Hello i did this question on my own because I thought I understood it but it was wrong I got 1/2
Answers
Given a number 'a', we have the following general rule for exponent:
[tex]a^{-n}=\frac{1}{a^n}[/tex]in this case, we have:
[tex]3^{-4}=\frac{1}{3^4}=\frac{1}{81}[/tex]Related Questions
A figure has vertices (2,1), (5,1), and (2,4). What are the coordinates of the vertices of the nee figure when it is reflected over the y-axis
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The co-ordinates when reflected over the y-axis are (-2,1), (-5,1) and (-2,4).
The co-ordinates of the figure given are (2,1), (5,1), and (2,4). It is clear that the figure is a triangle as (2,1) and (2,4) has same x-co-ordinates and (2,1) and (5,1) has same y-co-ordinates.
So this figure is reflected over the y-axis and we need to find the co-ordinates of the new transformed figure.
The reflection over y-axis does not change the y-co-ordinates but the x-co-ordinates are changed into their corresponding opposite signs. That is,
x ----> -x.
So the reflection over y-axis can be represented as (x, y) ----> (-x, y)
Hence the co-ordinates of the reflected figure are:
(-2,1), (-5,1), and (-2,4).
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Amrita wants to raise more than $200 for a charity by walking dogs in her neighborhood. She charges $7 per walk.What is an inequality that can be used to find the number of walks, w, that Amrita needs to complete?
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Given:
Amrita wants to raise more than $200 for a charity.
She charges $7 per walk.
[tex]\begin{gathered} 7w>200 \\ \end{gathered}[/tex]j
knjfjfjfjfjfjf help me solve this thanks !!
Answers
Answer:
132 degrees
Step-by-step explanation:
102+30 = 132
Find the approximate area between the curve and the x-axis on the interval using 4 rectangles. Use the left endpoint of each rectangle to determine the height.
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We have to approximate the area under the curve using the given rectangles.
Each rectangle will have an area that is equal to the width (the interval Δx) times the height (that is f(xi)).
We can express the formula for the approximation as:
[tex]A=\sum_{i=1}^4f(x_i)\cdot\Delta x=\sum_{i\mathop{=}1}^4f(x_i)(x_{i+1}-x_i)[/tex]We will have to calculate f(x) for x = 0, 4, 8 and 12, which are the left endpoints of the interval for each rectangle.
Given that f(x) is defined as:
[tex]f(x)=-2x^2+32x+5[/tex]we can calculate each value as:
[tex]f(0)=-2(0)^2+32(0)+5=5[/tex][tex]\begin{gathered} f(4)=-2(4)^2+32(4)+5 \\ f(4)=-2(16)+128+5 \\ f(4)=-32+128+5 \\ f(4)=101 \end{gathered}[/tex][tex]\begin{gathered} f(8)=-2(8)^2+32(8)+5 \\ f(8)=-128+256+5 \\ f(8)=133 \end{gathered}[/tex][tex]\begin{gathered} f(12)=-2(12)^2+32(12)+5 \\ f(12)=-288+384+5 \\ f(12)=101 \end{gathered}[/tex]We can now calculate the approximation as:
[tex]\begin{gathered} A=f(0)(4-0)+f(4)(8-4)+f(8)(12-8)+f(12)(16-12) \\ A=5(4)+101(4)+133(4)+101(4) \\ A=20+404+532+404 \\ A=1360 \end{gathered}[/tex]Answer: the approximation is equal to 1360 square units [Fourth option].
The box plots below show the number of goals that two hockey players, Sam and Barry, Scored each season during their careers.Select all that are TRUE1) Barrys data is nearly symmetrical2) the median is Sams data is more than Barrys data3) Sam scored more goals in one season than berry did.4) Barrys chart shows more variable than Sams5) Sams distribution is skewed left
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From the given distribution, it is clear that
Sam scored more goals in one season than berry did.
and
Barrys data is nearly symmetrical
The point (a,b) is reflected across the line y=x and then across the x-axis. Which of the following are the coordinates of its final image point in terms of a and b?(1) (-b,-a)(2) (-b,a)(3) (b,-a)(4) (-a,-b)
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When a point is reflected across the line, y = x, the x and y coordinates changes places. Given that the coordinates of the original point is (a, b), the coordinate of the new point would be (b, a)
Again, this new point was reflected across the x axis. Recall, if reflection is done across the x axis, the sign of the x coordinate remains the same while the sign of the y coordinate is reversed,
Therefore, the coordinates of its final image point in terms of a and b is (b, - a)
The correct option is number 3
need answer asap ty
multiplying integers
1. 13 + (-20) =
2.29 + (-12) =
3.21 + (-13) =
4.-19 + (-26) =
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answer 1=-7
2=17
3=8
4=-45
0.149 divided 8,712
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PLSSS!! Help me with this question I’ve been on it for hours!! Pls show decimal form or fraction form
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Answer:
(6, 4)
Step-by-step explanation:
(x, y) = ((x1 + x2)/2, (y1 + y2)/2)
= ((10 + 2)/2, (7 + 1)/2)
= (12/2, 8/2)
= (6, 4)
Answer:8.5 and 2.5
Step-by-step explanation:7, 8, MD 9, 10 There are four numbers in this sequence and MD is the midpoint. To find MD we have to find what is in the middle of 8 and 9. The number between them is 8.5 or
8 1/2(which is also 8 and one half)
For 2 and 1 same thing, what is between 2 and 1? To find that the number line goes 2, 2.9, 2.8, 2.7, 2.6, 2.5, 2.4, 2.3, 2.2, 2.1, and 1.
What is the midpoint in all of this? 2.5!see imageThere were 400 people that tooka survey about quality ofrestaurants. 240 people said thatOutback was the beststeakhouse. What percent ofpeople said Outback was the beststeakhouse?
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total people(TOTAL) : 400
People that said that the outback was the best ( BEST) : 240
percent of people said Outback was the best steakhouse : BEST / TOTAL : 240/400 = 0.6
Percent = 0
I need help with this question and can you please answer it how the paper says so I can understand it better
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given points
[tex]\begin{gathered} \text{ points of origin}=(0,0) \\ (3-2i)\text{ means that the start point}=(3,-2) \end{gathered}[/tex]STEP 2: Write the formula for finding the modulus
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where (}x_{1,}y_1_{})=(0,0) \\ (x_2,y_2)=(3,-2) \end{gathered}[/tex]STEP 3: Substitute the values into the formula to get the answer
[tex]\begin{gathered} d=\sqrt[]{(3-0)^2+(-2-0)^2} \\ d=\sqrt[]{(3)^2+(-2)^2} \\ d=\sqrt[]{9+4} \\ d=\sqrt[]{13} \\ d=3.605551275 \\ d\approx3.6\text{ to the nearest tenth} \end{gathered}[/tex]Hence, the required modulus is approximately 3.6 to the nearest tenth.
Find the equation of the line with the following:slope = 2/5; passes through (-3, 1)
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Answer:
[tex]y=\frac{2}{5}x+\frac{11}{5}[/tex]Explanation:
Given the slope and a point on the line, we use the point-slope form to find the equation of the line:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ m=\frac{2}{5} \\ (x_1,y_1)=(-3,1) \end{gathered}[/tex]Substitute the given values:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1=\frac{2}{5}(x-(-3)) \\ y-1=\frac{2}{5}(x+3) \\ y=\frac{2}{5}(x+3)+1 \\ y=\frac{2}{5}x+\frac{6}{5}+1 \\ y=\frac{2}{5}x+\frac{11}{5} \end{gathered}[/tex]The equation of the line in slope-intercept form is:
[tex]y=\frac{2}{5}x+\frac{11}{5}[/tex]The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8100 ft, the liquid boils at 198.61°F. At an altitude of 4500 ft, the liquid boils at 205.45°F. Write an equation giving the boiling point b of the liquid, in degrees Fahrenheit, in terms of altitude a, in feet. What is the boiling point of the liquid at 2400 ft?
Write an equation.
b=
Answers
Answer:
What is the relationship between altitude and boiling point of a liquid?
At a higher elevation, the lower atmospheric pressure means heated water reaches its boiling point more quickly—i.e., at a lower temperature. Water at sea level boils at 212 degrees Fahrenheit; at 5,000 feet above sea level, the boiling point is 203 degrees F. Up at 10,000 feet, water boils at 194 degrees F.
Step-by-step explanation:
Answer:
[tex]\textsf{Equation}: \quad b=-0.0019a+214[/tex]
209.44 °F
Step-by-step explanation:
Define the variables:
a = altitude, in feet.b = boiling point, in degrees Fahrenheit.Given:
At an altitude of 8100 ft, the liquid boils at 198.61°F. At an altitude of 4500 ft, the liquid boils at 205.45°F.If the relationship between altitude (a) and boiling point (b) is linear, this can be modelled as:
[tex]\boxed{b=ma+c}[/tex]
where:
a is the independent variable.b is the dependent variable.c is a constant.Find the slope of the linear equation by substituting the given ordered pairs into the slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{b_2-b_1}{a_2-a_1}=\dfrac{205.45-198.61}{4500-8100}=\dfrac{6.84}{-3600}=-0.0019[/tex]
Substitute the found slope and one of the ordered pairs into the point-slope formula:
[tex]\implies b-b_1=m(a-a_1)[/tex]
[tex]\implies b-205.45=-0.0019(a-4500)[/tex]
[tex]\implies b-205.45=-0.0019a+8.55[/tex]
[tex]\implies b=-0.0019a+214[/tex]
Therefore, an equation giving the boiling point (b) of the liquid in terms of altitude (a) is:
[tex]\boxed{b=-0.0019a+214}[/tex]
To find the boiling point of the liquid at 2400 ft, substitute a = 2400 into the found equation:
[tex]\implies b=-0.0019(2400)+214[/tex]
[tex]\implies b=-4.56+214[/tex]
[tex]\implies b=209.44[/tex]
Therefore, the boiling point of the liquid at 2400 ft is 209.44 °F.
Plot the point given in polar coordinates.Find three additional polar representations of the point, using −2 < < 2. (Enter your answers in order from smallest to largest first by r-value, then by -value.)
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Correct graph: C
[tex]\begin{gathered} 1st\text{ alternative form:} \\ (-9,\frac{2}{3}\pi)\frac{}{} \\ 2nd\text{ alternative form:} \\ (9,\frac{5}{3}\pi) \\ 3rd\text{ alternative form:} \\ (-9,\frac{8}{3}\pi) \end{gathered}[/tex]
you invest 1,000 in an account that pays simple interest of 3% for 10 years. what is the amount of money you'll have at the end of the 10 years?
Answers
Given data:
The given principal is P=1,000.
The given rate of interest is r=3%.
The given time is t=10 years.
The expression for the final amount after 10 years is,
[tex]A=P+\frac{P\times r\times t}{100}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} A=1,000+\frac{1,000\times3\times10}{100} \\ =1,300 \end{gathered}[/tex]Thus, the final amount after 10 years is 1,300.
A soccer ball is kicked in the air such that its height, h, in metres, after t seconds can be modeled by the function h(t) = -4.9t^2 + 12t + 0.5
a) Determine the average rate of change of the height of the ball from 1s to 3s.
b) Estimate the instantaneous rate of change at 3s.
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Part a: Average rate of change = 7.2 m/sec(going downward)
part b: Instantaneous rate of change = -7.6 m/sec
What is termed as the average rate of change?The average rate of change is indeed the rate during which one value changes in relation to another within a function. The slope of a plotted function is usually calculated using the average rate of change.The instantaneous rate of change is the rate change at a specific instant, and it is the same as the derivative value change at a specific point.For the given question;
The height of ball kicked is given by equation;
h(t) = -4.9t^2 + 12t + 0.5
Where, h(t) = -4.9t^2 + 12t + 0.5
Part a: Average rate of change of the height of the ball from 1s to 3s.
For t = 1 sec
h(1) = -4.9(1)^2 + 12(1) + 0.5
h(1) = 7.6 m
For t = 3 sec
h(3) = -4.9(3)^2 + 12(3) + 0.5
h(3) = -7.6
Average rate of change = -7.6 - 7.6 m/3 - 1
Average rate of change = - 15.2/2
Average rate of change = 7.2 m/sec(going downward)
Part b : instantaneous rate of change at 3s.
h(3) = -4.9(3)^2 + 12(3) + 0.5
h(3) = -7.6
instantaneous rate of change = -7.6 m/sec
Thus, the instantaneous rate of change of the ball at 3s -7.6 m/sec.
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Multiply. Simplify, you may leave the numerator and denominator in answer in factored form.
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Step 1
Given;
Step 2
Multiply
[tex]\frac{x^3+1}{x^3-x^2+x}\times\frac{3x}{-15x-15}=\frac{3x^4+3x}{-15x^4-15x}[/tex]Simplify
[tex]\frac{3x\left(x+1\right)\left(x^2-x+1\right)}{-15x\left(x+1\right)\left(x^2-x+1\right)}=-\frac{1}{5}[/tex]Answer;
[tex][/tex]if you roll a dice twice, what is the possibility of getting a number less than 5 on both rolls?
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Solution
Step 1
Write an expression for the probability of an event
[tex]\begin{gathered} \text{If an event is A} \\ P(A)\text{ = }\frac{No\text{ of required events}}{No\text{ of total possible events}} \end{gathered}[/tex]
No of the required events can be found with the following table
The numbers(1,2,3,4,5,6) on the vertical are for one dice and the others on the horizontal are for the second dice
No of required of numbers on both dices less than 5 are : 1,1 1,2 1,3 1,4 2,1 2,2 2,3 2,4 3,1 3,2 3,3 3,3 3,4 4,1 4,2 4,3 4,4. The number of the events are therefore, = 16
No of total events = 36
Step 2
Substitute the values and find the required probability
[tex]\text{Probability of getting numbers less than 5 on both dice = }\frac{16}{36}=\text{ }\frac{4}{9}[/tex]What is a like terms to 15?a.15xb.5bc.22d.not enough information
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Those are like terms because are constants
[tex]25,x,3x^2[/tex]Those aren't like terms because 25 is a constant, x is a variable, and 3x² is a quadratic variable
Robin and Dovey have four pet pigeons that they train to race. They release the birds at Robin's house and then drive to Dovey's to collect them. To drive from Robin's to Dovey's, because of one-way streets, they go 3.1 km north, turn right and go 1.7 km east, turn left and go 2.3 km north, turn right and go 0.9 km east, turn left and go 1.2 km north, turn left and go 4.1 km west, and finally turn left and go 0.4 km south. How far do the pigeons have to fly to go directly from Robin's house to Dovey's house? Round your answer to the nearest tenth. (HINT: draw a picture!) *
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Let the north and east with a positive sign, so, the south and west are negative signs
Because of one-way streets, they go 3.1 km north, turn right and go 1.7 km east, turn left and go 2.3 km north, turn right and go 0.9 km east, turn left and go 1.2 km north, turn left and go 4.1 km west, and finally turn left and go 0.4 km south.
So, the resultant horizontal distance = 1.7 + 0.9 - 4.1 = -1.5 km
The resultant vertical distance = 3.1 + 2.3 + 1.2 - 0.4 = 6.2 km
So, the direct distance will be calculated using Pythagorean theorem :
So, the distance d =
[tex]\begin{gathered} d=\sqrt[]{(-1.5)^2+(6.2)^2}=\sqrt[]{2.25+38.44} \\ \\ d=\sqrt[]{40.69}=6.37887 \end{gathered}[/tex]Rounding the answer to the nearest tenth
so, the answer is : 6.4 km
11. The list price of an orange dial Luminox watch is $450. Katz Jewelers receives a tradediscount of 25%. Find the trade discount amount and the net price.
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In order to find the trade discount amount and the net price, you first calculate the 25% of $450. You proceed as follow:
(25/100) x 450 = 112.5
the percentage is divided by 100, an
Then, $112.5 is the 25% of $450. And $112.5 is the discount amount
Next, to calculate the net price, you simply calculate the difference between the intial price ($450) and the price after the discount ($112.5), just as follow:
net price = $450 - $112.5 = $337.5
Hence, the discount amount is $112.5 and the net price is $337.5
The probability of rolling an odd number with a six-sided number cube is 1/2 Choose the tikelihood that best describes the probability of this event.O A. Certain O B. Likely O C. Neither likeiy nor unlikety O D. Unlikely
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In a dice, obtain odd number
Its A CERTAIN probability, because can be calculated
P = (1,3,5) /(1,2,3,4,5,6) = 3/6 = 1/2
Then ANSWER IS OPTION A)
Nick bakes 3 dozen cookies for the bake sale. Each cookie requires 12 milliliters of water. How
many milliliters of water does he use?
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In linear equation, 432 milliliters of water does he use .
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18, for instance.With only a constant and a first-order (linear) term, a linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept.Nick bakes 3 dozen cookies for the bake sale.
1 cookie requires 12 milliliters of water.
water does he use = 3 × 12 × 12
= 432 milliliters of water
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helpppppppp ur gurlll out
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Answer:
Step-by-step explanation:
2(x-3) + 21 = -3
So:
My first step is to open the brackets
2x - 6 + 21 = -3
Then I plus two numbers in the equation:
2x + 15 = -3
Third step is: 2x = -3 - 15
2x = -18
The value of x that makes the equation true is:
x = -18/2
x = -9
24. lim
x-(1/2)-
|2x - 1|
2x - 1
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After evaluating the limit we have came to find that the limit of [tex]\lim_{x\rightarrow \left(1/2)^-} $$|2x-1| 2x-1[/tex] as x approaches 1/2- is -1.
What is limit?In mathematics, a limit is the value that a function, sequence, or index approaches as an input or as an index approaches a specific value. Limits, which are fundamental to calculus and mathematical analysis, are required for the definitions of continuity, derivatives, and integrals.
The concept of a limit of a sequence is further generalized to include the concept of a limit of a topological network, in addition to having a connection to the category theory concepts of limit and direct limit.
A function's limit is typically expressed in formulas as
[tex]{\displaystyle \lim _{x\to c}f(x)=L}[/tex]
We need to solve the given equation
⇒ [tex]\lim_{x\rightarrow \left(1/2)^-} $$|2x-1| 2x-1[/tex]
⇒ [tex]\lim_{x\rightarrow \left(1/2)^-} $$(2\times|2x-1| x) + \lim_{x\rightarrow \left(1/2)^-}}$$( -1)[/tex]
⇒ Evaluate for x
⇒ [tex]0+ \lim_{x\rightarrow \left(1/2)^-}}$$( -1)[/tex]
⇒ 0 - 1
⇒ -1
Thus, after evaluating the limit we have came to find that the limit of [tex]\lim_{x\rightarrow \left(1/2)^-} $$|2x-1| 2x-1[/tex] as x approaches 1/2- is -1
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A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then theunit cost is given by the function C (x) = 0,3x2 -96x+14,848. How many cars must be made to minimize the unit cost?Do not round your answer
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Answer:
[tex]160\text{ cars}[/tex]Explanation:
Here, we want to get the number of cars to be made so as to minimize the unit cost
What we have to do here is to find the first derivative of the given cost function
Mathematically, we have that as:
[tex]C^{\prime}(x)\text{ = 0.6x -96}[/tex]To get the minimum x value, we simply set the first derivative to zero and solve for x
Mathematically, that would be:
[tex]\begin{gathered} 0\text{ = 0.6x-96} \\ 0.6x\text{ = 96} \\ x\text{ = }\frac{96}{0.6} \\ x\text{ = 160 } \end{gathered}[/tex]Which shape is the most general of the quadrilaterals below?
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Given:
There are four shapes square, parallelogram, isosceles trapezoid and rectangle.
To find:
The shape is the most general of the quadrilaterals.
Explanation:
As we know,
If the quadrilateral has equal opposite sides and equal opposite angles, then it is a parallelogram.
So,
All squares are parallelograms.
All rectangles are parallelograms.
All rhombus is a parallelogram.
Therefore, the most general of the quadrilaterals is a parallelogram.
Final answer:
A parallelogram is the most general of the quadrilaterals.
Find the radius of the circle and the coordinates of its center
Answers
Hence, the radius of the circle is 10, and the coordinates of its centre is (6,-2)
Find the y-intercept of the line on the graph.
Answers
The y-intercept of the given line on the graph is -3.
What is the y-intercept?A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.So, the y-intercept of the given line:
Formula of slope: y = mx + bWhere m is the slope and b is the y-intercept.Let's now follow the graph's value of y at x = 0.
Now, according to the given graph (Graph is attached below).
When, x = 0 then, y = -3.Therefore, the y-intercept of the given line on the graph is -3.
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data collected for a study involving IQ scores of four year old girls produced a mean of 100 and a standard deviation of 10 what IQ score does a z-score of -1.5 represent
Answers
Answer:
85
Explanation:
First, recall the formula for Z-Score.
[tex]Z-\text{Score}=\frac{X-\mu}{\sigma}\text{ where }\begin{cases}X=\text{raw score} \\ \mu=\operatorname{mean} \\ \sigma=\text{standard deviation}\end{cases}[/tex]Substitute the given values:
[tex]\begin{gathered} -1.5=\frac{X-100}{10}\text{ } \\ X-100=-1.5\times10 \\ X-100=-15 \\ X=100-15 \\ X=85 \end{gathered}[/tex]A z-score of -1.5 represents an IQ score of 85.
