scores on an iq test are normally distributed. the test is designed so that the mean is 100 and standard deviation is 15. hat is the cutoff score so that only 5% of the population has a higher score?
Answers
The cutoff score so that only 5% of the population has a higher score is 124.7.
If 5% of the population has a higher score, then the probability of selecting these is 0.05.
Find the z-score that corresponds to the probability in the z-table. (see attached images)
probability = 1 - 0.05 = 0.95
z-score = 1.647
Using the formula for the z-score below, determine the cutoff score.
z-score = (x – μ) / σ
where x = individual data value = cutoff score
μ = mean = 100
σ = standard deviation = 15
1.647 = (x - 100) / 15
1.647(15) = x - 100
x = 24.705 + 100
x = 124.705
cutoff score = 125
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Related Questions
( 9 times 10 to the power of -7) (5 times 10 to the power of -4)
Answers
5 x 10^-4 = 1/2000
Consider the arithmetic sequence an = 5 + 3 (n − 1)
a. What are the first 5 terms of the sequence?
b. What is the 9th term in the sequence?
c. Rewrite the explicit formula as a function.
d. What is f(15)?
e. f(n) = 65 what is n?
Answers
The answers to the subparts of the arithmetic sequence are shown:
(A) a₅ = 17(B) a₉ = 28What is an arithmetic sequence?A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.So, the formula is: aₙ = 5 + 3 (n − 1)
Where n is the number of terms.So, 5th term or n = 5:
a₅ = 5 + 3 (n − 1)a₅ = 5 + 3 (5 − 1)a₅ = 5 + 3 (4)a₅ = 5 + 12a₅ = 17Similarly, the 9th term or n = 9:
a₉ = 5 + 3 (n − 1)a₉ = 5 + 3 (9 − 1)a₉ = 5 + 3 (8)a₉ = 5 + 24a₉ = 28Therefore, the answers to the subparts of the arithmetic sequence are shown:
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The correct question is given below:
Consider the arithmetic sequence an = 5 + 3 (n − 1)
a. What are the first 5 terms of the sequence?
b. What is the 9th term in the sequence?
Mr. Reed is drawing a blueprint of a rectangular patio. The width of the patio is 40 3/4 feet shorter than twice its length. The perimeter of the patio is 86 1/2 feet. What is the length of the patio?
Answers
Answer:
length = 28 feet
Step-by-step explanation:
let length = x
width = 2x - 40 3/4
= 2x - 163/4
= 2x - 40.75
perimeter of a rectangle = 2(l+w)
according to the question:
86 1/2 = 2(l+w)
86.5 = 2(x + 2x - 40.75)
86.5 = 2(3x - 40.75)
86.5 = 6x - 81.5
86.5 + 81.5 = 6x
thus, x = 28
Classify the triangle with sides of lengths 25 ft, 23 ft, and 8 ft.
equilateral triangle
O scalene triangle
isosceles triangle
Answers
all sides have different lengths
Pythagorean Theorem1 2 3 4 5OA 29.5 unitsOB23.4 unitsC. 24.4 unitsOD. 33.4 units
Answers
we know that the perimeter is the sum of all the sides, therefore:
[tex]\begin{gathered} P=10+9+3+\sqrt{7^2+9^2} \\ P=22+\sqrt{49+81} \\ P=22+\sqrt{130} \\ P=22+11.4=33.4 \end{gathered}[/tex]Therefore the answer is D. 33.4 units
A 6-foot- tall electric pole casts a shadow that is 24 feet long. What is the ratio
of the pole's height to its shadow?
Answers
The ratio of the pole's height to its shadow is 1:4.
What is a ratio?An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls).A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.So, the ratio of height:shadow:
The height of the pole is 6 feet.The shadow the pool creates is 24 feet.The ratio will be:
6:246/241/41:4
Therefore, the ratio of the pole's height to its shadow is 1:4.
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Hello, I was wondering if the fraction 5/2 x and 5x/2 have the same value.
Answers
We have:
[tex]\frac{5}{2}x\text{ and }\frac{5x}{2}[/tex]These fractions are equal because the x is found by multiplying and it is as if we have this:
[tex]\frac{5}{2}\times\frac{x}{1}\text{ and }\frac{5\times x}{2}[/tex]And as we already know:
[tex]\frac{5}{2}\times\frac{x}{1}=\frac{5\times x}{2\times1}=\frac{5\times x}{2}=\frac{5x}{2}[/tex]which of the statements are true of the residuals in a regression equation? multiple choice question. they measure the impact of firm-specific events. they are not part of regression analysis. they reflect systematic risk. they represent alpha.
Answers
The residuals in a regression equation measure the impact of firm-specific events.
Residuals = Actual y value - Predicted y value
Residual analysis is a helpful set of methods for assessing the quality of a fitted model. Checking the underlying assumptions is crucial because most linear regression estimators depend on independent errors with the same distribution and a correctly stated regression function in order to be consistent. Regression is a statistical technique used in finance, investing, and other fields that aim to ascertain the strength and nature of the relationship between a single dependent variable (often represented by Y) and a number of other factors (known as independent variables).
The residuals in a regression equation measure the impact of firm-specific events.
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Last night, the two dinner specials at Rhianna's favorite restaurant were salmon filet and steak. The restaurant served 52 specials in all, 25% of which were salmon filets. How many salmon filets did the restaurant serve?
Answers
There were 13 salmon fillets that the restaurant served.
How do we calculate how many salmon fillets the restaurant served?The solution to this math problem involves fractions, especially percentage. A percentage is a fraction of a hundred. The literal meaning of percentage is "per 100". Percentage is often referred to as percent. The symbol or sign for percentage is %. The number beside the symbol/sign is the numerator, so for example, 10% can also be written as 10/100.
We're given that 25% of the dinner specials served by the restaurant were salmon fillets. In order to find out how many salmon fillets were served, we only need to multiply 52 by 25%.
52 × 25% =
52 × 25/100 =
(52 × 25)/100 =
1,300/100 = 13
There were indeed thirteen salmon fillets served by the restaurant.
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i need help but my chromebook doesn't accept the ads
Answers
Answer:
Whats the question?
Solve the system of one linear- one Quadratic equations algebraically.
x-y=3
x^2-3y=19
Answers
Answer:
x=-2 y=-5
x=5 x=2
X=5 x=2
Cffccccf
I have a graph with the question. If the parent function is y= 2 to the power of x plus 2, which is the function of the graph
Answers
The parent function of the graph is
[tex]y=2^x[/tex]The function of the grapg will be
[tex]y=2^{x\text{ + a}}\text{ + b}[/tex]at x equals infinity y equals 1
Therefore
[tex]\begin{gathered} \text{x =}\infty\text{ then y = 1} \\ \text{this implies} \\ b\text{ = 1} \end{gathered}[/tex]Therefore the function will now be
[tex]y=2^{x\text{ + a}}\text{ + 1}[/tex]from the graph
x = 2 when y = 2
Therefore,
[tex]\begin{gathered} 2=2^{2\text{ + a}}\text{ + 1} \\ 2-1=2^{2\text{ + a}} \\ 1=2^{2\text{ + a}} \\ \text{recall 1 = 2}^0 \\ 2^0=2^{2\text{ + a}} \\ 2\text{ + a = 0} \\ a\text{ = - 2} \end{gathered}[/tex]Therefore, the function is
[tex]y=2^{x\text{ - 2}}\text{ + 1}[/tex]Tell whether the data in the table can be modeled by a linear equation. Explain. A table listing pairs of x and y values. First pair. Negative 3 and 16. Second pair. Negative 1 and 10. Third pair. 1 and 4. Fourth pair. 3 and negative 2. Fifth pair. 5 and negative 8. The data be modeled by a linear equation because the rate of change constant. Question 2 If possible, write a linear equation that represents y as a function of x. If not possible, leave blank.
Answers
The table is a linear function and the equation is y = -3(x - 1) + 4
How to determine if the table represents a linear equation?From the question, we have the pairs to be
First pair = (-3, 16)Second pair.= (-1, 10)Third pair = (1, 4)Fourth pair = (3, -2)Fifth pair = (5, -8)From the above representations, we can see that:
As the values of x increase by +2, the values of y constantly increase by -6
This means that the table has a constant rate
By the definition of a linear function, the table represents a linear function
The linear equation of the functionIn (a), we have
x = +2
y = -6
The slope is calculated as
Slope = y/x
So, we have
Slope = -6/2
Evaluate
Slope = -3
The equation is then calculated as
Y = Slope * (X - x) + y
Where
(x, y) = (1, 4)
So, we have
y = -3(x - 1) + 4
Hence, the linear function is y = -3(x - 1) + 4
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(08.07) 10 8 6 + 4 3 -2 2 2 -8 -10 -12 - 14 + -16 Which of the following functions best represents the graph? (4 points) Of(x) = x3 + x2 - 9x - 9 f(x) = x3 + 4x2 - X-4 Of(x) = x3 + 3x2 – 3x - 9 Of(x) = x3 + 2x2 - 4x - 8
Answers
Given data:
The given graph of the polynomial.
The value of the given polynomial is zero, at x=-3, -1, and 3.
Substitute -3 for x in the expression of the first polynomial.
[tex]\begin{gathered} f(-3)=(-3)^3+(-3)^2-9(-3)-9 \\ =-27+9+27-9 \\ =0 \end{gathered}[/tex]Substitute -1 for x in the expression of the first polynomial.
[tex]\begin{gathered} f(-1)=(-1)^3+(-1)^2-9(-1)-9 \\ =-1+1+9-9 \\ =0 \end{gathered}[/tex]Substitute 3 for x in the expression of the first polynomial.
[tex]\begin{gathered} f(3)=(3)^3+(3)^2-9(3)-9 \\ =27+9-27-9 \\ =0 \end{gathered}[/tex]As all the points are satisfied for the first option.
TThus, the first option is correct.
what is the answer for n? 5i + 7i =n
Answers
Answer: [tex]n=12i[/tex]
Step-by-step explanation:
Combine like terms.
8. The smaller of two numbers is five less than half the larger number. Their sum is 13. Find the numbers,
Answers
Larger number: 12
Smaller number: 1
Let Statements:
Let x = the larger number
Let 1/2x - 5 = the smaller number
Equation:
x + (1/2x - 5) = 13
1.5x - 5 = 13
1.5x = 18
x = 12
Solutions:
The larger number = x = 12
The smaller number = 1/2x - 5 = 1/2(12) - 5 = 6 - 5 = 1
Simplify using order of operation 10^2-2[12-(3-2)]
Answers
Given the expression:
[tex]10^2-2\lbrack12-(3-2)\rbrack[/tex]We start from the parenthesis inside the brackets. We know that 3-2=1, then:
[tex]10^2-2\lbrack12-(3-2)\rbrack=10^2-2\lbrack12-(1)\rbrack=10^2-2\lbrack11\rbrack[/tex]now, we have that 10^2=100 and 2*11 =22, then:
[tex]10^2-2\lbrack11\rbrack=100-22=78[/tex]therefore, the result of simplifying the expression is 78
What is the slope of -2,1 and 2,1
Answers
Is should be 50% slope
Answer:
m=0
Step-by-step explanation:
(-2,1) (2,1)
x1=-2,x2=2,y1=1,y2=1
Gradient/slope
m=y2-y1/x2-x1
m=1 - 1/2-(-2)
m=0/2+2
m=0/4
m=0
eli needs to order some new supplies for the restaurant where he works. .Therestaurant needs at least 546 knives. There are currently 312 knives. If each set on
sale contains 10 knives, write and solve an inequality which can be used to determine
x, the number of sets of knives Eli could buy for the restaurant to have enough
knives.
Answers
Eli could buy is at least 24 sets of knives
How to determine the number of sets of knives Eli could buy?From the question, we have the following parameters:
Number of knives needed = At least 546Number of knives in the restaurant = 312Number of knives per set = 10Let the number of sets be x
So, we have the following representations
Number of knives needed = Number of knives needed + Number of knives per set x Number of set
So, we have
312 + 10x ≥ 546
Evaluate the like terms
10x ≥ 234
Divide by 10
x ≥ 23.4
Rewrite as
x ≥ 24
Hence, the number of sets of knives Eli could buy is at least 24
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Answer:
Inequality: 312+10x≥546
x≥24
Step-by-step explanation:
its the same as the bottom
Helppppppppppppppoopppppppppppp
Answers
Answer:
-7, -6, -4, -2, 7
Step-by-step explanation:
f(-4) = -4 - 3
f(-4) = -7
f(-3) = -3 - 3
f(-3) = -6
f(-1) = -1 - 3
f(-1) = -4
f(1) = 1 - 3
f(1) = -2
f(10) = 10 - 3
f(10) = 7
Taylor works on an art project that uses only rectangular pieces of paper. The first rectangle ha length 3/8 and width of 3in. Detriment wether the dimensions of each rectangle described as a proportional to the dimensions of tailors first rectangle
Answers
By comparing the dimensions above with the dimensions of Taylor's first rectangle, we have the following:
No, a length of 6 in, width 3/4 in. is not proportional.Yes, a length of 1/2 in, width 4 in. is not proportional.No, a length of 1 1/8 in, width 9 in. is not proportional.No, a length of 3 in, width 5 5/8 in. is not proportional.What is a direct proportion?Mathematically, a direct proportion (direct variation) can be represented the following mathematical expression:
y = kx
Where:
y and x are the variables or dimensions.k represents the constant of proportionality.For the dimensions of the rectangular pieces of paper to be proportional, the length and width must remain in a constant ratio.
Next, we would determine the constant of proportionality (k) as follows:
k = y/x
k = (3/8)/3
k = 3/24
k = 1/8
For dimension 1, we have:
k = y/x
k = (6)/(3/4)
k = 24/3
k = 8 (No).
For dimension 2, we have:
k = y/x
k = (1/2)/4
k = 1/2 × 1/4
k = 1/8 (Yes).
For dimension 3, we have:
k = y/x
k = (1 1/8)/9
k = (9/8)/8
k = 9/8 × 1/8
k = 9/64 (No).
For dimension 4, we have:
k = y/x
k = (3)/(5 5/8)
k = 3/(45/8)
k = 3 × 8/45
k = 24/45 (No).
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Complete Question:
Taylor works on an art project that uses only rectangular pieces of paper. The first rectangle has length 3/8 in. and width 3 in. Determine which dimensions below are proportional to the dimensions of Taylor's first rectangle.
The sum of three consecutive even integers is 20 less than four times the
first. What are the integers?
Answers
The most appropriate choice for linear equation will be given by -
The integers are 26, 28, 30
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here,
Let the integers be x - 2, x, x + 2
Sum = x - 2 + x + x + 2 = 3x
20 less than Four times the first = 4(x - 2) - 20
By the problem,
[tex]3x = 4(x - 2) -20\\3x = 4x - 8 -20\\4x - 3x = 28\\x = 28[/tex]
The integers are 28 - 2, 28, 28 + 2
The integers are 26, 28, 30
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Shona has 14 dresses.
50% of these dresses are red.
She gives 5 of her red dresses to a charity shop.
She buys 1 new red dress.
What percentage of the dresses she has now are red?
Answers
Answer:
She has 3 dresses for sure! But I don't know the percentage!
She gives 5 red dresses away leaving 2 red out of 9 dresses
Now buys another red dress resulting in 3 red out of 10 dresses.
3/10 = 30% of her dresses are now red
Need help on this question with some explanation "Graph the image of the figure on the right under the given translation". T(3,2) (x,y) . Thanks in advance!
Answers
ANSWER
[tex]A[/tex]EXPLANATION
The given translation
[tex](3,2)[/tex]This means the shape will be translated 3units to the right and 2 units up.
That is;
[tex]\begin{gathered} (x+3) \\ (y+2) \end{gathered}[/tex]Maria has already written Two-fifths of her 1,000 word essay. If she continues writing at the same pace of 6One-half words per minute, which expression shows the amount of time it will take her to write the rest of the essay?
1000 times two-fifths times StartFraction 13 Over 2 EndFraction
1000 times two-fifths divided by StartFraction 13 Over 2 EndFraction
1000 times three-fifths times StartFraction 13 Over 2 EndFraction
1000 times three-fifths divided by StartFraction 13 Over 2 EndFraction
Answers
1000 times three-fifths divided by Start Fraction 13 Over 2 End Fraction is the required expression.
What is Expression?An expression is a combination of numbers, variables and operators.
Given that,
Maria has already written Two-fifths of her 1,000 word essay.
It means she has completed 2/5 of essay.
She has 3/5 more to do.
she continues writing at the same pace of 6One-half words per minute
So Her speed is 13/2 words per minute.
So 1000*3/5 (600 words) at 13/2 words per minute
we need to divide the number of words by the speed to work out the time: 1000*3/5/(13/2),
Hence 1000 times three-fifths divided by Start Fraction 13 Over 2 End Fraction is the required expression.
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Answer:
c
Step-by-step explanation:
50 POINTS!!!!!
decide whether the statement about the diagram is true explain your answer
ES ≅ ST
Answers
Answer: No
Step-by-step explanation:
The segments are not indicated to be congruent.
Explain the meaning of the expression tan 32°= 0.624
Answers
The meaning of the expression tan 32°=0.624 is the adjacent side of ratio is 0.624m.
What is ratio?
the ratio is the number that can be used to express one is quantity as a fraction of the other ones. The two of numbers in a ratio can only be compared when they have the same unit. We are make use of ratios o compare two things.
Sol- let's take an example first
In a triangle abc
C is 32°
tan 32° = AB/BC =0.624m
By applying the theorem we know that
In a right triangle , tan 32° is the ratio of the constant to the adjacent side the ratio is
0.624 m.
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what is the answer
5+3=3+5
Answers
Answer:
They are equal
Step-by-step explanation:
5+3=8 and 3+5=8
If you are seeking the answer in terms of evaluation, then the answer would be 8 = 8. Both sides of the equation are equal, so in addition to this, the given equation is true.
5 + 3 = 8
3 + 5 = 8
So, if you were to attempt breaking down the equation, you could easily write it as 8 = 8.
Hope this helps!
8v < 40 solve the inequality for v and simplify your answer as much as possible
Answers
Hey there!
8v < 40
DIVIDE 8 to BOTH SIDES
8v/8 < 40/8
v < 40/8
v < 5
It is an open circle starting at 5 and it is going down to the left side of the number line
Therefore, your answer should be:
v < 5
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Solve for b.
1.34(b + 2) = 9.38
Answers
Answer:
Step-by-step explanation:
1.34(b + 2) = 9.38
=> (b+2) = [tex]\frac{9.38}{1.34}[/tex]
=> (b+2) = [tex]\frac{9.38}{1.34}[/tex] x [tex]\frac{100}{100}[/tex]
=> b+2 = 7
=> b = 7-2
=> b = 5
To solve the equation, we must subject b
so as 1.34 is in multiplication form with (b+2), if we take it to the other side of equals sign, it will be inverse which means it will be dividing 9.38
by multiplying 100/100 with the fraction, the decimals can be removed (100 because the dot of decimal is considered one and there are two digits after dot, so two zeroes)
then by simple division we can find 7
then as 2 is added with be if it goes to other side it will be inverted and be subtracted from 7
so we get 5