One stats class consists of 52 women and 28 men. Assume the average exam score on Exam 1 was 74 (σ = 10.43; assume the whole class is a population). A random sample of 16 students yielded an average of a 75 on the first exam (s=16). What is the z-score of the sample mean? Is this sample significantly different from the population? (Hint: Use the z-score formula for locating a sample mean)

Answers

Answer 1

Answer:

(A) What is the z- score of the sample mean?

The z- score of the sample mean is 0.0959

(B) Is this sample significantly different from the population?

No; at 0.05 alpha level (95% confidence) and (n-1 =79) degrees of freedom, the sample mean is NOT significantly different from the population mean.

Step -by- step explanation:

(A) To find the z- score of the sample mean,

X = 75 which is the raw score

¶ = 74 which is the population mean

S. D. = 10.43 which is the population standard deviation of/from the mean

Z = [X-¶] ÷ S. D.

Z = [75-74] ÷ 10.43 = 0.0959

Hence, the sample raw score of 75 is only 0.0959 standard deviations from the population mean. [This is close to the population mean value].

(B) To test for whether this sample is significantly different from the population, use the One Sample T- test. This parametric test compares the sample mean to the given population mean.

The estimated standard error of the mean is s/√n

S. E. = 16/√80 = 16/8.94 = 1.789

The Absolute (Calculated) t value is now: [75-74] ÷ 1.789 = 1 ÷ 1.789 = 0.559

Setting up the hypotheses,

Null hypothesis: Sample is not significantly different from population

Alternative hypothesis: Sample is significantly different from population

Having gotten T- cal, T- tab is found thus:

The Critical (Table) t value is found using

- a specific alpha or confidence level

- (n - 1) degrees of freedom; where n is the total number of observations or items in the population

- the standard t- distribution table

Alpha level = 0.05

1 - (0.05 ÷ 2) = 0.975

Checking the column of 0.975 on the t table and tracing it down to the row with 79 degrees of freedom;

The critical t value is 1.990

Since T- cal < T- tab (0.559 < 1.990), refute the alternative hypothesis and accept the null hypothesis.

Hence, with 95% confidence, it is derived that the sample is not significantly different from the population.


Related Questions

A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after submersion is 120°F. After 1 min submerged, the temperature has cooled to 100°F. A) Determine the cooling constant k.B) What is the differential equation satisfied by the temperature F(t) of the bar?C) What is the formula for F(t)?D) Determine the temperature of the bar at the moment it is submerged.

Answers

Answer:

A) cooling constant =  0.0101365

B) [tex]\frac{df}{dt} = k ( 60 - F )[/tex]

c)  F(t) = 60 + 77.46[tex]e^{0.0101365t}[/tex]

D)137.46 ⁰

Step-by-step explanation:

water temperature = 60⁰F

temperature of Bar after 20 seconds = 120⁰F

temperature of Bar after 60 seconds = 100⁰F

A) Determine the cooling constant K

The newton's law of cooling is given as

= [tex]\frac{df}{dt} = k(60 - F)[/tex]

= ∫ [tex]\frac{df}{dt}[/tex] = ∫ k(60 - F)

= ∫ [tex]\frac{df}{60 - F}[/tex] = ∫ kdt

= In (60 -F) = -kt - c

       60 - F = [tex]e^{-kt-c}[/tex]

      60 - F = [tex]C_{1} e^{-kt}[/tex]       ( note : [tex]e^{-c}[/tex] is a constant )

after 20 seconds

[tex]C_{1}e^{-k(20)}[/tex] = 60 - 120 = -60  

therefore [tex]C_{1} = \frac{-60}{e^{-20k} }[/tex] ------- equation 1

after 60 seconds

[tex]C_{1} e^{-k(60)}[/tex] = 60 - 100 = - 40  

therefore [tex]C_{1} = \frac{-40}{e^{-60k} }[/tex] -------- equation 2

solve equation 1 and equation 2 simultaneously

= [tex]\frac{-60}{e^{-20k} }[/tex] = [tex]\frac{-40}{e^{-60k} }[/tex]

= 6[tex]e^{20k}[/tex] = 4[tex]e^{60k}[/tex]

= [tex]\frac{6}{4} e^{40k}[/tex] = In(6/4) = 40k

cooling constant (k) = In(6/4) / 40 = 0.40546 / 40 = 0.0101365

B) what is the differential equation  satisfied

substituting the value of k into the newtons law of cooling)

60 - F = [tex]C_{1} e^{0.0101365(t)}[/tex]  

F(t) = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]

The differential equation that the temperature F(t) of the bar

[tex]\frac{df}{dt} = k ( 60 - F )[/tex]

C) The formula for F(t)

t = 20 , F = 120

F(t ) = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]

120 = 60 - [tex]C_{1} e^{0.0101365(t)}[/tex]

[tex]C_{1} e^{0.0101365(20)}[/tex] = 60

[tex]C_{1} = 60 * 1.291[/tex] = 77.46

C1 = - 77.46⁰ as the temperature is decreasing

The formula for f(t)

= F(t) = 60 + 77.46[tex]e^{0.0101365t}[/tex]

D) Temperature of the bar at the moment it is submerged

F(0) = 60 + 77.46[tex]e^{0.01013659(0)}[/tex]

F(0) = 60 + 77.46(1)

     = 137.46⁰

find the coordinate of W' after a 90° rotation of the triangle about the origin and then a reflection about the line y= -3​

Answers

Answer:

(4, -8).

Step-by-step explanation:

If point W were to be rotated 90 degrees, it would rotate 90 degrees clockwise. The current point of W is (-2, 4). After a 90 degree rotation about the origin, the point will be (4, 2).

y = -3 is a horizontal line where y = -3. The y-value of the newly rotated point is 2. That is five units above the line where y = -3. So, a reflection would result in a y-value of y = -3 - 5 = -8. The x-value does not change.

So, the coordinate of W' is (4, -8).

Hope this helps!

cual es la derivada de ()=√x sin

Answers

Answer:

[tex] f(x) =\sqrt{x} sin (x)[/tex]

And on this case we can use the product rule for a derivate given by:

[tex] \frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)[/tex]

Where [tex] f(x) =\sqrt{x}[/tex] and [tex] g(x) =sin (x)[/tex]

And replacing we have this:

[tex] f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)[/tex]

Step-by-step explanation:

We assume that the function of interest is:

[tex] f(x) =\sqrt{x} sin (x)[/tex]

And on this case we can use the product rule for a derivate given by:

[tex] \frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)[/tex]

Where [tex] f(x) =\sqrt{x}[/tex] and [tex] g(x) =sin (x)[/tex]

And replacing we have this:

[tex] f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)[/tex]

The price of a particular model car is $13,857 today and rises with time at a constant rate of $1203 per year. How much will a new car cost in 4.7 years?

Answers

Answer:

It should be about $19,500

Step-by-step explanation:

Answer:

$19,511.10

Step-by-step explanation:

1203*4.7= The total change over 4.7 years.

1203*4.7=5654.10

5654.10+13857=The total price after 4.7 years.

5654.10+13857=19,511.10

what is the answer to 100×338 ​

Answers

Answer:

33800

Step-by-step explanation:

100 x 338 = 33800

Answer:

33800

Step-by-step explanation:

338x10=3380 then 3380x10=33800

-------------------------------------------------------

Good luck with your assignment...

Someone help me please​

Answers

Answer:

3

Step-by-step explanation:

If the cube has 54 stickers across its six faces, and each face has the same number of stickers, first we can find the number of stickers in each face by dividing the number of stickers by the number of faces:

[tex]stickers\ per\ face = number\ of\ stickers / number\ of\ faces[/tex]

[tex]stickers\ per\ face = 54/6 = 9[/tex]

Each face has 9 stickers.

If each row and column has the same number of stickers, we can find the numbers of rows and columns by finding the square root of the number of stickers in the face:

[tex]\ number\ of\ rows = \sqrt{9} = 3[/tex]

If we have 3 rows, and each roll has the same number of stickers, the number of stickers per row or column is:

[tex]stickers\ per\ row = stickers\ per\ face / number\ of\ rows[/tex]

[tex]stickers\ per\ row = 9/3 = 3[/tex]

What is the vertex of the graph of g(x) = |x – 8| + 6?

Answers

Answer:

(8,6)

Step-by-step explanation:

g(x) = |x – 8| + 6 was transformed from the parent function g(x) = |x|:

8 unit right

6 units up

a parent absolute value function has a vertex at (0,0)

if the function is moved so is the vertex:

(0+8,0+6)

(8,6)

So, the vertex of this function is at (8,6)

Answer:  vertex = (8, 6)

Step-by-step explanation:

The Vertex form of an absolute value function is: y = a|x - h| + k   where

a is the vertical stretch(h, k) is the vertex

g(x) = |x - 8| + 6 is already in vertex form where

h = 8 and k = 6

so the vertex (h, k) = (8, 6)

One number is 2 more than another. The difference between their squares is 52. What are the numbers?

Answers

The numbers are 12 and 14.

Answer:

The aprox, numbers:

4.1633   and    8.3266

Step-by-step explanation:

a = 2b

a² - b² = 52

then:

(2b)² - b² = 52

4b² - b² = 52

3b² = 52

b² = 52/3

b² = 17.333

√b² = √17.333

b = 4.1633        aprox.

a = 2b

a = 2*4.1633

a = 8.3266

Check:

8.3266² - 4.1633² = 52

69.333 - 17.333 = 52

Write an equation perpendicular to 5x+6y=18 that passes through the point (10,7)

Answers

Answer:

Step-by-step explanation:

6y = -5x + 18

y = -5/6x + 3

perp slope: 6/5

y - 7 = 6/5(x - 10)

y - 7 = 6/5x - 12

y = 6/5x - 5

Here, we are required to write an equation perpendicular to 5x + 6y = 18.

The equation perpendicular to 5x+6y=18 that passes through the point (10,7) is;

6x - 5y = 25.

By rearranging 5x+6y=18 to resemble the end of a straight line; y = Mx + c; we have;

y = (-5/6)x +3

Therefore, slope of equation 5x + 6y = 18 is -5/6.

However, the product of the slopes of 2 perpendicular lines is -1.

Therefore, m1m2 = -1

Therefore, the slope of the required line, m2 is;

m2 = -1/(-5/6)

m2 = 6/5

Therefore, the equation of a line perpendicular to the equation 5x+6y=18 and passes through the point (10,7) is given as;

6/5 = (y - 7)/(x - 10).

By cross product; we have;

6x - 60 = 5y - 35

6x - 5y = 25.

Read more:

https://brainly.com/question/17619748

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

Answers

Answer:A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

Step-by-step explanation:

The cylinder is given by A = pi/4 the volume of the prism or π/4  x (4r²h) or π x r² x h

What is a Cylinder?

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Area circle is A = πr²

Area square with side s = s²

The side of the square is equal to the diameter of the circle

Area square = D²

A diameter of square is always twice the radius

Area square = (2r)² = 2²r² = 4r²

So , on simplifying , we get

Area circle/Area square = (πr²)/(4r²)

Area circle/Area square = π/4

Now , The volume Prism = Area Square x h

Volume Prism =  4r²h

Volume of Cylinder= Area Circle x h

Volume of Cylinder = π x r² x h

So , Volume Cylinder/Volume Prism = π x r² x h/4r² x h

Volume of Cylinder/Volume of Prism = π/4

Volume of Cylinder = π/4 x Volume Prism

And , The volume of Cylinder = π/4  x (4r²h)

Hence , the volume of cylinder is V = π/4  x (4r²h)

To learn more about cylinder click :

https://brainly.com/question/16134180

#SPJ5

a guy wire makes a 67 degree angle with the ground. walking out 32 ft further grom the tower,the angle of elevation to the top of the tower is 39 degrees. find the height of the tower

Answers

Answer:

  39.5 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between angles and sides of a right triangle.

  Tan = Opposite/Adjacent

This lets us write two equations in two unknowns:

  tan(67°) = AD/CD . . . . . . . . . . angle at guy point

  tan(39°) = AD/(CD+32) . . . . . .angle 32' farther

__

Solving the first equation for CD and using that in the second equation, we can get an equation for AD, the height of the tower.

  CD = AD/tan(67°)

  tan(39°)(CD +32) = AD . . . . eliminate fractions in the second equation

  tan(39°)(AD/tan(67°) +32) = AD

  32·tan(39°) = AD(1 -tan(39°)/tan(67°)) . . . simplify, subtract left-side AD term

  32·tan(39°)tan(67°)/(tan(67°) -tan(39°)) = AD . . . . divide by AD coefficient

  AD ≈ 39.486 . . . . feet

The tower is about 39.5 feet high.

Amina sold 1/3 of her goats to a butcher and gave 1/6 of the remaining goats to her children. If she was left with 90 goats how many goats had she at the beginning?​

Answers

Answer:

180 goats

Step-by-step explanation:

3/3-1/3=2/3.

2/3=4/6 remaining.

4/6-1/6=3/6 which also equals 1/2.

If 90=1/2 then 90*2=180.

Hope this helps!! <3

the mean monthly income of trainees at a local mill is 1100 with a standard deviation of 150. find rthe probability that a trainee earns less than 900 a month g

Answers

Answer:

The  probability is  [tex]P(X < 900 ) = 0.0918[/tex]

Step-by-step explanation:

From the question we are told that

   The sample mean is  [tex]\= x = 1100[/tex]

    The  standard deviation is  [tex]\sigma = 150[/tex]

     The random number value is  x =900

The probability that a trainee earn less than 900 a month is mathematically represented as

       [tex]P(X < x) = P(\frac{X -\= x}{\sigma} < \frac{x -\= x}{\sigma} )[/tex]

Generally the z-value for the normal distribution is mathematically represented as

       [tex]z = \frac{x -\mu }{\sigma }[/tex]

So From above we have

      [tex]P(X < 900 ) = P(Z < \frac{900 -1100}{150} )[/tex]

      [tex]P(X < 900 ) = P( Z <-1.33)[/tex]

Now from the z-table

    [tex]P(X < 900 ) = 0.0918[/tex]

8. Let X be the number of cars per minute passing a certain point of some road between 8am and 10am on a Sunday. Assume that X has a Poisson distribution with mean 5. Find the probability of observing 3 or fewer cars during any given minute.

Answers

Answer:

P (3 or fewer) =0.2650

Step-by-step explanation:

Mean = x` = 5

The Poisson distribution formula  is given by

P(X) = e-ˣ` x`ˣ/ x!

The mean is 5 and the X takes the values 0,1,2,and 3 which means 3 or fewer, so we add the probability of all the values of X to get the desired Value of X.

P(3 or fewer ) = e-⁵ (5)³/3!+  e-⁵ (5)²/2! +e-⁵ (5)/1!+e-⁵ (5)⁰/0!

Putting the Values

P (3 or fewer) = 0.006737 . 125 / 6 + 0.006737 . 25 / 2 +0.006737 . 5 / 1 + 0.006737 . 1 / 1

P (3 or fewer) = 0.140374 + 0.08422+ 0.03369 +0.006737

P (3 or fewer) =0.2650

1. What is an inequality? Give one example of an inequality? How would you graph this? 2. What is a compound inequality? Give an example of "and" and an "or" inequality. 3. Identify the independent and dependent variables in the following situation: The more hours Beth studies, the higher the GPA she has.

Answers

Answer:  see below

Step-by-step explanation:

1) An inequality is an equation that uses >, ≥, <, or ≤ instead of an equal sign.

Example:  3x + 2 ≥ 10

2) A compound inequality is when 2 inequalities are combined using either "and" or "or".  

And → means it must satisfy both inequalitiesOr → means it must satisfy at least one of the inequalities

Example:     x > -2  and  x < 4       rewrite as: -2 < x < 4

Graph:        -2 o-----------------o 4        one line segment between the #'s

Example:          x < -2 or x > 4

Graph:        ←-----------o -2    4 o----------→      two lines in opposite directions

3) The GPA is dependent on the number of hours she studies.

Independent: hours Beth studies

Dependent: GPA

Simplify the expression using the order of operations. 2[16-5⋅2]÷4

Answers

Answer:

3.

Step-by-step explanation:

Solve in the order of pemdas.

Answer:

[tex]\boxed{\sf 3}[/tex]

Step-by-step explanation:

Solve brackets first.

[tex]2[16-5 \cdot 2]\div4[/tex]

Multiply the terms in the brackets.

[tex]2[16-10]\div4[/tex]

Subtract the terms in the brackets.

[tex]2[6]\div4[/tex]

Divide the numbers.

[tex]2(\frac{6}{4} )[/tex]

Multiply.

[tex]\frac{12}{4} =3[/tex]

Which right circular cylinder has the greater volume?
r = 2
h = 4
r= 1
h = 8
O A) The red cylinder.
OB) The blue cylinder.
OC) They have the same volume
OD) There is not enough information to tell.

Answers

Answer:

r = 2

h = 4

vol for r = 2  and h = 4 has the greater volume

Step-by-step explanation:

vol for r = 2, h = 4

= pi * r ² * h

= 50

vol for r = 1, h= 8

= pi * r ² * h

= 25

therefore : vol for r = 2  and h = 4 has the greater volume

subtract these polynomials (x^2+5x+2)- (5x^2-x-2)

Answers

Step-by-step explanation:

Here,

the given polynomials are;

(x^2+5x+2)-(5x^2-x-2)

now, when we open bracket of second polynomial we get,

=x^2+5x+2-5x^2+x+2

combining like terms and simplifying them we get;

=x^2-5x^2+5x+x+2+2

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

Therefore, the answer is-3x^2+6x+4 or, taking - (minus) commo it will be -(3x2-6x-4).

Hope it helps....

29% of workers got their job through networking. A researcher feels this percentage has changed. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage).

Answers

Answer: [tex]H_0:p=0.29[/tex]

[tex]H_a: p \neq0.29[/tex]

Step-by-step explanation:

A null hypothesis[tex](H_0)[/tex] is a type of statement used in statistics that proposes that there is no difference between particular characteristics of a population whereas the alternative hypothesis[tex](H_a)[/tex] proposes that there is a difference.

Let p be the population proportion of workers got their job through networking.

Given: 29% of workers got their job through networking.

i.e. [tex]H_0:p=0.29[/tex]

A researcher feels this percentage has changed.

i.e. [tex]H_a: p \neq0.29[/tex]

Hence, the required null and alternative hypotheses in symbolic form for this claim:

[tex]H_0:p=0.29[/tex]

[tex]H_a: p \neq0.29[/tex]

Which is equivalent to 64 1/4 ?

Answers

Answer:

[tex]\frac{257}{4}[/tex]

Step-by-step explanation:

[tex]64\frac{1}{4}=\frac{64*4+1}{4}=\frac{256+1}{4}=\frac{257}{4}[/tex]

The conversion of this mixed number 64 1/4 into an improper fraction is 257/4.

What is a fraction?

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In this exercise and scenario, we would convert the given mixed fraction into an improper fraction into a  by multiplying and adding as follows;

64 1/4 = ((4 × 64) + 1)/4

64 1/4 = 257/4

Read more on fraction here: brainly.com/question/29367657

#SPJ6

What is the first stepin solving the quadratic equations x2-40=0

Answers

Answer:

+40 to both sides of the = sign.

Step-by-step explanation:

x2-40=0

    +40=+40

x2=40

 /2=/2

x=20

Which of the following equations is equivalent to 4/5a - 8 = 1/5?

Answers

Answer:

a = 10 1/4

Step-by-step explanation:

So with the following equation,

4/5a - 8 = 1/5,

we need to use the commutative property.

Which is the moving of whole numbers or variables.

So we add 8 to both sides.

4/5a = 41/5

Divide 4/5 by both sides

a = 10 1/4

So on of the equations could look like a = 10 1/4

Thus,

a = 10 1/4 could be one of the equations given which are equal to 4/5a - 8 = 1/5.

Hope this helps :)

Answer:

[tex]\huge\boxed{a=\dfrac{41}{4}=10\dfrac{1}{4}=10.25}[/tex]

Step-by-step explanation:

[tex]\dfrac{4}{5}a-8=\dfrac{1}{5}\qquad\text{multiply both sides by 5}\\\\5\!\!\!\!\diagup\cdot\dfrac{4}{5\!\!\!\!\diagup}a-(5)(8)=5\!\!\!\!\diagup\cdot\dfrac{1}{5\!\!\!\!\diagup}\\\\4a-40=1\qquad\text{add 40 to both sides}\\\\4a-40+40=1+40\\\\4a=41\qquad\text{divide both sides by 4}\\\\\dfrac{4a}{4}=\dfrac{41}{4}\\\\a=10.25[/tex]

The perimeter of a rectangular field is 344m . If the width of the field is 75m, what is its length?

Answers

Answer:

97 m

Step-by-step explanation:

Perimeter = 2 * (length + width); perimeter = 344, width = 75 (solving for length)

344 = 2(length + 75)

172 = length + 75

length = 97

What is an example of force causing a change in the size of the body (P.S. what is the difference between shape and size?)

Answers

Answer:

shape is how it looks like Square is a shape and size is how big something in like my size of my foot is 6 inches

Step-by-step explanation:

well idk your real question i think it is that your shape and size can change

box with a a square base and open top must have a volume of 62,500 cm3. Find the dimensions of the box that minimize the amount of material used. sides of base

Answers

Answer:

The dimensions of the box that minimize the amount of material used is 39.69 cm

Step-by-step explanation:

This problem is on the mensuration of solids, a box

we know that the volume of a box is give by the expression

[tex]Volume= L^3[/tex]

now to find the dimension of the box, we need to find L

Given data

volume = [tex]62,500 cm^3[/tex].

[tex]62,500 cm^3= L^3\\L=\sqrt[3]{62500} \\\L=39.69 cm[/tex]

Answer:

The dimensions of box that will minimize the amount of material used is [tex]39.69cm[/tex]

Step-by-step explanation:

Given information

Volume [tex]V=62500cm^3[/tex]

As given in question the box is of square shape:

So the volume will be

[tex]V=L^3[/tex]

where, L is the side of the square

[tex]V=L^3=62500\\L=\sqrt[3]{62500} \\L=39.69 cm\\[/tex]

Hence, The dimensions of box that will minimize the amount of material used is [tex]39.69cm[/tex].

For more information visit

https://brainly.com/question/23245822?referrer=searchResults

If sinθ = 12/13 and θ is an acute angle, find cotθ.

Answers

Answer:

[tex]\displaystyle \cot \theta = \frac{5}{12}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \sin \theta = \frac{12}{13}[/tex]

Where θ is an acute angle, and we want to find cot(θ).

Recall that sine is the ratio of the opposite side over the hypotenuse. In other words, our opposite side is measures 12 units and our hypotenuse measures 13 units.

Find the adjacent side:

[tex]\displaystyle \begin{aligned} a^2 + b^2 & = c^2 \\ \\ (12)^2 + b^2 & = (13)^2 \\ \\ b & = 5\end{aligned}[/tex]

Hence, our adjacent side is 5, our opposite side is 12, and our hypotenuse is 13.

Recall that cotangent is the ratio of the adjacent side to the opposite side. Therefore:

[tex]\displaystyle \cot \theta = \frac{5}{12}[/tex]

In conclusion:

[tex]\displaystyle \cot \theta = \frac{5}{12}[/tex]

Answer:

-5/12

Step-by-step explanation:

I just completed Quiz 2: Evaluation of Functions. Of which, this was one of the questions.

Consider the density curve plotted below:

Find PX < 6.4):
Find P(X> 4.8):

Answers

Answer:

[tex] P(X<6.4)= \frac{6.4*0.2}{2}= 0.64[/tex]

[tex] P(X>4.8) =1-P(X<4.8)= 1- \frac{4.8*0.15}{2}= 1-0.36= 0.64[/tex]

Step-by-step explanation:

Part a

We want to find:

[tex] P(X<6.4)[/tex]

And we just need to find the area below the curve until x=6.4, since we have a triangle we can do this:

[tex] P(X<6.4)= \frac{6.4*0.2}{2}= 0.64[/tex]

Part b

For this case we want to find this probability:

[tex] P(X>4.8)[/tex]

And we can use the complement rule and we got:

[tex] P(X>4.8) =1-P(X<4.8)= 1- \frac{4.8*0.15}{2}= 1-0.36= 0.64[/tex]

rewrite (21+31).4 using the disbributive property of multiplication over addition

Answers

Answer: evaluate it is 52

Step-by-step explanation:

determining the probability of events. please help :)​

Answers

Answer:

C. 1/8

Step-by-step explanation:

Probability of shooting a goal on a throw is 2/4 = 1/2.

Probability of 3 in a row is (1/2)³ = 1/8.

Let x represent the number of times a student visits a gym in a one month period. Assume that the probability distribution of X is as follows: x 0 1 2 3 p(x) 0.17 0.33 0.32 0.18 Determine the probability the student visits the gym at most twice in a month. Report your answer to two decimal places.

Answers

Answer: Probability of visiting at most twice = 0.82

Step-by-step explanation: The probability distribution is of the form:

 X      0         1           2            3

P(X)  0.17   0.33      0.32       0.18

It wants the probability of visiting the gym at most twice in a month, which means the probability of never going to the gym, P(X=0), or going once, P(X=1), or going twice, P(X=2).

Using the "OR" probability:

P(visiting at most twice) = P(X=0) + P(X=1) + P(X=2)

P(visiting at most twice) = 0.17 + 0.33 + 0.32

P(visiting at most twice) = 0.82

Therefore, the probability of visiting the gym at most twice in a month is 0.82 or 82%

Other Questions
In Central City, Elm Street and Maple Street are parallel to one another. Oak Street crosses both Elm Street and Maple Street as shown.Choose True Or False for each statement Why was George Washington famous? According to Piaget, a(n) ______ is an organized system of mental representations used to understand the world. UWhich statements are true about x? Select threeoptionsBXEBUCOxencOXEAUCOxeanc In case of a tie in the electoral return, thechooses the president, with each state havingvote(s). Find the product. (6xyz4)(5xy3)PLEASE HELP!!! ASAP!! A bridge on a prominent public roadway in the city of Springfield, Ohio, was deteriorating and in need of repair. The city posted notices seeking proposals for an artistic bridge design and reconstruction. Bridges by Madison LLC, owned and managed by Madison Mason and his wife, May Mason, decided to submit a bid for a decorative concrete project that incorporated artistic metalwork. They contacted Pablo Hand, a local sculptor who specialized in large-scale metal designs, to help them design the bridge. The city selected their bridge design and awarded them the contract for a commission of $184,000. Bridges by Madison and Hand then entered into an agreement to work together on the bridge project. Bridges by Madison agreed to install and pay for concrete and structural work, and Hand agreed to install the metalwork at his expense. They agreed that overall profits would be split, with 25 percent to Hand and 75 percent going to Bridges by Madison. Hand designed numerous metal pig sculptures that were incorporated into colorful decorative concrete forms designed by May Mason, while Madison Mason performed the structural engineering. The group worked together successfully until the completion of the project. Suppose Hand had entered into an agreement to rent space in a warehouse that was close to the bridge so that he could work on his sculptures near the location at which they would eventually be installed. He entered into the contract without the knowledge or consent of Bridges by Madison. In this situation, would a court be likely to hold that Bridges by Madison was bound by the contract that Hand entered? Help please here is the multiple choices Consider issues around prayer in public schools. Then, write a half-page essay to summarize the Supreme Court case Engel v. Vitale. Include a description of the case, discuss the majority opinion and the dissenting opinion, and include your own personal thoughts on the matter. The economic prosperity enjoyed by _____ during the 1980s and 1990s strained the world trading system and created the demand for increased protectionist measures. find the slope y=2x+5 There are chemical reactions that take place within a cell? Mickey is not concerned about the environment. He has no problem with the pollution coming from his 1965 Chevy, and he refuses to recycle. To which environmental activism segment would Mickey belong Write the rule for this sequence '32,16,8,4' n rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB=11 and BC=2, what is the area of the shaded region? Write your answer as a decimal, if necessary. Need help, there are also two more questions to answer after those but I couldnt put them in the picture, they are semicircle and radius. Thanks which expression is equivalent to 2(5)^4 Solving by fractions Which equation represents a line parallel to the line shown on the graph? On a coordinate plane, a line goes through (negative 6, 0) and (negative 8, 6). y = 3 x minus 7 y = negative 3 x + 3 y = one-third x + StartFraction 7 Over 9 EndFraction y = negative one-third x + 12 if elf =gjh ef=12 and Lf=7.8 find ij Light with a frequency of 5.7010^14 Hz travels in a block of glass that has an index of refraction of 1.56. What is the wavelength of the light in the glass?