PLEASE HELP ME!!!!!!!!!!!!

In 1981 number of ways a committee of five members of the department if at least one woman must be on the committee.

By choosing some items from a set and creating subsets, permutation and combination are two approaches to express a collection of things. It outlines the numerous configurations for a certain set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.

The number of ways of picking 5 from 14 is what the question is actualy asking minus combinations of 5 from 7 , because there must be 1 woman

so 5 from 14 is given by :

= [tex]\frac{14*13*12*11*10}{5*4*3*2*1}[/tex]

which is :

14 x 13 x 11 = 2002

combinations of 5 from 7 is :

(9x8x7x6x5) / (5x4x3x2x1)

[tex]\frac{7*6*5*4*3}{5*4*3*2*1}[/tex]

which is :

7 x 3= 21

so the final answer is 2002 - 21 = 1981.

Therefore, in 1981 ways a committee of five members of the department if at least one woman must be on the committee.

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We can use the Pythagorean theorem to find the distance between the game store and the skate park.

Let's call the distance between the game store and the skate park "d". Then we have:

d^2 = (distance between school and game store)^2 + (distance between school and skate park)^2

d^2 = 7.3^2 + 8.7^2

d^2 = 106.18

d ≈ 10.3

Therefore, the game store is approximately 10.3 kilometers from the skate park.

Step 1: Find the cost of 1 pie

1 pie = 4 cups of fruit + 1 pie crust

1 pie = 4(0.75) + 1(2.50)

1 pie = 3 + 2.50

1 pie = 5.50

Step 2: Find the amount of money a baker makes by selling 1 pie

1 pie cost = 5.50

1 pie revenue = 10.25

1 pie profit = 4.75

Step 3: Find the amount of money a baker makes by selling 10 pies

1 pie profit = 4.75

10 pies profit = 47.5

Answer: $47.50

Hope this helps!

Answer:

B

Step-by-step explanation:

3x 5

_ + _

4 2

Answer: (670 -110)/8

Step-by-step explanation:

Months: 110 the first month

*Now since she paid 670 in total she subtracts the 110 from the first month which is 560, and now there is an event amound paid in the other months so you divide 560 by 8 since 8 months are left over resulting in $70 each month.

January,

February,

March,

April,

May,

June,

July,

August,

The concentration of salt in the tank at the end of 10 minutes is 0.01 pounds per gallon

We can use the formula:

(concentration of salt in tank) * (gallons of water in tank) = (total pounds of salt in tank)

To solve this problem. At the beginning, the tank contains 500 gallons of salt-free water, so the total pounds of salt in the tank is 0. After 10 minutes, 20 gallons of brine have entered the tank, and 20 gallons of the mixture have left the tank. As a result, the amount of water in the tank remains constant at 500 gallons.

The amount of salt that enters the tank in 10 minutes is:

(0.25 lb/gal) * (2 gal/min) * (10 min) = 5 lb

The total pounds of salt in the tank after 10 minutes is:

0 + 5 = 5 lb

Therefore, the concentration of salt in the tank at the end of 10 minutes is

(concentration of salt in tank) * (500 gallons) = 5 lb

Solving for the concentration of salt in the tank, we get:

concentration of salt in tank = 5 lb / 500 gallons

Simplifying this expression, we get:

concentration of salt in tank = 0.01 lb/gal

Therefore, the concentration of salt in the tank at the end of 10 minutes is 0.01 pounds per gallon.

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There are 4 possible combinations of coins that Suki could use to get exactly $2.50.

Let's denote the number of $2 coins as x, the number of $1 coins as y, and the number of quarters as z.

We need to find all the possible combinations of x, y, and z that satisfy the equation:

2x + y + 0.25z = 2.50

Here's the corrected organized list of combinations:

(1, 0, 2) → $2 + $1 + $0 = $2.50

(0, 2, 2) → $0 + $2 + $0.50 = $2.50

(0, 1, 6) → $0 + $1 + $1.50 = $2.50

(0, 0, 10) → $0 + $0 + $2.50 = $2.50

There are 4 possible combinations of coins that Suki could use to get exactly $2.50.

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We get:

[tex]y' = [x k_1 sin(k_1 x + k_2 y) - cos(k_1 x + k_2 y)] / [cos x - y sin x][/tex]

To find the first derivative of [tex]x^{(2/3)} + y^{(2/3)} = k_1^2[/tex], we can use implicit differentiation with respect to x. Taking the derivative of both sides, we get:

[tex](2/3)x^{(-1/3)} dx/dx + (2/3)y^{(-1/3)} dy/dx = 0[/tex]

Simplifying and solving for [tex]dy/dx[/tex], we get:

[tex]dy/dx = - (x/y)(y/x)^{(-2/3)} = - (x/y) (y/x)^{(2/3)}[/tex]

which can also be written as:

[tex]dy/dx = - (y/x)^{(1/3)}[/tex]

To find the first derivative of [tex]x cos(k_1 x + k_2 y) = y sin x[/tex], we can also use implicit differentiation with respect to x. Taking the derivative of both sides, we get:

[tex]cos(k_1 x + k_2 y) - x k_1 sin(k_1 x + k_2 y) = y \cos x[/tex]

Solving for y' (i.e., [tex]dy/dx[/tex]), we get:

[tex]y' = [x k_1 sin(k_1 x + k_2 y) - cos(k_1 x + k_2 y)] / [cos x - y sin x][/tex]

Note that we could have also solved for x' (i.e., [tex]dx/dy[/tex]) if we had chosen to differentiate with respect to y instead of x

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Answer:

3x

Step-by-step explanation

The time taken for $400 to amount to $650 at 6% compound interest annually is 8.33 years.

Compound interest is expressed as below:

[tex]A = P(1+\frac{r}{n})^{nt[/tex]

where A is the amount

P is principal

r is the rate of interest

n is the frequency with which interest is compounded per year

t is the time

A = $650

P = $400

r = 0.06

n = 1 because the interest is compounded annually. Thus the frequency of interest compounded per year is 1

650 = 400 [tex](1+0.06)^t[/tex]

1.625 = [tex]1.06^t[/tex]

t = 8.33 years

Thus, it takes 8.33 years for $400 to convert to $650 at 6% compound interest annually.

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The estimate from direct proportionality is higher than the prediction from KLEIBER's law.

a. For a 180 kilogram lion, we can use KLEIBER's law: R = 73.3*(180^0.75) = 6136.5 Calories per day. For an 80 kilogram human, we can use the same formula: R = 73.3*(80^0.75) = 1537.6 Calories per day.

b. If metabolic rate and mass were directly proportional, we could use the ratio of the masses to find the basal metabolic rate for an 80 kilogram human.

The ratio of the masses is 80/180 = 0.44. We can multiply this by the basal metabolic rate for the lion to get an estimate for the human: 0.44*6136.5 = 2701.26 Calories per day.

This estimate is higher than the prediction from Kleiber's law for an 80 kilogram human (1537.6 Calories per day). KLEIBER's law indicates that smaller organisms have a higher metabolic rate per kilogram of mass than do larger organisms.

Therefore, the estimate from direct proportionality is higher than the prediction from KLEIBER's law.

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The total cubic centimeters of space the tissue box requires is 500 cubic centimeters, under the condition that the box is half full.

The volume of a cube is evaluated by multiplying its length by its width by its height. If all sides of a cube are equal,

we can use the formula

V = s³

here

s = length of one side of the cube.

If we let s be the length of one side of the cube and V be its volume,

V = s³

If we know that the tissue box is half full, then let us consider that half of its volume is occupied by tissues. Then

V' = 0.5 × V

Staging V = s³ in the equation

V' = 0.5 × s³

s = 10 cm (given)

V' = 0.5 × 1000 = 500 cubic centimeters

Hence, if Patrick's tissue box has a volume of 1000 cubic centimeters and it is half full, then the tissues occupy 500 cubic centimeters of space.

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The complete question is

Patrick buys a tissue box in the shape of a cube of side 10 centimeters. How many cubic centimeters of space do the tissues occupy if the box is half full? Show all work

If x² + bx - 9 is factorable, then the possible values for b are -6 and 6.

To factor x² + bx - 9, we need to find two numbers that multiply to -9 and add up to b. We can write this as (x + a)(x + b) = x² + bx - 9. Since the coefficient of x² is 1, the two numbers that multiply to -9 must add up to the coefficient of x, which is b. We can find the factor pairs of -9 to see which ones add up to b:

-1 and 9 add up to 8

-3 and 3 add up to 0

-9 and 1 add up to -8

3 and -3 add up to 0

1 and -9 add up to -8

9 and -1 add up to 8

Only -6 and 6 add up to b, so the possible values for b are -6 and 6. Therefore, x² - 6x - 9 and x² + 6x - 9 are both factorable.

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________________________________

________________________________

About the equation used to estimate the height E of the tramway t seconds after it left the station, we first need to calculate the rate of elevation gain per second.

Elevation difference: 5632 feet (Range Peak) - 4692 feet (tramway station) = 940 feet
Time: 4 minutes * 60 seconds/minute = 240 seconds

Rate of elevation gain: 940 feet / 240 seconds = 3.9167 feet/second (approximately 3.9 feet/second)

Now, we can write the equation to estimate the height E of the tramway t seconds after it left the station:

E = initial elevation + (rate of elevation gain * t)
E = 4692 + 3.9t

So, the correct equation is: E = 4692 + 3.9t

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Answer:

That's the correct order.

Step-by-step explanation:

2x+20+5=55

2x+25=55

2x=30

x=15

The amount of cashews needed to be mixed with the peanuts so that the mixture will produce the same revenue as selling the nuts separately is 10 pounds.

To solve this problem, we need to use the equation:

$3(20) + 6x = 4(20 + x)$

where x is the number of pounds of cashews needed.

First, we simplify the equation by multiplying:

$60 + 6x = 80 + 4x$

Then we isolate x by subtracting 4x from both sides and subtracting 60 from both sides:

$2x = 20$

Finally, we solve for x by dividing both sides by 2:

$x = 10$

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The value of the definite integral 2t sin(-9t)dt from 0 to π is 5.25π.

To evaluate the definite integral 2t sin(-9t)dt using integration by parts, we first need to choose u and dv.

Let u = 2t and dv = sin(-9t)dt. Then du/dt = 2 and v = (-1/9)cos(-9t).

Using the integration by parts formula ∫udv = uv - ∫vdu, we can evaluate the definite integral as follows: ∫2t sin(-9t)dt = [-2t/9 cos(-9t)] - ∫(-2/9)cos(-9t)dt

Next, we need to evaluate the integral on the right-hand side.

Let u = -2/9 and dv = cos(-9t)dt. Then du/dt = 0 and v = (1/9)sin(-9t).

Using integration by parts again, we get: ∫cos(-9t)dt = (1/9)sin(-9t) + ∫(1/81)sin(-9t)dt = (1/9)sin(-9t) - (1/729)cos(-9t)

Substituting this result back into the original equation, we get: ∫2t sin(-9t)dt = [-2t/9 cos(-9t)] - [(-2/9)(1/9)sin(-9t) + (2/9)(1/729)cos(-9t)]

Now, we can evaluate the definite integral by plugging in the limits of integration (0 and π) and simplifying:

∫π0 2t sin(-9t)dt

= [-2π/9 cos(-9π)] - [(-2/9)(1/9)sin(-9π) + (2/9)(1/729)cos(-9π)] - [(-2/9)cos(0)]

= [-2π/9 cos(9π)] - [(-2/9)(1/9)sin(9π) + (2/9)(1/729)cos(9π)] - [(-2/9)cos(0)]

= [-2π/9 (-1)] - [(-2/9)(1/9)(0) + (2/9)(1/729)(-1)] - [(-2/9)(1)]

= (2π/9) + (2/6561) + (2/9) = 5.25π

Therefore, the value of the definite integral 2t sin(-9t)dt from 0 to π is 5.25π.

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The situation that can be represented by a proportional relationship is given as follows:

B: Justin saves $5:50 every month to contribute to his college fund.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

A proportional relationship is a linear function with an intercept of zero, meaning that the initial amount should be of zero, meaning that option B is the correct option for this problem.

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Jorge's older brother's watering can holds approximately 165.33 cups of water. And since Jorge's watering can holds half as much water as his older brother's watering can, Jorge's watering can holds approximately (1/2) × 165.33 = 82.67 cups of water, which we can round to 4 cups.

Let's represent the amount of water that Jorge's older brother's watering can holds by x. According to the problem, Jorge's watering can holds half as much water as his older brother's watering can. Therefore, Jorge's watering can holds (1/2)x cups of water.

We also know that Jorge's younger brother's watering can holds 8 cups of water. Altogether, the watering cans hold 2 gallons, which is equal to 2 × 128 = 256 fluid ounces (since there are 128 fluid ounces in a gallon).

We can write an equation based on the given information:

x + (1/2)x + 8 = 256

Simplifying the equation, we get:

(3/2)x = 248

x = 248 × 2/3 = 165.33

Therefore, jorge's watering can holds 4 cups of water.

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The Unique or Many for each description by placing a check or X in the appropriate box is given below.

We are given that;

Measurements=  30°, 60°, 90°

Side lengths 5 cm, 5 cm, 5 cm Side lengths 3 in and 4.

Now,

If three angle measures are given, and they add up to 180 degrees, then there are infinitely many similar triangles with those angle measures, but they differ in size. This is called the AAA (angle-angle-angle) similarity criterion.

If two angles and a non-included side are given, then there may be zero, one, or two possible triangles with those measurements, depending on the length of the side and the position of the angles. This is called the AAS (angle-angle-side) or SSA (side-side-angle) criterion.

Using criteria, we can fill in the table as follows:

Conditions | Unique | Many Side lengths 3 cm, 6 cm, 7 cm | ✓ | Angle measures 30°, 60°, 90° | | ✓ Angle measures 35º, 35°, 110° | | ✓ Side lengths 5 cm, 5 cm, 5 cm | ✓ | Side lengths 3 in and 4 in with an included 95° angle | ✓ |

Therefore, by the angle the answer will be given.

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So, the final answer is:

(1/2)(-√(4 - x^2) / x) + C. To evaluate the integral ∫dx / (x^2√(4-x^2)), we will use the trigonometric substitution x = 2sin(θ). This substitution is chosen because it simplifies the expression under the square root, as 4 - x^2 becomes 4 - 4sin^2(θ) which can be factored into 4cos^2(θ).

Now, we need to find dx in terms of dθ. Differentiating x with respect to θ, we get:

dx/dθ = 2cos(θ) => dx = 2cos(θ)dθ

Substituting x = 2sin(θ) and dx = 2cos(θ)dθ into the integral:

∫(2cos(θ)dθ) / ((2sin(θ))^2√(4(1-sin^2(θ))))
= ∫(2cos(θ)dθ) / (4sin^2(θ)√(4cos^2(θ)))

Simplifying the integral, we get:

= (1/2) ∫(cos(θ)dθ) / (sin^2(θ)cos(θ))
= (1/2) ∫dθ / sin^2(θ)

Now, use the identity csc^2(θ) = 1/sin^2(θ) and integrate:

= (1/2) ∫csc^2(θ) dθ
= (1/2)(-cot(θ)) + C

To find cot(θ), we draw a right triangle with the opposite side x, the adjacent side √(4 - x^2), and the hypotenuse 2:

cot(θ) = adjacent / opposite = √(4 - x^2) / x

So, the final answer is:

(1/2)(-√(4 - x^2) / x) + C

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The amount of compound remaining from a 75-ounce sample after three weeks is 0.52 oz. The correct option is c) 0.52 oz.

To find the amount of compound remaining after three weeks, we need to first convert three weeks into days. Since one week is equal to seven days, three weeks is equal to 21 days. The exponential decay function is given by: N = [tex]N0e^(-kt)[/tex]

Where N is the amount of compound remaining after time t, N0 is the initial amount of compound, k is the decay constant, and t is time. The half-life of the compound is given as four days, which means that k = ln(2)/4 = [tex]0.1733 day^-1.[/tex]

Substituting the values, we get: N =[tex]75e^(-0.1733*21[/tex]. N = 0.52 oz to find the amount of compound remaining after a certain amount of time, we can use the exponential decay function N =[tex]N0e^(-kt)[/tex]. We first need to convert the given time into the appropriate units and calculate the decay constant using the half-life. We can substitute the values to find the answer.

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The option that represents the resulting transformation is: Option C

A reflection over line is defined as a transformation in which each point of the original figure which is also called the pre-image possesses an image that is the essentially the same distance from the reflection line as the original point, but then is on the opposite side of the line. In a reflection, the image is the same size and shape as the pre-image.

Now, looking at the letter Q, when we reflect it once, it should be the mirror image but when reflect it the second time about same line, it becomes exactly the original copy.

Thus, we can conclude that Option C represents the resulting transformation.

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The explanation of the continuous range is added below

Continuous ranges are expressed in inequality notation because they represent a set of infinitely many numbers between two endpoints.

Inequality notation allows us to describe this range using mathematical symbols to show that the values can be any number between the two endpoints, including the endpoints themselves.

For example, a continuous range might be described as "all real numbers between 0 and 1, including 0 and 1".

This can be expressed in inequality notation as 0 ≤ x ≤ 1, where x is a real number.

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The platelet count is 652 x 10^3.

Based on the information provided, it seems that the platelet count from a test result is 652, and the normal range for platelet count is 150,000 to 450,000 platelets per microliter of blood. The value "10(3)" likely refers to the measurement being in thousands.

To convert the measurement to the standard unit of platelet count, we need to multiply the given value by 1,000. Thus, 652 * 1,000 = 652,000 platelets per microliter.

It's important to note that platelet counts can vary depending on various factors, and medical professionals typically interpret the results in conjunction with other clinical information. If the obtained value of 652,000 platelets per microliter is accurate, it would be significantly higher than the upper limit of the normal range.

It's crucial to consult a healthcare professional or a qualified medical practitioner for an accurate interpretation of test results and any necessary medical advice or treatment.

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Answer:

96 percent

Step-by-step explanation:

If you divide 816 by 850 you get 0.96. If you multiply 0.96 by 100% you get 96%.

The quadratic function for the graph and the duration the ball is in the air are;

Function; f(t) = -16·(t - h)² + k

Duration the ball is in the air is about 3.02 seconds

A quadratic function is a function that can be expressed in the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.

The height at which the ball Alex releases the ball = 4 feet above the ground

The time it takes the ball to reach maximum height = 1.5 seconds

The required form of the function to be obtained based on the graph is f(t) = a·(t - h)² + k

f(t) = The height of the ball at time t

The required form of the function is the vertex form of a quadratic equation, where;

(h, k) = The coordinates of the vertex = (1.5, 40)

The points on the graph are; (0, 4), (3, 3)

Therefore; f(0) = a·(0 - 1.5)² + 40 = 4

a·(0 - 1.5)²  = 4 - 40 = -36

a = -36/(1.5²) = -16

The equation is; f(t) = -16·(t - 1.5)² + 40

The time the ball is in the air can be obtained from the function f(t) = -16·(t - 1.5)² + 40 as follows;

f(t) = -16·(t - 1.5)² + 40 = 3

-16·(t - 1.5)² = 3 - 40 = -37

(t - 1.5)² = -37/(-16)

(t - 1.5) = (√(37))/4

t = (√(37))/4 + 1.5 ≈ 3.02

The time the ball is in the air about 3.02 seconds

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Selika spends £565.85 on labour costs.

Given, Selika spends money on plants, materials, and labor in the ratio of 1:5:12 and spends a total of £848.75. We have to find how much money she spends on labor costs.

Let the amount of money Selika spends on plants be x. Then, the amount of money she spends on materials is 5x, and the amount of money she spends on labor is 12x.

The total amount of money she spends is £848. 75

x + 5x + 12x = 848.75

18x = 848.75

x = 848.75/18

x = 47.15

She spend on labour 12x = 12 × 47.15

= 565.85

Therefore, Selika spends £565.85 on labour costs.

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The MAD for Doctor A's data set is 0.67 and the MAD for Doctor B's data set is 0.83. Doctor A's data set has less variation than Doctor B's data set, as indicated by their respective MADs.

To calculate the mean absolute deviation (MAD) for a data set, we first find the mean of the data set, and then find the absolute deviation of each value from the mean. We then find the mean of these absolute deviations.

a) For Doctor A's data set on corrective lenses, the mean is:

Mean = (15+18+17+16+14)/5 = 16

The absolute deviations from the mean are:

|15-16| = 1

|18-16| = 2

|17-16| = 1

|16-16| = 0

|14-16| = 2

The mean of these absolute deviations is:

MAD = (1+2+1+0+2)/5 = 1.2

Therefore, the MAD for Doctor A's data set is 1.2.

b) For Doctor B's data set on corrective lenses, the mean is:

Mean = (17+19+20+16+18)/5 = 18

The absolute deviations from the mean are:

|17-18| = 1

|19-18| = 1

|20-18| = 2

|16-18| = 2

|18-18| = 0

The mean of these absolute deviations is:

MAD = (1+1+2+2+0)/5 = 1.2

Therefore, the MAD for Doctor B's data set is also 1.2.

Comparing the two data sets using their MAD, we can see that they have the same amount of variation or dispersion from the mean. Both sets have a MAD of 1.2, indicating that the average absolute deviation of each value from the mean is the same for both sets.

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Answer:

Doctor A MAD: 11.8

Doctor B MAD: 9.32

Step-by-step explanation:

This is what I got on the assignment.