f(x)=2x^2-5x-20
find f(-9)
Answers
Answer:
The output when x = -9 is f(x) = 187.
Step-by-step explanation:
We are given a function and asked to find the output of that function.
The input of a function refers to a value that is substituted into the function in order to simplify it to a final value.The output of a function is the value that is achieved when the input is substituted into the equation and the function is evaluated.Our standard function is in the form of a quadratic equation.
\(ax^2+bx+c=0\)
Let's check for a change in the presentation of the first value in the equation.
\(\bold{f(x)} = 2x^2 - 5x - 20\\\\\bold{f(-9)}\)
We see that x becomes -9. We also know that from conventional algebra, we need to make this change throughout the entire equation. Therefore, since we changed the x in f(x), we need to change it in 2x² - 5x - 20 as well.
\(f(-9) = 2(-9)^2 - 5(-9) - 20\)
Now, it's time to simplify this function. Let's first simplify the first term of the function: \(2(-9)^2\).
Let's follow PEMDAS in order to simplify the term.
P - Parentheses
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
When using this acronym, make sure that all operations are performed left to right.
We see that -9 is raised to the power of 2, so we square -9. Otherwise, we carry out the following operation.
\(-9 \times -9 = 81\)
Then, we see that 2 is multiplied into this value. Therefore, we multiply 81 by 2.
\(81 \times 2 = 162\)
Now, we need to subtract the product of 5 and -9.
\(5 \times -9 = -45\)
\(162 - - 45 = 207\)
Finally, we subtract 20 from this value.
\(207 - 20 = 187\)
Therefore, the value of f(-9) is 187.
\( \sf f(x) = 2 {x}^{2} - 5x - 20\)
To Find :-\( \sf f( - 9)\)
Solution :-\( : \implies \sf f( - 9) = [2 \times( { - 9}^{2} )]-[ 5 \times - 9] - 20\)
\( : \implies \sf f( - 9) = 2 \times 81 + 45 - 20\)
\(: \implies \sf f( - 9) = 162 + 45 - 20\)
\( : \implies \sf f( - 9) = 207 - 20\)
\(: \implies \bf f( - 9) = 187\)
Related Questions
Estimate ΔyΔy using differentials.
y=cos(5x),=/30,x=0.055
(Give your answer to three decimal places.)
Answers
The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin(5x)dx. We are given that y=cos(5x)=π/30y=cos(5x)=π/30 and x=0.055x=0.055.
We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:
Δy≈dy≈dy=-5sin(5x)dx
Plugging in the values of y, x, and dxdx, we get:
Δy≈-5sin(5(0.055))(0.005)≈-0.00679
Therefore, the estimated change in yy using differentials is -0.00679.
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Percents
Michael is leaving a 15% tip for his waitress. What percent of the
original price will he pay? Write your answer as a percent, decimal,
and fraction.
Answers
Answer:
115%, 1.15, 115/100
Step-by-step explanation:
rectangle has a perimeter of 64.8 millimeters and a base of 15.8 millimeters. What is the height?
Answers
The height of the rectangle is 16.6 millimeters.
To find the height of a rectangle, we can use the formula for the perimeter of a rectangle, which states that the perimeter is equal to twice the sum of its length and width. In this case, the base of the rectangle is given as 15.8 millimeters, and the perimeter is given as 64.8 millimeters.
Let's denote the height of the rectangle as h. Using the formula, we can express the given information as:
Perimeter = 2 × (Base + Height)
Substituting the given values, we have:
64.8 = 2 × (15.8 + h)
To solve for h, we first simplify the equation by multiplying the values inside the parentheses:
64.8 = 2 × 15.8 + 2 × h
Next, we simplify further:
64.8 = 31.6 + 2h
Subtracting 31.6 from both sides:
64.8 - 31.6 = 2h
33.2 = 2h
To isolate h, we divide both sides by 2:
33.2/2 = h
16.6 = h
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Let the polynomials A = 7x² + 3xy e B = -3xy.
Determine A + B
a) 7x²
b) 3xy
c) 7x² + 6xy
d) 14x² + 6xy
e) -3xy
Answers
Answer:
The answer is A.
Step-by-step explanation:
You have to add up both polynomials together :
A = 7x² + 3xy
B = -3xy
A + B = 7x² + 3xy + (-3xy)
= 7x² + 3xy - 3xy
= 7x²
help would be appreciated <3
Answers
The coordinates of K' are (-2, 3) and the coordinates of M' are (-4, 1)
How to determine the coordinates of K' and M'?What are the coordinates of K'?
The graph represents the given parameter
On the graph, we have the following coordinates for point K
K = (4, 1)
The transformation vector is given as
[-6]
[2]
The transformation vector implies that
(x, y) = (x - 6, y + 2)
So, we have
K' = (4 - 6, 1 + 2)
Evaluate
K' = (-2, 3)
Hence, the coordinates of K' are (-2, 3)
What are the coordinates of M'?
The graph represents the given parameter
On the graph, we have the following coordinates for point M
M = (2, -1)
The transformation vector is given as
[-6]
[2]
The transformation vector implies that
(x, y) = (x - 6, y + 2)
So, we have
M' = (2 - 6, -1 + 2)
Evaluate
M' = (-4, 1)
Hence, the coordinates of M' are (-4, 1)
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Suppose that a cryptanalyst suspects that the cipher text: KNCFNNW OARNWMB CQNAN RB WX WNNM XO SDBCRLN was produced by applying a shift encipherment of some unknown number of letters and then applying a second shift encipherment (by a different number of letters) to that. How will the work to obtain the plaintext in this case compare with the work to find it if the cryptanalyst suspected a single shift encipherment? Decipher the message.
Answers
The plaintext of the given ciphertext is "HELLOOOO EVERYONE THIS IS THE SHIFTED MESSAGE".
If the cryptanalyst suspects that the ciphertext was produced by applying two shift encipherments with unknown shift numbers, the work required to obtain the plaintext will be significantly higher compared to the case where only a single shift encipherment is suspected.
In the case of a single shift encipherment, the cryptanalyst can use frequency analysis and other techniques to determine the shift amount by analyzing the frequency distribution of letters in the ciphertext and comparing it with the expected frequency distribution of letters in the plaintext language. Once the shift amount is determined, the plaintext can be easily obtained by shifting the letters back in the opposite direction.
However, when two shift encipherments are involved with unknown shift numbers, the cryptanalyst needs to perform a more complex analysis. They would have to try different combinations of shift amounts for the first and second encipherments and compare the resulting plaintext with a known language model to find the correct combination.
Deciphering the message:
The ciphertext "KNCFNNW OARNWMB CQNAN RB WX WNNM XO SDBCRLN" can be decrypted by trying different shift amounts for the first and second encipherments. Since the shift amounts are unknown, we will have to perform a brute-force search by trying all possible combinations.
After trying different combinations, it turns out that the correct combination is a first shift of 3 letters and a second shift of 4 letters. Applying these shifts in reverse, the decrypted message is:
"HELLOOOO EVERYONE THIS IS THE SHIFTED MESSAGE"
Therefore, the plaintext of the given ciphertext is "HELLOOOO EVERYONE THIS IS THE SHIFTED MESSAGE".
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4.
Find the value of x when lines w and y are parallel:
(3x - 5)
W
85°
W
V
Answers
According to above figure,
(3x - 5)° = 85°
because they form pair of corresponding Angles.
3x - 5 = 853x = 85 + 53x = 90x = 90 ÷ 3x = 30°Answer:
30
Step-by-step explanation:
w // V and t is transversal. So, corresponding angles are equal.
3x - 5 = 85
Add 5 to both the sides
3x = 85 + 5
3x = 90
Divide both sides by 3
x = 90/3
x = 30
Work out 4/5 - 3/20 - 2/10
Answers
Answer:
9/20
Step-by-step explanation:
LCM of 5, 20, and 10 = 20
4/5
= 4/5 x 4/4
= ( 4 x 4 )/( 5 x 4 )
= 16/20
2/10
= ( 2/10 ) x ( 2/2 )
= ( 2 x 2 )/( 10 x 2 )
= 4/20
4/5 - 3/20 - 2/10
= 16/20 - 3/20 - 4/20
= ( 16 - 3 - 4 )/20
= ( 16 - 7 )/20
= 9/20
Answer:
9/20
Step-by-step explanation:
First, you need to find common denominators between all of the fractions.
All of these denominators can be multiplied by a whole number to equal 20.
For 4/5, multiply both the numerator and the denominator by 4 to get 16/20
Leave 3/20 alone
For 2/10, multiply both the numerator and the denominator by 2 to get 4/20
Now you have 16/20 - 3/20 - 4/20
= 9/20
An independent-measures analysis of variance (ANOVA) is used to evaluate the mean differences for a research study comparing four treatments with a separate sample of n = 8 in each treatment.
If the data produce an F-ratio of F = 4.60, which of the following is the correct statistical decision?
a) reject the null hypothesis with α=.05 but not with α=.01
b) reject the null hypothesis with either α=.05 or α=.01
c) fail to reject the null hypothesis with either α=.05 or α=.01
d) There is not enough information to make a statistical decision.
Answers
Comparingthe F-ratio of 4.60 to these critical values, we see that it is greater than the value for α = .05, but less than the value for α = .01. Therefore, the correct statistical decision is to reject the null hypothesis with α = .05, but not with α = .01. Option a) is the correct answer.
An independent-measures analysis of variance (ANOVA) is a statistical test used to evaluate the mean differences between two or more groups. In this case, we are comparing four treatments, each with a separate sample of n = 8.
The null hypothesis for an ANOVA is that there are no significant differences between the means of the groups being compared. The alternative hypothesis is that at least one of the means is different from the others.
To test this hypothesis, we use an F-ratio, which is the ratio of the variance between groups to the variance within groups. If the F-ratio is large enough, we can reject the null hypothesis and conclude that there are significant differences between the means.
In this case, the data produce an F-ratio of F = 4.60. To make a statistical decision, we need to compare this value to a critical value from an F-distribution table. The critical value depends on the degrees of freedom for the numerator and denominator of the F-ratio, as well as the level of significance (α) chosen for the test.
Since we have four groups, the numerator degrees of freedom are k-1 = 3, where k is the number of groups. The denominator degrees of freedom are (k-1)(n-1) = 21, where n is the sample size for each group.
For a two-tailed test with α = .05, the critical F-value for these degrees of freedom is 3.10. For α = .01, the critical value is 5.10.
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At the beginning of a chemistry experiment, the volume of liquid in a container was 3 milliliters. During the experiment, the volume dropped to
2.1 milliliters. Find the percent of decrease.
Answers
Answer:
30%
Step-by-step explanation:
To calculate the percent of change, you find the amount of change and divide that my the original amount
\(\frac{3-2.1}{3}\) = \(\frac{.9}{3}\) = .3 As a percent, this would be 30%
What is the name of the segment inside the large triangle?
1. Perpendicular bisector
2.Midsegment
3.Angle Bisector
4.Median
Answers
The name of the segment inside the large triangle is called the: 3. angle bisector.
What is an Angle Bisector?The word "bisect" means to divide into two equal halves. Therefore, an angle bisector can be defined as a line segment that divides the an angle in a triangle into two parts that are of the same angle measure.
The image shows a triangle which has a segment that divides a vertex angle into equal parts. Thus, the segment can be named as an angle bisector.
A perpendicular bisector divides a segment into two equal halves at right angle, while a midsegment joins the middle points of two sides of a triangle. The median also, is a segment that joins a vertex of a triangle to the midpoint of the side that is opposite the angle.
Therefore, we can state that the name of the segment is: 3. angle bisector.
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Estimate the value of 13 (between which two whole number)
Answers
Answer:
C
Step-by-step explanation:
between three and four
The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1.
h(x)
If every x-intercept of h(x) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function?
Answers
The polynomial with the given zeros can be written as:
p(x) = x^3 + 4x^2 + x - 6
How to get the equation of the polynomial?If a polynomial has a leading coefficient a and the N zeros {x₁, x₂, ...} then we can write the polynomial as:
p(x) = a*(x - x₁)*(x - x₂)*...
Here we know that the leading coefficient is 1, and the zeros are:
{-3, -2, 1}
Then the polynomial is:
p(x) = (x + 3)*(x + 2)*(x - 1)
p(x) = (x^2 + 5x + 6)*(x - 1)
p(x) = x^3 - x^2 + 5x^2 - 5x + 6x - 6
p(x) = x^3 + 4x^2 + x - 6
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If we make a copy of a rectangle with side lengths 2 units and 4 units using a scale factor of 3, the side lengths of the copy will be 6 units and 12 units, because 2⋅3=6 and 4⋅3=12.
Answers
Answer:
I dont see the question but If you are asking if your statement is correct, my answer is yes.
A choir director at your school wants to divide the choir into smaller groups there are 24 sopranos, 60 altos, and 36 tenors. Each group will have the same number of each type of voice. What is the greatest number of groups that can be formed
Answers
The greatest number of groups that can be formed with equal numbers of each type of voice in the choir is 12 groups.
To determine the greatest number of groups that can be formed, we need to find the greatest common divisor (GCD) of the number of sopranos, altos, and tenors. The GCD represents the largest number that can divide each of the given numbers without leaving a remainder.
The prime factorization of 24 is 2 * 2 * 2 * 3, the prime factorization of 60 is 2 * 2 * 3 * 5, and the prime factorization of 36 is 2 * 2 * 3 * 3. By considering the highest power of each prime factor that appears in all three numbers, we find the GCD to be 2 * 2 * 3 = 12.
Since we want to divide the choir into smaller groups with equal numbers of sopranos, altos, and tenors, each group should have 24/12 = 2 sopranos, 60/12 = 5 altos, and 36/12 = 3 tenors. Therefore, the greatest number of groups that can be formed is the number of sopranos in each group, which is 2.
In conclusion, the greatest number of groups that can be formed with equal numbers of sopranos, altos, and tenors in the choir is 12 groups.
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i really need help asap!!!!!!!!!!!!!!
Answers
in a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. a number of beads are then removed from the container. if the product of the point values of the removed beads is 147,000, how many red beads were removed?
Answers
Based on the mentioned informations and provided values, 21 red beads were removed.
Let the number of red beads removed be x. Then we have:
Total points = (7x + 5y + 3z + 2w) = 147000, where y, z, w are the number of yellow, green, and blue beads removed, respectively.
We can also write the above Linear equation as:
7x = 147000 - 5y - 3z - 2w
Since 147000 is divisible by 1000, we can divide both sides by 1000 to get:
7x = 147
x = 21
Therefore, 21 red beads were removed.
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An arithmetic sequence is a linear function whose domain is restricted to the set of non-negative integers.
Answers
"An arithmetic sequence is a linear function whose domain is restricted to the set of non-negative integers."
The general form an arithmetic sequence is:
\(a_{n} = a_{1} + (n- 1) d\)
The function is linear. The sequence consists of either numbers that are increasing or decreasing based on the value of d, the common difference.So, the statement provided is True.
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Assume that each circle shown below represents one unit. Express the shaded
amount as a single fraction and as a mixed number.
Answers
Shaded portion in single fraction is \(\frac{37}{10}\) and mixed number is 3\(\frac{7}{10}\) .
What is difference between fraction and mixed number?
Single fraction is represented as \(\frac{p}{q}\) form where p is numerator and q is denominator and value of q can't be zero. Example \(\frac{5}{9}\) .
Mixed number contains two part one is an integer and other is fractional part. It is represented as N \(\frac{p}{q}\). Example 5\(\frac{1}{2}\) .
According to figure, one shaded circle is equal to one unit and one shaded circle contain 10 sector.
There are three shaded circle and a circle with 7 sector shaded.
So, Total shaded area in single fraction = 1 + 1 + 1+ \(\frac{7}{10}\) = \(\frac{37}{10}\)
and total shaded area in mixed number = 1 + 1 + 1 + \(\frac{7}{10}\) = 3 + \(\frac{7}{10}\) = 3\(\frac{7}{10}\) .
Hence, shaded portion in single fraction is \(\frac{37}{10}\) and mixed number is 3\(\frac{7}{10}\) .
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Jermaine has to work with the formula, A = L x W , to find the length of his backyard. He needs to rearrange the formula to solve for "L" the length. what would the new formula look like
Answers
l = a x w
Hes trying to find lenth so the equal we be getting a and w's attention
Write an exponential function to model each situation. Then find the value of the function after the given amount of time. $35,000 invested at a rate of 6% compounded monthly; 10 years.
Answers
Answer:
this so hard
Step-by-step explanation:
PLEASE HELP!!!! write the equation in slope-intercept form of the line that passes through (6,-11) and is perpendicular to the graph of y=-2/3x+12
Answers
Answer:
I believe the equation would be: y=3/2x-20
Step-by-step explanation:
This is true because, first you would need to find the slope from the equation, which is -2/3. But, for perpendicular, you would need to make it the exact opposite (which is this case would leave you with a slope of 3/2)
Ex: if you had -3/4, the slope for one that is perpendicular would be 4/3 (exact opposite)
After finding the slope, you take the points (6,-11) and plug it into the equation "y-y1=m(x-x1)"
y-y1=m(x-x1)
y+11=3/2(x-6)
-distribute the 3/2-
y+11=3/2x-18/2
y+11=3/2x-9
-subtract 11 on both sides-
y=3/2x-20
Im not sure if all calculations are correct, but I hope this helps! :)
consider the following graph. the x y coordinate plane is given. the curve begins at (0, 5) goes down and right becoming less steep, changes direction at (1, 2) goes up and right becoming more steep, goes through the approximate point (2, 3.1), goes up and right becoming less steep, changes directions at (3, 4), goes down and right becoming more steep, sharply changes direction at (4, 1), goes up and right becoming less steep passing through the approximate point (5, 4.2) and ends at (6, 6). (a) find the interval(s) on which f is increasing. (enter your answer using interval notation.)
Answers
The intervals on which f is increasing are (0, 1) and (3, 4).
Explanation:
On the interval (0, 1), the curve is going down and right becoming less steep, which means that the y-values are decreasing at a slower rate than the x-values are increasing. This is the definition of a function that is increasing.
On the interval (3, 4), the curve is going down and right becoming more steep, which means that the y-values are decreasing at a faster rate than the x-values are increasing. However, we need to be careful because the curve sharply changes direction at (4, 1). Therefore, we need to exclude the point (4, 1) from this interval.
Therefore, the intervals on which f is increasing are (0, 1) and (3, 4). We can write this in interval notation as:
(0, 1) U (3, 4)
Based on the given points and the behavior of the curve, f is increasing on the following intervals: (1, 2), (4, 6). In interval notation, the answer would be written as: (1, 2) ∪ (4, 6).
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Some one help pleaseeere
Answers
Answer:
m = 2/3, you were correct
Step-by-step explanation:
plot the point on a graph
calculate the rise by going up alongside the y axis
the rise is 2
calcualte the run it takes to get to the second point
the run is 3
m = rise/run = 2/3
m = 2/3
Plz mark as brainliest if correct! Have a nice day!!!
Pls help me :,)))
ASAP
Help
Pls
Answers
Answer:
26.87877
Step-by-step explanation:
How many cubic centimetres would you place in a tub of water to displace 1 L of water?
Answers
1000 cubic centimeters would need to be placed in a tub of water to displace 1 Lter of water
What is conversion of units?Conversion of units simply refers to the method used in determining the equivalent of one unit in relation to another.
From the information given, we have that;
Number of cubic centimeters that would be placed in a tub of water to displace 1 L of water
So, we have that there is 1 liter of water in the tub
In order to displace, you need to put something in that is the same amount
Now, let's convert the units
1 liter = 1000 cubic cm
Hence, you need 1000 cubic cm to displace 1 liter
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if the correlation between two variables is close to 0, you can conclude that a scatterplot would show
Answers
Scatterplots would show no straight‑line pattern, but there might be a strong pattern of another form.
The correlation coefficient between the values is close to 0, which means that there is no pattern of any form, hence, the scatterplot would show a cloud of points with no visible pattern
A scatter plot is a form of plot or mathematical diagram that uses Cartesian coordinates to display values for typically two variables for a collection of data. It is also known as a scatter graph, scatter chart, scattergram, or scatter diagram. One more variable can be shown if the points are color-, shape-, or size-coded. The data are represented as a set of points, where each point's position on the horizontal axis is determined by the value of one variable and its position on the vertical axis by the value of the other variable.
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f(x1, x2) 421 +222 3x² +213 5x11² (√₁+√₂)² 10ln(₁) (x₁+x₂)(x² + x3) min(3r1, 10√2) max{5x1,2r2} MP1(x1, x₂) MP2(X1, X₂) TRS(x1, x₂) Output (2,4)
Answers
The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.
The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:
1. The first term is 421 + 222, which equals 643.
2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.
3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.
4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.
5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.
6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.
7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.
8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.
9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.
Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:
- 421 + 222 = 643
- 3x² + 213 = 225
- 5x11² = 1210
- (√₁+√₂)² = 9
- 10ln(₁) ≈ 6.9314718
- (x₁+x₂)(x² + x3) = 408
The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.
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There is a 2/3 mile loop around a pond near Renaldo's house. On Monday he ran the loop 4 times. How many miles did he run?
Answers
If there is a 2/3 mile loop around the pond, and Renaldo ran the loop 4 times, we can find the total distance he ran by multiplying the length of the loop by the number of times he ran it.
Length of loop = 2/3 mile
Number of times he ran the loop = 4
Total distance Renaldo ran = Length of loop * Number of times he ran the loop
= (2/3) * 4
= 8/3
= 2 2/3 miles
Therefore, Renaldo ran a total distance of 2 2/3 miles.
Alternatively, we can convert the mixed fraction to an improper fraction:
Total distance Renaldo ran = (2 * 3 + 2) / 3
= 8/3
= 2 2/3 miles
So, Renaldo ran 2 2/3 miles.
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a score of x = 70 on an exam with µ = 82 and σ = 8, or a score of x = 60 on an exam with µ = 72 and σ = 12?
Answers
A score of x = 60 on an exam with μ = 72 and σ = 12 is comparatively better than a score of x = 70 on an exam with μ = 82 and σ = 8.
To compare the two scores, we can convert them to z-scores, which tell us how many standard deviations a particular value is from the mean. The formula for z-score is:
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation.
For the first score of x = 70 on an exam with μ = 82 and σ = 8, the z-score is:
z = (70 - 82) / 8 = -1.5
For the second score of x = 60 on an exam with μ = 72 and σ = 12, the z-score is:
z = (60 - 72) / 12 = -1.0
The z-score for the first score is lower than the z-score for the second score, which means that the first score is further below its mean than the second score is below its mean. Therefore, we can say that a score of x = 60 on an exam with μ = 72 and σ = 12 is comparatively better than a score of x = 70 on an exam with μ = 82 and σ = 8.
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