The volume of a rectangular prism is the products it’s dimensions. If the dimensions of a rectangle prism are approximately 1.08 feet,5.25 feet, and 3.3 feet ,what is the approximate volume of the cube?Express your answer using an approximate level of accuracy.

[tex]10[/tex] divisions between $389$ and $390$ so each division is $\frac{390-389}{10}=0.1$

A is 8 division from $389$, so, A is $389+8\times 0.1=389.8$

similarly, C is one division behind $389$ so it is $389-1\times 0.1=388.9$

and B is $390.3$

Answer:

$25

Step-by-step explanation:

.5 * 50 = 25

25<27.5<30

The cheapest supplier is the first one.

Answer:

Yes it can be concluded that state employees earn on average less than federal employees

  The critical value is  [tex]Z_{\alpha } = - 2.33[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean is  [tex]\mu = \$ 59593[/tex]

   The sample size is  n =  30

    The  sample mean is [tex]\= x = \$ 58800[/tex]

     The  standard deviation is  [tex]\sigma = \$ 1500[/tex]

     The significance level is  [tex]\alpha = 0.01[/tex]

The null hypothesis is  [tex]H_o : \mu = \$ 59593[/tex]

 The  alternative hypothesis is  [tex]H_a : \mu < \$ 59593[/tex]

The critical value of [tex]\alpha[/tex] from the normal distribution table is  [tex]Z_{\alpha } = - 2.33[/tex]

 Generally the test statistics is  mathematically evaluated as

            [tex]t = \frac{\= x - \mu}{ \frac{ \sigma }{ \sqrt{n} } }[/tex]

=>         [tex]t = \frac{ 58800 - 59593 }{ \frac{ 1500 }{ \sqrt{30} } }[/tex]  

=>          [tex]t = -2.896[/tex]

The  p-value is obtained from the z-table

   [tex]p-value = P(t < -2.896) = 0.0018898[/tex]

Since [tex]p-value < \alpha[/tex] , we reject the null hypothesis, hence it can be concluded that state employees earn on average less than federal employees  

Answer:

n + 1

Step-by-step explanation:

Starting with the integer 'n,' we represent the "next integer" by n + 1.

Answer:

  isosceles

Step-by-step explanation:

The point B is located on the perpendicular bisector of AC. No calculation is necessary. AC has a slope of 1, so it is easy to count grid squares to see where the perpendicular bisector goes.

When the altitude of the triangle bisects the side opposite the vertex, it is an isosceles triangle.

_____

Apparently, you're to use the distance formula to determine the lengths of the sides of the triangle. Doing that, you would find ...

  AB² = (6-4)² +(1 -6)² = 4 + 25

  CB² = (6-1)² +(1-3)² = 25 + 4

At this point, it doesn't require much thought to realize these sides are the same length: √29.

Greetings from Brasil...

In this problem we have 2 translations: 4 units horizontal to the left and 3 units vertical to the bottom.

The translations are established as follows:

→ Horizontal

F(X + k) ⇒ k units to the left

F(X - k) ⇒ k units to the right

→ Vertical

F(X) + k ⇒ k units up

F(X) - k ⇒ k units down

In our problem, the function shifted 4 units horizontal to the left and 3 units vertical to the bottom.

F(X) = X³

4 units horizontal to the left: F(X + 4)

3 units vertical to the bottom: F(X + 4) - 3

So,

F(X) = X³

The transformed function is f ( x ) = ( x + 4 )³ - 3 and the graph is plotted

Every modification may be a part of a function's transformation.

Typically, they can be stretched (by multiplying outputs or inputs) or moved horizontally (by converting inputs) or vertically (by altering output).

If the horizontal axis is the input axis and the vertical is for outputs, if the initial function is y = f(x), then:

Vertical shift, often known as phase shift:

Y=f(x+c) with a left shift of c units (same output, but c units earlier)

Y=f(x-c) with a right shift of c units (same output, but c units late)

Vertical movement:

Y = f(x) + d units higher, up

Y = f(x) - d units lower, d

Stretching:

Stretching vertically by a factor of k: y = k f (x)

Stretching horizontally by a factor of k: y = f(x/k)

Given data ,

Let the function be represented as g ( x )

Now , the value of g ( x ) = x³

And , the transformed function has coordinates as A ( -4 , -3 )

So , when function is shifted 4 units to the left , we get

g' ( x ) = ( x + 4 )³

And , when the function is shifted vertically by 3 units down , we get

f ( x ) = ( x + 4 )³ - 3

Hence , the transformed function is f ( x ) = ( x + 4 )³ - 3

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Answer:

[tex]\Large \boxed{\mathrm{C) \ D: (-7, 3] \ R: (-10, 9.2]}}[/tex]

Step-by-step explanation:

The domain is the set of all possible x values.

The range is the set of all possible y values.

For the domain, we observe the graph, the graph will contain all the x values shown on the x-axis.

[tex]\mathrm{D= (-7,3] }[/tex]

For the range, we observe the graph, the graph will contain all the y values shown on the y-axis.

[tex]\mathrm{R= (-10,9.2] }[/tex]

Answer:

k=8

Step-by-step explanation:

Since y and x are in direct proportions, the equation is

y= kx, where k is a constant.

when y= 33.6, x=4.2,

33.6= k(4.2)

k= 33.6 ÷4.2

k=8

Answer:

k=8

Step-by-step explanation:

Answer:

length times width

Step-by-step explanation:

Answer:

L = 29,550 mm

Step-by-step explanation:

i think i've done this before.. but anyway Lets make it simple and easy.

Let A = 600mm

Let B = 300mm

Let C = 16 as number turns

Let d = 20mm

L = sqrt ((3.14 * (600 - 20))² + 300³)    * 16

L = 29,550 mm

Answer:

[tex](-\infty,1/4)\cup(1/4,\infty)[/tex]

The answer is C.

Step-by-step explanation:

We are given the rational function:

[tex]\displaystyle f(x) = \frac{x-3}{4x-1}[/tex]

In rational functions, the domain is always all real numbers except for the values when the denominator equals zero. In other words, we need to find the zeros of the denominator:

[tex]\displaystyle \begin{aligned}4x -1 & = 0 \\ \\ 4x & = 1 \\ \\ x & = \frac{1}{4} \end{aligned}[/tex]

Therefore, the domain is all real number except for x = 1/4.

In interval notation, this is:

[tex](-\infty,1/4)\cup(1/4,\infty)[/tex]

The left interval represents all the values to the left of 1/4.The right interval represents all the values to the right of 1/4. The union symbol is needed to combine the two. Note that we use parentheses instead of brackets because we do not include the 1/4 nor the infinities.  

In conclusion, our answer is C.

Answer:

The third one

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Option D is correct. Slope of the line shown in the graph is 3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run.

It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=(y₂-y₁)/(x₂-x₁)

The line is passing through point (2, 2) and (4, 8).

Lets find the corresponding point values y₂= 8, y₁ = 2, x₂= 4 and x₁ =2.

Plug in the values in slope formula:

Slope = (8-2)/(4-2)  

=6/2

=3

Hence, slope of the line shown in the graph is 3. Option D is correct.

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Answer:

x= -20

Step-by-step explanation:

x/2=3x/4+5

Multiply both sides of the equation by 4, the least common multiple of 2,4.

2x=3x+20

Subtract 3x from both sides.

2x−3x=20

Combine 2x and −3x to get −x.

−x=20

Multiply both sides by −1.

x=−20

Answer:

0.4207149;0.7271136; 0.3063987; 0.04979 ; 0.01832

Step-by-step explanation:

For an exponential distribution:

IF Mean time until failure = 23100

λ = 1/ 23100 = 0.0000432900

What is the probability that a randomly selected fan will last at least 20,000 hours

x ≥ 20000

P(X ≥ 20000) = 1 - P(X ≤ 20000)

1 - P(X ≤ 20000) = [1 - (1 - e^(-λx))]

1 - P(X ≤ 20000) = [1 - (1 - e^(-0.0000432900*20000)

1 - P(X ≤ 20000) = [1 - (1 - 0.4207148)]

1 - P(X ≤ 20000) = 1 - 0.5792851

1 - P(X ≤ 20000) = 0.4207149

11) What is the probability that a randomly selected fan will last at most 30,000 hours?

x ≤ 30000

P(X ≤ 30000) = 1 - e^(-λx)

P(X ≤ 20000) = 1 - e^(-0.0000432900*30000)

= 1 - e^(−1.2987)

= 1 - 0.2728863

= 0.7271136

111) What is the probability that a randomly selected fan will last between 20,000 hours and 30,000 hours?

0.7271136 - 0.4207149 = 0.3063987

B) What is the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations?

More than two standard deviation

X = 23100 + 2(23100) = 23100 + 46200 = 69300

Using the online exponential probability calculator :

P(X > 69300) = 0.04979

C) What is the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations?

X = 23100 + 3(23100) = 23100 + 69300 = 92400

P(X > 92400) = 0.01832

volume of a cone

.

.

.

volume of sphere

.

.

number of spheres that can be made......

.

.

hence a hemisphere can be formed

Answer:

14

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

12*x = 8 * (x+2)

Distribute

12x = 8x+16

Subtract 8x

12x-8x = 8x+16-8x

4x = 16

Divide by 4

4x/4 = 16/4

x = 4

We want NT

NT = 8+x+2

     = 10 +x

    = 10 +4

    = 14

Answer:

a) and b)  Look step by step explanation

c) z(s) = - 12,07

d) z(c) = - 1,64

e) Final decision: Reject H₀

Step-by-step explanation:

We assume Normal Distribution

Data:

Sample population  n   = 1200

Sample mean         μ  =    3

Sample Standard deviation   2,87

Claim mean      μ₀  =  4

α = 0,05  then from z-table we find  z(c) = 1,64   ( critical value )

We need to develop a one tail-test to the left

Test Hypothesis

The General Society developed a survey ( in all cases that is an indication of a sample)

Null hypothesis                    H₀                      μ   =  μ₀

Alternative hypothesis        Hₐ                       μ  <  μ₀

To calculate the  z(s)

z(s) =  ( μ  -  μ₀ )/ 2,87/√n

z(s) =  ( 3 - 4 )/ 2,87/√1200

z(s) =   -1 * 34,64 / 2,87

z(s) = - 12,07

To compare  z(s) and z(c)

z(s)  <  z(c)           - 12,07 < - 1,64

z(s) is in the rejection region (quite far away) we reject H₀

Data provide enough evidence to disprove the claim

Answer:

the answer to the question is "C"

[tex]\displaystyle\\(a+b)^n\\T_{r+1}=\binom{n}{r}a^{n-r}b^r\\\\\\(x+2)^7\\a=2x\\b=3\\r+1=4\Rightarrow r=3\\n=5\\T_4=\binom{5}{3}\cdot (2x)^{5-3}\cdot3^3\\T_4=\dfrac{5!}{3!2!}\cdot 4x^2\cdot27\\T_4=\dfrac{4\cdot5}{2}\cdot 4x^2\cdot27\\\\T_4=1080x^2[/tex]

Answer:

At 3 hours, the trains will be equidistant from the station.

Step-by-step explanation:

The first train leaves at 75 miles per hour and has a 2 hour head start.  This will put the first train at mile marker 150 (75 * 2) when the second train leaves the station at 125 mph.

To solve when they will be near each other, we set up an equation to solve for t.

150 + 75t = 125t

150 = 50t

3 = t

So given this value, we know the trains will be equidistant from the train station on parallel tracks after 3 hours.

Cheers.

Answer:

mean=87

median=87

Step-by-step explanation:

mean=sum of test score/number of subject

mean=79+91+93+85+86+88/6

mean=522/6

mean=87

Literal meaning of median is medium.

To find the number which lies in the medium, we must rearrange the number in ascending.

79, 91, 93, 85, 86, 88

79, 85, 86, 88, 91, 93

86+88/2=87

Hope this helps ;) ❤❤❤

Let me know if there is an error in my answer.

Answer:

option B

everyone has different opinions about different things, since we only recorded the survey of a fourth of the total people, the survey will definitely have bias since the people who dont have to answer survey will not be able to record their opinions

Answer:

495.56 should be p[aid for 40 hours.

Step-by-step explanation:

concept used

In ratio

a:b = c:d

__________________________________________

Given

IS PAID 473.88 FOR 38 1/4 HOURS OF WORK

38 1/4 hour = 38.25 hours

if we get ratio for payment per hour

we have

473.88 / 38.25 or  473.88 : 38.25

___________________________________

now we have to find payment for 40 hours

let that payment be x

thus,  ratio for payment per hour in this case will be

x/40 or x:40

since

x:40 and  473.88 : 38.25 is representative of same program enhancement unit both ratio will be equal

thus

x:40 =  473.88 : 38.25

x/40 =  473.88 / 38.25

=> x = 40*(473.88 / 38.25 ) = 495.56

Thus,  495.56 should be p[aid for 40 hours.

Answer:

0.16

Step-by-step explanation:

See the picture attached for reference.

As you see the best points are the green areas which covers 2 out of 5 zones.

Since it is same for both broken points, the probability of  this is:

Answer is 0.16

Answer:

The calculated Z= 10/4.61 = 2.169

The P value is 0.975 .

Since the calculated value of z= 2.169 falls in the rejection region we therefore reject the null hypothesis at 5 % significance level . On the basis of this we conclude that the students at University A do not spend more on textbooks then the students at University B.

Step-by-step explanation:

We set up our hypotheses as

H0 : x 1= x2 and Ha: x1 ≠ x2

We specify significance level ∝= 0.05

The test statistic if H0: x1= x2 is true is

Z =  [tex]\frac{x_1-x_2}\sqrt\frac{s_1^2}{n_1}+ \frac{s_2^2}{n_2}[/tex]

Z = 260-250/ √400/50 + 529/40

Z= 10 / √8+ 13.225

Z= 10/4.61 = 2.169

The critical value for two tailed test at alpha=0.05 is ± 1.96

The P value is 0.975 .

It is calculated by dividing alpha by 2 for a two sided test and subtracting from 1. When we subtract   0.025 ( 0.05/2)from 1 we get 0.975

Since the calculated value of z= 2.169 falls in the rejection region we therefore reject the null hypothesis at 5 % significance level . On the basis of this we conclude that the students at University A do not spend more on textbooks then the students at University B.

Answer:

A) C1 = 0.00187 m = 0.187 cm,  C2 = 0.0062 m = 0.62 cm

B)  A sample of how the graph looks like is attached below ( periodic sine wave )

C) w = [tex]\sqrt[4]{3}[/tex] is when the amplitude of the forced response is maximum

Step-by-step explanation:

Given data :

mass = 5kg

length of spring = 10 cm = 0.1 m

f(t) = 10sin(t) N

viscous force = 2 N

speed of mass = 4 cm/s = 0.04 m/s

initial velocity = 3 cm/s = 0.03 m/s

Formulating initial value problem

y = viscous force / speed = 2 N / 0.04 m/s = 50 N sec/m

spring constant = mg/ Length of spring = (5 * 9.8) / 0.1 = 490 N/m

f(t) = 10sin(t/2) N

using the initial conditions of u(0) = 0 m and u"(0) = 0.03 m/s to express the equation of motion

the equation of motion = 5u" + 50u' + 490u = 10sin(t/2)

A) finding the solution of the initial value

attached below is the solution and

B) attached is a periodic sine wave replica of how the grapgh of the steady state solution looks like

C attached below

Answer: ABCD is a parallelogram.

Step-by-step explanation:

First we plot these point on a graph as given in attachment.

From the attachment we can observe that AD || BC || x-axis .

also, AB ||CD, that will make ABCD a parallelogram ,  but to confirm we check the property of parallelogram "diagonals bisect each other" , i.e . "Mid point of both diagonals are equal".

Mid point of AC= [tex](\dfrac{-5+4}{2},\dfrac{2+5}{2})=(\dfrac{-1}{2},\dfrac{7}{2})[/tex]

Mid point of BD= [tex](\dfrac{-3+2}{2},\dfrac{5+2}{2})=(\dfrac{-1}{2},\dfrac{7}{2})[/tex]

Thus, Mid point of AC=Mid point of BD

i.e. diagonals bisect each other.

That means ABCD is a parallelogram.

Answer: ABCD is a parallelogram.

Step-by-step explanation:

First, we plot these points on a graph as given in the attachment. From the attachment, we can observe that AD || BC || x-axis. Also, AB ||CD, which will make ABCD a parallelogram, but to confirm, we check the parallelogram property "diagonals bisect each other," i.e., "Midpoint of both diagonals is equal."

The midpoint of AC=. The midpoint of BD=. Thus, the Midpoint of AC=Mid point of BD diagonals bisects each other. That means ABCD is a parallelogram.

Answer:

this? hope it helps ........

Answer:

The answer is area=32pi-64 and the perimeter is 8pi

Step-by-step explanation:

Answer:

The second graph is a function.

Step-by-step explanation:

This is the only one that passes the vertical line test.

(If there exits a vertical line which passes through more than one point, then the relation is NOT a function).

Answer:

2x^2 + x - 6 = rectangular garden: length = 2x – 3 feet; width = x + 2 feet

Step-by-step explanation:

(2x - 3)(x + 2) = 2x^2 + x - 6 =

2x^2 + 4x - 3x - 6 = 2x^2 + x - 6 =

2x^2 + x - 6

You get the original equation from the two sides multiplied. :)

Hope this helps, have a good day.

The length and width of the rectangle will be (2x – 3) and (x + 2). Then the correct option is D.

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L × W square units

The area is 2x² + x – 6 square feet. Then the factor of the equation is given as,

A = 2x² + x – 6

A = 2x² + 4x – 3x – 6

A = 2x(x + 2) – 3(x + 2)

L × W = (2x – 3)(x + 2)

The length and width of the rectangle will be (2x – 3) and (x + 2). Then the correct option is D.

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