Hannah and Becky are learning to type on a computer keyboard. Hannah's
typing speed is represented by the equation y = 11x where y is the number of
words she types and x is the number of minutes. Becky's typing speed is
given by the graph.
Number of words
60
48
36
24
12
2
3
Time (minutes)
Choose the statement that correctly compares their unit rates.
Adr
A. Hannah's unit rate is 2 more words per minute than Becky's unit
rate.
B. Hannah's unit rate is 1 more word per minute than Becky's unit
rate.
C. Hannah's unit rate is equal to Becky's unit rate.
D. Hannah's unit rate is 1 fewer word per minute than Becky's unit
rate
The correct statement is D. Hannah's unit rate is 1 fewer word per minute than Becky's unit rate.
To compare the unit rates, we need to determine the rate at which each person types words per minute.
For Hannah, the equation y = 11x represents her typing speed, where y is the number of words and x is the number of minutes. This means that Hannah types 11 words per minute (11 words/minute).
Looking at Becky's graph, we can determine her unit rate by calculating the change in the number of words divided by the change in time.
The change in words is 48 - 2 = 46, and the change in time is 3 - 2 = 1. So, Becky's unit rate is 46 words per minute (46 words/minute).
Comparing the unit rates:
Hannah's unit rate: 11 words/minute
Becky's unit rate: 46 words/minute
Therefore, Hannah's unit rate is 35 words per minute less than Becky's unit rate.
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Consider this equation
1/x-1 = | x-2 |
Using three iterations of successive approximation, what is the approximate solution to the equation? Use the graph as a starting point.
A. x ≈ 43/16
B. x ≈ 21/8
C. x ≈ 41/16
D. x ≈ 19/8
The approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.
To solve the equation 1/x-1 = |x-2| using three iterations of successive approximation, we will start with an initial guess and refine it using an iterative process.
Given that the equation involves absolute value, we will consider two cases:
Case 1: x - 2 ≥ 0
In this case, |x-2| simplifies to x-2, and the equation becomes 1/(x-1) = x-2.
Case 2: x - 2 < 0
In this case, |x-2| simplifies to -(x-2), and the equation becomes 1/(x-1) = -(x-2).
Now, let's perform the successive approximation:
Iteration 1:
Let's start with an initial guess, x = 2.
Case 1: When x - 2 ≥ 0,
1/(2-1) = 2-2,
1/1 = 0,
which is not true.
Case 2: When x - 2 < 0,
1/(2-1) = -(2-2),
1/1 = 0,
which is not true.
Since our initial guess did not satisfy the equation in either case, we need to choose a different initial guess.
Iteration 2:
Let's try x = 3.
Case 1: When x - 2 ≥ 0,
1/(3-1) = 3-2,
1/2 = 1,
which is not true.
Case 2: When x - 2 < 0,
1/(3-1) = -(3-2),
1/2 = -1,
which is not true.
Again, our guess did not satisfy the equation in either case.
Iteration 3:
Let's try x = 2.5.
Case 1: When x - 2 ≥ 0,
1/(2.5-1) = 2.5-2,
1/1.5 = 0.5,
which is true.
Case 2: When x - 2 < 0,
1/(2.5-1) = -(2.5-2),
1/1.5 = -0.5,
which is not true.
Our guess of x = 2.5 satisfies the equation in Case 1.
Therefore, the approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.
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Cameron sorts 56 books into groups of 5, but has some books left over
How many books are left over?
Cameron has 1 book left over after sorting it into group of 5
To determine the number of book left,
we need to first divide 56 by 5 [56 ÷ 5]
Quotient = 11
then find the remainder which is 1
therefore there os only 1 book left over
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2AI + 3H₂SO4
To show that the reaction conserves matter, how many hydrogen (H) atoms
will the right side of the equation need to have?
A. 6
B. 3
C. 2
OD. 5
Answer:
A. 6
Step-by-step explanation:
You have 3 molecules of H2SO4, each molecule has two atoms of H and you have 3 molecules, so 3*2=6 atoms of H
In order to compute a sample mean by hand, first the data values must be added up. Then the sum is divided by the
sample size.
x = xx
Given the data set below, compute the summation, identify the sample size, and calculate the sample mean.
19
10
15
17
16
a.) Ex =
b.) n =
c.) x =
a) The summation (Ex) of the given data set, we add up all the values
Ex = 77
b) n = 5
c) x = 15.4
a) To compute the summation (Ex) of the given data set, we add up all the values:
19 + 10 + 15 + 17 + 16 = 77
b) The sample size (n) is the total number of data points in the set. In this case, there are 5 data points, so:
n = 5
c) To calculate the sample mean (x), we divide the summation (Ex) by the sample size (n):
x = Ex / n
x = 77 / 5
x = 15.4
Therefore, the answers are:
a) Ex = 77
b) n = 5
c) x = 15.4
The summation is 77, the sample size is 5, and the sample mean is 15.4.
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Choose an amount between $60.00 and $70.00 to represent the cost of a grocery bill for a family. Be sure to include dollars and cents.
Part A: If the family has a 25% off coupon, calculate the new price of the bill. Show all work or explain your steps. (6 points)
Part B: Calculate a 7% tax using the new price. What is the final cost of the bill? Show all work or explain your steps. (6 points)
Answer:
A: $51.00
B: $54.57
Step-by-step explanation:
Let amount = $68.00
Part A:
Since the coupon is for 25%, the family pays 75% of $68.00
75% of $68.00 = 0.75 × $68.00 = $51.00
The new price is $51.00
Part B:
The tax is 7% of $51.00
7% of $51.00 = $3.57
The total price is the sum of $51.00 and the amount of tax, $3.57
Total price = $51.00 + $3.57 = $54.57
Calc II Question
Find the average value of the function on the given interval
F(x) = sin4x, [-pi, pi]
Correct answer is 45/28 but I'm not sure how to get to that answer
Answer:
0
Step-by-step explanation:
[tex]\displaystyle \frac{F(b)-F(a)}{b-a}\\\\=\frac{F(\pi)-F(-\pi)}{\pi-(-\pi)}\\\\=\frac{\sin(4\pi)-\sin(-4\pi)}{2\pi}\\\\=\frac{0-0}{2\pi}\\\\=0[/tex]
Not sure how the correct answer is stated as 45/28, but the answer is definitely 0.
5h-6-8+7h what’s the answer ?
Suppose the bear population in the Allegheny National Forest have weights that produce a normal density curve as shown.
74——————-200————————-326
From the graph shown, use the 69-95-99.7% (empirical) rule to estimate the standard deviation of the bear weights.
The estimated standard deviation of the bear weights, based on the given graph and using the 69-95-99.7% rule, is approximately 63.
The 69-95-99.7% (empirical) rule, also known as the 3-sigma rule, is a rule of thumb that applies to data that follows a normal distribution. According to this rule:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
In the given graph, if we assume the bear weights follow a normal distribution, we can estimate the standard deviation using the 69-95-99.7% rule.
Based on the graph, we know that the midpoint of the distribution (mean) is 200. Assuming the graph is symmetric, we can estimate one standard deviation as half the distance between the mean (200) and either end (74 or 326).
To calculate this, we subtract the mean from one of the endpoints and divide by 2:
Standard Deviation ≈ (326 - 200) / 2 ≈ 126 / 2 ≈ 63
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Work out the height, y, of the isosceles triangle shown below. Give your answer in metres to 2 d.p. 57° 11.5 m Not drawn accurately
The height of the isosceles triangle is approximately 9.70 meters.
To find the height (y) of an isosceles triangle given its slant height and two angles, we can use trigonometry. Here are the steps to solve this problem:
Start by drawing a sketch of the isosceles triangle. Label the base as "b," the height as "y," and the slant height as "s."
Since the triangle is isosceles, the two base angles are congruent, meaning each angle measures 57 degrees. Label one of these angles as "θ."
We know that the slant height (s) is given as 11.5 m.
Apply the sine function to relate the slant height (s) to the angle (θ) and the height (y) of the triangle. The sine of an angle is defined as the ratio of the opposite side (y) to the hypotenuse (s). So, we have sin(θ) = y/s.
Substitute the given values into the equation: sin(57 degrees) = y/11.5.
Solve the equation for y by multiplying both sides by 11.5: y = 11.5 * sin(57 degrees).
Use a calculator to find the value of sin(57 degrees) and multiply it by 11.5 to obtain the height (y) of the triangle.
Performing the calculation, y = 11.5 * sin(57 degrees) ≈ 9.70 meters (rounded to two decimal places).
Therefore, the height of the isosceles triangle is approximately 9.70 meters.
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3,20,110 _1715 This is an mathematics question
The pattern between the numbers 3, 20, 110, and 1715 can be found using a mathematical method. In order to get the following number from each, there is a sequence that must be applied.Let's take a look at the sequence that was used to generate these numbers:
The first number is multiplied by 2 and then increased by 14 to get the second number. For example:
3 x 2 + 14 = 20
Then, the second number is multiplied by 3 and 20, and 110 is added.
20 x 3 + 110 = 170
The third number is multiplied by 4 and then increased by 110.
110 x 4 + 110 = 550
Finally, the fourth number is multiplied by 5 and then increased by 110.
550 x 5 + 110 = 2825
Therefore, using the above formula, the next number in the sequence can be calculated:
1715 x 6 + 110 = 10400
As a result, the sequence of numbers 3, 20, 110, 1715, 10400 can be calculated using the mathematical formula stated above.
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Given the following equation of a line x+6y= 3, determine the slope of a line that is perpendicular.
The slope of a line that is perpendicular to the given line x + 6y = 3 is 6.
To determine the slope of a line that is perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line.
The equation of the given line is x + 6y = 3.
To find the slope of the given line, we can rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope:
x + 6y = 3
6y = -x + 3
y = (-1/6)x + 1/2
From the equation y = (-1/6)x + 1/2, we can see that the slope of the given line is -1/6.
To find the slope of a line that is perpendicular, we take the negative reciprocal of -1/6.
The negative reciprocal of -1/6 can be found by flipping the fraction and changing its sign:
Negative reciprocal of -1/6 = -1 / (-1/6) = -1 * (-6/1) = 6
Therefore, the slope of a line that is perpendicular to the given line x + 6y = 3 is 6.
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Juan has some dimes and some quarters. He has no less than 20 coins worth a maximum of $2.75 combined. If Juan has 18 dimes, determine the maximum number of quarters that he could have. If there are no possible solutions, submit an empty answer.
Juan could have a maximum of 3 quarters.
1. Let's assume Juan has x quarters.
2. The value of x quarters in dollars would be 0.25x.
3. We are given that Juan has 18 dimes, which have a value of 0.10 * 18 = $1.80.
4. The combined value of Juan's dimes and quarters should be less than or equal to $2.75.
5. We can write the equation: 0.25x + 1.80 ≤ 2.75.
6. Subtracting 1.80 from both sides of the equation, we have: 0.25x ≤ 2.75 - 1.80.
7. Simplifying, we get: 0.25x ≤ 0.95.
8. Dividing both sides of the inequality by 0.25, we have: x ≤ 0.95 / 0.25.
9. Evaluating the expression, we find: x ≤ 3.8.
10. Since Juan cannot have a fraction of a quarter, the maximum number of quarters he could have is 3.
11. However, we need to check if the combined value of the dimes and quarters is at least $0.20.
12. If Juan has 3 quarters (0.25 * 3 = $0.75) and 18 dimes ($1.80), the combined value is $0.75 + $1.80 = $2.55.
13. Since $2.55 is less than $2.75, Juan can have 3 quarters.
14. Therefore, the maximum number of quarters Juan could have is 3.
Note: There are no possible solutions where Juan has more than 3 quarters and still satisfies the conditions.
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Suitable average for averaging the shoe sizes of children is
Select one:
a. Mean
b. Harmonic Mean
c. Geometric Mean
d. Percentile
e. Mode
Question #2
Solve for x
2
O Saved 1
4
3
Q
69x + 2
R
70°
2.3.5 Quiz: Cross-Sections of Geometric Solids
OA. Triangle
OB. Circle
OC. Trapezoid
OD. Rectangle
The cross section of the geometric solid is (d) rectangle
How to determine the cross section of the geometric solidFrom the question, we have the following parameters that can be used in our computation:
The geometric solid
Also, we can see that
The geometric solid is a cylinder
And the cylinder is divided vertically
The resulting shape from the division is a rectangle
This means that the cross section of the geometric solid is (d) rectangle
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The shape of the cross-section for the geometric solid given in the diagram is a rectangle.
The cross section of the geometric solid represents the shape which extends beyond the actual geometric solid which is a cylinder.
A rectangle has opposite side being equal. This means that the width and and length are of different length.
Therefore, the shape of the cross-section is a rectangle.
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Emma gets $9 per hour for the first 40 hours worked per week and time and a half for the hours..
determine the value of x
The hypotenuse (x) of the right triangle is 10 units
Finding the hypotenuse of the right triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The hypotenuse (x) of the right triangle can be calculated using the following sine equation
sin(30) = 5/x
Using the above as a guide, we have the following:
x = 5/sin(30)
Evaluate
x = 10
Hence, the hypotenuse of the right triangle is 10
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PLS HELP WILL GIVE BRAINLIEST IF ANSWER IS CORRECT (NO LINKS)
Identify the arc length of MA◠ in terms of a and rounded to the nearest hundredth.
The length of the arc in terms of π and the actual length is as follows;
8.17π m²
25.68 m²
How to find arc length?Let's find the length of the arc of the circle as follows:
Therefore,
length of an arc = ∅ / 360 × 2πr
where
r = radius∅ = central angleHence,
∅ = 180 - 88 = 92 degrees
r = 16 m
length of an arc MA = 92 / 360 × 2 × π × 16
length of an arc MA = 2944π / 360
length of an arc MA = 8.17π
Therefore,
length of an arc MA = 25.68 m²
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Consider the following pair of points.
(8,−8)
and (−5,−1)
Step 2 of 2 : Determine the midpoint of the line segment joining the pair of points.
The midpoint of the line segment joining the pair of points (8, -8) and (-5, -1) is (1.5, -4.5).
To find the midpoint, we need to take the average of the x-coordinates and the average of the y-coordinates of the two given points.
For the x-coordinate: (8 + (-5))/2 = 3/2 = 1.5
For the y-coordinate: (-8 + (-1))/2 = -9/2 = -4.5
Thus, the midpoint of the line segment is (1.5, -4.5).
In more detail, the midpoint formula is derived by averaging the x-coordinates and y-coordinates separately. For a line segment with endpoints (x1, y1) and (x2, y2), the midpoint (xm, ym) is given by:
xm = (x1 + x2)/2
ym = (y1 + y2)/2
In this case, the x-coordinates are 8 and -5, and their average is (8 + (-5))/2 = 1.5. The y-coordinates are -8 and -1, and their average is (-8 + (-1))/2 = -9/2 = -4.5.
Therefore, the midpoint of the line segment joining the two given points is (1.5, -4.5).
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Will give brainlieest. 50 points. (8x + 2x³ - 4x²) - (4 + x³ + 6x)
Answer:
[tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] + 2x - 4
Step-by-step explanation:
(8x + 2[tex]x^{3}[/tex] - 4[tex]x^{2}[/tex]) - (4 + [tex]x^{3}[/tex] + 6x)
= 8x + 2[tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] - 4 - [tex]x^{3}[/tex] - 6x
= 2x + [tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] - 4
= [tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] + 2x - 4
You just inherited a sum of money from a distant uncle. The only stipulation is that you need to save it for 10 years and then you can do whatever you want with it. The amount of the inheritance is $25,000.
Option one: You can put it into a saving account that earns 6% compounded quarterly.
Option two: You can put it into a checking account that earns 4% compounded monthly.
Option three: You can place it into a money market account that earns 3% compounded daily.
Which option is best for you? Why?
Submit a report detailing the reasons you have for the decision you make.
This flexibility of a money market account makes it an ideal option for people who need to save money without risking their inheritance.
After inheriting $25,000 from a distant uncle, you would like to save it for ten years before doing anything with it. Since you want to save the money, there are several options for keeping it safe and earning interest, including a savings account, a certificate of deposit (CD), and a money market account.
Money market accounts, in my opinion, would be the best place to keep the inheritance. The money market account is a low-risk account with high-interest rates, making it an attractive option for someone who wants to save their money. As a result, it would be reasonable to place the inheritance into a money market account that pays a daily compounded rate of 3%.There are several reasons for choosing this option.
Firstly, the daily compounded interest will generate a higher return over the ten-year period than the simple interest or monthly compounded interest offered by other accounts. Second, the account is FDIC-insured, which means that the account holder is guaranteed to receive their money in the event of a bank failure.
Furthermore, the money market account provides easy access to the account holder's money while still earning interest. Most money market accounts have a limit on the number of withdrawals a person can make per month. Still, the account holder can easily transfer funds into a checking account or withdraw money from an ATM if needed.
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faste او انوار کو کسی Q2. 3 balls are drawns from the box containing six white balls five red balls and four blue balls find the probabi- lity. that they are draw from the other blue red and white if each ball is (i) Replaced (ii) Not replace.
The probability of drawing blue, red, and white balls consecutively is 120/3375 with replacement and 120/2730 without replacement.
To calculate the probability of drawing three balls from a box containing six white balls, five red balls, and four blue balls, we need to consider two scenarios: with replacement and without replacement.
(i) With replacement:
When each ball is replaced after it is drawn, the total number of balls remains the same for each draw. Therefore, the probability of drawing a specific color on each draw remains constant.
The probability of drawing a blue ball on each draw is 4/15, the probability of drawing a red ball is 5/15, and the probability of drawing a white ball is 6/15 (assuming all colors are equally likely to be drawn).
To find the probability of drawing a blue, red, and white ball consecutively, we multiply the probabilities together since the events are independent:
P(Blue, Red, White) = (4/15) * (5/15) * (6/15) = 120/3375
(ii) Without replacement:
When the balls are not replaced after being drawn, the total number of balls decreases for each subsequent draw. This affects the probability of each color being drawn on subsequent draws.
For the first draw, the probability of drawing a blue ball is 4/15, a red ball is 5/15, and a white ball is 6/15.
For the second draw, the probability of drawing a blue ball is 3/14, a red ball is 5/14 (as one blue ball is already drawn), and a white ball is 6/14.
For the third draw, the probability of drawing a blue ball is 2/13, a red ball is 4/13 (as two blue balls and one red ball are already drawn), and a white ball is 6/13.
To find the probability of drawing a blue, red, and white ball consecutively without replacement, we multiply the probabilities together:
P(Blue, Red, White) = (4/15) * (5/14) * (6/13) = 120/2730
Therefore, the probability of drawing blue, red, and white balls consecutively is 120/3375 with replacement and 120/2730 without replacement.
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find the inverse of each function
Answer:
c
Step-by-step explanation:
assume base 10
-logy = x
[tex] \frac{1}{ log(y) } = x[/tex]
log base x y = 5 turns into the format x^ 5 = y
implement that to get c
Measurement techniques used to measure extent of skewness in data set values are called
Select one:
a. Measure of skewness
b. Measure of median tail
c. Measure of tail distribution
d. Measure of distribution width
e. Measure of peakdness
Note: Answer C is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
Answer:
a. Measure of skewness
Step-by-step explanation:
Skewness is a measure of the asymmetry of a probability distribution. It quantifies the extent to which a dataset's values deviate from a symmetric distribution. Various measures of skewness exist, including the Pearson's skewness coefficient, the Bowley skewness coefficient, and the moment coefficient of skewness. These measures provide a numerical indication of the skewness present in the dataset.
The cost to buy p pounds of potatoes at $0.32 per pound and n
pounds of onions at $0.48 per pound can be determined by using
the expression 0.32p + 0.48n. How much will it cost to buy 4.5
pounds of potatoes and 2.5 pounds of onions?
In an election 177 votes are cast. How many votes are needed
The number of votes needed in an election can vary depending on various factors such as the type of election, voting rules, and specific requirements.
Without additional context or information about the specific election, it is challenging to provide an exact number of votes needed.The number of votes needed in an election is typically determined by factors such as the majority threshold, minimum vote requirement, or any specific criteria outlined in the election rules.
For example, in some elections, a candidate may need a simple majority (more than half) of the votes cast to win, while in others, a candidate may need a specific number or percentage of votes to secure victory.To determine the number of votes needed, it is essential to refer to the specific guidelines or rules established for that particular election.
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The mean height of an adult giraffe is 19 feet. Suppose that the distribution is normally distributed with standard deviation 1 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X - N b. What is the median giraffe height? ft. c. What is the Z-score for a giraffe that is 22 foot tall?
d. What is the probability that a randomly selected giraffe will be shorter than 18.9 feet tal?
e. What is the probability that a randomly selected giraffe will be between 18.6 and 19.5 feet tall?
f. The 80th percentile for the height of giraffes is ft.
a. The distribution of X is a normal distribution.
b. The median giraffe height is also 19 feet.
c. The Z-score for a giraffe that is 22 foot tall is 3.
d. The probability that a randomly selected giraffe will be shorter than 18.9 feet tall is less than -0.1.
f. The 80th percentile represents the value below which 80% of the data falls.
a. The distribution of X is a normal distribution (or Gaussian distribution) with a mean of 19 feet and a standard deviation of 1 foot. This can be denoted as X ~ N(19, 1).
b. The median of a normal distribution is equal to its mean.
c. To find the Z-score for a giraffe that is 22 feet tall, we can use the formula: Z = (X - μ) / σ, where X is the observed value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get Z = (22 - 19) / 1 = 3.
d. To find the probability that a randomly selected giraffe will be shorter than 18.9 feet tall, we need to calculate the area under the normal curve to the left of 18.9. This can be done using the Z-score and a standard normal distribution table or a calculator.
Alternatively, we can use the Z-score formula from the previous question. The Z-score for 18.9 feet can be calculated as Z = (18.9 - 19) / 1 = -0.1. We can then look up the corresponding probability in the standard normal distribution table or use a calculator to find the probability that Z is less than -0.1.
e. To find the probability that a randomly selected giraffe will be between 18.6 and 19.5 feet tall, we need to calculate the area under the normal curve between these two values.
Again, we can use the Z-score formula to standardize the values and then find the corresponding probabilities using a standard normal distribution table or a calculator.
f. To find the height at the 80th percentile, we can use the standard normal distribution table or a calculator to find the Z-score that corresponds to the 80th percentile.
Once we have the Z-score, we can use the formula Z = (X - μ) / σ to solve for X. Rearranging the formula, we have X = Z * σ + μ. Plugging in the values for Z (obtained from the percentile) and μ (mean) and σ (standard deviation), we can calculate the height at the 80th percentile.
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PLS HELP WILL GIVE BRAINLIEST IF ANSWER IS CORRECT (NO LINKS )
Find the measure of arc GW.
Answer:c
Step-by-step explanation:
Can some please help me I don’t understand this?
Please due tmr morning thanks!
The numbers to complete the pythagorean triple in the equation (n² - 1)² + k² = (n² + 1)² are B. 35 and 37
What is the pythagorean triple?A pythagorean triple is a set of 3 numbers that obey the pythagorean theorem.
Given the equation
(n² - 1)² + k² = (n² + 1)², we need to find the remaining numbers generated by the equation when k = 12. So, we proceed as follows/
Since we have the equation
(n² - 1)² + k² = (n² + 1)²
Subtracting (n² + 1)², from both sides, we have that
(n² - 1)² - (n² + 1)² + k² = (n² + 1)² - (n² + 1)²
(n² - 1)² - (n² + 1)² + k² = 0
Now, subtracting k from both sides, we have that
(n² - 1)² - (n² + 1)² + k² = 0
(n² - 1)² - (n² + 1)² + k² - k² = 0 - k²
(n² - 1)² - (n² + 1)² + 0 = - k²
(n² - 1)² - (n² + 1)² = - k²
Using the difference of two squares a² - b² = (a + b)(a - b)
(n² - 1)² - (n² + 1)² = - k²
(n² - 1 + n² + 1)[n² - 1 - (n² + 1)] = - k²
(n² + n² - 1 + 1)[n² - n² - 1 - 1)] = - k²
(2n² + 0)[0 - 2)] = - k²
(2n²)(- 2) = - k²
-4n² = - k²
4n² = k²
n² = k²/4
Taking square root of both sides, we have that
n = √(k²/4)
n = k/2
Since k = 12, we have that
n = 12/2
n = 6
So, the first number is (n² - 1) = (6² - 1)
= 36 - 1
= 35
The second number is (n² + 1) = (6² + 1)
= 36 + 1
= 37
So, the numbers are B. 35 and 37
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