All sides of the building shown above meet at right angles. If three of the sides measure 2 meters, 7 meters, and 11 meters as shown, then what is the perimeter of the building in meters?

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:

[tex]\boxed{x^2+y^2 = 49}[/tex]

Step-by-step explanation:

First, we'll find the length of the radius using distance formula and the coordinates (0,0) and (7,0)

Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

R = [tex]\sqrt{(7-0)^2+(0-0)^2}[/tex]

R = [tex]\sqrt{7^2}[/tex]

Radius = 7 units

Now, Equation of circle:

[tex](x-a)^2+(y-b)^2 = R^2[/tex]

Where (a,b) = (0,0) So, a = 0, b = 0 and R = 7 units

=> [tex](x-0)^2+(y-0)^2 = (7)^2[/tex]

=> [tex]x^2+y^2 = 49[/tex]

This is the required equation of the circle.

Answer:

x^2 + y^2 = 49

Step-by-step explanation:

We can write the equation of a circle as

( x-h) ^2 + ( y-k) ^2 = r^2

where ( h,k) is the center and r is the radius

The radius is the distance from the center to a point on the circle

(0,0) to (7,0) is 7 units

so the the radius is 7

( x-0) ^2 + ( y-0) ^2 = 7^2

x^2 + y^2 = 49

Answer:

The least common multiple of $6!$ and $(4!)^2.$

is 6×4! or 144

Answer:

A

Step-by-step explanation:

the graph of x'3 is B

the graph of x'(-1/3) is C

Answer:

The Central Limit Theorem says that if the sample size is more than 30, the data follows a normal sampling distribution. Since the sample size is 180, and that is more than 30, a Normal sampling distribution can be used.

Since a normal sampling distribution can be used, we should FAIL TO REJECT the null hypothesis because p = 0.20, which is more than the significance level of α = 0.08. There is NOT sufficient evidence to suggest that the alternative hypothesis is true.

Hope this helps!

Answer:

125

Step-by-step explanation:

30+25+x=180

55+x=180

x=180-55

x=125

Answer:

Step-by-step explanation:

To find x we use tan

tan ∅ = opposite / adjacent

From the question

x is the adjacent

30 is the hypotenuse

So we have

tan 25 = 30/x

x = 30/tan 25

x = 64.33

x = 64.3 to the nearest tenth

Hope this helps you

Answer:

12

Step-by-step explanation:

let

x= no. for English

y= no. for maths

z= no. for fine arts

a= no. for all subjects

x= 22

y= 21

z= 17

x+y+z= 39

x intersect y= 11

y intersect z= 8

x intersect z= 7

(4+a)+ (11-a)+ (7-a)+ (8-a)+ (2+a)+ (2+a)+ a= 39

34+a =39

a= 5

no.of teachers who teaches all & fine art only

= a + (2+a)

= 5+7

= 12

Answer:  3/(28) ≈ 10.7%

Step-by-step explanation:

3 blue + 2 red + 3 green = 8 total pens

   First pick    and           Second pick

 [tex]\dfrac{3\ blue\ pens}{8\ total\ pens}\quad \times \quad \dfrac{2\ remaining\ blue\ pens}{7\ remaining\ total\ pens}\quad =\large\boxed{\dfrac{3}{28}}[/tex]  

Answer:

[tex]Mean = 344[/tex]

Step-by-step explanation:

Given

[tex]Population = 1013[/tex]

Let p represents the proportion of those who worry about identity theft;

[tex]p = 66\%[/tex]

Required

Mean of those who do not worry about identity theft

First, the proportion of those who do not worry, has to be calculated;

Represent this with q

In probability;

[tex]p + q = 1[/tex]

Make q the subject of formula

[tex]q = 1 - p[/tex]

Substitute [tex]p = 66\%[/tex]

[tex]q = 1 - 66\%[/tex]

Convert percentage to fraction

[tex]q = 1 - 0.66[/tex]

[tex]q = 0.34[/tex]

Now, the mean can be calculated using:

[tex]Mean = nq[/tex]

Where n represents the population

[tex]Mean = 1013 * 0.34[/tex]

[tex]Mean = 344.42[/tex]

[tex]Mean = 344[/tex] (Approximated)

Hi,

f°g means :  apply first g then f . so calculate  "g" and then use result as "x" in f.  

g°f  means :   you apply first  f then g  

so :  f°g =    2(3x²-x) -5  =   6x²-2x- 5

To improve in math, you need practice. have a try with  g°f  :)

give the answer in comments, and I will tell you if you are correct.

good luck.

Answer:

3s-4bbb=17

Step-by-step explanation:

brother=4bbb

sister=3s

3s-4bbb=17

Answer:

The answer is:

The fourth option,

{s | s <90}

Step-by-step explanation:

yes

Answer:

[tex]\boxed{s|s<90}[/tex]

Step-by-step explanation:

1/3s-6<24

Add 6 on both sides.

1/3s<30

Multiply both sides by 3.

s<90

Answer:

(1.5, -13.5)

Step-by-step explanation:

Midpoint Formula: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]

Simply plug in our coordinates into the formula:

x = (17 - 14)/2

x = 3/2

y = (-11 - 16)/2

y = -27/2

Answer:

(-1.5, -13.5)

Step-by-step explanation:

To find the x coordinate of the  midpoint, add the x coordinates and divide by 2

( 17+-14)/2 = 3/2 =1.5

To find the y coordinate of the  midpoint, add the x coordinates and divide by 2

( -11+-16)/2 = -27/2= - 13.5

Answer:

h = 7 degrees

Step-by-step explanation:

To find h, we know that it is positive because it increases in value, not decreases:

h = 65 - 58

h = 7

Answer:

h = 7°F

Step-by-step explanation:

58 + h = 65

h = 65 - 58

h = 7

Check:

68 + 7 = 65

Answer:

He stitched 1 shirt in 6 hours.

He can stitch 1/6 of a shirt in one hour

Step-by-step explanation:

Given Mike can stitch 7 shirts in 42 hours

No. of shirt stitch in one hour = total no of shirt stitch/total time taken

No. of shirt stitch in one hour = 7/42 = 1/6

Thus, he can stitch 1/6 of a shirt in one hour

Time taken to stitch 1 shirt = total time taken by him to stitch 7 shirts/ total no. of shirt stitch(i.e 7)  = 42/6 = 6 hours.

Thus, he stitched 1 shirt in 6 hours.

Answer:

He can stitch 1/6 of a shirt in one hour

Step-by-step explanation:

Because he stitched  7 shirts in 42 hours

42/7 = 6

so 6 hours per shirt

In one hour:

1/6

Answer:

2

Step-by-step explanation:

We are given that a graph which represents f(x).

Interval:[-4,-1]

We have to find the average rate of   change of the function f(x).

From the graph we can see that

f(-4)=-3

f(-1)=3

We know that the average rate of change of the function

Average rate =[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Using the formula

Average rate of change of f=[tex]\frac{3-(-3)}{-1-(-4)}[/tex]

Average rate of change of f=[tex]\frac{6}{3}=2[/tex]

Answer:

0.9

Step-by-step explanation:

First, convert them all into fractions:

[tex]2\frac{1}{3}=\frac{7}{3}[/tex]

[tex].5=\frac{1}{2}[/tex]

Now, we have:

[tex]\frac{4x+9}{\frac{7}{3} } =\frac{3x}{\frac{1}{2} }[/tex]

Cross multiply:

[tex]\frac{1}{2} (4x+9)=\frac{7}{3} (3x)[/tex]

On the left, distribute. On the right, notice that the 3 in the denominator and the coefficient 3 cancel:

[tex]2x+4.5=7x[/tex]

[tex]4.5=5x[/tex]

[tex]x=0.9=9/10[/tex]

Answer and step-by-step explanation:

Photo

Answer:

Answer E

Step-by-step explanation:

If you think about it, the origin is just (0,0). Now, think which one is the closest to that. (0,1/2), or answer E, should be your assumption.

The difference of the rational expressions 6/x - 5x/x+2 is (x + 12)/(x(x+2)).

Thus, the correct option would be:

C. (x + 12)/(x(x+2))

To find the difference of the rational expressions, we need to subtract the second expression from the first expression.

Let's simplify the expressions first:

The first expression is 6/x - 5x/(x+2).

To combine the terms, we need a common denominator, which is (x)(x+2).

Converting the first term, 6/x, to have a denominator of (x)(x+2), we get (6(x+2))/(x(x+2)).

Now, we can combine the terms:

[(6(x+2))/(x(x+2))] - [5x/(x+2)]

To subtract the fractions, we need to have a common denominator, which is (x)(x+2).

Expanding the numerators, we get:

[(6x + 12)/(x(x+2))] - [5x/(x+2)]

Now, we can subtract the fractions:

[(6x + 12 - 5x)/(x(x+2))]

Simplifying the numerator, we have:

(6x - 5x + 12)/(x(x+2))

Combining like terms, we get:

(x + 12)/(x(x+2))

Therefore, the difference of the rational expressions 6/x - 5x/x+2 is (x + 12)/(x(x+2)).

Thus, the correct option would be:

C. (x + 12)/(x(x+2))

For similar question on rational expressions.  

https://brainly.com/question/29061047

#SPJ8

Answer:

my best answer for this is B. False.

I calculated as fast as i can.

Answer:

B. Y = 6/4 X

Step-by-step explanation:

Well to find its parallel line we need to put,

2y - 3x = 4 into slope-intercept.

+3x to both sides

2y = 3x + 4

Now we divide everything by 2,

y = 3/2x + 2

So a line that is parallel to the given line will have the same slope but different y intercept, meaning we can cross out choices A and C.

To check look at the image below ↓

Thus,

answer choice B. Y = 6/4 X is correct.

Hope this helps :)

Answer:

0.081

Step-by-step explanation:

To solve this question, we would use the z score formula

z score = (x-μ)/σ, where

x is the raw score = 36.32cm

μ is the population mean = 34.5 cm

σ is the population standard deviation = 1.3cm

z score = (36.32cm - 34.5cm)/1.3cm

z = 1.4

Using the normal distribution to find the z score for 1.4

P(z = 1.4) = 0.91924

Therefore, the probability that a boy has a head circumference greater than 36.32cm at birth is

P(x>36.32) = 1 - P(z = 1.4)

= 1 - 0.91924

= 0.080757

Approximately ≈ 0.081

Answer:

j/2+7= -12

(j+14)/2= -12

cross-multiply

j+14= -24

j= -38

Answer:

[tex]\boxed{j=-38}[/tex]

Step-by-step explanation:

[tex]\frac{j}{2} +7=-12[/tex]

Subtract 7 on both sides.

[tex]\frac{j}{2} +7-7=-12-7[/tex]

[tex]\frac{j}{2}=-19[/tex]

Multiply both sides by 2.

[tex]\frac{j}{2}(2)=-19(2)[/tex]

[tex]j=-38[/tex]

Answer:

60 ounces

Step-by-step explanation:

A certain mixture of paint contains 5 parts white paint for every 4 parts blue paint, that is, the white paint (w) to blue paint (b) ratio is 5:4. We can apply this ratio to different units such as ounces. This means that the mixture has 5 ounces of white paint to 4 ounces of blue paint. If a can of paint contains 75 ounces of white paint, the ounces of blue paint in the can are:

75 oz w × (4 oz b/5 oz w) = 60 oz b

Answer:

The answer is

Step-by-step explanation:

3+ – 5(4+ – 3v) can be written as

3 - 5( 4 - 3v)

Expand and simplify

That's

3 - 20 + 15v

15v - 17

Hope this helps you

Answer:

b.  y = |x+4| - 10

Step-by-step explanation:

When you see a v-shaped graph, it could very well relate to an absolute-value function.

The value of the absolute value function has the vertex at x= -4, meaning that it has a minimum value when x=-4, which means that the absolute value function is of the form |x+4|  giving a zero when x= -4.

Also, the minimum of the function occurs at y = -10, meaning that the function has been translated by -10.

Therefore the function is

y = |x+4| - 10

Answer:

B

Step-by-step explanation:

EDGE unit review

Answer:

1,-1,3,4

1,6,-2,-4

-4,6,-6,6

Step-by-step explanation:

I believe you just put in the values into the box. Watch the video to see how they did it to make sure it looks like how I did it.

Answer:

C.

Step-by-step explanation:

It's the most reasonable answer.

Answer:

12100

Step-by-step explanation:

If the number B of federally insured banks could be approximated by B ( t ) = − 329.4 t + 13747 from 1985 to 2007 where t = 0 correspond to year 1985

In order to determine the amount of federally insured banks that were there in 1990, we will first calculate the year range from initial time 1985 till 1990

The amount of time during this period is 5years. Substituting t = 5 into the modeled equation will give;

B ( t ) = − 329.4 t + 13747

B(5) = -329.4(5) + 13747

B(5) = -1647+13747

B(5) = 12100

This shows that there will be 12100 federally insured banks are there in the year 1990.

Answer:

Step-by-step explanation:

(3,-2)

plug in 3 for x and -2 for y

-2< -1/2x3+2

-2<-1.5+2

-2<0.5