Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation 20. Find P15, which is the IQ score separating the bottom 15% from the top 85%.

Answers

Answer 1

Taking the given data into consideration we reach the conclusion that the IQ score ranging the bottom 15% from the top 85% is approximately 79.2, under the standard deviation 20.

Let us assume that adults have IQ scores that are normally expressed  with a mean of 100 and a standard deviation of 20, we need to calculate the IQ score ranging the bottom 15% from the top 85%, which is denoted as [tex]P_{15}[/tex]
To find the answer for this problem, we need to evaluate the z-score that corresponds to the 15th percentile. We can utilise a standard normal distribution table to  evaluate this value.
Implementing a standard normal distribution table, we could evaluate that the z-score corresponding to the 15th percentile is approximately -1.04.
[tex]z = (P_{15} - mean) /standard deviation[/tex]
[tex]-1.04 =( P_{15} - 100) /20[/tex]
[tex]- 20.8 = P_{15} - 100[/tex]
[tex]P_{15} = 79.2[/tex]
Hence, the IQ score separating the bottom 15% from the top 85% is approximately 79.2.
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Related Questions

4. Evaluate the expression for the given value of each variable.


5a2 -7 -b3

when a = -2 and b = -3

please help!
NO LINKS!!!

Answers

Answer:

-18

Step-by-step explanation:

5a2-7-b3

[tex]5*a*2-7-b*3[/tex]

[tex]5\cdot \left(-2\right)\cdot \left(2\right)-7-\left(-3\right)\cdot 3[/tex]

Therefore, -18 is your answer.

Hope this helped! :)

The null hypothesis is that the laptop produced by HP can run on an average 120 minutes without recharge and the standard deviation is 25 minutes. In a sample of 50 laptops, the sample mean is 130 minutes. Test this hypothesis with the alternative hypothesis that average time is not equal to 120 minutes. What is the p- value?

Answers

The p-value for testing the hypothesis that the average runtime of HP laptops is not equal to 120 minutes, based on a sample mean of 130 minutes from a sample of 50 laptops, is approximately 0.0006 (rounded to four decimal places).

To calculate the p-value, we use the t-test. Given the null hypothesis that the average runtime is 120 minutes, the alternative hypothesis is that it is not equal to 120 minutes. We compare the sample mean to the hypothesized population mean using the t-distribution.

Using the formula for the t-statistic:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

t = (130 - 120) / (25 / sqrt(50))

t = 10 / (25 / 7.0711)

t = 2.8284

The degrees of freedom for the t-distribution are (sample size - 1) = (50 - 1) = 49.

Using the t-distribution table or statistical software, we find that the two-tailed p-value for a t-value of 2.8284 with 49 degrees of freedom is approximately 0.0006.

Therefore, the p-value for this hypothesis test is approximately 0.0006.

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Question is in picture

Answers

200 :)
Because I’m guessing that the house is 90m and the store is 110m so add that and it’s 200
Hope this helps

ect
Use the number line interactive to evaluate the
following expressions.
8 + 3 =
+
16
(-8) + (-5) =
<
(-8) + 2 =

Answers

Answer:

1. 11

2. -13

3. -6

Step-by-step explanation:

Hope this helps. Have a great day! (I got this correct on edge :})

Answer fast plsssssss

Answers

Answer:

i cat see it

Step-by-step explanation:

what is the solution
a: (6,5)
b: (5,6)
c: (1,2)
d: (2,1)

Answers

Answer:

(5,6)

Step-by-step explanation:

I'm guessing you mean the coordinates for the point where the lines intersect

Answer:

I believe it is b: (5,6)

Explanation:

The point (5,6) is the only point on the graph that both lines go through.

If n e z, use modulo to show that -13n2 +5n+23 is odd.

Answers

The given expression -13n^{2}+5n+23[/tex] is odd using modulo.

We are given to show that -13n2 + 5n + 23 is odd by using modulo.

Let's try to understand what modulo means:Modulo is a mathematical operation that finds the remainder when one number is divided by another. It is represented by the percentage symbol (%).

Now we can use the concept of modulo to show that -13n2 + 5n + 23 is odd.Note:An integer is odd if it is not even. In other words, odd numbers can't be divided evenly by 2. They leave a remainder of 1 when divided by 2.To show that -13n2 + 5n + 23 is odd, we need to take the given expression modulo 2.$$-13n^2 + 5n + 23 \; \mathrm{mod} \; 2$$We know that every odd integer can be written in the form of 2n + 1 where n is an integer. Now we just have to show that the expression -13n2 + 5n + 23 can be written in the form 2n + 1.$$-13n^2 + 5n + 23 \equiv 1 \; \mathrm{mod} \; 2$$Let's assume k is an integer such that $$-13n^2 + 5n + 23 = 2k + 1$$Rearranging the above expression, we get$$-13n^2 + 5n + 22 = 2k$$Now, we can use the concept of odd and even numbers. We know that an even number can be represented in the form 2n, where n is an integer. Now we just have to show that the expression -13n2 + 5n + 22 can be represented in the form 2n.$$-13n^2 + 5n + 22 = -13n^2 + 13n - 8n + 22$$$$= 13(n-1)(n-2) - 8$$We know that the product of two odd numbers is odd, and the subtraction of an even number from an odd number is odd. Here, (n-1) and (n-2) are consecutive integers, which means one of them is even and the other is odd. Therefore, the product (n-1)(n-2) is even. Hence, the above expression is odd.Since -13n2 + 5n + 23 is equivalent to 1 modulo 2, which means it can be represented in the form of 2n+1. Therefore, -13n2 + 5n + 23 is odd.

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Kallen was invited to a birthday party for his best friend. He wanted to buy a gift that was $43.87 and wrapping paper that was $2.94. If he earns $8.25 for each lawn he mows and his mom agrees to match all his earnings how many lawns will he need to complete to buy the gift and wrapping

Answers

Answer: 6

Step-by-step explanation:

The total amount needed by Kallen for the gift and the wrapping paper will be:

= $43.87 + $2.94

= $46.81

Since he earns $8.25 for each lawn he mows, the number of lawns they he will need to complete to buy the gift and wrapping will be:

= $46.81 / $8.25

= 5.67

= 6 lawns approximately

He'll need to mow 6 lawns

A circle with a shaded sector has a circumference of 12 pi millimeters. What is the area of the shaded sector? Express the answer in terms of Pi.

Answers

Answer:

The answer is C. 8 mm

Step-by-step explanation:

For me, i was able to divide the 80 by 12 and get 6.667 thus i was able to round up and conclude the answer in the answer choices

Answer:

c

Step-by-step explanation:

A scientist used 60 grams of sodium nitrate during an experiment. One ounce is approximately equal to 28.3 grams. Which measurement is closest to the number of ounces of sodium nitrate the scientist used?

Answers

Answer:

2

Step-by-step explanation:

60 divided by 28.3 which gives u 2.120141342756184

so round it which gives u 2

PLEASE HELP ME!!! I REALLY NEED TO KNOW THIS...



So my math teacher hates me and i did this for a answer:
5x³ + x² + 16 , this is a different question, and i got the points.
But for a answer that was right and she mared wrong i did this:
2x²+4
(I know it is right because my sister and me have the same math. and she got a 10/10 on this)
My sister's answer : 2x^2 + 4.

Are they the same or not?!

Answers

Answer:

The exact same

Step-by-step explanation:

^ just means put it up like 3^2=3²

A tree casts a shadow that is 231 cm long. Janet is 170 cm tall and she casts a shadow that is 102 cm long. How tall is the tree?

Answers

Answer:

139 cm

Step-by-step explanation:

Plz help I’ll give brainliest

Answers

Answer:

2) 4/5

3) 3

Step-by-step explanation:

2) 4/8-3=4/5

3)5x-4=3x+2

2x=6

x=3

Answer:

2) 4/5

3)x=3

Step-by-step explanation:

1) 4/8-3= 4/5

2) 5x-4=3x+2

bring 3x to left side and bring -4 to right side (remember signs will be reversed that is 3x becomes -3x and -4 will be 4

5x-3x=4+2

2x=6

x=6/2

x=3

put 3 in place of x

5*3-4=3*3+2

15-4=9+2

11=11

if an equation indicates addition in its presentation, in order to solve for the unknown you must: a. add b. subtract c. multiply d. divide

Answers

If an equation indicates addition in its presentation, in order to solve for the unknown, you must perform the inverse operation, which is subtraction.

Equations typically involve an equality between two expressions, with one or more unknown variables.

To isolate the unknown variable and determine its value, you need to perform operations on both sides of the equation to simplify and solve for the variable.

When an equation shows addition, you can undo that operation by subtracting the same value from both sides of the equation. This ensures that the equation remains balanced and maintains equality.

For example, consider the equation:

x + 5 = 10

To solve for x, you need to eliminate the 5 added to x. To do so, you subtract 5 from both sides of the equation:

x + 5 - 5 = 10 - 5

x = 5

By subtracting 5 from both sides, you isolate the variable x and find that its value is 5.

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Help pleaseeeeeeeeeee

Answers

Answer:

5 is c 6 is b

Step-by-step explanation:

Answer:

5) C 6) B

Step-by-step explanation:

Yw

Let f be the function given by f(x) = 2 cos x +1. What is the approximation for f(1.5) found by using 1 the tangent line to the graph off at x = ? 2 (A) -2 (B) 1 (C) 1-2 (D) 4-2

Answers

To approximate the value of f(1.5) using the tangent line to the graph of f at x = 1, we first find the derivative of f(x) to determine the slope of the tangent line at x = 1. The derivative is f'(x) = -2 sin x. Evaluating f'(x) at x = 1, we find the slope to be approximately -1.6829.

Next, we use the point-slope form of a line to find the equation of the tangent line. We have the point (1, f(1)) ≈ (1, 1.5839) and the slope -1.6829. Plugging these values into the point-slope form, we obtain the equation of the tangent line as y ≈ -1.6829x + 3.2668.

Finally, we substitute x = 1.5 into the equation of the tangent line to approximate f(1.5). After calculation, we find that f(1.5) is approximately 0.0009.

Therefore, the approximation for f(1.5) using the tangent line to the graph at x = 1 is approximately 0.0009.

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You earn $10 per hour working as a manager at a grocery store. You are required to work at the grocery store at least 8 hours per week. You also teach music lessons for $15 per hour. You need to earn at least $120 per week, but you do not want to work more than 20 hours per week. a. Write a system of linear inequalities that represents the situation. Use x for hours worked at the grocery store and y for hours teaching music lessons. i need the inequility for total work. please fast

Answers

Answer:

without numbers= 10x + 15y = 120

Step-by-step explanation:

grocery store= 10x (x=8 in this case)

music lessons= 15y

Write an equation for two angles A and B that are supplementary.

A. a + b = 180

B. a + b = 100

C. 2ab = 180

D. a + b = 90​

Answers

Answer:

A. a + b = 180 is the correct option.

Find the midpoint of the segment with the following endpoints.
(9,6) and (5,2)

Answers

Answer:

[tex]M(7 ; 4)[/tex]

Step-by-step explanation:

midpoint -M

[tex]M(\frac{x_{1}+x_{2}}{2} ; \frac{y_{1}+y_{2}}{2} )[/tex]

[tex]M(\frac{9+5}{2} ; \frac{6+2}{2} )[/tex]

[tex]M(7 ; 4)[/tex]

Answer:

(7, 4 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

Here (x₁, y₁ ) = (9, 6) and (x₂, y₂ ) = (5, 2) , then

midpoint = ( [tex]\frac{9+5}{2}[/tex] , [tex]\frac{6+2}{2}[/tex] ) = ([tex]\frac{14}{2}[/tex] , [tex]\frac{8}{2}[/tex] ) = (7, 4 )

3. A piece of wire 16 feet long is strung from
the top of the side of a house to the
ground. The distance from the base of the
house to where the wire meets the ground
is 9 feet, as shown in the picturt.
st
19 lei
(The figure is not drawn to scale.)
How tall, in feet, is the house?
B. 20
C. 175
D. 337​

Answers

Answer:

its c  because its not a b or d  and its alround 13 feet

Step-by-step explanation:

A local fast food chain had revenue represented by the polynomial 6x ^ 2 + 5x - 8 for one fiscal year and expenses for that same fiscal year represented by the polynomial 4x ^ 2 - 3x + 7 7. What was the company's profit for the fiscal year?

Answers

Answer:

2x^2+8x - 16

Step-by-step explanation:

Profit = Revenue - Cost

P(x) = R(x) - C(x)

Given

R(x) = 6x ^ 2 + 5x - 8

C(x) = 4x ^ 2 - 3x + 7

P(x) = 6x ^ 2 + 5x - 8-(4x ^ 2 - 3x + 7)

P(x) = 6x ^ 2 + 5x - 8 - 4x ^ 2 + 3x - 8

Collect the like terms;

P(x) = 6x^2-4x^2+5x+3x-8-8

P(x) = 2x^2+8x - 16

Hence the company's profit for the fiscal year is 2x^2+8x - 16

or each of the following functions, find the constant c such that f(x)is a pdf; find the cdf, f(x)= p(x ≤ x); graph the pdf and cdf; and find μ and σ2: (a) f(x)= 4xc for 0 ≤ x ≤ 1

Answers

c = 1/2 ,the mean is μ = 1/2,  the CDF of f(x) is 2x^2   and the variance is σ² = 1/6.

The given pdf is f(x) = 4xc for 0 ≤ x ≤ 1.

To find the constant c such that f(x) is a pdf: We know that, For f(x) to be a pdf, it must satisfy the following two conditions:

The integral of f(x) over its support should be equal to 1. f(x) must be greater than or equal to 0 for all values of x. So,

Let us find the value of c first integral of f(x) from 0 to 1 should be equal to 1, therefore∫f(x)dx = ∫(4xc)dx for 0 ≤ x ≤ 1∫f(x)dx = 4∫xc dx for 0 ≤ x ≤ 1∫f(x)dx = 4[c(x^2/2)]_0^1∫f(x)dx = 2c

Therefore,∫f(x)dx = 1 implies 2c = 1 or c = 1/2.

Now we know the value of c. Let us find the CDF of f(x): CDF of f(x) = P(x ≤ X) = ∫f(t)dt from -∞ to x= ∫f(t)dt from 0 to x= ∫(4xt)dt from 0 to x= 2x^2 from 0 to x= 2x^2Therefore, the CDF of f(x) is 2x^2.

Graph of the PDF of f(x)For graphing the PDF of f(x), we need to know the values of x for which f(x) is defined as well as its shape and maximum value.f(x) = 4xc for 0 ≤ x ≤ 1The given function is a straight line with a slope of 4c and intersects the x-axis at 0 and the y-axis at 0.

We know that c = 1/2, thus (x) = 2x for 0 ≤ x ≤ 1The graph of f(x) will look as follows: Graph of the CDF of f(x)The graph of the CDF of f(x) will look as follows:

We can find the mean and variance of the PDF of f(x) using the following formulae: Mean, μ = ∫xf(x)dx from -∞ to ∞.Variance, σ² = ∫(x - μ)²f(x)dx from -∞ to ∞.

Substituting f(x) and its limits in the above formulae, we get: Mean, μ = ∫xf(x)dx from 0 to 1= ∫(2x^2)x dx from 0 to 12(1^4 - 0^4)/4= 1/2.

Variance, σ² = ∫(x - μ)²f(x)dx from 0 to 1= ∫(x - 1/2)²(2x)dx from 0 to 1= 1/6.

Therefore, the mean is μ = 1/2, and the variance is σ² = 1/6.

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consider recurrence (and no such that for every non negative integer ny 2 an = 400-1 - 5an-2 +200-3 suppose recurrence (an) has the following initial value a=1 a2=2 in what follows, let a (n) dehote term an for each nonnegative integern write an explicit formula for a(n)

Answers

The given recurrence relation is an = 400 - 5an-2 + 200-3, with initial values a0 = 1 and a1 = 2. We need to find an explicit formula for a(n).

To find an explicit formula for a(n), we will first solve the recurrence relation and then generalize the pattern. Let's expand the relation for a few terms to observe the pattern:

a2 = 400 - 5a0 + 200-3 = 400 - 5(1) + 200-3 = 397

a3 = 400 - 5a1 + 200-3 = 400 - 5(2) + 200-3 = 388

a4 = 400 - 5a2 + 200-3 = 400 - 5(397) + 200-3 = -9603

a5 = 400 - 5a3 + 200-3 = 400 - 5(388) + 200-3 = -1260

From the given examples, we can observe that the recurrence relation alternates between positive and negative values. This suggests that the relation might have a periodic pattern. Since the given recurrence is a second-order relation (in terms of n), it is reasonable to assume that the pattern repeats every two terms.

Based on this observation, we can establish the following explicit formula for a(n):

a(n) = (-1)^(n mod 2) * (200n - 5^(n/2) + 200-3)

In this formula, the term (-1)^(n mod 2) alternates between -1 and 1 depending on the parity of n, ensuring the alternating pattern. The other terms account for the linear and exponential components of the recurrence relation.

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Beth filled 48 jars with paint. If each jar holds 1 pint of paint, how many gallons of paint did Beth use?

Answers

The gallons of paint that Beth used is 6 gallons.

How many gallons did Beth use?

The first step is to convert pint to gallon:

1 pint = 0.125 gallon

The second step is to multiply 0.125 by 48 : 0.125 x 48 = 6 gallons

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What are the solutions to the quadratic equation 4(x + + 2)2 = 36
O x= -11 and x = 7
Ox= -7 and x = 11
O x= -5 and x = 1
Ox= -1 and x = 5

Answers

Answer:

x= -1 and 5

hope that helps

The solutions to the quadratic equation [tex]4(x+2)^2=36[/tex] are x = -5 and x = 1.

Given the following data:

[tex]4(x+2)^2=36[/tex]

How to solve a quadratic equation.

In this exercise, you're required to determine the value of x by solving for the factors (roots) of the given quadratic equation.

In Mathematics, the standard form of a quadratic equation is given by;

[tex]ax^2 + bx + c =0[/tex]

Where:

a = 4.b = 16.c = -20.

Dividing both sides by 4, we have:

[tex]4(x+2)^2=36\\\\(x+2)^2=9[/tex]

Taking the square root of both sides, we have:

[tex]x+2=\pm3\\\\x=\pm 3-2[/tex]

x = -5 or 1.

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The product of 3x^3-5x² + 3 and 2x² + 5x – 4 in Z7[x] / < x² +1 > is_________a. 2x + 3 b.2x+2 c. 2x d. 2x + 1

Answers

The product of 3x³-5x² + 3 and 2x² + 5x – 4 in Z7[x] / < x² +1 > is 2x + 1.

The product of the polynomials 3x³-5x² + 3 and 2x² + 5x – 4 in Z7[x] / < x² +1 > can be determined using polynomial long division.

To perform the division, we divide 3x³-5x² + 3 by x² + 1. The result of this division gives us the quotient and the remainder. In this case, the quotient is 2x and the remainder is 2x + 1.

The quotient represents the coefficient of x in the resulting product, while the remainder represents the constant term. Therefore, the resulting product is d. 2x + 1.

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Which equation is not equivalent to 2x+10=-8

Answers

Answer:

2x+10=-8

x=9

3x=9

x=3

2x=8

x=4

4x=20

x=5

Step-by-step explanation:

i dont have a question for this. look at the photo​

Answers

Answer:

first is no second is yes third is no fourth is yes

Step-by-step explanation:

I'm not sure btw

Calculate the volume of a cube with side lengths of 2.8 yards.

Answers

Answer:

21.952 [tex]yards^{3}[/tex]

Step-by-step explanation:

The volume of a cube is side length cubed.

So [tex]2.8^{3}[/tex] = 21.952

f (x) = -3x + 1
g(x) = x2 + 2x – 5
Find g (f (x))

Answers

Answer: f

=  x = − 3 x + 1 = x = 1 4 g = x 2 + 2 x − 5f( x ) = f ( x )

Step-by-step explanation:

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P(X Hartman, Inc. has prepared the following comparative balance sheets for 2020 and 2021:2021 2020Cash $ 282,000 $ 153,000Accounts receivable 139,000 117,000Inventory 150,000 180,000Prepaid expenses 18,000 27,000Plant assets 1,295,000 1,050,000Accumulated depreciation (450,000) (375,000)Patent 153,000 174,000$1,587,000 $1,326,000Accounts payable $ 153,000 $ 168,000Accrued liabilities 60,000 42,000Mortgage payable 450,000Preferred stock 525,000 Additional paid-in capitalpreferred 120,000 Common stock 600,000 600,000Retained earnings 129,000 66,000$1,587,000 $1,326,000The Accumulated Depreciation account has been credited only for the depreciation expense for the period. The Retained Earnings account has been charged for dividends of $138,000 and credited for the net income for the year.The income statement for 2021 is as follows:Sales revenue $1,980,000Cost of sales 1,089,000Gross profit 891,000Operating expenses 690,000Net income $ 201,000REQUIRED(a) From the information above, prepare a statement of cash flows (indirect method) for Hartman, Inc. for the year ended December 31, 2021.(b) From the information above, prepare a schedule of cash provided by operating activities using the direct method. technically it can be said that death results from a lack of Five friends equally share 20 strawberries. How many strawberries does each friend get Square Hammer Corp. shows the following information on its 2018 income statement: Sales $222,000; Costs = $132,000; Other expenses = $7,900; Depreciation expense $19,700, Interest expense = $14,000, Taxes = $16,940; Dividends = $11,000. In addition, you're told that the firm issued $5,500 in new equity during 2018 and redeemed $4,000 in outstanding long-term debt. a. What is the 2018 operating cash flow? (Do not round intermediate calculations.) b. What is the 2018 cash flow to creditors? (Do not round intermediate calculations.) c. What is the 2018 cash flow to stockholders? (Do not round intermediate calculations.) d. If net fixed assets increased by $20,000 during the year, what was the addition to NWC? (Do not round intermediate calculations.) Find the general solution of the nonhomogeneous differential equation, 2y"' + y" + 2y' + y = 2t + 3. Which of the following is implied from the standard error of the mean formula? A. that true means of populations can be found easier than those of samples B. that standard deviation increases with increase in sample size C. that larger sample sizes provide greater accuracy in estimating the true population mean D. that the true mean of the population can only be calculated using smaller sample sizes Asif is travelling to New York from Toronto to purchase a laptop that is only available in America. The laptop is being sold for $799 in US dollars. Calculate the price of the laptop in Canadian dollars if one American dollar is worth 1.29 Canadian dollars. a. Convert 250 from degrees to radians.b. Convert 3/5 from radians to degrees. Write a C++ program to keep asking for a number until you enter a negative number. At the end, print the sum of all entered numbers. You need to use a while loop for this Lab.