An IQ test is designed so that the mean is 100 and the standard deviation is 12 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95 % confidence that the sample mean is within 5 IQ points of the true mean. Assume that σ = 12 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

What is the required sample size?

Answer:

8 units²

Step-by-step explanation:

What you have is a square with two triangles. We will break them apart, calculate the area and then add them together.

Square: A = l · w

2 · 2 = 4 un²

Triangle: A = (b · h) ÷ 2

(2 · 2) ÷ 2 = 2 un²

4 un² + 2 un² + 2 un²

8 un²

Answer:

F = 160 pounds

B. 160 pounds

Step-by-step explanation:

F = k / l

Where,

F = amount of force needed

l = length of the lever

k = constant of proportionality

F = 240 when l = 24 inch

F = k / l

240 = k / 24

Cross product

240*24 = k

k = 5,760

Find F when l = 36 inch

Recall, k = 5,760

F = k / l

= 5,760 / 36

= 160

F = 160 pounds

The correct answer is B. 160 pounds

The variation is an inverse variation.; so, 160 pounds of force is needed for a 36-inch long lever

Given that F varies inversely as L, the variation is represented as:

\(F\ \alpha\ \frac 1L\)

Express as an equation

\(F\ =\ \frac kL\) -- where k represents the constant of variation

Make k the subject

\(k =FL\)

When F = 240, L = 24.

So, we have:

\(k =240 \times 24\)

\(k =5760\)

Substitute 5760 for k in \(k =FL\)

\(5760 = FL\)

When L = 36, we have:

\(5760 = 36F\)

Divide both sides by 36

\(160 = F\)

Rewrite as:

\(F = 160\)

Hence, 160 pounds of force is needed for a 36-inch long lever

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Answer:

The sound in a loud part of the room is 10000 times louder than sound in a quiet part of the same place.

Step-by-step explanation:

The acoustic intensity sound is a logarithmic function whose form is:

\(L = 10\cdot \log_{10}\left(\frac{I}{I_{o}} \right)\)

Where:

\(L\) - Acoustic intensity sound, measured in decibels.

\(I_{o}\) - Reference sound intensity, measured in watts per square meter.

\(I\) - Real sound intensity, measured in watts per square meter.

Sound intensity is now cleared:

\(10^{\frac{L}{10} } = \frac{I}{I_{o}}\)

The ratio of the sound intensity in a loud part to the sound intensity in a quiet part is:

\(\frac{I_{100}}{I_{60}} = \frac{10^{\frac{100\,dB}{10} }}{10^{\frac{60\,dB}{10}}}\)

\(\frac{I_{100}}{I_{60}} = \left(10^{100\,dB-60\,dB}\right)^{\frac{1}{10} }\)

\(\frac{I_{100}}{I_{60}} = (10^{40\,dB})^{\frac{1}{10} }\)

\(\frac{I_{100}}{I_{60}} =10^{4}\)

The sound in a loud part of the room is 10000 times louder than sound in a quiet part of the same place.

Answer:

1/3

Step-by-step explanation:

4/15 + 1/15 = 5/15

simplified its 1/3

Answer:

Step-by-step explanation:

The sum of exterior angles in a quadrilateral is always 360 degrees.

So, 2x+x+4x+3x=10x=360

Soling for x, we get x=36 degrees.

Answer:

$73915.40

Step-by-step explanation:

→ Find the multiplier

( 3 + 100 ) ÷ 100 = 1.03

→ Multiply by principal amount and raise it to the power of years

55000 × 1.03¹⁰ = 73915.40

Answer: $630,513.36

Step-by-step explanation:

Let's make a table of values to see how much he earns every year after graduation.

1 year -> $55,000

2 years -> 55,000 * 103% = $56,650

3 years -> 56,650 * 103% = 55000 * 103% * 103% = $58,349.50

4 years ->  58349.50 * 103% = 55,000 * 103% * 103% * 103% = 55000(1.03)³

Here, we see that every year, he gets 103% of what he got the previous year, which is also 1.03 times his previous salary.

We also see that we multiply 55000 by 1.03 three times in the fourth year, and two times in the third year. This means that we multiply 55000 by 1.03 n-1 times.

Using this, let's generalize this for n.

n years -> \(55000(1.03)^{n-1}\)

We are trying to find his total income after ten years, or the sum of his salary from year 1 to year 10. We can represent this in sigma notation like this

\(% Adjusted limits of summation$\displaystyle\sum_{n=1} ^{10} 55000(1.03)^{n-1}$\)

This essentially translates to the sum of the first ten terms in the sequence \(55000(1.03)^{n-1}\), starting at n=1.

Since this is a geometric sequence, or a sequence where we need to multiply by the same number to get to the next term, we can find the sum using the sum of geometric series formula. This formula is as follows:

\(S_n=a_1\frac{1-r^n}{1-r}\)

where \(S_n\) is the sum of the first n terms, \(a_1\) is the first term, r is the common ratio, and n is the number of terms. In this question, \(S_n\) is the total income after n years, \(a_1\) is his salary after the first year, r is how much his salary increases by each year, and n is the number of years we are calculating the sum for.

\(a_1\) -> 55000

r -> 1.03

n -> 10

Now that we have the values for each variable, let's plug them in and solve

\(S_{10}=55000(\frac{1-1.03^{10}}{1-1.03})\\S_{10}=630513.36\)

The total income he will have received after ten years is $630,513.36.

a) The sum of the measures of the interior angles of the regular nonagon is given by S₉ = 1260°

b) The measure of each interior angle of the regular nonagon is a = 140°

c) The measure of each exterior angle of the regular nonagon​ is b = 40°

Given data ,

Sum of the measures of the interior angles of a regular nonagon:

The Polygon Interior Angle Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is given by the formula:

Sum of interior angles = (n - 2) * 180°

For a nonagon, which has 9 sides, we can plug in n = 9 into the formula:

Sum of interior angles = (9 - 2) * 180

Sum of interior angles = 7 * 180

Sum of interior angles = 1260°

So, the sum of the measures of the interior angles of a regular nonagon is 1260°

Measure of each interior angle of a regular nonagon:

Since a regular nonagon has 9 sides, we can divide the sum of the interior angles (which we calculated as 1260 degrees) by the number of sides to find the measure of each interior angle:

Measure of each interior angle = Sum of interior angles / Number of sides

Measure of each interior angle = 1260 / 9

Measure of each interior angle = 140°

So, the measure of each interior angle of a regular nonagon is 140°

Measure of each exterior angle of a regular nonagon:

The Polygon Exterior Angle Sum Theorem states that the sum of the measures of the exterior angles of a polygon with n sides is always 360°

Since a regular nonagon has 9 sides, we can divide 360 degrees by the number of sides to find the measure of each exterior angle:

Measure of each exterior angle = 360 / Number of sides

Measure of each exterior angle = 360 / 9

Measure of each exterior angle = 40°

Hence , the measure of each exterior angle of a regular nonagon is 40°

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Answer:

5.5

Step-by-step explanation:

29.5-13=16.5 16.5÷3=5.5

Answer:

Step-by-step explanation:

smallest value=-240

critical number=(4.5,-240)

relative maximum=200

critical number=(-0.5,200)

relative minimum=-240

largest value=200

Answer:

Let's solve your inequality step-by-step.

x+5≥10

x+5−5≥10−5

x≥5

Step-by-step explanation:

\( \longmapsto\sf x + 5 \geqslant 10\)

\( \longmapsto \sf x \geqslant 10 - 5\)

\( \longmapsto\bf x \geqslant 5\)

Answer:

6\(\sqrt{17}\) or 24.738634

Step-by-step explanation:

We can use the Pythagorean theorem to find the length of the sides. We will only need to find the length of AB and AD, as AB = DC and AD = BC.

The picture shows the Pythagorean theorem being used to find AB and AD.

AB = \(\sqrt{17}\)

AD = \(\sqrt{68}\)

Now we can find the perimeter

2(\(\sqrt{17}\)) + 2(\(\sqrt{68}\)) = 6\(\sqrt{17}\)

Answer:

graph D.

Step-by-step explanation:

The inequality that is being shown in the question means that the value of x is equal to or greater than 9. Greater values are represented as all of the values to the right of a certain number. On a number line "equal to" is represented by  a closed circle. Therefore, with this knowledge we can see that out of all of the provided options the only one that follows these set of rules would be graph D.

Answers:

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

Explanation:

When we translate 4 units down, we're subtracting 4 from the y coordinate. Point A(-6,5) moves to (-6,1) after applying this translation.

Then we add 5 to the x coordinate because we're shifting 5 units to the right. This means (-6,1) moves to (-1,1) which is the location of point A'.

The other three points follow the same pattern: add 5 to the x coordinate, subtract 4 from the y coordinate.

The translation rule can be written as \((x,y) \to (x+5, y-4)\)

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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Answer:

dh/dt =  0.4 m/min

Step-by-step explanation:

The volume of the cone is:

V(c) = (1/3)*r² *h              if always  h = 3r    then    r = h/3

The volume of the cone as a function of h will be:

V(h)  =  (1/3)* (h/3)²*h

V(h) =  (1/27)*h³

The increasing rate of the volume is equal to the rate of sand added the:

D(V)/dt   = (1/27)*3*h²*dh/dt

D(v) / dt  =  10 m³/min

h =  15 m      and   dh/dt is the rate of increasing of the height

By substitution

10 m³/min  = ( 1/9)* 225 * dh/dt  (m²)

dh/dt =  90 / 225   m/min

dh/dt =  0.4 m/min

EDITED: Answer: Phillip can order 12 different ways of ice cream.

Step-by-step explanation:

Ahem.

He can only have Vanilla or Chocolate. So let's pet them in a separate Row.

Vanilla

Chocolate

1.With Sprinkles

2.With Almonds

3.With Hot Fudge

4.With Sprinkles and Almonds

5.With Sprinkles and Hot Fudge

6.With Almonds and Hot Fudge

The treatment groups should be comparable, and any differences in the outcomes of the telemarketing calls can be attributed to the different scripts and not to any systematic differences in the characteristics of the subjects.

The statement that best describes the composition of the treatment groups in this scenario is: "The treatment groups should be comparable because characteristics of the subjects should be roughly equivalent among the three groups."

Randomly assigning the subjects to the three new scripts using a table of random digits helps ensure that there is no bias in the selection process and that the characteristics of the subjects should be roughly equivalent among the three groups.

The fact that there are 25 subjects in each group and a relatively large number of subjects in total (75) also supports the comparability of the treatment groups.

Thus, the treatment groups should be comparable, and any differences in the outcomes of the telemarketing calls can be attributed to the different scripts and not to any systematic differences in the characteristics of the subjects.

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Answer: Its A

Step-by-step explanation: i got it right on edge 2023, keep going u got thisss <3

Answer:

4th graph

6th graph

3rd graph

Step-by-step explanation:

Linear = y = x + 3

it is 4th graph

when you substitute x = 0 y is 3

and when y = 0 x is -3

Quadratic = y = 3x^2

It is 6th graph

for both positive and negative values of x, y is rapidly increasing

Exponential = y = 3^x

it is 3rd graph

for x = 0 y value is 1 because 3^0 = 1

for positive values of x, y is exponentially rising

for negative values of x it is nearly almost touches zero

Answer:

Step-by-step explanation:

Similar triangles have the same shape but different sizes.

A is incorrect. We don't know the length of the sides, or if it is equilateral so we can't say that fg/lm=fh/ln

B is correct. FH and LN may be different sizes but they are similar

C is correct. Since the triangles are similar the angles are similar.

D is incorrect. The triangle is the same shape, not neccesarily the same size

E is correct. See C for explanation.

Answer:

Triangles = 4

Rectangles = 2

Step-by-step explanation:

Triangle.

8/2 = 4 . ratio = 4:1 or fraction form as 4

Rectangle.

4/2 = 2. ratio = 2:1 or fraction form as 2

If my answer is incorrect, pls correct me!

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Answer:

it is impossible as when we multiply two prime numbers other than 2 we get the number odd but 3128 is an even number

Step-by-step explanation:

The two tanks differ in terms of Filling rates and initial volumes.

We can work with the equation for tank A, which represents a linear relationship between the volume of liquid in the tank (y) and the time it has been filling (x).

The equation y = 75x + 110 tells us that the tank A is filling at a constant rate of 75 units per minute, starting with an initial volume of 110 units.

To analyze the data for tank B, we would need to know the volumes of the tank at different times as it is being filled.

If the relationship for tank B is also linear, we could find the equation that represents it by using two points from the table and the slope-intercept form of a linear equation (y = mx + b). Once we have both equations, we can compare them to see how the two tanks differ in terms of filling rates and initial volumes.

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The value of the variable in the given equation is x = 25/3.

To determine the value of the variable in the given equation, we need to solve it.

The equation is:

6x - 15 = 3x + 10

To simplify the equation, we can start by subtracting 3x from both sides:

6x - 3x - 15 = 3x - 3x + 10

This gives us:

3x - 15 = 10

Next, we can add 15 to both sides of the equation:

3x - 15 + 15 = 10 + 15

This simplifies to:

3x = 25

Finally, to isolate x, we divide both sides of the equation by 3:

(3x)/3 = 25/3

This gives us:

x = 25/3

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If each classroom can accommodate less than 15 kids, then we can assume that the maximum number of kids in each classroom is 14 (since 15 is not allowed). Therefore, the maximum number of kids in all 12 classrooms would be:

Max number of kids = 14 kids/classroom x 12 classrooms = 168 kids

So the kindergarten section can accommodate a maximum of 168 kids.

We can write this as an inequality as follows:

Let K be the number of kids in the kindergarten section. Then:

K ≤ 168

This inequality says that the number of kids in the kindergarten section (K) is less than or equal to 168. As long as the number of kids is less than or equal to 168, the kindergarten section can accommodate them all.

Original total of building = $35

Discount = 60% = 60/100 = 0.6 ( decimal form)

First, multiply the original total (35) by the discount in decimal form

35 x 0.6 = 21

Subtract it to the original total

35-21= $14

The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

Given that;

The sequence is,

11, 13, 15, 17, ....

Here, Common difference is,

13 - 11 = 2

15 - 13 = 2

Hence, Sequence is in Arithmetic sequence.

So, the nth term of 11,13,15,17 is,

⇒ T (n) = a + (n - 1)d

⇒ T (n) = 11 + (n - 1) 2

⇒ T (n) = 11 + 2n - 2

⇒ T (n) = 9 + 2n

Thus, The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

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