Calculate the volume of this prism.

Answer:

10.44cm lon

Step-by-step explanation:

Given data

Height of house= 10cm

Distance of ladder from wall= 3cm

We can apply the Pythagoras theorem to get the length of the ladder

Also, the length of the ladder is the hypothenuse

z^2= x^2+y^2

z^2= 10^2+ 3^2

z^2= 100+9

z^2= 109

square both sides

z= √109

z= 10.44cm

Hence the ladder is 10.44cm long

Answer:

the answer to the question is A.Rs.648.67

Answer:

The p-value of the test is of 0.2776 > 0.01, which means that the we accept the null hypothesis, that is, the manager's claim that this is only a sample fluctuation and production is not really out of control.

Step-by-step explanation:

A manufacturer considers his production process to be out of control when defects exceed 3%.

At the null hypothesis, we test if the production process is in control, that is, the defective proportion is of 3% or less. So

[tex]H_0: p \leq 0.03[/tex]

At the alternate hypothesis, we test if the production process is out of control, that is, the defective proportion exceeds 3%. So

[tex]H_1: p > 0.03[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.03 is tested at the null hypothesis

This means that [tex]\mu = 0.03, \sigma = \sqrt{0.03*0.97}[/tex]

In a random sample of 100 items, the defect rate is 4%.

This means that [tex]n = 100, X = 0.04[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.04 - 0.03}{\frac{\sqrt{0.03*0.97}}{\sqrt{100}}}[/tex]

[tex]z = 0.59[/tex]

P-value of the test

The p-value of the test is the probability of finding a sample proportion above 0.04, which is 1 subtracted by the p-value of z = 0.59.

Looking at the z-table, z = 0.59 has a p-value of 0.7224

1 - 0.7224 = 0.2776

The p-value of the test is of 0.2776 > 0.01, which means that the we accept the null hypothesis, that is, the manager's claim that this is only a sample fluctuation and production is not really out of control.

Answer:

There are 35 of each color.

Step-by-step explanation:

If the number of each color is the same  there are 140 / 4 = 35 balloons of each color.

Answer:

Step-by-step explanation:

The formula for this is

[tex]N=N_0(.5)^{\frac{t}{H}[/tex] where

N is the amount of the element left after a certain amount of time (for us it is measured in days),

N₀ is the initial amount of the element in grams,

t is the number of days gone by, and

H is the half life of the element. Filling in:

[tex]N=42(.5)^{\frac{16}{8}[/tex] which simplifies a bit to

[tex]N=42(.5)^2[/tex] and a bit more to

N = 42(.25) which gives us a remaining amount of

N = 10.5

Answer:

13.5 pounds

Step-by-step explanation:

90% of 15 is 13.5 or if you need to round then 14 pounds of lettuce

Answer: hi your question is incomplete below is the complete question

Use the Divergence Theorem to calculate the surface integral S F dS   with F x y z = , , and S is a sphere centered at the origin with a radius of 2. Confirm your answer by computing the surface integral

answer : surface integral = 384/5 π

Step-by-step explanation:

Representing  the vector field as

F ( x, y , z ) = ( a^3 + y^3 ) + ( y^3 + z^3 ) + ( Z^3 + x^3 ) k

assuming the sphere ( s) with radius = 2 be centered at Origin of the vector field.

Hence the divergence will be represented as :

Attached below is the detailed solution

Answer:

53

Step-by-step explanation:

848 students/16 buses=53 students per bus

Answer:

121.50

Step-by-step explanation:

Let x be the earnings

2x+10 = 253

Subtract 10 from each side

2x+10-10 = 253-10

2x = 243

Divide by 2

2x/2 = 243/2

x = 121.50

Answer:

B=23.19

Step-by-step explanation:

First, find the last side of the triangle using the Pythagorean theorem.

[tex]a^{2} +b^{2} =c^{2} \\21^{2} +9^{2} =c^{2} \\441+81=c^{2} \\\sqrt[3]{58}=c[/tex]

Then, find the missing angle, lets name it B.

The angle B can be found using the inverse sine function.

B=arcsin(opp/hyp)

[tex]B=arcsin(\frac{9}{\sqrt[3]{58} } )\\B=23.19[/tex]

Answer:

Option a.

Step-by-step explanation:

By looking at the options, we can assume that the function y(x) is something like:

[tex]y = \sqrt{4 + a*x^2}[/tex]

[tex]y' = (1/2)*\frac{1}{\sqrt{4 + a*x^2} }*(2*a*x) = \frac{a*x}{\sqrt{4 + a*x^2} }[/tex]

such that, y(0) = √4 = 2, as expected.

Now, we want to have:

[tex]y' = \frac{x*y}{2 + x^2}[/tex]

replacing y' and y we get:

[tex]\frac{a*x}{\sqrt{4 + a*x^2} } = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}[/tex]

Now we can try to solve this for "a".

[tex]\frac{a*x}{\sqrt{4 + a*x^2} } = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}[/tex]

If we multiply both sides by y(x), we get:

[tex]\frac{a*x}{\sqrt{4 + a*x^2} }*\sqrt{4 + a*x^2} = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}*\sqrt{4 + a*x^2}[/tex]

[tex]a*x = \frac{x*(4 + a*x^2)}{2 + x^2}[/tex]

We can remove the x factor in both numerators if we divide both sides by x, so we get:

[tex]a = \frac{4 + a*x^2}{2 + x^2}[/tex]

Now we just need to isolate "a"

[tex]a*(2 + x^2) = 4 + a*x^2[/tex]

[tex]2*a + a*x^2 = 4 + a*x^2[/tex]

Now we can subtract a*x^2 in both sides to get:

[tex]2*a = 4\\a = 4/2 = 2[/tex]

Then the solution is:

[tex]y = \sqrt{4 + 2*x^2}[/tex]

The correct option is option a.

Answer:

Length = 5 feet

Breadth = (5/3) feet

Height(depth) = 2 feet

Volume of the entire tank = Length x Breadth x Height  

                                         = [tex]5 \times \frac{5}{3} \times2 = \frac{50}{3}[/tex]   ----------(1)

Water is filled upto a height of (1/3) feet

Volume of water in the tank = Length x Breadth x Height  

                                           = [tex]5 \times \frac{5}{3} \times \frac{1}{3} = \frac{25}{9}[/tex]     -------------(2)

Volume of space needed to be filled = (1) - (2)

                                                         = [tex]\frac{50}{3} -\frac{25}{9} = \frac{150-25}{9} = \frac{125}{9} cubic feet[/tex]

                                           OR

Height of tank needed to be filled = 2 - (1/3) = (5/3) feet

Volume of space =  Length x Breadth x Height of empty tank

                           =  [tex]5 \times \frac{5}{3} \times \frac{5}{3} = \frac{125}{9} cubic \ feet[/tex]

Answer:

Step-by-step explanation:

since they are in continued proportion the ratio will be

3/8=9/x

do cross multiplication

8*9=3*x

72=3x

72/3=x

24=x

therefore x =24

Answer:

ans is 24

Step-by-step explanation:

soln

the 3 8 9 and x are in proportion

so 3/8=9/x

3x=72

x=72/3

x=24

Answer: 121.5 ft^2

Step-by-step explanation:

Area= L x W

12.8 X 9.5

= 121.6

35 is the answer

have a wonderful day

Answer:

The researcher determines relationships among variables.

The individuals are observed the exact way they act in real life.

Step-by-step explanation:

An observational study can be defined as a type of study in which a researcher observes and measures the effect of a diagnostic test, risk factors, or treatments on individuals without intervening, changing or manipulating who are or aren't exposed to it (controlled conditions).

Hence, the statements which best describes a characteristic of an observational study are;

I. The researcher determines relationships among variables.

II. The individuals are observed the exact way they act in real life.

Additionally, an unobtrusive data collection is a data collection technique used mainly in the social sciences to obtain or gather data without the researcher directly interfering or interfacing with the subject being studied. Thus, it doesn't influence the behavior, action or response of the subjects under study.

=======================================

Explanation:

As mentioned earlier (in a previous post) the triangle with sides 2,5,7 is not a right triangle. So we can rule out choice A.

For choice B, we have a = 6, b = 8, c = 10, and that leads to...

a^2+b^2 = c^2

6^2+8^2 = 10^2

36+64 = 100

100 = 100

The true equation at the end means the beginning equation is true as well for those a,b,c values. Therefore, we have a right triangle and the answer is choice B

Choices C and D are similar to choice A. They make a^2+b^2 = c^2 to be false.

Answer:

6 3/4 cm³

Step-by-step explanation:

I'm assuming value means volume, so if I'm wrong, let me know ;).

To find volume, you multiply length x height x width. So you multiply 2 1/4 three times.

Convert 2 1/4 to an improper fraction.

2 1/4 = 9/4

9   x   3        27

--        --     =

4   x    1        4

Now convert 27/4 to a mixed fraction.

27/4 = 6 3/4

So the volume of the cube is 6 3/4 cm³.

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hope it helps

Answer:

2.15cm^3

Step-by-step explanation:

V = Mass / Density

21.93g / 10.2 g/cm^3

2.15cm^3

Answer:

A, B, D, E, F

Step-by-step explanation:

48/64 can be simplified into all of them except C

Answer:

B

Step-by-step explanation: Net worth is the total assets minus total liabilities of an individual or entity.

Answer:

1 11/12

Step-by-step explanation:

convert to common denominators.

1 1/6 = 7/6 = 14/12

3/4 = 9/12

14+9=23

23/12

1 11/12

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hope it helps

Answer:

4p +2

Step-by-step explanation:

(2p + 1)(2)

Distribute

2p * 2 + 1*2

4p +2

Answer:

4p+2

Step-by-step explanation:

See the steps below:)

Welcome back....♡

Surface area = 2( 4 × 2 ) + ( 3 × 4 )

+ 2( 4 × 4 ) + 3( 10 × 4 )

+ 3( 4 × 7 )

Surface area = 16 + 12 + 32 + 120 + 84

Surface area = 264 in^2

9514 1404 393

Answer:

Step-by-step explanation:

The only given angle is between the two given sides, so the Law of Cosines must be used to find the side opposite the angle. It tells you ...

  e² = d²+f² -2df·cos(E)

  e² = 7² +6² -2·7·6·cos(95°) ≈ 92.321082

  e ≈ 9.608

The remaining angles can be found from the law of sines.

  sin(D)/d = sin(E)/e

  D = arcsin(d/e·sin(E)) ≈ arcsin(7/9.608·sin(95°)) ≈ 46.5°

  F = 180° -95° -46.5° = 38.5°