The volume of the box shown in the diagram is 40π3 cubic units. Find the length of ‘x’.

Answer:

x = -30/7

Step-by-step explanation:

-7x+3y=30

Let y=0

-7x +0 = 30

Divide by -7

-7x /-7 = 30/-7

x = -30/7

Answer:

[tex]-\frac{30}{7}[/tex]

Step-by-step explanation:

y equals zero => y = 0

-7x+3y=30

-7x +3.0 = 30

-7x + 0 = 30

-7x = 30

-7x/-7 = 30/-7

x = -30/7

Hope this helps ^-^

FINDING THE SURFACE AREA OF A COMPOSITE SOLID

About "Finding the surface area of a composite solid"

Finding the surface area of a composite solid :

A composite solid is made up of two or more solid figures.

To find the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.

Finding the surface area of a composite solid - Examples

Example 1 :  

Daniel built the birdhouse shown below. What was the surface area of the birdhouse before the hole was drilled ?

Solution :  

Step 1 :

Identify the important information.

• The top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.

• The bottom is a rectangular prism with h = 18 cm. The base is a 30 cm by 24 cm rectangle.

• One face of each prism is not on the surface of the figure.

Step 2 :  

Find the surface area of each prism.

Add the areas. Subtract the areas of the parts not on the surface.

Step 3 :  

Find the area of the triangular prism.

Perimeter  =  17 + 17 + 30  =  64 cm

Base area  =  (1/2)(30)(8)  =  120 sq.cm

Surface area  =  Ph + 2B

Surface area  =  64(24) + 2(120)

Surface area  =  1,776 sq.cm

Step 4 :  

Find the area of the rectangular prism.

Perimeter  =  2(30) + 2(24)  =  108 cm

Base area  =  30(24)  =  720 sq.cm

Surface area  =  Ph + 2B

Surface area  =  108(18) + 2(720)

Surface area  =  3,384 sq.cm

Step 5 :  

Add. Then subtract twice the areas of the parts not on the surface.

Surface area  =  1,776 + 3,384 - 2(720)  =  3,720 sq.cm

The surface area before the hole was drilled was 3,720 sq.cm.

The surface area before the hole was drilled was; 3,720 sq.cm.

A composite solid is made up of two or more solid figures.

To determine the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.

Given that the top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.

The bottom is a rectangular prism with h = 18 cm.

The base is a 30 cm x 24 cm rectangle.

One face of each prism is not on the surface of the figure.

Then the surface area of each prism.

Add the areas. Subtract the areas of the parts not on the surface.

The area of the triangular prism.

Perimeter  =  17 + 17 + 30  =  64 cm

Base area  =  (1/2)(30)(8)  =  120 sq.cm

Surface area  =  Ph + 2B

Surface area  =  64(24) + 2(120)

Surface area  =  1,776 sq.cm

Now the area of the rectangular prism.

Perimeter  =  2(30) + 2(24)  =  108 cm

Base area  =  30(24)  =  720 sq.cm

Surface area  =  Ph + 2B

Surface area  =  108(18) + 2(720)

Surface area  =  3,384 sq.cm

Now,

Surface area  =  1,776 + 3,384 - 2(720)  =  3,720 sq.cm

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Answer:1977.60

Step-by-step explanation:

24x8= 192

192x 10.30= 1977.60

Answer:

Option 2 is correct

Step-by-step explanation:

One number is 2 times another number plus 3. Their sum is 21.

"One number is 2 times another number plus 3" translated to

x = smaller number = another number

It is also given that: Their sum is 21.

Combine like terms:

3x+3 = 21

Answer:

I do questions like these everyday so I have too much experience. Let me explain step by step for you.

Brainliest?

First lets set 2 variables x and y

Lets make 2 equations.

x=3+2*y

Thats because it says 'x' is 3 more (+) than 2 times(*) 'y'

Now lets set second, we know both of them add up to 27.

x+y = 27

Since we know what x is equal to (look above equation)

We can replace it.

x is replaced with 3+2*y

3+2y+y = 27

3+4y = 27

Simplify 27-3 = 24

24/4 = 6

Now lets plug in for x

3+2*6 = 15

15 - x

6 - y

:))

Answer:

√130 is the distance between (9,-3) (0,-10)

Answer:

Step-by-step explanation:

From the given question;

Given that:

Jan's All You Can Eat Restaurant charges ​$9.10 per customer to eat at the restaurant.

Distribution  is skewed and and has a mean of $8.10 and a standard deviation of ​$4.

A.  If the 100 customers on a day have the characteristics of the random sample from their customer base, find the mean and standard error of the sampling distribution of the restaurant's sample mean expense per customer.

the mean by using the central limit theorem is 8.10

the standard error of the sampling distribution  = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]

the standard error of the sampling distribution = [tex]\dfrac{4}{\sqrt{100}}[/tex]

= 4/10

= 0.4

B.  

P(X > $8.95) = P (Z > 8.95 - 8.10/0.4)

P(X > $8.95) = P (Z > 2.1)

P(X > $8.95) = 1 - P (Z < 2.1)

P(X > $8.95) = 1 - 0.9821

P(X > $8.95) = 0.0179

Answer:

D. It would be less steep.

Step-by-step explanation:

→When the absolute value of the number in front of x is greater than 1, the function on the graph narrows. When the absolute value of the number in front of x is less than 1, the function on the graph widens.

In this case, the number is less than 1, making it grow wider. And as a result of it growing wider, it also becomes less steep.

Answer:

Step-by-step explanation:

a circle will satisfy the conditions of Green's Theorem since it is closed and simple.

Let's identify P and Q from the integral

[tex]P=x^2 y[/tex], and [tex]Q= xy^2[/tex]

Now, using Green's theorem on the line integral gives,

[tex]\oint\limits_C {x^2ydx-xy^2dy } =\iint\limits_D {y^2-x^2} \, dA\\\\[/tex]

Answer:

21 x^2

Step-by-step explanation:

12x^2+9x^2

Combine like terms

x^2(12+9)

x^2(21)

21 x^2

Answer:

[tex]y-4p[/tex]

Step-by-step explanation:

Add/subtract like terms.

[tex]5y+2p-4y-6p\\5y-4y+2p-6p\\y-4p[/tex]

Answer:

a) N(33,15).

b) 37.33% probability that a randomly selected LA worker has a commute that is longer than 38 minutes

c) 45.6 minutes.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 33, \sigma = 15[/tex]

a. What is the distribution of X?

Normal with mean 33 and standard deviaton 15. So

N(33,15).

b. Find the probability that a randomly selected LA worker has a commute that is longer than 38 minutes

This is 1 subtracted by the pvalue of Z when X = 38. So

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

[tex]Z = \frac{38 - 33}{15}[/tex]

[tex]Z = 0.333[/tex]

[tex]Z = 0.333[/tex]  has a pvalue of 0.6267.

1 - 0.6267 = 0.3733

37.33% probability that a randomly selected LA worker has a commute that is longer than 38 minutes

c. Find the 80th percentile for the commute time of LA workers.

This is X when Z has a pvalue of 0.8. So it is X when Z = 0.84.

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

[tex]0.84 = \frac{X - 33}{15}[/tex]

[tex]X - 33 = 0.84*15[/tex]

[tex]X = 45.6[/tex]

45.6 minutes.

Answer:

11×-9y=14

Step-by-step explanation:

123hsvwjwjbe

Answer:

(-2,-4)

Step-by-step explanation:

add the equations in order to solve the first variable. put the value into the other equations in order to solve the other variables.

Answer:

Step-by-step explanation:

I am not really sure because u did not finish the question but is u are asking how much time it takes to fit one tyre:

answer is time/tyres

56min./4

14 min. Per type

Answer:

Graph A

Step-by-step explanation:

The common ratio is less than 1, so the graph will be decreasing. The initial value is 2, so the y-intercept will be 2. Graph A fits this criteria.

I hope this helps :))

The graph A is correct.

A diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables.

The equation is,

[tex]y=2(0.5)^{x}[/tex]

Plotting the graph, we get,

Option A

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Answer:

y = x+15

Step-by-step explanation:

y - 15=x

Add 15 to each side

y - 15+15=x+15

y = x+15

Answer:

[tex]y=x+15[/tex]

Step-by-step explanation:

[tex]y - 15=x[/tex]

Add [tex]15[/tex] on both sides of the equation.

[tex]y - 15+15=x+15[/tex]

The [tex]y[/tex] should be isolated on one side of the equation.

[tex]y=x+15[/tex]

Answer:

f

Step-by-step explanation:

Answer:

Null hypothesis: [tex]\mu_1 \leq \mu_2[/tex]

Alternative hypothesis: [tex]\mu_1 > \mu_2[/tex]

The statistic is given by:

[tex]t= \frac{\bar X_1 -\bar X_2}{\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}}[/tex]

And replacing we got:

[tex] t=\frac{72.86-67.34}{\sqrt{\frac{15.98^2}{150} +\frac{35.67^2}{275}}}=2.194[/tex]

And the best option would be:

2.19

Step-by-step explanation:

We have the following info given:

n1 = 150 n2 = 275

[tex]\bar x_1 = 72.86, \bar x_2 = 67.34[/tex]

s1 = 15.98 s2 = 35.67

We want to test the following hypothesis:

Null hypothesis: [tex]\mu_1 \leq \mu_2[/tex]

Alternative hypothesis: [tex]\mu_1 > \mu_2[/tex]

The statistic is given by:

[tex]t= \frac{\bar X_1 -\bar X_2}{\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}}[/tex]

And replacing we got:

[tex] t=\frac{72.86-67.34}{\sqrt{\frac{15.98^2}{150} +\frac{35.67^2}{275}}}=2.194[/tex]

And the best option would be:

2.19

Answer:

D

Step-by-step explanation:

Lines EF and GH are already parallel. Translating them 2 units to the side without changing how far apart they are vertically means they won't intersect and will remain the same distance apart.

Answer:

D

Step-by-step explanation:

They are parallel lines

Hey there!

First, let's take all of the expenses and change the ones that aren't monthly into monthly.

Groceries: $800/month

Car insurance: $87.5/month

Gasoline: $100/month

Now, let's add together all of our expenses

1090+800+125+87.5+100+200+50=2452.5

Now, we subtract that from her salary.

2300-2452.5=-152.5

Therefore, Rebecca's net monthly cash flow is -$152.5. She should spend a bit less on groceries, not do so much miscellaneous, find a place that charges less rent, drive less, etc. so she isn't spending more than she earns.

I hope that this helps! Have a wonderful day!

Answer:

18.66 ft/s

Step-by-step explanation:

The distance between you and the elevator is given by:

[tex]h=\sqrt{x^2+y^2}[/tex]

The rate of change for the distance between you and the elevator is given by:

[tex]\frac{dh}{dt}=\frac{dh}{dy}*\frac{dy}{dt}[/tex]

[tex]-16=\frac{dh}{dy}*\frac{dy}{dt}[/tex]

[tex]\frac{dh}{dy}=\frac{d}{dy} (\sqrt{x^2+y^2})\\[/tex]

Applying the chain rule:

[tex]u=x^2+y^2\\\frac{dh}{dy}=\frac{d\sqrt u}{du} *\frac{du}{dy}\\\frac{dh}{dy}=\frac{1}{2\sqrt u} *2y\\\frac{dh}{dy}=\frac{y}{\sqrt {(x^2+y^2)}}[/tex]

Therefore, at x=300 and y = 500, dy/dt is:

[tex]-16=\frac{y}{\sqrt {(x^2+y^2)}}*\frac{dy}{dt}\\-16=\frac{500}{\sqrt {(300^2+500^2)}}*\frac{dy}{dt}\\\frac{dy}{dt}=-18.66\ ft/s[/tex]

The elevator is descending at 18.66 ft/s.

Answer:

The percentage of the employee will experience a lost-time accident in both years is 0.0%

Step-by-step explanation:

Let A denote events that employees suffered lost-time accidents during the last year

Let B denote events that employees suffered lost-time accidents during the current year

P(A) = 5% = 0.05

P(B) = 4% = 0.04

P(B | A) = 15% = 0.15

(a) P (A ∩ B) = P(B | A) × P(A)

= 0.15 × 0.05

= 0.0075

= 0.0 (1 decimal place)

The probability that an employee will experience a lost- time accident in both years is 0.0

Answer:

Which statements?

Step-by-step explanation:

Can you write the statements please?

Answer:

[tex]t=\frac{183-160}{\frac{12}{\sqrt{25}}}=9.58[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=25-1=24[/tex]  

And the p value would be:

[tex]p_v =P(t_{(24)}>9.58)\approx 0[/tex]  

Since the p value is very low at any significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 160

Step-by-step explanation:

Information provided

[tex]\bar X=183[/tex] represent the sample mean

[tex]s=12[/tex] represent the sample standard deviation

[tex]n=25[/tex] sample size  

[tex]\mu_o =160[/tex] represent the value to test

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to verify if the true mean is greater than 160, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 160[/tex]  

Alternative hypothesis:[tex]\mu > 160[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info we got:

[tex]t=\frac{183-160}{\frac{12}{\sqrt{25}}}=9.58[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=25-1=24[/tex]  

And the p value would be:

[tex]p_v =P(t_{(24)}>9.58)\approx 0[/tex]  

Since the p value is very low at any significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 160

Answer:

The 85% confidence interval is ( 7.7 , 8.0 )

Step-by-step explanation:

In order to find the 85% confidence interval you use the following formula:

[tex]\overline{x}\pm Z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]       (1)

where

[tex]\overline{x}[/tex]: mean of number of bacteria reproduces per hour = 7.8

σ: standard deviation = 2.2

n: sample size = 967

α: 1 - 0.85 = 0.15

Zα/2: Z factor of the density distribution = 1.44

You replace the values of all parameters in the equation (1):

[tex]7.8\pm (1.44)\frac{2.2}{\sqrt{697}}\\\\7.8\pm0.119\\\\[/tex]

Then, the confidence interval is:

[tex](7.8-0.119,7.8+0.119)\\\\(7.7,8.0)[/tex]

Answer:

46 degrees

Step-by-step explanation:

Add 31 + 15 together to find the total angle

31 + 15 = 46

= 46 degrees

Answer:

That is 46°.

Step-by-step explanation:

31 + 15 = 46

So, 46°.

Answer:

[tex]58,464 \: \: miles[/tex]

Step-by-step explanation:

[tex]speed = \frac{distantce}{time} \\ [/tex]

[tex]distance = speed \times time \\ x = 72 \times 812 \\ x = 58,464 \: \: miles[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

10 square inches

Step-by-step explanation:

cost of a plain t-shirt = $10

cost of 1 square inch of design addition = $1.50

let there be x square inches of design

then cost of x square inches of design = x*cost of 1 square inch of design

                                                                 = 1.50*x = 1.5x

Total cost for t-shirt with x square inches of design = cost of a plain t-shirt + cost of x square inches of design   = 10 + 1.5 x

It is given that Makeeya has only $25, then total cost which can be afforded by him will be $25 only

Thus,

10 + 1.5 x = 25

=> 1.5x = 25-10 = 15

=> x = 15/1.5 = 10

Thus, Makeeya can  put 10 square inches of design on her T-shirt.

Answer:

4 pizza recipes

Step-by-step explanation:

It shows 4 Xs after the [tex]\frac{3}{4}[/tex] mark. So there are 4 recipes that use MORE than [tex]\frac{3}{4}[/tex] cups of cheese.

Answer:

4 cups of cheese

Step-by-step explanation:

More than 3/4 are (3+1) = 4 cups of cheese

Mark Wishing the Brainliest because he deserves it :)

Answer:

i hope this helps you

The Equation of the line is 2y = -x.

Suppose the given points are (x_1, y_1) and (x_2, y_2), then the equation of the straight line joining both two points is given by

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

Given Points of the line are (0,0) and (4,-2).

Since we are given two points.

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)\\\\\\(y - (-2)) = \dfrac{-2- 0}{4 - 0} (x -4)\\\\\\(y - (-2)) = \dfrac{-1}{2} (x -4)\\\\2(y + 2) =-1(x -4)\\\\2y + 4 = -x + 4\\\\2y = -x\\\\[/tex]

Therefore, Equation of the line is 2y = -x.

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