Use the estimated angle to find the distance of the life-raft from the lighthouse.

Answer:

Here's a set of five numbers, each of which is divisible by 3:

{ 3, 6, 9, 12, 15 }

All the numbers in this set are multiples of 3, so they are all divisible by 3.

The matrix formed by performing the row operation 2R₁ + R₂ — R₂ on M will have a new R₂ = [ -8 -1 -3]

A rectangular array of numbers or mathematical objects which are arranged in rows and columns is called a matrix. Each row of a matrix is a horizontal sequence of numbers or objects that are separated by commas and enclosed within square brackets, and it represents a vector in the row space of the matrix.

performing the row operation 2R₁ + R₂ — R₂ on M, we have;

2(-3) + (-2) = -8 {row 2 column 1}

2(-1) + 1 = -1 {row 2 column 2}

2(-4) + 5 = -3 {row 2 column 3}

Therefore, the matrix formed by performing the row operation 2R₁ + R₂ — R₂ on M will have a new R₂ = [ -8 -1 -3]

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Answer:

6 out of 36 or 1 out of 6

Step-by-step explanation:

There are 36 possible ways two dice can roll, so the probability of the sum of seven is 6 out of 36, or 1/6.

[tex]\boxed{\sf 16.67\%}.[/tex]

So since we have a pair of dice, assuming they are standard 6 faced dices, the total amount of outcomes is given by just multiplying the number of faces or different numbers that the dices can present:

6 x 6 = 36 possible outcomes.

Now, here we need to count all the possible cases where the outcome of both dices will equal 7. And there are said cases:

1 + 6 = 7

Explanation. Here the first dice presented number 1 and the second presented number 6, adding up to 7.

Other cases that meet the requirement:

2 + 5 = 7

3 + 4 = 7

4 + 3 = 7

5 + 2 = 7

6 + 1 = 7

So the total amount of events that will meet the requirement is 6.

So if we have an event with 36 possible outcomes, and only 6 of those 36 outcomes will mean a success on the experiment. Then, to find the probability of those 6 events from happening all we need to do is divide the amount of events considered "success" which is the numbers adding up to 7 by the total amout of outcomes (36).

So, the probability of rolling a sum of 7 with 2 dices is:

[tex]\sf P(\dfrac{6}{36} )=\dfrac{1}{6} =\boxed{\sf 16.67\%}.[/tex]

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The incorrect statement is

In mathematics, dilation can be defined as a transformation which alters the size of an object, though its shape remains unchanged. It is described as a specific similarity transformation where all dimensions associated with the given object (i.e. height, width and length) are increased or decreased uniformly by a particular scale factor.

A dilation thus produces an alteration in size, with the figure being either magnified or diminished while keeping its unique shape intact.

The scale factor used in the dilation is 9/7 instead of 7/3.

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Comparing each pair of expressions using >, <, or = is given below:

-32 < |-32| (because -32 is negative and |-32| is positive)

5 - 5 = 0 (because subtracting the same number results in zero)

15 > |___15| (because |___15| is equal to 15)

|5| = |___|-5|| (because both expressions are equal to 5)

2 - 17 < ▾ (because 2 - 17 equals -15, which is less than the square root symbol)

2 > |____|-17|| (because 2 is positive and |-17| is also positive)

|-27| > ||-45|| (because |-27| is 27 and ||-45|| is 45)

-27 > -45 (because -27 is closer to zero than -45)

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Step-by-step explanation:

[tex] {( ({3})^{4} })^{8} \\ = {3}^{32} [/tex]

Answer:

C

Step-by-step explanation:

the prime factorization of 84 is 2 x2 x 3 x 7

I can rewrite the problem

-3[tex]\sqrt{84x^{3} }[/tex]

-3[tex]\sqrt{(2)(2)(3)(7)xxx}[/tex]  pull out the pairs

-3(2)x[tex]\sqrt{(3)(7)x}[/tex]

-6x[tex]\sqrt{21x}[/tex]

Helping in the name of Jesus.

Since the calculated t-value is greater than the critical t-value, we reject the null hypothesis, concluding that there's convincing evidence that the new treatment results in a higher mean MSI value than standard care.

a. The 95% confidence interval for the proportion of teenagers using video streaming services daily is (0.5579, 0.6221). This means we're 95% confident that 55.79% to 62.21% of US teenagers use such services daily.

b. The results demonstrate that the proportion is not 0.5 because the full confidence interval is higher than 0.5.2. We obtain a t-value of roughly 2.51 with 108.52 degrees of freedom using a two-sample t-test.

At a significance level of 0.05, the critical t-value for a one-tailed test is approximately 1.66.

Since the calculated t-value is greater than the critical t-value, we reject the null hypothesis, concluding that there's convincing evidence that the new treatment results in a higher mean MSI value than standard care.

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Using a system of equations, the quantities of each type of gas sold by the gas station for the business day are as follows:

A system of equations refers to two or more equations solved concurrently.

A system of equations is also known as simultaneous equations because they can be solved at the same time.

                              Regular    Premium

Price per gallon      $2.20       $2.75

Total number of gallons of gas sold = 340

The total receipts for the 340 gallons = $803.

Let the number of gallons of the regular gas = x

Let the number of gallons of the premium gas = y

x + y = 340 ...Equation 1

2.2x + 2.75y = 803 ...Equation 2

Multiply Equation 1 by 2.2:

2.2x + 2.2y = 748 ...Equation 3

Subtract Equation 3 from Equation 2:

2.2x + 2.75y = 803

-

2.2x + 2.2y = 748

0.55y = 55

y = 100

x = 240 (340 - 100)

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Answer:

To find the value of "a" when you know the perimeter of a shape, you need to know the specific shape you're referring to. Please provide more information about the shape in question, such as whether it's a rectangle, triangle, or another geometric figure. Additionally, if you have any specific measurements or relationships between the sides of the shape, please provide them as well.

Answer:  36600 = E

Step-by-step explanation:

Given:

T=.2 (E - 10600)      

T=5200  

Find:  E

Solution:  

>substitute into thequation.  You know T=5200

5200 = .2(E-10600)     > Divide both sides by .2

26000 = E- 10600       > add 10600 to both sides

36600 = E                    

Using the given random variable and the mean the required probability in the given situation is 0.9772.

A probability is a numerical representation of the likelihood or chance that a specific event will take place.

Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

= P(x>36) = P(X-μ/σ>36-50/7)

= P(Z>-14/7) Z=X-μ/σ

= P(Z>-2)

= P(Z<2)  [P(Z<z) = P(Z>-z)]

= 0.9772 by the p-value table

Therefore, using the given random variable and the mean the required probability in the given situation is 0.9772.

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Correct question:

Assume the random variable x is normally distributed with mean 50 and a standard deviation 7. Find the indicated probability. P(X>36)

Answer: 29

Step-by-step explanation:

<F is 29 degrees because 180-58=122 and 180-122= 58, so then you divide 58 by 2 to get 29 for each x. The x's are each equal to 29.

Answer:

29 degrees

Step-by-step explanation:

The problem shows angle HGE as 58 degrees.

Segment HF is 180 degrees so we can subtract 58 from 180 to get 122 degrees for angle g

Now, the sum of all angles in a triangle is 180.

So, there are 3 angles in the triangle:

g(we know this is 122)

e

f

the graph denotes that the measures of angle e and f are the same because they are the same variable.

Lets subtract 122 from 180 to get 58.

So, angle e and f together combine to make 58 degrees.

But we also know that e and f have the same measure.

So, to find the measure of f, simply divide 58/2 to get 29 degrees.

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Harriet ate a total of 3/4 of the total pizza

Given data ,

On Monday Harriet ate 1/4 of a 8 slice of pizza

And , on Tuesday she ate 1/2 of the same pizza

Now , If the pizza has 8 slices, then Harriet ate 1/4 of 8 slices on Monday, which is 2 slices.

On Tuesday, Harriet ate 1/2 of the same pizza, which is 4 slices.

So, in total, Harriet ate 2 + 4 = 6 slices of pizza

On simplifying the equation , we get

The whole pizza has 8 slices, so Harriet ate 6/8 of the pizza, which simplifies to 3/4.

Hence , Harriet ate 3/4 of the whole pizza

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The statements that are true include the following:

B. Lisa paints more square feet per minute than Sally.

C. Lisa will finish painting before Sally.

D. After 10 minutes of painting Sally will have less to paint than Lisa.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 - 360)/(30 - 0)

Slope (m) = -360/30

Slope (m) = -12

At data point (0, 360) and a slope of -12, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 360 = -12(x - 0)  

y = -12x + 360

A = 360 - 12x

For Sally, the time to finish;

360 = 12x

x = 360/12 = 30 min.

For Lisa, the time to finish;

392 = 14x

x = 392/14 = 28 min (Lisa will finish painting before Sally)

For Sally, when x = 10;

A = 360 - 12(10)

A = 240 sq. feet.

For Lisa, when x = 10;

A = 392 - 14(10)

A = 252 sq. feet.

For Sally, when x = 20;

A = 360 - 12(20)

A = 120 sq. feet.

For Lisa, when x = 20;

A = 392 - 14(20)

A = 112 sq. feet.

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As a result, the prism's volume is given by V = lwh = 3 x 5 x 5.5 = 82.5 cubic yards. Thus, option C—eighty two and a half yards—is the correct response.

The quantity of room an object takes up in three dimensions is measured by its volume. It is frequently expressed in cubic units like cubic metres, cubic feet, and cubic centimetres. Mathematics formulas that are particular to the shape of the object can be used to calculate its volume, such as V = l w h for a rectangular shape or V = (4/3)r3 for a sphere.

given

V = lwh is the formula for calculating the volume of a rectangular prism, where l, w, and h stand for the prism's length, width, and height, respectively.

Here, the dimensions are 3 yards in length, 5 yards in breadth, and 5.5 yards in height.

As a result, the prism's volume is given by V = lwh = 3 x 5 x 5.5 = 82.5 cubic yards.

Thus, option C—eighty two and a half yards—is the correct response.

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Answer:

We can use Bayes' theorem to calculate P(R), which states that the probability of an event A given event B is equal to the probability of B given A multiplied by the probability of A, divided by the probability of B:

P(R|T) = P(T|R) * P(R) / P(T)

We can rearrange this equation to solve for P(R):

P(R) = P(R|T) * P(T) / P(T|R)

We are given that P(RI-T) = 0.25, which can be written as:

P(R∩T) = P(R|T) * P(T) = 0.25

We are also given that P(-R|T) = 0.2, which can be written as:

P(-R∩T) = P(-R|T) * P(T) = 0.2 * 0.1 = 0.02

We can use the law of total probability to find P(T|R):

P(T|R) = P(RI-T) / P(R) = 0.25 / P(R)

We can substitute these values into the equation for P(R) to get:

P(R) = P(R|T) * P(T) / P(T|R)

= 0.25 / [P(T|R) * P(T) + P(-R|T) * P(T)]

= 0.25 / [0.25 + 0.02]

= 0.1060

Therefore, the answer is option C: 0.1060.

The probabilities are given as follows:

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem is given as follows:

[tex]\mu = 957, \sigma = 193[/tex]

The probability is the p-value of Z when X = 1000.1 subtracted by the p-value of Z when X = 964.6, hence:

Z = (1000.1 - 957)/193

Z = 0.22.

Z = 0.22 has a p-value of 0.5871.

Z = (964.6 - 957)/193

Z = 0.04.

Z = 0.04 has a p-value of 0.5160.

Hence:

0.5871 - 0.5160 = 0.0711.

For the sample of 58, the standard error is obtained as follows:

s = 193/sqrt(58) = 25.34.

Hence:

Z = (1000.1 - 957)/25.34

Z = 1.7.

Z = 1.7 has a p-value of 0.9554.

Z = (964.6 - 957)/25.34

Z = 0.3.

Z = 0.3 has a p-value of 0.6179.

Hence:

0.9554 - 0.6179 = 0.338.

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the probability that the marble is not green is 0.9 or 90%. This means that if we were to randomly select a marble from the box, there is a 90% chance that it will not be green.

How to solve probability?

To calculate the probability that a marble is not green, we need to first determine the total number of marbles in the box, which is given by:

Total number of marbles = 8 + 6 + 2 + 4 = 20

Next, we need to determine the number of marbles that are not green. Since there are 2 green marbles, the number of marbles that are not green is given by:

Number of marbles that are not green = 20 - 2 = 18

Finally, we can calculate the probability of selecting a marble that is not green by dividing the number of marbles that are not green by the total number of marbles in the box, as follows:

Probability of selecting a marble that is not green = Number of marbles that are not green / Total number of marbles

= 18 / 20

= 0.9 or 90%

Therefore, the probability that the marble is not green is 0.9 or 90%. This means that if we were to randomly select a marble from the box, there is a 90% chance that it will not be green.

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Answer: To factorize 3h² + 12h, we can first find the greatest common factor (GCF) of the two terms, which is 3h:

3h(h + 4)

This is the fully factorized form of 3h² + 12h.

The use of calculations to show that the height of the barrel of oil is 96.82cm is given below:

The volume is given as V = 42 gal

The radius is given as r = 18/2 = 9 in

The height is given as h= 96.83 cm

Using the formula:

V = πr²h

h = V/(πr²)

The volume is given as V = 42 gal

42 gal x 3.7854 l/gal = 158.987 l

158.987 l = 158,987 ml = 158,987 cm³

The radius is given as r = 18/2 = 9 in

9 in x 2.54 cm/in = 22.86 cm

The height is given as h = (158987 cm³) / π(22.86 cm)² ≈ 96.82 cm

depending on how you round, the more precise answer is 96.8285 ≈ 96.83 cm

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The surface area of the rectangular prism is 24.62 square units

From the question, we have the following parameters that can be used in our computation:

2.5 by 2.14 by 1.5

The surface area of the rectangular prism is calculated as

Area = 2 * (Length * Width + Length * Height + Height  * Width )

substitute the known values in the above equation, so, we have the following representation

Area = 2 * (2.5 * 2.14 + 2.5 * 1.5 + 2.14 * 1.5)

Evaluate

Area = 24.62

Hence, the surface area is 24.62 square units

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The length of the other legs of the isosceles right triangle is 13 + 13√2 centimetres.

The hypotenuse of an isosceles right triangle is 13 centimetres longer than either of its legs.

An isosceles right triangle is a right triangle whose legs are the same length. The sides of a right triangle can be found using Pythagoras's theorem.

Therefore,

let

y = other legs

Therefore,

(x + 13)² = x² + x²

(x + 13)(x + 13) = 2x²

x² + 13x + 13x + 169 = 2x²

x² - 26x - 169 = 0

Therefore, using the quadratic formula,

[tex]\frac{-b+\sqrt{b^{2} - 4ac } }{2a}[/tex]

where

x = 13 ± 13√2

Therefore, we can only use positive values

x = 13 + 13√2

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Step-by-step explanation:

[tex] { ({4}^{ - 4} )}^{3} \\ = {4}^{ - 12} [/tex]

[tex] \frac{ {4}^{15} }{ {4}^{5} } \\ = {4}^{10} [/tex]

[tex] {4}^{ - 5} \times {4}^{ - 4} \\ = {4}^{ - 9} [/tex]

[tex] \frac{1}{ {4}^{ - 12} } \\ = {4}^{12} [/tex]

least to greatest

[tex]1)\: {4}^{ - 12} \\ 2) \: {4}^{ - 9} \\ 3) \: {4}^{10 } \\ 4) \: {4}^{12} [/tex]

The equation of a parabola with a vertical axis and vertex (h, k) is given by:

(x - h)² = 4p(y - k)

In the equation, where p is the distance from the vertex to the focus (and also the distance from the vertex to the directrix).

If the vertex is at the origin (h=0, k=0), then the equation simplifies to:

x² = 4py

where p is still the distance from the vertex to the focus (and also the distance from the vertex to the directrix).

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The endpoints of the latus rectum of the parabola are (3, -2) and (3, -4)

Given data ,

Let the equation of the parabola be (y + 3)² = (x - 2)

Now , y² + 6y + 9 = x - 2

y² + 6y = x - 11

Now we can see that the vertex of the parabola is (2, -3), and the axis of symmetry is parallel to the y-axis. This means that the focus and directrix will also be parallel to the y-axis.

x = h - p

where (h, k) is the vertex and "p" is the distance between the vertex and the focus. In this case, (h, k) = (2, -3) and p = 1, so

x = 2 - 1

x = 1

Therefore, the equation of the directrix is x = 1

And , the axis of symmetry of the parabola is parallel to the y-axis, the latus rectum will be parallel to the directrix, and its endpoints will be equidistant from the focus and the directrix

The distance between the focus and the directrix is 1 unit, so the distance between the endpoints of the latus rectum will also be 1 unit

Therefore, the endpoints of the latus rectum will be at the points where the perpendiculars drawn from the focus to the directrix intersect the parabola

To find the points of intersection between this line and the parabola, we can substitute x = 3 into the equation of the parabola and solve for y

(y + 3)² = (x - 2)

(y + 3)² = (3 - 2)

(y + 3)² = 1

y + 3 = ±1

y = -2 or y = -4

Hence , the points of intersection between the perpendicular and the parabola are (3, -2) and (3, -4)

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Answer: I believe the only option would be Length.

The length determines the distance between the two endpoints.

I can't think of a reason why you'd need to use height or width when measuring a line on a graph. Besides if it were height, it'll just be the length of the line when vertical. And all generated graphed lines have the same width. You wouldn't need to measure it.

Hopefully it's correct.

5. The answer is option D (12.53, 61.39°)

6. Option D. ((7√2)/2, (-7√2)/2)

7. Option C. (104.40, -16.70°)

Question 5:

Apply the Pythagorean theorem to find the distance r from the fire station to the destination:

r = √(62 + 11²) = 12.53 (rounded to the nearest hundredth)

The angle θ between the positive x-axis and the line connecting the fire station to the destination is found using tangent:

tan(θ) = ¹¹/₆

θ = arctan(¹¹/₆) = 61.39° (rounded to the nearest hundredth)

Therefore, the answer is (12.53, 61.39°), which is option D.

Answer: D. (12.53, 61.39°)

Question 6:

Convert from polar coordinates to rectangular coordinates using the following formulas:

x = r cos(θ)

y = r sin(θ)

Plugging in the values, we get:

x = -7 cos(3π/4) = -7√(2)/2) = 3.5√(2)

y = -7 sin(3π/4) = -7√(2)/2) = -3.5√(2)

Therefore, the rectangular coordinates of the point are (3.5sqrt(2), -3.5sqrt(2)), which can also be written as (-4.95, -4.95) (rounded to the nearest hundredth).

Answer: (7√(2)/2), -7√(2)/2))

Question 7:

Use the Pythagorean theorem to find the distance r from the starting point to the current position:

r = √(100² + 30²) = 104.40 (rounded to the nearest hundredth)

The angle θ between the positive x-axis and the line connecting the starting point to the current position can be found using tangent:

tan(θ) = 30/100

θ = arctan(30/100) = 16.70° (rounded to the nearest hundredth)

However, since the woman is south of the starting point, the angle should be in the negative direction, so we have:

θ = -16.70°

Therefore, the answer is (104.40, -16.70°), which is option C.

Answer: C. (104.40, -16.70°)

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The interest for the month is:  $2.59

The balance for the month is: $598.18.

We have the information from the question is:

The interest rate is 1.4% per month.

June 1 Balance $352.12

June 4 Sears $331.89

June 8 eBay $81.58

June 15 Outback $30

June 18 Payment $200

Now, According to the question:

The average daily balance for June is $184.89.

To calculate the interest for the month,

Multiply the average daily balance by the interest rate:

$184.89 × 1.4% = $2.59.

To find the balance for the month :

Add the initial balance, transactions, and interest, then subtract the payment:

$352.12 + $331.89 + $81.58 + $30 + $2.59 - $200 = $598.18.

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