How do I do this problem? Two similar pyramids have matching sides in the ratio 5:7. If the surface area of the larger pyramid is 441 cm^2. find the surface area of
the smaller pyramid.
S Area
cm²

Hey there! I'm happy to help!

It appears that we are trying to figure out which triangles are similar, which means that their side lengths have the same ratio. In ΔABC, we see that two sides have a length of 10 and the shorter has a length of 5. This means that the ratio between the long sides and the short sides must be 2:1 to be similar to this triangle.

Let's look at ΔJKL. Our long side has to be double our short side. If we double 2.5, it will be 5, not six, so JKL is not similar with ABC.

Now, let's look at ΔDEF. We see that it's long sides are double the short sides because 6 is double three. This means that the triangles ABC and DEF are similar.

The answer is A) ΔABC ~ ΔDEF.

I hope that this helps! Have a wonderful day!

Answer:

a) Null hypothesis:[tex]\mu \geq 3[/tex]  

Alternative hypothesis:[tex]\mu < 3[/tex]  

This hypothesis test is a left tailed test.

b) [tex]t=\frac{2.8-3}{\frac{2.6}{\sqrt{1310}}}=-2.784[/tex]  

The p value for this case can be calculated with this probability:  

[tex]p_v =P(z<-2.784)=0.0027[/tex]  

We can conduct the test with the Ti84 using the following steps:

STAT>TESTS>T-test>Stats

We input the value [tex]\mu_o =3, \bar X= 2.8, s_x = 2.6, n=1310[/tex] and for the alternative we select [tex]< \mu_o[/tex]. Then press Calculate.

And we got the same results.  

Step-by-step explanation:

Information given

[tex]\bar X=2.8[/tex] represent the sample mean

[tex]s=2.6[/tex] represent the population standard deviation  

[tex]n=1310[/tex] sample size  

[tex]\mu_o =3[/tex] represent the value to test

[tex]\alpha=0.5[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic

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

Part a) System of hypothesis

We want to test if the true mean is less than 3, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 3[/tex]  

Alternative hypothesis:[tex]\mu < 3[/tex]  

This hypothesis test is a left tailed test.

Part b

The statistic is given by:

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

Replacing the info given we got:

[tex]t=\frac{2.8-3}{\frac{2.6}{\sqrt{1310}}}=-2.784[/tex]  

The p value for this case can be calculated with this probability:  

[tex]p_v =P(z<-2.784)=0.0027[/tex]  

We can conduct the test with the Ti84 using the following steps:

STAT>TESTS>T-test>Stats

We input the value [tex]\mu_o =3, \bar X= 2.8, s_x = 2.6, n=1310[/tex] and for the alternative we select [tex]< \mu_o[/tex]. Then press Calculate.

And we got the same results.  

Answer:

total surface area Stot = 753.9816 m2

lateral surface area Slat = 351.85808 m2

top surface area Stop = 201.06176 m2

bottom surface area Sbot = 201.06176 m2

Answer:

Lateral area = 352 Square m

Surface area = 756. 3 square m

Volume = 1408 cubic m

Step-by-step explanation:

[tex]lateral \: area = 2\pi \: rh \\ = 2 \times \frac{22}{7} \times \frac{16}{2} \times 7 \\ = 22 \times 16 \\ = 352 \: {m}^{2} \\ \\ surface \: area = 2\pi \: r(h + r) \\ = 2 \times 3.14 \times 8(7 + 8) \\ = 6.28 \times 8 \times 15 \\ = 6.28 \times 120 \\ = 756.3 \: {m}^{2} \\ \\ volume = \pi {r}^{2} h \\ = \frac{22}{7} \times {8}^{2} \times 7 \\ = 22 \times 64 \\ = 1408 \: {m}^{3} \\ [/tex]

The question is incomplete. Here is the complete question.

Find the measurements (the lenght L and the width W) of an inscribed rectangle under the line y = -[tex]\frac{3}{4}[/tex]x + 3 with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.

Answer: L = 1; W = 9/4; A = 2.25;

Step-by-step explanation: The rectangle is under a straight line. Area of a rectangle is given by A = L*W. To determine the maximum area:

A = x.y

A = x(-[tex]\frac{3}{4}.x + 3[/tex])

A = -[tex]\frac{3}{4}.x^{2} + 3x[/tex]

To maximize, we have to differentiate the equation:

[tex]\frac{dA}{dx}[/tex] = [tex]\frac{d}{dx}[/tex](-[tex]\frac{3}{4}.x^{2} + 3x[/tex])

[tex]\frac{dA}{dx}[/tex] = -3x + 3

The critical point is:

[tex]\frac{dA}{dx}[/tex] = 0

-3x + 3 = 0

x = 1

Substituing:

y = -[tex]\frac{3}{4}[/tex]x + 3

y = -[tex]\frac{3}{4}[/tex].1 + 3

y = 9/4

So, the measurements are x = L = 1 and y = W = 9/4

The maximum area is:

A = 1 . 9/4

A = 9/4

A = 2.25

Answer:

D

Step-by-step explanation:

The diagramatic representation of the life cycle of a darkling beetle is shown in the attached file below.

The metamorphosis of the darkling bettle takes four stages:

egg → larva → pupa→ adult

After laying the eggs by an adult darkling bettle, the eggs are encased in a fluid-like covering to prevent it from damage as a result of environmental factors. The egg metamorphosize into the larva stage; a period of feeding and growth. They then in turn proceed into the pupa stage where they are being enclosed in a cocoon. In the cocoon, they undergo modifications and become sexually matured before they enters into adulthood.

Thus, the stage that represent the change fromm larva to adult is the pupa stage and it is shown in the diagram as option D

Answer:

55.95 ft²

Step-by-step explanation:

Circumference formula:  C = 2πr  =>  r = C / (2π)

Area formula:  A = πr²

Substituting C / (2π) for r in the above equation, we get:

               C                        47 ft

A = π( ----------- )²  =  π ( -------------- )²

              2π                       (2π)

or ...

          π(47 ft)²                   2209 ft²

A = ----------------------  =  --------------------  =  55.95 ft²

               4π²                   4(3.14159)²

Use the law of cosines to find the missing length, which we'll call [tex]d:[/tex]

[tex]d^2=100^2+120^2-2(100)(120)\cos 45^\circ[/tex]

[tex]d^2=24400-12000\sqrt{2}[/tex]

[tex]\boxed{d\approx 86\text{ cm}}.[/tex]

Answer: Three have a right angle. These are the green rectangle, the pinkish square, and the orange trapezoid.

Step-by-step explanation:

Answer:

PO = 36

Step-by-step explanation:

Since both the chords are equal in length so they must be equidistant from the centre.

And

PG = GO

-x+10 = -3(x+2)

-x+10 = -3x-6

-x+3x = -6-10

2x = -16

Dividing both sides by 2

x = -8

Now

PO = PG + GO

PO = -(-8)+10+(-3)((-8)+2)

PO = 8+10+(-3)(-6)

PO = 18+18

PO = 36

Answer:

[tex]y = 2x + \frac{x^2}{2} - 6[/tex]

Step-by-step explanation:

Solution:-

- We are given the following initial value problem:

                             [tex]\frac{dy}{dx} = 2 + x , y ( 2 ) = -6[/tex]

- We will first isolate the variables:

                            [tex]dy = ( 2 + x ).dx[/tex]

- Perform integration for both sides of the equation:

                          [tex]\int {dy} = \int {( 2 + x )}.dx + c\\\\y = 2x + \frac{x^2}{2} + c\\[/tex]

Where,

                         c: The constant of integration

- We will solve for the constant of integration by using the initial value y ( 0 ) = -6 as follows:

                         [tex]-6 = 2(0) + \frac{0^2}{2} + c\\\\c = -6[/tex]

- The final solution can be expressed  as follows:

                         [tex]y = 2x + \frac{x^2}{2} - 6[/tex]

Answer:

Additional cubes added to the rectangular prism= 72cubes

Volume of new rectangular prism = 108in³

Step-by-step explanation:

The question is incomplete without the diagram and not clear to understand.

Let's determine how to find answers to the above using the following:

The diagram used for solving the question has been attached.

From the diagram, the base of the rectangular prism has length =6inches and width = 6inches

Height = 1inch

If 2more layers are added, then height becomes 3inches sinch the two additional layer has same dimensions as the base.

The bottom layer has 6 by 6 dimension

Area = 6×6 = 36in²

Since 1 cube = 1 inch

Number of cubes in the base = 36cubes

Since two layers were added, Additional cubes added to the rectangular prism = 2×36 = 72cubes

Volume of rectangular prism = length×breadth×height

= l×b×h

dimension of new rectangular prism

Length = 6in

Breadth = 6in

Height = 3in

Volume of new rectangular prism = 6×6×3

Volume = 108in³

Answer:

Wade

Step-by-step explanation:

Wade equals to 165

Naomi equals to 112

Gail equals to 123

And bailey equals to 150

Answer:

Each of the students absent for 1, 2, 4 and 5 days get 57, 53, 45 and 40 copies of the the reading books respectively.

Step-by-step explanation:

English Translation

The team of teachers from the Humanistic Training Area decides to distribute 195 copies of reading books to 4 students previously classified on their own merits. But the distribution will be made taking into account absences from classes during the first cycle. How many books does each student receive if their absences have been 1; two; 4 and 5 days, respectively?

Solution

Because the more the number of days absent, the less the number of books each of the 4 students deserve, we have to employ an elaborate scheme.

If 195 copies are distributed equally between 4 People, each person gets 48.75 copies of the books.

Now, if we add another 48.75 copies of books to the total number of books, each person gets 60.9375 books.

But, we can then divide 48.75 extra books on top according to the number of days absent and subtract each person's number from the assumed 60.9375 books, with an extra 48.75 books.

Total number of days absent = 1 + 2 + 4 +5 = 12

(48.75/12) = -4.0625 copies for each absent day.

The student with only 1 absent day gets 60.9375 - 4.0625 = 56.875 copies = 57 copies

The student with 2 absent days, gets = 60.9375 - (2×4.0625) = 52.8125 copies = 53 copies

The student with 4 absent days, gets = 60.9375 - (4×4.0625) = 44.6875 copies = 45 copies

The student with 5 absent days, gets = 60.9375 - (5×4.0625) = 40.425 copies = 40 copies

Hence, each of the students absent for 1, 2, 4 and 5 days get 57, 53, 45 and 40 copies of the the reading books respectively.

Hope this Helps!!!

Answer:

[tex]t=\frac{(4-3.5)-0}{\sqrt{\frac{1.5^2}{11}+\frac{1^2}{9}}}}=0.890[/tex]  

The p value for this case would be:

[tex]p_v =P(t_{18}>0.890)=0.193[/tex]  

The p value is higher than the significance level so then we can conclude that we can FAIL to reject the null hypothesis and then the true mean for group A is not significantly higher than the mean for B

Step-by-step explanation:

Information given

[tex]\bar X_{1}=4[/tex] represent the mean for sample A

[tex]\bar X_{2}=3.5[/tex] represent the mean for sample B

[tex]s_{1}=1.5[/tex] represent the sample standard deviation for A

[tex]s_{2}=1[/tex] represent the sample standard deviation for B  

[tex]n_{1}=11[/tex] sample size for the group A

[tex]n_{2}=9[/tex] sample size for the group B  

[tex]\alpha=0.1[/tex] Significance level provided

t would represent the statistic

Hypothesis to test

We want to verify if the student who graduates from college A has taken more math classes, on the average, the system of hypothesis would be:  

Null hypothesis:[tex]\mu_{1}-\mu_{2} \leq 0[/tex]  

Alternative hypothesis:[tex]\mu_{1} - \mu_{2}> 0[/tex]  

The statistic is given by:

[tex]t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}[/tex] (1)  

And the degrees of freedom are given by [tex]df=n_1 +n_2 -2=11+9-2=18[/tex]  

Replacing we got:

[tex]t=\frac{(4-3.5)-0}{\sqrt{\frac{1.5^2}{11}+\frac{1^2}{9}}}}=0.890[/tex]  

The p value for this case would be:

[tex]p_v =P(t_{18}>0.890)=0.193[/tex]  

The p value is higher than the significance level so then we can conclude that we can FAIL to reject the null hypothesis and then the true mean for group A is not significantly higher than the mean for B

Answer:

P(A∣D) = 0.667

Step-by-step explanation:

We are given;

P(A) = 3P(B)

P(D|A) = 0.03

P(D|B) = 0.045

Now, we want to find P(A∣D) which is the posterior probability that a computer comes from factory A when given that it is defective.

Using Bayes' Rule and Law of Total Probability, we will get;

P(A∣D) = [P(A) * P(D|A)]/[(P(A) * P(D|A)) + (P(B) * P(D|B))]

Plugging in the relevant values, we have;

P(A∣D) = [3P(B) * 0.03]/[(3P(B) * 0.03) + (P(B) * 0.045)]

P(A∣D) = [P(B)/P(B)] [0.09]/[0.09 + 0.045]

P(B) will cancel out to give;

P(A∣D) = 0.09/0.135

P(A∣D) = 0.667

9514 1404 393

Answer:

  (c)  G(x) = x³ -x

Step-by-step explanation:

Replacing x with x+1.5 will shift the graph back left by 1.5 units.

  G(x) = ((x +1.5) -1.5)³ -((x +1.5) -1.5)

  G(x) = x³ -x . . . . . . equation of graph before shift right

Answer:

7.5 feet

Step-by-step explanation:

Scale of the Model =5 in: 25 ft.

If we divide both sides by 5

[tex]\dfrac{5 in.}{5} : \dfrac{25 ft.}{5}\\\\$1 inch: 5 feet[/tex]

If a window on the model is 1.5 inch wide, from the unit ratio derived above we then have that:

1 Inch X 1.5 : 5 feet X 1.5 feet

1.5 Inch : 7.5 feet

Therefore, if a window in the model is 1.5 in. wide, the actual window is  7.5 feet wide.

Answer:

180 ways

Step-by-step explanation:

U just multiply the number of sauce, noodle, vegetable, and meat

So 3 times 3 times 4 times 5

Correct me if this is wrong

Answer:

180

Step-by-step explanation:

you multiply 3X3X4X5 thus it equals 180

Answer:

i dont get it

Step-by-step explanation:

[tex]g(x) = \sqrt{x - 4}[/tex]

[tex]h(x) = 2x - 8[/tex]

g x h = [tex]\sqrt{x-4}.(2x-8)[/tex]

Looking at the equation we know that there's no way to have a negative root, so we need x - 4 to be greater than or equal to 0

[tex] x - 4 \geq 0[/tex]

[tex]x \geq 4[/tex]

Answer:

It's 6

Step-by-step explanation:

Answer:

a) The null and alternative hypothesis are:

[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]

b) Sample proportion (p) = 0.6

Sample size (n) = 200

P-value = 0.0029

c) Conclusion: there is enough evidence to support the claim that the proportion of physicians over the age of 55 that have been sued at least once is significantly higher than 0.5.

Step-by-step explanation:

The question is incomplete: there is no attached file with the data.

a) We want to test if more than half of the physiscians over the age of 55 have been sued at least once.

Then, the claim that will be stated in the alternative hypothesis should be that the proportion of physicians over the age of 55 that have been sued at least once is significantly higher than 0.5.

The null hypothesis should state that this proportion is not signficantly different from 0.5.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]

b) As we do not have the file, we will work with a sample with size n=200 and sample proportion of 0.6.

This sample proportion can be calculated from the data as

[tex]p=x/n=120/200=0.6[/tex]

where x is the number of subjects in the sample that have been sued at least once.

The claim is that the proportion of physicians over the age of 55 that have been sued at least once is significantly higher than 0.5.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]

The significance level is 0.01.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{200}}\\\\\\ \sigma_p=\sqrt{0.00125}=0.035[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.6-0.5-0.5/200}{0.035}=\dfrac{0.098}{0.035}=2.758[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>2.758)=0.0029[/tex]

As the P-value (0.0029) is smaller than the significance level (0.01), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of physicians over the age of 55 that have been sued at least once is significantly higher than 0.5.

Answer:

  [tex]\dfrac{x^3-5x^2 +4x}{2x+8}[/tex]

Step-by-step explanation:

The basic idea is to factor each expression and cancel common factors from numerator and denominator.

  [tex]\dfrac{x^2-16}{2x+8}\cdot\dfrac{x^3-2x^2 +x}{x^2+3x-4}=\dfrac{(x-4)(x+4)}{2(x+4)}\cdot\dfrac{x(x-1)^2}{(x+4)(x-1)}\\\\=\dfrac{(x-4)x(x-1)}{2(x+4)}\cdot\dfrac{(x+4)(x-1)}{(x+4)(x-1)}\\\\=\boxed{\dfrac{x^3-5x^2 +4x}{2x+8}}[/tex]

Answer: r=d/t

Step-by-step explanation:

This is an equation manipulation problem. Since you are looking for r, you want to get it alone. To do so, you would divide t on both sides. Therefore, you get r=d/t.

Answer:

2 litre = 200 ml

so 200/50 = 4 glasses

Answer:

It's 40 of 50ml glass

Step-by-step explanation:

It's basically 2 litre/50ml

But 1000ml = 1 litres ;

Meaning 2 litres = 1000 × 2 = 2000ml

Therefore 2 litre/50ml = 2000/50

= 40

Answer:

(C)

Step-by-step explanation:

We want the probability of at least one hit in  

missiles to be at least 80%.

Step-by-step explanation:

21

may be, I am not sure about this answer. But it can be

Answer:

719/47 is 15.29787234

Answer:

[tex]z=\frac{0.462 -0.35}{\sqrt{\frac{0.35(1-0.35)}{78}}}=2.074[/tex]  

Now we can calculate the p value with this probability:

[tex]p_v =P(z>2.074)=0.019[/tex]  

If we use a significance level os 0.05 we see that the p value is lower than the significance level so then we can conclude that the true proportion of students with jobs is higher than 0.35 for this case. If we decrease the significance level to 1% the result changes otherwise not.

Step-by-step explanation:

Information given

n=78 represent the random sample taken

X=36 represent the students with jobs

[tex]\hat p=\frac{36}{78}=0.462[/tex] estimated proportion of students with jobs

[tex]p_o=0.35[/tex] is the value that we want to test

z would represent the statistic

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

Hypothesis to test

We want to test if the proportion of students with jobs is higher than 0.35, the system of hypothesis are:  

Null hypothesis:[tex]p \leq 0.35[/tex]  

Alternative hypothesis:[tex]p > 0.35[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info we got:

[tex]z=\frac{0.462 -0.35}{\sqrt{\frac{0.35(1-0.35)}{78}}}=2.074[/tex]  

Now we can calculate the p value with this probability:

[tex]p_v =P(z>2.074)=0.019[/tex]  

If we use a significance level os 0.05 we see that the p value is lower than the significance level so then we can conclude that the true proportion of students with jobs is higher than 0.35 for this case. If we decrease the significance level to 1% the result changes otherwise not.

Answer:

x = 30

Step-by-step explanation:

4x + 2x = 180

6x = 180  

x = 30

Answer:

tanA = sinA / cosA = 3/5 / 4/5 = 3/4.