Find the square root of each number.
√81
√169

The area of the region that is outside of r = 1 + cos(e) and inside of r = 3cos(e) is 3π - (π/2 + 3/2) ≈ 2.858 square units.

a) The region can be visualized by plotting the polar equations r = 1 + cos(e) and r = 3cos(e) on a graphing tool. The region lies between the curves and is bounded by the values of e.

b) To determine the limits of integration, we need to find the points of intersection between the two curves. Set the equations equal to each other and solve for e:

1 + cos(e) = 3cos(e)

2cos(e) = 1

cos(e) = 1/2

e = π/3 or e = 5π/3

c) The appropriate integral to evaluate the area is:

A = ∫[π/3, 5π/3] (1/2) (3cos(e)² - (1 + cos(e))²) de

Simplifying the integral and evaluating it yields the area of the region.

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Answer:

Answer: For me, the number who chose a design with black was greater than the number who chose a design with blue.

Step-by-step explanation:

I don't exactly know what you're asking but if you need help with rotating a shape 180 degrees here is the little "formula":

(x, y) -> (-x, -y)

Answer:

The answer is -8/3.

Step-by-step explanation:

First, you have to make y the subject :

8x + 3y = 9

3y = -8x + 9

y = (-8/3)x + 3

In a linear equation, y = mx + b, m represent gradient (slope). So in this equation the slope is -8/3.

Complete Question

Carmen is putting together a business plan for her sandwich restaurant, Subs Away, so she can expand to another location. She wants to include some information about recent sales but only has certain information about last month's sales. She currently offers ham, turkey and vegetarian sandwiches. She sells the ham sandwiches for $10 each and the turkey sandwiches for $11.25.

Last Month's Vegetarian Sales

Total Sandwiches Sold 75

Total Income $712.50

How much does Carmen charge for the vegetarian sandwich?

Answer:

 \(X=9.5\)

Step-by-step explanation:

From the question we are told that:

Total Vegetarian Sandwiches Sold \(T_{vs}=75\)

Total Vegetarian Sandwiches Income \(T_{vi}=$712.50\)

Generally the equation for Cost of vegetarian sandwich is mathematically given by

 \(X=\frac{Total\ income\ from\ vegetarian\ sandwich}{No.\ of\ vegetarian\ sandwich\ sold}\)

 \(X=\frac{T_{vi}}{T_{vs}}\)

 \(X=\frac{712.50}{75}\)

 \(X=\$9.5\)

Answer:

\(2p^2\)

Step-by-step explanation:

Step 1: Apply the exponentiation property:

\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)

Step 2: Simplify the cube root of 8:

The cube root of 8 is 2:

\(8^\frac{1}{3} =2\)

Step 3: Simplify the cube root of \((p^6)\):

The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)

Step 4: Combine the simplified terms:

\(2 * p^2\)

So, the simplified expression is \(2p^2\).

Answer:

(675°F − 32) × 5/9 + 273.15 = 630.372K

Hope it's right if not so sorry :)

Answer:

Step-by-step explanation:

6ax +12by -9ay -8bx

=6ax -8bx -9ay +12by

=2x(3a -4b)-3y(3a -4b)

=(2x-3y)(3a-4b)

Answer:

10 days: ofc there is an easier way to do this but i did my own way down below :)

Step-by-step explanation:

in 1 day

cowboys: 300+25 is 325

saints: 700-15=685

in 2 days:

cowboys: 325+25 is 350

saints: 685-15 is 670

in 3 days:

cowboys: 350+25 is 375

saints: 670-15 is 655

in 4 days:

cowboys: 375+25 is 400

saints: 655-15 is 640

in 5 days:

cowboys: 400+25 is 425

saints: 640-15 is 625

in 6 days:

cowboys: 425+25 is 450

saints: 625-15 is 610

in 7 days:

cowboys: 450+25=475

saints: 610-15 is 595

in 8 days:

cowboys: 475+25 is 500

saints: 595-15 is 580

in 9 days:

cowboys: 500+25 is 525

saints: 580-15 is 565

in 10 days:

cowboys: 525+25 is 550

saints: 565-15 is 550

in 10 days, they will have the same number of followers

The proportion of students who scored higher than Willa is 0.7389. Hence, Option B is correct.

The given information is:

Mean (μ) = 78, Standard deviation (σ) = 5, and Willa scores = 74.8

The formula for the Z-score is:

Z = (x-μ) / σ

Where, x is the value, μ is the mean and σ is the standard deviation.

Substitute the values in the above formula, we get:

Z = (74.8 - 78) / 5

= -0.64

The negative sign indicates that Willa's score is less than the mean score.

Now, find the proportion of students who scored higher than Willa.

It can be done in two steps as shown below:

Step 1: Find the area under the standard normal distribution curve corresponding to the calculated Z-score.

The Z-table gives the area to the left of Z = -0.64.

The area to the right of Z is 1 - area to the left of Z.= 1 - 0.2611

= 0.7389

Therefore, the proportion of students who scored higher than Willa is 0.7389.

Hence, Option B is correct.

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Answer:

A

Step-by-step explanation:

as one number being added on both sides

The equation that represents the situation in which case the percent of successful free throws is 75% during the game is; ( 8 + x ) = 0.75 ( 15 + x ).

It follows from the task content that the equation which represents the situation in which case the percent of successful free throws rises to 75% is to be determined.

As evident in the task content; Initially, Shaq made 8 out of 15 free throws he attempted.

Therefore, let the number of consecutive free throws he has to make to raise the success rate to 75% be; x.

Therefore, it follows from percent proportion that;

( 8 + x ) / ( 15 + x ) = 75 / 100

The simplified equation which represents the required situation is therefore;

( 8 + x ) = 0.75 ( 15 + x ).

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Answer:

35 + 37

Step-by-step explanation:

if you try any other number like: 37 + 39 = 76 that doesn't work well because its higher that 75.

for ever 12 elephants there is 11 lions

so it would be 12:11

Answer:

To determine the missing coefficient "a" in the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, we can use the SOLVE process as follows:

S: Write down the given information and identify the problem.

We are given the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, and we need to find the value of the missing coefficient "a".

O: Organize the information and decide on a plan.

To find the value of "a", we can substitute specific values for x into the polynomial and solve for a.

L: Carry out the plan.

For example, let's say we substitute x = 2 into the polynomial. We get:

P(2) = 2^4 - 32^3 + a2^2 - 6*2 + 14

= 16 - 24 + 4a - 12 + 14

= -4 + 4a + 2

= 4a - 2

We are given that P(2) = 4a - 2 = 0, so 4a = 2.

Solving for a, we get:

a = 2 / 4

= 0.5

V: Check the solution.

We can check the solution by substituting 0.5 for a in the original polynomial and verifying that it gives us the correct result for P(x) when x = 2.

P(x) = x^4 - 3x^3 + 0.5x^2 - 6x + 14

Substituting x = 2 and a = 0.5, we get:

P(2) = 2^4 - 32^3 + 0.52^2 - 6*2 + 14

= 16 - 24 + 1 - 12 + 14

= 0

Since P(2) = 0, our solution appears to be correct.

Therefore, the missing coefficient "a" in the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14 is 0.5.

Answer:

its the first option, y = -3/2x+6

Step-by-step explanation:

A)

If the order of choice is taken into consideration, we consider four possibilities for the first choice and three for the second. Then the total number of ways is given by:

B)

If the order of choices is not taken into consideration, we must divide the the previous result by 2, which is the total number of ways by which we can organize two letters (ex: AB and BA):

Answer:

24t = amount earned

Step-by-step explanation:

12 dollars per hour

so 12*t

since coach would double all the money they earned, it would mean multiplying 12t by 2 which would make the answer 24t= amount earned

The equation 15s + 34t = 1 has infinitely many integer solutions, which can be represented as (s, t) = (-7/15 - 2k, k), where k is an integer.

To find integers s and t such that 15s + 34t = 1, we can use the extended Euclidean algorithm.

We start by applying the Euclidean algorithm to the original equation. We divide 34 by 15 and get a quotient of 2 and a remainder of 4. Therefore, we can rewrite the equation as:
15s + 34t = 1
15s + 2(15t + 4) = 1
15(s + 2t) + 8 = 1

Now, we have a new equation 15(s + 2t) + 8 = 1. We can ignore the 8 for now and focus on solving for s + 2t. We can rewrite the equation as:
15(s + 2t) = 1 - 8
15(s + 2t) = -7

To find the multiplicative inverse of 15 modulo 7, we can use the extended Euclidean algorithm. We divide 15 by 7 and get a quotient of 2 and a remainder of 1. We then divide 7 by 1 and get a quotient of 7 and a remainder of 0.

Working backward, we can express 1 as a linear combination of 15 and 7:
1 = 15 - 2(7)

Now, we can substitute -7 with the linear combination of 15 and 7:
15(s + 2t) = 1 - 8
15(s + 2t) = 15 - 2(7) - 8
15(s + 2t) = 15 - 14 - 8
15(s + 2t) = -7

Since 15 is relatively prime to 7, we can divide both sides of the equation by 15:
s + 2t = -7/15

To find integer solutions for s and t, we can set t as a parameter, say t = k, where k is an integer. Then, we can solve for s:
s + 2k = -7/15
s = -7/15 - 2k

Therefore, for any integer value of k, we can find corresponding integer solutions for s and t:
s = -7/15 - 2k
t = k

This means that there are infinitely many integer solutions to the equation 15s + 34t = 1, and they can be represented as (s, t) = (-7/15 - 2k, k), where k is an integer.

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The speed in rad/s will be;25.13 / 62.86= 0.398 rad/s= 0.40 rad/s (approx)

Given:

Diameter of open cylinder (D) = 20cm

Radius of open cylinder (r) = D/2 = 20/2 = 10 cm

Height of open cylinder (h) = 90 cm

Speed of rotation = 240 rpm

Formula used:

The formula for the speed of rotation is given by;

Speed of rotation = 2πn Where, n = Number of revolutions per secondπ = 22/7

From the given diameter, we can find the circumference of the base of the cylinder as follows:

Circumference of base = πD= 22/7 × 20= 62.86 cm

We know that the water is contained in the cylinder which is open at the top. So, the water will form a parabolic surface whose height will vary with the radius.In order to find the speed of rotation of the cylinder, we need to find the velocity of the water at a distance r from the axis of rotation. The velocity of the water at any point depends on the distance of the water particle from the axis of rotation.

The maximum velocity of the water will be at the top and the minimum velocity will be at the bottom. The velocity at different points will be given by:v = rωWhere, r = distance of water particle from the axis of rotationω = angular velocity of the cylinder at that point= (240 × 2π) / 60= 8π rad/s

So, the velocity of the water at a distance of 10 cm from the axis of rotation will be;v = rω= 10 × 8π= 80π cm/s= 251.3 cm/s

Therefore, the speed of rotation of the cylinder is 25.13 rad/s (Option C)

Note: In order to convert the answer to rad/s, divide the answer by the circumference of the base of the cylinder. The circumference of the base is 62.86 cm.

So, the speed in rad/s will be;25.13 / 62.86= 0.398 rad/s= 0.40 rad/s (approx)

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Answer:

900

Step-by-step explanation:

There are 50(8/2) = 200 sheep.

So, there are 200(9/2) = 900 cows.

Answer:

x = 8

Step-by-step explanation:

4(x + 3) = 44 ( divide both sides by 4 )

x + 3 = 11 ( subtract 3 from both sides )

x = 8

The value of x is greater than -3. i.e., x > -3.

Inequality is a statement that shows the relationships the two expressions are not equal. It is defined by the symbols like <, >, ≤, ≥.

The given inequality is 5 -x < 8.

To solve:

5 - x < 8

Subtract 5 from both sides of an inequality we get,

-x < 8-5, subtract 5 from 8 we get as 3.

Then the inequality becomes,

-x < 3.

Divide both sides by -1.

⇒x > -3.

Since -1 is negative, the inequality direction is changed.

Hence, the value of x is greater than -3.

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98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792)

mean x = 16

standard deviation σ = 2.4

sample size n = 65

z score for 98% = 2.576

Interval = x±z*s/

= 16±2.576*2.4/

= 16±2.576*0.39629

= 16±1.0208

Interval = (21.0208,18.9792)

Therefore 98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792).

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Answer:

0.0357

Step-by-step explanation:

Answer:

3375 cubic inches & 121.5 ( rounding to 122)

Step-by-step explanation: