Out of a group of 120 students that were surveyed about winter sports, 28 said they ski and 52 said they snowboard.


Sixteen of the students who said they ski said they also snowboard. If a student is chosen at random, find each


probability

Answers

Answer 1

The probability of  P(Ski) is 7 / 30, P(Snowboard) is 13 / 30,P(Ski & Snowboard) is 2/15 and P(ski or snowboard) is  8/15.

1. Probability of a student skiing (P(Ski)):
  P(Ski) = number of students who ski / total number of students = 28 / 120 = 7 / 30

2. Probability of a student snowboarding (P(Snowboard)):
  P(Snowboard) = number of students who snowboard / total number of students = 52 / 120 = 13 / 30

3. Probability of a student skiing and snowboarding (P(Ski & Snowboard)):
  P(Ski & Snowboard) = number of students who ski and snowboard / total number of students = 16 / 120 = 4 / 30

=2/15

4.Probability(ski or snowboard) = (7/30) + (13/30) - (2/15)

P(ski or snowboard) = 8/15
Therefore, the probabilities are:

P(ski) = 7/30

P(snowboard) = 13/30

P(ski and snowboard) = 2/15

P(ski or snowboard) = 8/15

Learn more about probability : https://brainly.com/question/13604758

#SPJ11


Related Questions

Use any method to determine whether the series converges а. น k2 sk (5 pts) b 6. Ex 2+(-1){ 5k (5 pts)"

Answers

To determine whether the series น k2 sk converges, we can use the Integral Test. Let f(x) = x2, then f'(x) = 2x. Since 2x is continuous, positive, and decreasing on [1,∞), In summary, the series Σ (1/k^2) converges, while the series Σ (2 + (-1)^{5k}) does not converge.

∫1∞ f(x) dx = ∫1∞ x2 dx = lim (t → ∞) [1/3 x3]1t = ∞
Since the integral diverges, the series น k2 sk also diverges.
b. To determine whether the series 2+(-1){ 5k converges, we can use the Alternating Series Test. The series has alternating signs and the absolute value of each term decreases as k increases. Let ak = 2+(-1){ 5k, then:
|ak| = 2+1/32k ≤ 2
Also, lim (k → ∞) ak = 0. Therefore, by the Alternating Series Test, the series 2+(-1){ 5k converges.

a. For the series Σ (1/k^2) (denoted as น k2 sk), we can use the p-series test. A p-series is a series of the form Σ (1/k^p), where p is a constant. If p > 1, the series converges, and if p ≤ 1, the series diverges. In this case, p = 2, which is greater than 1. Therefore, the series Σ (1/k^2) converges.
b. For the series Σ (2 + (-1)^{5k}), we can use the alternating series test. An alternating series is a series that alternates between positive and negative terms. In this case, the series alternates because of the (-1)^{5k} term. However, the series does not converge to zero as k goes to infinity, since there is a constant term 2. Therefore, the series Σ (2 + (-1)^{5k}) does not converge.
In summary, the series Σ (1/k^2) converges, while the series Σ (2 + (-1)^{5k}) does not converge.

Visit here to learn more about integral test:

brainly.com/question/28157842

#SPJ11

Solve for x.
2x²8x+5=0
Enter your answers in the boxes.
x = |or x =
T

Answers

We can solve the quadratic equation 2x² - 8x + 5 = 0 by using the quadratic formula, which states that for an equation of the form ax² + bx + c = 0, the solutions are given by:

x = (-b ± sqrt(b² - 4ac)) / 2a

In this case, a = 2, b = -8, and c = 5. Substituting these values into the formula, we get:

x = (-(-8) ± sqrt((-8)² - 4(2)(5))) / (2(2))

x = (8 ± sqrt(64 - 40)) / 4

x = (8 ± sqrt(24)) / 4

x = (8 ± 2sqrt(6)) / 4

Simplifying the expression by factoring out a common factor of 2 in the numerator and denominator, we get:

x = (2(4 ± sqrt(6))) / (2(2))

x = 4 ± sqrt(6)

Therefore, the solutions to the equation 2x² - 8x + 5 = 0 are:

x = 4 + sqrt(6) or x = 4 - sqrt(6)

High school competency test a mandatory competency test for high school sophomores has a normal distribution with a mean of 400 and a standard deviation of 100. the top 3% of students receive $500. what is the minimum score you would need to receive this award? the bottom 1.5% of students must go to summer school. what is the minimum score you would need to stay out of this group?

Answers

A score of at least 183 is required to stay out of the bottom 1.5%. To find the minimum score required to receive the award, we need to determine the z-score corresponding to the top 3% of students.

Since the distribution is normal, we can use the standard normal distribution table to find the z-score. From the table, we find that the z-score corresponding to the top 3% is approximately 1.88.

Therefore, we can use the formula z = (x - μ) / σ, where μ = 400 and σ = 100, to find the minimum score required: 1.88 = (x - 400) / 100

Solving for x, we get: x = 1.88(100) + 400 = 488. Therefore, a score of at least 488 is required to receive the award.

To find the minimum score required to stay out of the bottom 1.5%, we need to determine the z-score corresponding to the bottom 1.5%.

From the standard normal distribution table, we find that the z-score corresponding to the bottom 1.5% is approximately -2.17. Therefore, we can use the same formula as before to find the minimum score required: -2.17 = (x - 400) / 100.

Solving for x, we get: x = -2.17(100) + 400 = 183. Therefore, a score of at least 183 is required to stay out of the bottom 1.5%.

To know more about standard normal distribution, refer here:

https://brainly.com/question/29509087#

#SPJ11

Find the area of the composite figure.Round Your Answer To The Nearest Hundreth if needed

Answers

Answer:

[tex]A = 68.75 \text{ square inches}[/tex]

Step-by-step explanation:

First, we need to identify the trapezoid's dimensions:

base 1 = 16

base 2 = 11.5

height = 5

Then, we can plug these values into the trapezoid area formula:

[tex]A = \dfrac{b_1+b_2}{2} \cdot h[/tex]

[tex]A = \dfrac{16 + 11.5}{2} \cdot 5[/tex]

[tex]A = \dfrac{27.5}{2} \cdot 5[/tex]

[tex]A = \dfrac{137.5}{2}[/tex]

[tex]\boxed{A = 68.75 \text{ square inches}}[/tex]

Megha bikes 20km north, 30km east, 20 km south and then 30 km west and then stopped. What is her displacement​

Answers

Megha's total movement involves biking 20km north, 30km east, 20km south, and 30km west, resulting in a displacement of zero as she ends up back at her starting point.

Given that,

Megha bikes 20km north.

Megha then bikes 30km east.

After that, Megha bikes 20km south.

Lastly, Megha bikes 30km west.

Megha stops after completing the above movements.

Megha's displacement can be calculated by finding the straight-line distance between her starting point and ending point.

In this case,

She initially bikes 20km north, then 30km east, followed by 20km south, and finally 30km west.

Let's break it down:

The north and south distances cancel each other out, as she ends up back at her starting point vertically.

The east and west distances also cancel each other out, as she ends up back at her starting point horizontally.

Hence,

Megha's displacement is zero. She has returned to her original position.

To learn more about number straight lines visit:

https://brainly.com/question/32029748

#SPJ12

Find the coordinates of a point P on the line and a vector v parallel to the line. X-7 - Y + 2 = 2 + 6 = 5 4 P(x, y, z) = V ="

Answers

To find the coordinates of point P on the line, we can solve for x and y in the equation X-7 - Y + 2 = 2 + 6 = 5. Adding 7 to both sides, we get X - Y + 2 = 12. Subtracting 2 from both sides, we get X - Y = 10. We can choose any value for x, and then solve for y using this equation. For example, if we choose x = 0, then y = -10.

So the coordinates of point P on the line could be (0, -10, z), where z is any real number.

To find a vector v parallel to the line, we can take two points on the line and find the vector between them. For example, we could use the points (0, -10, 0) and (1, -9, 0). The vector between these points is (1-0, -9-(-10), 0-0) = (1, 1, 0).

So a vector v parallel to the line is v = (1, 1, 0).
To find the coordinates of a point P on the line and a vector v parallel to the line, we first need to rewrite the given equation in a more standard form. The equation provided seems to be incorrect, but let's assume it's meant to be in the format of Ax + By = C, then we can proceed as follows:

1. Identify the normal vector of the line (A, B): Since the given equation is X - Y = 3 (combining the constants), the normal vector is (1, -1).

2. Determine the direction vector of the line, which is perpendicular to the normal vector. One possible direction vector is the one obtained by swapping the components and negating one of them, so v = (1, 1).

3. To find a point P on the line, we can choose a value for either x or y and solve for the other coordinate. Let's choose x = 0, then we have 0 - Y = 3, which gives Y = -3. Therefore, P(x, y) = (0, -3).

In summary, the point P on the line is (0, -3), and a vector v parallel to the line is (1, 1).

Learn more about coordinates here: brainly.com/question/16634867

#SPJ11

8. Brock placed a 20 foot ladder against the side of the house. The base of the ladder was 6 foot from the base of the house. How high does the ladder reach on the side of the house? Draw a picture and solve. (Round to tenth) ​

Answers

Step-by-step explanation:

1st i think u divide 20 and 6 and then round tht to the tenth place because we already know our answer is going to be a decimal bc 6 cant go into 20.

Why do Markets behave in the same ways as Individual Consumers?

Answers

Answer:

Markets behave the same way as individual customers because markets are made up of individual consumers.

Step-by-step explanation:

Solich sandwich shop had the following long-term asset balances as of december 31, 2021: accumulated cost depreciation book value land $ 77,000 − $ 77,000 building 442,000 $ (83,980 ) 358,020 equipment 245,000 (46,400 ) 198,600 patent 160,000 (64,000 ) 96,000 solich purchased all the assets at the beginning of 2019 (3 years ago). the building is depreciated over a 20-year service life using the double-declining-balance method and estimating no residual value. the equipment is depreciated over a 10-year useful life using the straight-line method with an estimated residual value of $13,000. the patent is estimated to have a five-year service life with no residual value and is amortized using the straight-line method. depreciation and amortization have been recorded for 2019 and 2020. problem 7-7a part 1 required: 1. for the year ended december 31, 2021, record depreciation expense for buildings and equipment. land is not depreciated. (if no entry is required for a transaction/event, select "no journal entry required" in the first account field.)

Answers

No journal entry is required for the land since it is not depreciated.

To record depreciation expense for buildings and equipment for the year ended December 31, 2021, we need to calculate the depreciation amounts for each asset based on their respective methods.

For the building, we will use the double-declining-balance method. The annual depreciation expense is calculated as (2 / 20) x $442,000 = $44,200. Since depreciation has already been recorded for 2019 and 2020, the accumulated depreciation balance for the building as of December 31, 2020 is $83,980. Therefore, the 2021 depreciation expense for the building is $44,200 - $83,980 = $(-39,780). We record this as follows:

Building Depreciation Expense: $39,780
 Accumulated Depreciation - Building: $39,780

For the equipment, we will use the straight-line method. The annual depreciation expense is calculated as ($245,000 - $13,000) / 10 = $23,200. Since depreciation has already been recorded for 2019 and 2020, the accumulated depreciation balance for the equipment as of December 31, 2020 is $46,400. Therefore, the 2021 depreciation expense for the equipment is $23,200, and we record it as follows:

Equipment Depreciation Expense: $23,200
 Accumulated Depreciation - Equipment: $23,200

No journal entry is required for the land since it is not depreciated.
Learn more about straight-line method,

https://brainly.com/question/30243743

#SPJ11

A right triangle has legs that are 17 centimeters and 28 centimeters long.

What is the length of the hypotenuse?

Enter your answer as a decimal, Round your answer to the nearest hundredth.

Answers

Answer: 4.5

Step-by-step explanation:

.PLEASEEEEEEEEEEEEEE

Answers

Answer:

#1        (176 - x)°

#2       m∠3 = m∠4 = 90°

Step-by-step explanation:

If a pair of parallel lines are cut by a transversal, there are several angles that are either equal to each other or are supplementary(angles add up to 180°).

For the specific questions...
For #1.

Angles ∠1 and ∠2 are supplementary angles since they are adjacent to each other and lie on the same straight line

Therefore
m∠1 + m∠2= 180°

Given m∠1 = (x + 4)° this becomes

(x + 4)° + m∠2 = 180°

m∠2 = 180° - (x + 4)°

= 180° - x° - 4°

= (176 - x)°

For #2

∠3 and ∠4 are supplementary angles so m∠3 + m∠4 = 180°

If m∠3 = m∠4 each of these angles must be half of 180°

So
m∠3 = m∠4 = 180/2 = 90°

Find the value(s) of k for which u(x.t) = e-³sin(kt) satisfies the equation Ut=4uxx

Answers

When k = 0, both sides of the equation equal 0:
3cos(0) = 4(0)sin(0)
3 = 0

There are no other values of k for which the equation holds true, the only value of k that satisfies the given equation is k = 0.

To find the value(s) of k for which u(x, t) = e^(-3)sin(kt) satisfies the equation Ut = 4Uxx, we first need to calculate the partial derivatives with respect to t and x.
[tex]Ut = ∂u/∂t = -3ke^(-3)cos(kt)Uxx = ∂²u/∂x² = -k^2e^(-3)sin(kt)[/tex]
Now, we will substitute Ut and Uxx into the given equation:

[tex]-3ke^(-3)cos(kt) = 4(-k^2e^(-3)sin(kt))[/tex]
Divide both sides by e^(-3):

[tex]-3kcos(kt) = -4k^2sin(kt)[/tex]

Since we want to find the value(s) of k, we can divide both sides by -k:

3cos(kt) = 4ksin(kt)

Now we need to find the k value that satisfies this equation. Notice that when k = 0, both sides of the equation equal 0:

3cos(0) = 4(0)sin(0)
3 = 0

Since there are no other values of k for which the equation holds true, the only value of k that satisfies the given equation is k = 0.

To learn more about partial derivatives, refer below:

https://brainly.com/question/29652032

#SPJ11

HERE IS A HARD QUESTION , COULD U PLEASE ANSWER B PLEASE? I DID A ! 1ST ANSWER WOULD BE MARKED BRAINLIEST AND GET 5/5 WITH A THANKS! ILL ALSO COMMENT ON YOUR ANSWER ! BUT IF IT ISNT CORRECT , I WONT MARK BRAINLIEST! Thank you for your answers!!!!

Answers

Plot D at coordinates 6,4

Answer:

D(6,4).

Step-by-step explanation:

The shape ABCD is a square.

By definition, the diagonals are equal.

The diagonal from A to C is 6 units long. Therefore, you should get your point D by drawing across from B to the right by 6.

D(6,4).

The population of dolphins in the Gulf of Mexico has been decreasing at a rate of 4% every 10


years. In 2020 there were 4,670 dolphins. If things continue this way, how many dolphins will there


be in the year 2100?

Answers

The number of dolphins that will be there in the year 2100 is 1003, under the condition that in the Gulf of Mexico has been decreasing at a rate of 4% every 10
years.

Here the population of dolphins in the Gulf of Mexico in 2020 was 4,670.The rate of decrease is 4% every 10 years.
Therefore, the population would  decrease by 4% every 10 years.
We want to evaluate the population in 2100, which is  80 years from now, which is eight 10-year periods.
Now, we have to calculate the population after eight 10-year periods.
Each period would decrease the population by 4%.
Hence, the population after eight periods is
4670 × (1 - 0.04)⁸
= 4670 × (0.96)⁸
= 1003

Then, if things progress like this, the population of dolphins in the Gulf of Mexico in the year 2100 will be close to 1000.
To learn more about population
https://brainly.com/question/29885712
#SPJ4

A backyard swimming pool has a diameter of 16 feet and a height of 4 feet. A hose is used to fill the pool with a flow rate of 30 gallons per minute. A. How long will it take to fill the pool? B. If h represents the depth of the water, find dh/dt

Answers

Hose will take about 63.7 minutes to fill the pool and the the depth of the water is increasing at a rate of about 0.0079 feet per minute.

First, let's find the volume of the pool. The pool is in the shape of a cylinder with a height of 4 feet and a diameter of 16 feet, so its radius is half of the diameter, or 8 feet. The volume of a cylinder is given by

V = πr^2h

Plugging in the values, we get

V = π(8 ft)^2(4 ft)

V = 256π cubic feet

Next, let's convert the flow rate to cubic feet per minute. One gallon is equal to 0.1337 cubic feet, so the flow rate is

30 gallons/min x 0.1337 ft^3/gallon = 4.011 ft^3/min

Finally, we can use the formula

time = volume/flow rate

Plugging in the values, we get

time = 256π ft^3 / 4.011 ft^3/min

time ≈ 63.7 minutes

So it will take about 63.7 minutes to fill the pool.

Let's use the formula for the volume of a cylinder again to relate the volume of the water in the pool to its depth

V = πr^2h

We can solve this formula for h

h = V/πr^2

Taking the derivative of both sides with respect to time, we get

dh/dt = d/dt (V/πr^2)

The radius of the pool does not change, so we can treat it as a constant and take it out of the derivative

dh/dt = (1/πr^2) dV/dt

We know the flow rate is constant at 4.011 cubic feet per minute, so the rate of change of the volume of water in the pool is

dV/dt = 4.011

Plugging in the values, we get

dh/dt = (1/π(8 ft)^2) (4.011 ft^3/min)

dh/dt ≈ 0.0079 ft/min

So the depth of the water is increasing at a rate of about 0.0079 feet per minute.

To know more about rate here

https://brainly.com/question/30125255

#SPJ4

This data is an example of (?)

Answers

The given data is an example of a nonlinear function. Therefore, the answer is A.

The given data consists of two sets of numbers, X and Y, where each value of X has a corresponding value of Y. We can observe that the points do not lie on a straight line. Instead, the plotted points form a curved shape, which indicates that the relationship between X and Y is not a linear function.

A linear function is a function where the relationship between the input variable (X) and output variable (Y) is a straight line. In this case, we can observe that as the value of X increases, the value of Y increases at an increasing rate, which means the relationship between X and Y is not linear.

In particular, the relationship between X and Y is a quadratic function since the values of Y are the squares of the corresponding values of X.

Therefore, the answer is A.

To learn more about linear/non-linear click on,

https://brainly.com/question/276828

#SPJ1

a) ¿Cuál es el coeficiente del término 23x5?

Answers

Answer:

El coeficiente del término 23x^5 es 23.

Step-by-step explanation:

In an expansion of (2a-5b)^2 the coefficient of ab is

Answers

In the expansion of the given expression, (2a - 5b)², the coefficient of ab is -20

Determining the coefficient of a term in an expansion

From the question, we are to determine the coefficient of ab in the expansion of the given expression.

The given expression is

(2a - 5b)²

To determine the coefficient of ab, we will expand the expression

Expand the expression

(2a - 5b)²

(2a - 5b)(2a - 5b)

Applying the distributive property, we get

2a(2a - 5b) -5b(2a - 5b)

Distribute the expression outside

4a² - 10ab - 10ab + 25b²

Simplify the expression

4a² - 20ab  + 25b²

Hence, the coefficient of ab is -20

Learn more on Determining the coefficient in an expansion here: https://brainly.com/question/30601451

#SPJ1

The table shown below gives the approximate distance from the sun for a few different planets how much further (in km) from the sun is Saturn than Venus

Answers

The distance that shows how much farther (in km) from the sun is Saturn than Venus is: [tex]1.2 * 10^9[/tex] km.

How to calculate the distance

According to the table, the distance of Saturn from the Sun is [tex]1.4 * 10^{9}[/tex] and the distance of Venus from the Sun is [tex]1.1 * 10^{8}[/tex] .

Now to determine how much further from the Sun is Saturn than Venus, we will subtract the distance of the planet with the higher distance span from the one with the lower distance.

So our calculation will go thus:

[tex]1.4 * 10^9 - 1.1 * 10^8 = \\140000000 - 11000000 = 1290000000\\= 1.29 * 10^9[/tex]

From the calculation above, we can see how much further from the sun, is Saturn than Venus.

Complete Question:

The table shown below gives the approximate distance from the sun for a few different planets. How much farther (in km) from the sun is Saturn than Venus? Express your answer in scientific notation.

_______km

Learn more about distance calculation here:

https://brainly.com/question/26046491

#SPJ1

Assinale a alternativa que melhor julga a sentença abaixo:

"as frações 3/9 e 7/18 são equivalentes, pois representam a mesma parte do todo"
( ) verdadeiro
( ) falso

ajuda pfvrrrrrrr

Answers

The statement is true as 3/9 and 7/18 represent the same part of the whole.

How to determine if the fractions 3/9 and 7/18 are equivalent?

A sentença é falsa. As frações 3/9 e 7/18 não são equivalentes, pois não representam a mesma parte do todo. Para determinar se duas frações são equivalentes, é necessário simplificar as frações e verificar se os resultados são iguais.

No caso das frações 3/9 e 7/18, podemos simplificar ambas dividindo o numerador e o denominador pelo máximo divisor comum (MDC).

A fração 3/9 pode ser simplificada dividindo ambos por 3, resultando em 1/3. Já a fração 7/18 não pode ser simplificada ainda mais. Portanto, as frações 3/9 e 7/18 não são equivalentes, pois não representam a mesma parte do todo.

Learn more about frações

brainly.com/question/11201112

#SPJ11

Part C

What does the absolute value of the correlation coefficient say about the predictions in part B? How do you know? Write

an explanation of about one to two sentences.

BI U x

х

Font Sizes

A-A-DEE 3



Characters used: 0 / 15000

Submit

o

Answers

The shows that Luther can expect the speed to be 51 miles/hour when he throws 80 pitches and 64 miles/hour when he throws 54 pitches.

How to calculate the speed?

The average speed of Luther's pitches when he throws 80 pitches will be:

y = -0.511x + 91.636

= -0.511(80) + 91.636

= 50.756

= 51

Also, the number of pitches that Luther can throw when the speed is 64 miles per hour will be:

y = -0.511x + 91.638

64 = -0.511x + 91.638

0.511x = 91.638 - 64

0.511x = 27.636

x = 54

Therefore, the number of pitches will be 54.

Learn more about line of best fit on:

brainly.com/question/21241382
#SPJ4

Answer:

Because the absolute value of the correlation coefficient, 0.9672, is very close to 1, Luther can be very confident in the predictions.

Step-by-step explanation: Edmentum Answer

Give the Laplace transform of f(x)= (-2x-3)/4

Answers

The Laplace transform of f(x)= (-2x-3)/4 is (-2L{x}-3L{1})/4, where L{x} is the Laplace transform of x and L{1} is the Laplace transform of 1.
Hi! The Laplace transform of a given function f(t) is denoted by L{f(t)} and is defined as the integral of f(t) multiplied by e^(-st), where s is a complex variable. For the function f(x) = (-2x - 3)/4, the Laplace transform can be calculated as follows:

L{f(t)} = L{(-2t - 3)/4}

To find the Laplace transform, we will treat the function as two separate parts:

L{(-2t - 3)/4} = (-2/4) * L{t} + (-3/4) * L{1}

The Laplace transforms of t and 1 are well-known:

L{t} = 1/s^2
L{1} = 1/s

Now, substitute these transforms back into our expression:

L{f(t)} = (-1/2) * (1/s^2) + (-3/4) * (1/s)

L{f(t)} = -1/(2s^2) - 3/(4s)

And that's the Laplace transform of f(x) = (-2x - 3)/4.

To learn more about Laplace transform visit;

brainly.com/question/31041670

#SPJ11

The distance from Earth to Mercury is 9.21×10^7 kilometers. How long would it take a rocket, traveling at 3.35×10^4 kilometers per hour to travel from Earth to Mercury? Round your answer to the nearest whole number of hours.

Answers

it would take approximately 2,749 hours for a rocket traveling at 3.35×10⁴ kilometers per hour to travel from Earth to Mercury.

what is approximately ?

Approximately means "about" or "roughly". It is used to indicate that a number or value is not exact, but rather an estimate or approximation. When a value is given as approximately a certain number

In the given question,

To calculate the time it would take a rocket traveling at 3.35×10⁴ kilometers per hour to travel from Earth to Mercury, we need to divide the distance between Earth and Mercury by the speed of the rocket:

Time = Distance / Speed

Distance = 9.21×10⁷kilometers

Speed = 3.35×10⁴ kilometers per hour

Time = 9.21×10⁷ km / (3.35×10⁴ km/h)

Time = 2,748.66 hours

Rounding this value to the nearest whole number of hours gives:

Time = 2,749 hours

Therefore, it would take approximately 2,749 hours for a rocket traveling at 3.35×10⁴ kilometers per hour to travel from Earth to Mercury.

To know more about approximately  , visit:

https://brainly.com/question/30945002

#SPJ1

15 POINTS IM GOING TO BE BROKE AFTER THESE QUESTIONS



Two cars leave from the same location with one car traveling north and the other traveling west. When the northbound car has traveled 18 miles, the straight-line distance between the two cars is 30 miles. How far has the westbound car traveled?

Answers

We know that the westbound car has traveled 24 miles.

When the northbound car has traveled 18 miles and the straight-line distance between the two cars is 30 miles, you can use the Pythagorean theorem to determine the distance the westbound car has traveled. The theorem states that a² + b² = c², where a and b are the legs of a right triangle and c is the hypotenuse.

In this case, the northbound car's distance (18 miles) represents one leg (a) and the westbound car's distance represents the other leg (b). The straight-line distance between the cars (30 miles) represents the hypotenuse (c). The equation can be set up as follows:

18² + b² = 30²

Solving for b:

324 + b² = 900
b² = 900 - 324
b² = 576
b = √576
b = 24

So, the westbound car has traveled 24 miles.

To know more about miles refer  here

https://brainly.com/question/23245414#

#SPJ11

A circle with center (7,3) and radius of 5 is graphed below with a square inscribed in
the circle.
Part A: Dillon and Chelsey are discussing how to write the equation of a tangent line
to circle A through point B. Both agree that they start the problem by drawing the
radius AB and find the slope of that segment. They also know that a tangent line is
perpendicular to the radius.

Answers

The area of the shaded region is (9/500)π.

To find the area shaded below in circle K, we first need to find the radius of the circle.

Let O be the center of the circle, and let N be the midpoint of segment LM. We can draw a radius ON to segment LM such that it is perpendicular to LM, and then draw another radius OL to point L. This forms a right triangle LON with the hypotenuse equal to the radius of circle K.

Since segment LM is given to have a length of 11/9π, we can find the length of LN by dividing it in half:

LN = (11/9π)/2 = 11/18π

We can then use trigonometry to find the length of OL:

sin(55°) = OL / LN

OL = LN sin(55°)

OL = (11/18π) sin(55°)

Next, we can use the Pythagorean theorem to find the length of ON:

ON² = OL² + LN²

ON² = [(11/18π) sin(55°)]² + [11/18π]²

ON ≈ 1.022

Therefore, the radius of circle K is approximately 1.022.

The area of the shaded region can now be found by subtracting the area of sector LOM from the area of triangle LON:

Area of sector LOM = (110/360)π(1.022)² ≈ 0.317π

Area of triangle LON = (1/2)(11/18π)(1.022) ≈ 0.326π

Area of shaded region = (0.326π) - (0.317π) = (9/500)π

So the area of the shaded region is (9/500)π.

To learn more about trigonometry here

https://brainly.com/question/31896723

#SPJ1

The Volume, V, in liters, of air in the lungs is approximated by the the model, V = -0.0374+3 +0.1525+2 +0.1729t, during a five second respiratory cycle. In here, t is measured in second

Answers

The model approximates the volume, V, in liters, of air in the lungs during a five-second respiratory cycle using the equation V = -0.0374t + 3 + 0.1525t^2 + 0.1729t.

The given equation represents a mathematical model for estimating the volume of air in the lungs during a respiratory cycle. It is a quadratic equation with three terms: -0.0374t, 0.1525t^2, and 0.1729t.

The term -0.0374t represents the linear decrease in volume over time, indicating that the volume decreases by 0.0374 liters for every second of the respiratory cycle.

The term 0.1525t^2 represents the quadratic relationship between volume and time squared, indicating that the rate of change of volume with respect to time is influenced by the square of time.

The term 0.1729t represents the linear increase in volume over time, indicating that the volume increases by 0.1729 liters for every second of the respiratory cycle.

Overall, this model provides an approximation of the volume of air in the lungs during a five-second respiratory cycle, taking into account both linear and quadratic relationships with time.

For more questions like Volume click the link below:

https://brainly.com/question/1578538

#SPJ11

MARKING BRAINLEIST IF CORRECT PLS ANSWER ASAP

Answers

Answer:

7.6 cm

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]a^{2}[/tex] + [tex]6.5^{2}[/tex] = [tex]10^{2}[/tex]

[tex]a^{2}[/tex] + 42.25 = 100 Subtract 42.25 from both sides

[tex]a^{2}[/tex] = 57.57

[tex]\sqrt{\a^{a} }[/tex] = [tex]\sqrt{57.57}[/tex]

a ≈ 7.6

Helping in the name of Jesus.

Answer:

7.6 cm

Step-by-step explanation:

a^2+ b^2=c^2

a^2+6.5^2=10^2

a^2+42.25=100 subtract 42.25 from both sides

a^2=57.57

a=√57.57

a=7.6 cm

In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student chosen randomly from the class passed the test and completed the homework? Passed the test Failed the test Completed the homework 11 3 Did not complete the homework 2 5

Answers

The probability that a student chosen randomly from the class passed the test or completed the homework is 20/27.

What is the probability?

The probability that a student chosen randomly from the class passed the test or completed the homework is calculated as follows:

Let the probability that a student completed the homework be P(B).

Also, let the probability that a student passed the test be P(A)

P(A or B) = P(A) + P(B) - P(A * B)

From the data table:

The number of students who passed the test = 18

The number of students who completed the homework = 17

The number of students who both passed the test and completed the homework = 15.

Total number of students = 27

P(A) = 18/27

P(B) = 17/27

P(A*B) = 15/27

Therefore,

P(A or B) = 18/27 + 17/27 - 15/27

P(A or B) = 20/27

Learn more about probability at: https://brainly.com/question/24756209

#SPJ1

The table shows the purchases made by two customers at a meat counter. you want to buy 2 pounds of sliced ham and 3 pounds of sliced turkey. can you determine how much you will pay? explain.​

Answers

The cost of purchasing 2 pounds of sliced ham and 3 pounds of sliced turkey from the meat counter is $30.95.

The table provided shows the purchases made by two customers at a meat counter. To determine how much you will pay for 2 pounds of sliced ham and 3 pounds of sliced turkey, you need to first look at the prices listed in the table. For sliced ham, the price per pound is $4.99, and for sliced turkey, the price per pound is $6.99.

To calculate the cost of 2 pounds of sliced ham, you can multiply the price per pound ($4.99) by the number of pounds (2), which gives you a total cost of $9.98. Similarly, to calculate the cost of 3 pounds of sliced turkey, you can multiply the price per pound ($6.99) by the number of pounds (3), which gives you a total cost of $20.97.

Therefore, the total cost for 2 pounds of sliced ham and 3 pounds of sliced turkey would be $9.98 + $20.97 = $30.95.

In conclusion, by using the prices listed in the table, it is possible to determine the cost of purchasing 2 pounds of sliced ham and 3 pounds of sliced turkey from the meat counter. It is important to remember to multiply the price per pound by the number of pounds needed for each item, and then add the costs together to get the total price.

Know more about cost here:

https://brainly.com/question/15135554

#SPJ11

Find ∫∫D 2xy dA, where D is the region between the circle of radius 2 and radius 5 centered at the origin that lies in the first quadrant. Find the exact value.

Answers

The exact value of the double integral ∫∫D 2xy dA is 0.

To evaluate the double integral ∫∫D 2xy dA, where D is the region between the circles of radius 2 and 5 centered at the origin that lies in the first quadrant, we need to use polar coordinates.

In polar coordinates, the region D is defined by 2 ≤ r ≤ 5 and 0 ≤ θ ≤ π/2. The double integral can be expressed as:

∫∫D 2xy dA = ∫θ=0^(π/2) ∫r=[tex]2^5 2r^3[/tex] cosθ sinθ dr dθ

Solving the inner integral with respect to r, we get:

∫r=[tex]2^5[/tex] 2[tex]r^3[/tex] cosθ sinθ dr = [r^4 cosθ sinθ]_r=[tex]2^5 = 5^4[/tex] cosθ sinθ - [tex]2^4[/tex] cosθ sinθ

Substituting this result into the double integral expression and solving the remaining integral with respect to θ, we get:

∫∫D 2xy dA = ∫θ=0^(π/2) (5^4 cosθ sinθ - 2^4 cosθ sinθ) dθ

= [5^4/2 sin(2θ) - 2^4/2 sin(2θ)]_θ=0^(π/2)

= (5^4/2 - 2^4/2) sin(π) - 0

= (5^4/2 - 2^4/2) * 0

= 0

Therefore, the exact value of the double integral ∫∫D 2xy dA is 0.

To learn more about double integral visit: https://brainly.com/question/30217024

#SPJ11

Other Questions
Please help! Daniel incorrectly solved the equations shown. Explain what he did wrong in each solution and then solve both equations correctly. 25x^2-16=9(25x^2 )-16=95x-4=35x=7x=7/5 z^3-2=6z^3=8(z^3 )=8z=2 Question 2 of 10When payroll expenses are journalized, each individual payable account isentered asOA. a debit and a creditOB. a debitC. neither a debit nor a creditD. a credit How are 401(k)s different from roth or traditional iras How can you solve x3-2=2? FAST I REALLY NEED HELP IM GONNA FAILThe Beatles emerged in Britain during the same era that rock and roll was sweeping the American music scene. What does the fact that both countries embraced a similar style of music in the same era suggest?Select one:a.Neither country was able to product any original music.b.Both nations were subject to similar cultural influences.c.The British would not have developed rock and roll without Americans.d.The 1960s were an era with many limitations on the type of music created. At the beginning of the poem, there is no clear message about the warrior problem. What actually happened to the warrior? Describe. Paragraph on rainy day you will never forget what is gastulaton stage in development of a chick? Write c program (without arrays or pointers) (Wattan Corporation) is an Internet service provider that charges customers a flat rate of $7. 99 for up to 10 hours of connection time. Additional hours or partial hours are charged at $1. 99 each. Write a function charges that computes the total charge for a customer based on the number of hours of connection time used in a month. The function should also calculate the average cost per hour of the time used (rounded to the nearest 0. 01), so use two output parameters to send back these results. You should write a second function round_money that takes a real number as an input argument and returns as the function value the number rounded to two decimal places. Write a main function that takes data from an input file usage. Txt and produces an output file charges. Txt. The data file format is as follows: Line 1: current month and year as two integers Other lines: customer number (a five-digit number) and number of hours used Here is a sample data file and the corresponding output file: Data file usage. Txt 10 2009 15362 4. 2 42768 11. 1 11111 9. 9 Output file charges. Txt Charges for 10/2009 15362 4. 2 7. 99 1. 90 42768 11. 1 10. 18 0. 92 11111 9. 9 7. 99 0. 81 Uppose the market demand function (expressed in dollars) for a normal product isP = 80 q, and the marginal cost (in dollars) of producing it is MC = 1q, where P is theprice of the product and q is the quantity demanded and/or supplied. A. B. C. D. 3. 4. 5. Suppose you were asked to comment on a proposed policy to control oil spills. Since theaverage cost of an oil spill has been computed as $X, the proposed policy would requireany firm responsible for a spill immediately to pay the government $X. Is this likely toresult in the efficient amount of precaution against oil spills? Why or why not?"In environmental liability cases, courts have some discretion regarding the magnitudeof compensation polluters should be forced to pay for the environmental incidents theycause. In general, however, the larger the required payments the better. " Discuss. Label each of the following propositions as descriptive or normative and defend yourchoice:a. B. C. D. E. 6. How much would be supplied by a competitive market?Compute the consumer surplus and producer surplus. Show that their sum ismaximized. Compute the consumer surplus and the producer surplus assuming this same productwas supplied by a monopoly. (Hint: The marginal revenue curve has twice the slopeof the demand curve. )Show that, when this market is controlled by a monopoly, producer surplus is larger,consumer surplus is smaller, and the sum of the two surpluses is smaller than whenthe market is controlled by competitive industry What is the molar mass of potassium hydroxide, KOH? 22 randomly picked people were asked if they rented or owned their own home, 9 said they rented. Obtain a point estimate of the proportion of home owners. Use a 95% level of confidence.point Which statement can be supported by using a position-time graph?O A negative slope results when an individual is moving away from the origin.O A horizontal line on the graph means the individual is moving at a non-zero velocity.O A positive slope results when an individual is moving away from the origin.O The speed of an individual cannot be determined from this type of graph.4 1. Suppose a government has no debt and a balanced budget. Suddenly it decides to spend $5trillion while raising only $4. 5 trillion worth of taxes. (a) What will be the government's deficit?(b) If the government finances the deficit by issuing bonds, what amount of bonds will itissue?(c) At a 4 percent rate of interest, how much interest will the government pay each year?(d) Add the interest payment to the government's $5 trillion expenditures for the next year,and assume that taxes remain at $4. 5 trillion. In the second year, compute the(i) Deficit(ii) Amount of new debt (bonds) issued. (iii) Total debt at end of year. (iv) Debt service requirement Write a numerical expression using at least three operations a parenthesis an exponent that when solved has a solution of 23 Why was the federal deposit insurance corporation started and what was the need? The main purpose of each of these texts is A. To educate the reader about Sybil Ludington's heroics. B. To show the kindness of General George Washington. C. To describe the many battles of the Continental Army. D. To explain how the British protected British loyalists. I need help! Solve for X A spring with an m-kg mass and a damping constant 5 (kg/s) can be held stretched 0.5 meters beyond its natural length by a force of 2 newtons. If the spring is stretched 1 meters beyond its natural length and then released with zero velocity, find the mass that would produce critical damping. m = kg how are all the properties of water are related?