Find the value of x.

Answer:

[tex]\mathbf{V = 1296 \pi }[/tex]

Step-by-step explanation:

Given that :

Find the volume of the region enclosed by the cylinder [tex]x^2 + y^2 =36[/tex] and the plane z = 0 and y + z = 36

From y + z = 36

z = 36 - y

The volume of the region can be represented by the equation:

[tex]V = \int\limits \int\limits_D(36-y)dA[/tex]

In this case;

D is the region given by [tex]x^2 + y^2 = 36[/tex]

Relating this to polar coordinates

x = rcosθ    y = rsinθ

x² + y² = r²

x² + y² = 36

r² = 36

r = [tex]\sqrt{36}[/tex]

r = 6

dA = rdrdθ

r → 0 to 6

θ to 0  to 2π

Therefore:

[tex]V = \int\limits^{2 \pi} _0 \int\limits ^6_0 (36-r sin \theta ) (rdrd \theta)[/tex]

[tex]V = \int\limits^{2 \pi} _0 \int\limits ^6_0 (36-r^2 sin \theta ) drd \theta[/tex]

[tex]V = \int\limits^{2 \pi} _0 [\dfrac{36r^2}{2}- \dfrac{r^3}{3}sin \theta]^6_0 \ d\theta[/tex]

[tex]V = \int\limits^{2 \pi} _0 [648- \dfrac{216}{3}sin \theta]d\theta[/tex]

[tex]V = \int\limits^{2 \pi} _0 [648+\dfrac{216}{3}cos \theta]d\theta[/tex]

[tex]V = [648+\dfrac{216}{3}cos \theta]^{2 \pi}_0[/tex]

[tex]V = [648(2 \pi -0)+\dfrac{216}{3}(1-1)][/tex]

[tex]V = [648(2 \pi )+\dfrac{216}{3}(0)][/tex]

[tex]V = 648(2 \pi )[/tex]

[tex]\mathbf{V = 1296 \pi }[/tex]

Answer:

x = log (7)/ 2log 5

Step-by-step explanation:

25^ x = 7

Replace 25 with 5^2

5^ 2x = 7

Take log  on each side

log (5 ^2x) = log ( 7)

We know that log a^ b = b log a

2x  log 5 = log (7)

Divide each side by log 5

2x  log 5/ log 5= log (7)/ log 5

2x = log (7)/ log 5

Divide each side by 2

x = log (7)/ 2log 5

Answer:

The demand function is  [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]

Step-by-step explanation:

A firm has the​ marginal-demand function [tex]D' x = \dfrac{-1200}{\sqrt{25-x^2 } }[/tex].

Find the demand function given that D = 16,000 when x = $4 per unit.

What we are required to do  is to find the demand function D(x);

If we integrate D'(x) with respect to x ; we have :

[tex]\int\limits \ D'(x) \, dx = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]

[tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]

Let represent   t  with [tex]\sqrt{25-x^2}}[/tex]

The differential of t with respect to x is :

[tex]\dfrac{dt}{dx}= \dfrac{1}{2 \sqrt{25-x^2}}}(-2x)[/tex]

[tex]\dfrac{dt}{dx}= \dfrac{-x}{ \sqrt{25-x^2}}}[/tex]

[tex]{dt}= \dfrac{-xdx}{ \sqrt{25-x^2}}}[/tex]

replacing the value of  [tex]\dfrac{-xdx}{ \sqrt{25-x^2}}}[/tex]  for dt in   [tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]

So; we can say :

[tex]D(x) = \int\limits{\dfrac{-1200 x}{\sqrt{25-x^2}} } \, dx[/tex]

[tex]D(x) = 1200\int\limits{\dfrac{- x}{\sqrt{25-x^2}} } \, dx[/tex]

[tex]D(x) = 1200\int\limits \ dt[/tex]

[tex]D(x) = 1200t+ C[/tex]

Let's Recall that :

t  = [tex]\sqrt{25-x^2}}[/tex]

Now;

[tex]\mathbf{D(x) = 1200(\sqrt{25-x^2}})+ C}[/tex]

GIven that:

D = 16,000 when x = $4 per unit.

i.e

D(4) = 16000

SO;

[tex]D(x) = 1200(\sqrt{25-x^2}})+ C[/tex]

[tex]D(4) = 1200(\sqrt{25-4^2}})+ C[/tex]

[tex]D(4) = 1200(\sqrt{25-16}})+ C[/tex]

[tex]D(4) = 1200(\sqrt{9}})+ C[/tex]

[tex]D(4) = 1200(3}})+ C[/tex]

16000 = 1200 (3) + C

16000 = 3600 + C

16000 - 3600 = C

C = 12400

replacing the value of C = 12400 into [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2}})+ C}[/tex], we have:

[tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]

∴ The demand function is  [tex]\mathbf{D(x) = 1200(\sqrt{25-x^2})+ 124000}[/tex]

Step-by-step explanation:

It is given that,

Total length of a board is 65 inches

It is sawed into two pieces such that one piece is 7 inches shorter than twice the length of the other piece.

Let x is the length of other piece and y is the length of first piece such that,

y = 2x-7 ....(1)

Also,

x+y = 65 .....(2)

Put the value of y from equation (1) to equation (2) such that,

x+2x-7 = 65

3x=65+7

3x=72

x = 24 inches

Put the value of x in equation (1)

y = 2(24)-7

y = 41 inches

So, the length of first piece is 41 inches while the length of other piece is 24 inches.

Answer:

I guess that we have the linear equation:

y = 32*x

Where y is the profit, and x is the number of games sold.

Then the first step may be doing a table.

Give x different values, then find the value of y.

if x = 0

y = 32*0 = 0

if x = 1, y = 32*1 = 32

if x = 2, y = 2*32 = 64

Then the points:

(0,0) (1,32) and (2, 64) belong to this line, now we need to conect them with a straigth line and its ready.

The graph will be:

Answer:

Likely

Step-by-step explanation: Mathematically it is likely because there are 4 options certain is the thing that will defiantly happen so it would be 4/4. The impossible thing would be 1/4 this is because 1/4 is the smallest so it is obviously going to be impossible. Likely would be 3/4 and unlikely would clearly be 2/4

Answer:

it is likely

Step-by-step explanation:

it is not certant because it is not 4/4 but it is not impossible because its not 0/4 so the answer is likely 3/4

Answer: There is no sufficient evidence to support the claim that loaded die behaves differently than a fair die

Step-by-step explanation:

Find explanations in the attached file

Answer:

z = 70°

y = 103°

Step-by-step explanation:

From the picture attached,

110° + z° = 180° [Supplementary angles]

z = 180 - 110

z = 70°

Since sum of interior angles of a polygon = (n - 2)×180°

where n = number of sides of the polygon

For a quadrilateral (n = 4),

Sum of interior angles = (4 - 2) × 180°

                                     = 360°

z° + y° + 100° + 87° = 360°

70° + y° + 187° = 360°

y = 103°

Therefore, measure of the angles x = 70° and y = 103°.

Hey there! :)

Answer:

4√3 in.

Step-by-step explanation:

Given:

-Equilateral triangle

-Side lengths of 8 in

Find the altitude using the Pythagorean Theorem (c² = a² + b²) where:

'a' is the shorter leg, or half of the base to find the altitude

'b' is the altitude

'c' is the Hypotenuse, or 8 in.

Therefore:

8² = 4² + b²

64 = 16 + b²

48 = b²

b = √48 or 4√3 in.

Therefore, the altitude of the triangle is 4√3 in.

Answer: -4/3

Step-by-step explanation:

Formula to find a slope of two given points is

y(sub2) - y(sub1) / x(sub2) - x(sub1)

Plug the values in to get the answer.

-2 - 2 / -1 - (-4)

-4/3

Answer:

x = 65°

Step-by-step explanation:

Naming the sides of the parallelogram formed ABCD as shown in the attached image to this solution.

Angle A = 2x (vertically opposite angles are equal)

Angle A = Angle C (opposite angles of a parallelogram are equal)

Angle A = Angle C = 2x

(Angle C) + 50° = 180° (Sum of angles on a straight line is 180°)

2x + 50° = 180°

2x = 180° - 50° = 130°

x = (130°/2) = 65°

Hope this Helps!!!

Answer:

65 degrees

Step-by-step explanation:

S = sample space = set of all possible outcomes

S = set of whole numbers 1 through 6

S = {1,2,3,4,5,6}

E = event space = set of outcomes we want to happen

E = set of odd numbers between 1 through 6

E = {1,3,5}

We have 3 items in set E and 6 items in set S. So there are 3 ways to get what we want to happen out of 6 ways total. The probability is therefore 3/6 = 1/2

Answer:

The answer is below

Step-by-step explanation:

Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. The white blood count (WBC) was measured using a Coulter Counter Model S. The mean WBC was 8.636 with a standard deviation of 3.9265. (a) Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to

Answer:

Given:

Mean (μ) = 8.636, standard deviation (σ) = 3.9265, Confidence (C) = 90% = 0.9, sample size (n) = 25

α = 1 - C = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05

From the normal distribution table, The z score of α/2 (0.05) corresponds to the z score of 0.45 (0.5 - 0.05) which is 1.645

The margin of error (E) is given by:

[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }\\ \\E=1.645*\frac{3.9265}{\sqrt{25} }=1.2918[/tex]

The confidence interval = μ ± E = 8.636 ± 1.2918 = (7.3442, 9.9278)

The 90% confidence interval is from 7.3442 to 9.9278

Answer:

m∠N = 51°

m∠M = 31°

m∠O = 98°

Step-by-step explanation:

It is given that ΔMNO is an isosceles triangle with base NM.

m∠N = (4x + 7)° and m∠M = (2x + 29)°

By the property of an isosceles triangle,

Two legs of an isosceles triangle are equal in measure.

ON ≅ OM

And angles opposite to these equal sides measure the same.

m∠N = m∠M

(4x + 7) = (2x + 29)

4x - 2x = 29 - 7

2x = 22

x = 11

m∠N = (4x + 7)° = 51°

m∠M = (2x + 9)° = 31°

m∠O = 180° - (m∠N + m∠M)

         = 180° - (51° + 31°)

         = 180° - 82°

         = 98°

Answer:

[tex](A)7.5 ft^2\\(C)20 ft^2[/tex]

Step-by-step explanation:

The diagram is attached below.

Area of the Rectangular Faces

[tex]8 X 6.5 =52$ ft^2\\8 X 2.5 =20$ ft^2\\8 X 6= 48$ ft^2[/tex]

Area of the Triangular face

[tex]=\dfrac12 X 2.5 X 6 =7.5$ ft^2[/tex]

Therefore, Options A and C could be the area of one lateral face of the triangular prism.

Answer:

C

Step-by-step explanation:

Answer:

Option(A) is correct

Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.

Step-by-step explanation:

The given data set in the question are ;33, 29, 97, 56, 26, 78, 83, 74, 65, 47, 58

the range can be determined by finding the highest value and subtract it to the lowest value. In this case the values are:

Highest = 97

Lowest = 71

Range = highest value - Minimum value

Range = 97 - 26 = 71

[tex] Range= 71[/tex]

mean of the data is the summation of all the numbers in the data set divided by the number of given samples.

Mean = (33 + 29 + 97 + 56+ 26 + 78 + 83 74+ 65 + 47 + 58)/11

= 647/11

[tex]Mean value =58.7[/tex]

Now to find the variance of the data set by using below formular

σ²=[ (xᵢ -mean)²]/n-1

[(33-58.7)² +(29-58.7)²+( 97-58.7)²+( 56-58.7)²+( 26 -58.7)²+(78-58.7)²+( 83 -58.7)²+(74-58.7)²+( 65-58.7)²+( 47 -58.7)²+(58 -58.7)²]/10

[tex]Variance=546[/tex]

Now, we will calculate standard deviation by taking square root over variance

σ =√(variance)

σ =√(546)

[tex]Standard deviation= 23.4[/tex]

Hence, the range is 71 ,variance is 546 and standard deviation is 23.4 therefore,

Option A is the answer that is Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.

Answer:

A)$ 45

B) $105

Step-by-step explanation:

Bag and a belt cost $255

Let bag = x

Let belt = y

X+y= 255 equation 1

Let total money be z first

Remaining money= z-255

X-30 = z-255

Y +15 = z-255

Equating the left side of the equation

X+30 = y+15

X-y= 45 equation 2

Solving simultaneously

X+y= 255

X-y= 45

2x = 300

X= 150

If x= 150

150-y= 45

150-45= y

105=y

Bag = $150

Belt = $105

Bag Is 150-105 more than the belt

150-105= $45

Hey there! I'm happy to help!

If the number of red marbles is 6 more than double the number of black marbles, we can create this equation, with r representing the red marbles and b representing the black marbles.

r=2b+6

We also know that r+b=33, and if we know that r is equal to 2b+6, we can just replace r with that and then solve for b.

2b+6+b=33

We combine like terms.

3b+6=33

We subtract six from both sides.

3b=27

We divide both sides by 3.

b=9

Now we just subtract 9 from 33 to see how many red ones there are.

33-9=24

So, there are 24 red marbles and 9 black marbles.

Now, let's see which of these options are correct.

The equation r+b=33 represents the total number of marbles.

This is true because r plus b is equal to the total, which is 33.

The equation r=2b+6 can be used to find the number of red marbles.

This is true because it we used this r-value to find how many black marbles there were.

The equation r=2b+6 represents the total number of marbles.

This is false because it does not have the total number, which is 33.

The equation r=b=33 can be used to find the number of red marbles.

This is true because we plugged in the r-value to solve for b with this equation.

There are 9 red marbles in the bag.

This is false. There are 24 red marbles.

There are 9 black marbles in the bag.

This is true.

There are 24 black marbles in the bag.

This is false. There are 9 black marbles.

There are 24 red marbles in the bag.

This is true.

Have a wonderful day! :D

Answer:

1,2,4,6,8

Step-by-step explanation:

Answer:

$0.26

Step-by-step explanation:

To find the unit price, divide the cost by the amount you have.

$2.86/11 = $0.26

The unit price is $0.26.

Answer:

i feel as if in the United States, both the metric system and the English system of measurement are used, although the English system predominates. This discussion question has three parts:

Look around you to find something in the U.S. that is measured in metrics. Describe it to the class.

Give an example of how you think the metric system will be used in your future career.

Do you think the U.S. should switch to metric system exclusively? Why or why not?

This week we learned about the metric and U.S. customary measurement systems. Please upload and submit your responses to the following questions in at least 150 words:

In reflecting on both measurement systems, what did you find most important?

Explain how both measurement systems could relate to your life, community, or current/future career.

Expert Answer

Step-by-step explanation:

Answer:

The correct option is (B).

Step-by-step explanation:

The p-value is well-defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic.

In this case, we need to test the claim that the majority of voters oppose a proposed school tax.

The hypothesis can be defined as follows:

H₀: The proportion of voters opposing a proposed school tax is not a majority, i.e. p ≤ 0.50.

Hₐ: The proportion of voters opposing a proposed school tax is a majority, i.e. p > 0.50.

It is provided that the test statistic value and p-value are:

z = 1.23

p-value = 0.1093

The probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic is 0.1093.

The significance level of the test is:

α = 0.05

The p-value of the test is larger than the significance level of the test.

p-value = 0.1093 > α = 0.05

The null hypothesis will not be rejected.

Concluding that there is not enough evidence to support the claim.

Thus, the correct option is:

"If the null hypothesis is true, then the probability of getting a test statistic that is as or more extreme than the calculated test statistic of 1.23 is 0.1093. This result is not surprising (or considered unusual) and could easily happen by chance"

Answer: a) Mean = [tex]=37.80[/tex]

Standard deviation=[tex]=1.9442[/tex]

b) Mean = [tex]56.00[/tex]

Standard deviation=[tex]4.0988[/tex]

c) Mean = [tex]=24[/tex]

Standard deviation=[tex]2.4495[/tex]

Step-by-step explanation:

To compute Mean and standard deviation , we use following formula:

Mean = [tex]n\pi[/tex]

Standard deviation=[tex]\sqrt{n\pi(1-\pi)}[/tex]

a. [tex]n=42,\ \pi=0.90[/tex]

Mean = [tex]42\times0.90=37.80[/tex]

Standard deviation=[tex]\sqrt{42(0.90)(0.10)}=\sqrt{3.78}\approx1.9442[/tex]

b. [tex]n=80,\ \pi=0.70[/tex]

Mean = [tex]80\times0.70=56.00[/tex]

Standard deviation=[tex]\sqrt{80(0.70)(0.30)}=\sqrt{16.8}\approx4.0988[/tex]

c. [tex]n=32,\ \pi=0.75[/tex]

Mean = [tex]32\times0.75=24[/tex]

Standard deviation=[tex]\sqrt{32(0.75)(0.25)}=\sqrt{6}\approx2.4495[/tex]

Answer:

Step-by-step explanation:

even function are symmetrical about the y axis or f(-x)=f(x)

odd function are symmetrical about the origin -f(-x)=f(x)

f(x)=x^6 + 10x^4-11x^2+19

f(-x)=(-x)^6+10(-x)^4+11(-x)^2+19=x^6 + 10x^4-11x^2+19

the function is even

Answer:

13.33

Step-by-step explanation:

As in the attached diagram,  we can see that the points belong to  [tex]\mu\pm \sigma[/tex] interval

Data provided in the question as per the details below:

[tex]\mu_{\bar x}[/tex] = 440

[tex]\mu_{\bar x} + \sigma_{\bar x}[/tex] = 480

So,

[tex]\sigma_{\bar x}[/tex] = 480 - 440

= 40

Now the standard deviation of the population is

[tex]V(\bar{x}) = \frac{\sigma}{\sqrt n} \\\\ = \frac{40}{\sqrt 9}[/tex]

= 13.33

Hence, the standard deviation of the population for which the sample is drawn is 13.33

Answer:

the car overtake the truck at time 11:40 am.

Step-by-step explanation:

We have both vehicules going at constant speed from city a to city b. The distance is unknown, but can be written as d.

We will express the time in hours (and decimals of hours).

The truck speed can be calculated estimating the time between arrival and start:

- The arrival time is 1.15 pm. This is t2=13.25.

- The starting time is 9:15 am. This is t1=9.25.

The truck took t2-t1=13.25-9.25=4 to go from city a to b.

The average speed is then:

[tex]v_t=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{4}[/tex]

We can write the equation for the position x(t) for the truck as:

[tex]x(t)=x_0+v_t\cdot t=x_0+\dfrac{d}{4}t\\\\\\x(13.25)=x_0+\dfrac{d}{4}(13.25)=d\\\\x_0=d-3.3125d=-2.3125d\\\\\\x(t)=-2.3125d+0.25d\cdot t[/tex]

For the car we have:

- The arrival time is 12:45 am. This is t2=12.75.

- The starting time is 10 am. This is t1=10.

The car took t2-t1=12.75-10=2.75.

The average speed is then:

[tex]v_c=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{2.75}[/tex]

We can write the equation for the position x(t) for the car as:

[tex]x(t)=x_0+v_c\cdot t=x_0+\dfrac{d}{2.75}t\\\\\\x(12.75)=x_0+\dfrac{d}{2.75}(12.75)=d\\\\x_0=d-4.6363d=-3.6363d\\\\\\x(t)=-3.6363d+0.3636d\cdot t[/tex]

The time at which the car overtake the car is the time when both vehicles have the same position:

[tex]x(t)/d=-2.3125+0.25\cdot t = -3.6363+0.3636\cdot t\\\\-2.3125+3.6363=(0.3636-0.25)t\\\\1.3238=0.1136t\\\\t=1.3238/0.1136\approx11.65[/tex]

The car overtakes the truck at t=11.65 hours or 11:39 am.

Answer:

[tex]7.5cm^2[/tex]

Step-by-step explanation:

Well using the following formula,

[tex]\frac{b*h}{2}[/tex]

5*3 = 15

15 / 2

7.5cm^2

Answer:[tex]7.5cm^{2}[/tex]

Step-by-step explanation:

h=3

b=5

area=1/2 x b x h

1/2 x 5 x 3

area=7.5

Answer:

Well if (a,b) is in Quadrant IV which is the last quadrant the a or x is a positive number and the b or y is a negative number.

Answer:

a should be a positive number

b should be a negative number

Answer:

0.2006

Step-by-step explanation:

The probability the first calculator is defective is 42/62.

The probability the second calculator is defective is 41/61.

The probability the third calculator is defective is 40/60.

The probability the fourth calculator is defective is 39/59.

The probability all four calculators are defective:

(42/62) (41/61) (40/60) (39/59) = 0.2006

Answer:

57.6 km/h

Step-by-step explanation:

We are told that At noon, ship A is 70 km west of ship B.

Thus, coordinates of initial position of A and B is;

A(0,0) and B(70,0)

Now, we are told that Ship A is sailing south at 35 km/h and ship B is sailing north at 25 km/h. Thus, the final position of ship A and B after t hours are;

A(0,-35t) and B(70,25t)

Thus, distance between the two ships at time t hours is;

d(t) = √[(70 - 0)² + (25t - (-35t))²]

d(t) = √(4900 + 3600t²)

Now, to find how fast the distance between the ships changing, let's differentiate using the chain rule;

d'(t) = [1/(2√(4900 + 3600t²))] × 7200t

d'(t) = 3600t/√(4900 + 3600t²)

d'(t) = 3600t/10√(49 + 36t²)

d'(t) = 360t/√(49 + 36t²)

Now, at 4pm,it would have been 4 hours from noon. Thus, t = 4.

So;

d'(t) = (360×4)/√(49 + 36(4²))

d'(t) = 1440/√(49 + 576)

d'(t) = 1440/√625

d'(t) = 1440/25

d'(t) = 57.6 km/h