Answer: To end up due north, the pilot will need to fly the plane 3.382 degrees east of north.
Step-by-step explanation:
don't know how to explain got it form chegg
Non mutually exclusive events !
The missing probability is P(A or B) = 131/200
How to calculate the probabilityIt should be noted that in order to find the probability of the union of two events A and B, i.e., P(A or B), we can use the following formula:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = P(A) + P(B) - P(A and B) = (9/20) + (1/4) - (9/200)
Simplifying the expression, we get:
P(A or B) = 45/100 + 25/100 - 9/200 = (90+50-9)/200 = 131/200
The probability is 131 / 200.
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Solve for x. Round to the nearest tenth, if necessary.
The calculated value of x in the right triangle is 8.7
Calculating the value of x in the right triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The value of x in the right triangle can be calculated using the following sine ratio
sin(75) = x/9
Cross multiply the equation
So, we have
x = 9 * sin(75)
Evaluate the products
x = 8.7
Hence, the value of x in the right triangle is 8.7
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Water flows from the bottom of a storage tank. After t minutes, the amount of water in the tank is
R(t)=8000-250t + 2t² liters, where 0 ≤ t ≤ 50. Find the amount of water (in liters) that flows from the tank
between the 14 minute mark and the 34 minute mark.
So, 3,280 liters of water flows from the tank between the 14 minute mark and the 34 minute mark.
What is function?In mathematics, a function is a rule or relationship that assigns a unique output or value for each input or value in its domain. In other words, a function is a mathematical object that takes an input value and produces a corresponding output value. Functions are commonly denoted by f(x), where x represents the input value, and f(x) represents the corresponding output value.
Here,
To find the amount of water that flows from the tank between the 14 minute mark and the 34 minute mark, we need to find the difference between the amount of water at the 14 minute mark and the amount of water at the 34 minute mark. At the 14 minute mark, t = 14, so we can substitute this value into the equation to get:
R(14) = 8000 - 250(14) + 2(14)²
R(14) = 5,720 liters
At the 34 minute mark, t = 34, so we can substitute this value into the equation to get:
R(34) = 8000 - 250(34) + 2(34)²
R(34) = 2,440 liters
Therefore, the amount of water that flows from the tank between the 14 minute mark and the 34 minute mark is:
R(14) - R(34) = 5,720 - 2,440
R(14) - R(34) = 3,280 liters
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You buy tomatoes in 25 pounds cases. One portion of salad requires.75 ounces of tomatoes. How many portions can be made with one case
Answer: 5.3 repeated portions or about 5 portions
Step-by-step explanation: 25 pounds = 400 ounces
400/75 = 5.3 repeated
Answer:33
Step-by-step explanation:
If a cylinder has a height of 5 inches and a radius of 3 inches, which equation can be used to find V, the volume of the cylinder in cubic inches?
The equation to find the volume of the cylinder is: V = 45π cubic inches.
What is cubic inches?The volume of things or containers is often measured in cubic inches in the United States. It is the amount of area that a cube with one inch sides takes up. A cubic inch is about equal to 16.387 millilitres or 0.016387064 litres. The displacement of an engine—a measurement of the total amount of air and fuel the engine can compress into its cylinders—is frequently discussed in terms of cubic inches.
According to given information:The formula to find the volume of a cylinder is:
V = πr²h
Where V is the volume, r is the radius, and h is the height.
Substituting the values given in the problem, we get:
V = π(3²)(5)
V = π(9)(5)
V = 45π
Therefore, the equation to find the volume of the cylinder is:
V = 45π cubic inches.
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PLS I NEED HELP WITH THIS I WILL MARK YOU AS THE BRAINLIEST!!
Answer:
linearlinearquadraticexponentialStep-by-step explanation:
You want to classify the functions shown in the tables as linear, quadratic, or exponential.
DifferencesWe notice all of the tables have x-values that are evenly spaced. this means we can look at the differences between y-values to determine the kind of function the table represents.
The differences have the following interpretation:
differences are constant — lineardifferences have a constant difference — quadraticdifferences (and terms) have a constant ratio — exponential5, 3, 1, ...The differences of y-terms are constant at 3 -5 = -2.
The function is linear.
2, 5, 8, ...The differences of y-terms are constant at 5 -2 = 3.
The function is linear.
5, 1, 5, ...We observe that the y-values have a minimum. We don't need to take differences to know this is not linear or exponential. Of the offered choices, the only one that makes sense is "quadratic."
The differences of y-terms are ...
1 -5 = -4, 5 -1 = 4, 17 -5 = 12, 37 -17 = 20
The differences of differences are ...
4 -(-4) = 8, 12 -4 = 8, 20 -12 = 8
The second differences are constant.
The function is quadratic.
1, 3, 9, ...The first differences are ...
3 -1 = 2, 9 -3 = 6, 27 -9 = 18, 81 -27 = 54
The second differences are
6 -2 = 4, 18 -6 = 12, 54 -18 = 36
We note that the first and second differences are not constant, but the ratio of terms at every level is 3/1 = 6/2 = 12/4 = 3.
The function is exponential.
You are running a fundraiser for your school, selling Reese’s and Skittles candies. You recorded you sold 34 candies and made $41, but didn’t tally how many of each candy you sold (and you don't remember the original amount of candy you had).
Below is the advertisement you used to sell the candy:
Reese's sells for $1 and skittles for $1.50
Write a system of equations to represent this situation. Then, solve it algebraically using either the substitution or elimination method.
Reese sold 20 candy and Skittles sold 14 candy for a total of $41. The equation for this is x + y = 34 and x + 1.5y = 41
What is an equation?An exponential equation is an expression that shows how numbers and variables using mathematical operators.
Let x represent the number of candy that Reese sell and y represent the number of Skittles candies
Reese's sells for $1 and skittles for $1.50
34 candies was sold, hence:
x + y = 34 (1)
He made $41, hence:
x + 1.5y = 41 (2)
Solving both equations simultaneously:
x = 20; y = 14
Reese had 20 candy and Skittles had 14 candy.
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A circle is represented by the equation (x + 6)2 + (y − 3)2= 121.
Which of the following statements is true?
Group of answer choices
The circle is centered at (−6, 3) and has a radius of 11.
The circle is centered at (−6, 3) and has a diameter of 11.
The circle is centered at (6, −3) and has a diameter of 11.
The circle is centered at (6, −3) and has a radius of 11.
The statement that is true about the given circle equation is:
Option A: The circle is centered at (−6, 3) and has a radius of 11.
How to find the equation of a circle?The standard form for finding the equation of a circle is given by the expression:
(x - h)² + (y - k)² = r²
where:
(h, k) represents the coordinates of the center of circle
r represents the radius of the circle
We are given the equation of the circle as:
(x - 6)² + (y - 3)² = 121
Now, 121 can also be written as 11². Thus, the equation of the circle can be rewritten as:
(x - 6)² + (y - 3)² = 11²
Comparing with the standard form of equation of a circle gives:
Coordinates of center = (-6, 3)
Radius = 11
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what is 2x multiplied by 7 with the exponent of 4
The simplified expression of 2x multiplied by 7 with the exponent of 4 is 4,802x.
What is the simplification of the expression?
The expression is simplified by applying the rules of multiplication and exponent rules.
the expression = 2x(7⁴)
simplify 7⁴ as follows = 7 x 7 x 7 x 7 = 2,401
Multiply the resultant solution of 2,401 as follows;
= 2,401 x (2x)
= 4,802x
Thus, the simplified expression of 2x multiplied by 7 with the exponent of 4 is determined by applying basis rules of multiplication.
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The mass of 12 packets of flour and 8 packets of salt is 19 kg. When 7 packets of flour are removed, the mass became 9.9 kg. Find the mass of each packet of salt in kilogram.
Answer:
1.235 kg
Step-by-step explanation:
Let's assume that each packet of flour and salt weighs the same.
When we remove 7 packets of flour, we are left with 5 packets of flour and 8 packets of salt. The total number of packets is 13 and their total mass is 9.9 kg.
Therefore, the average mass of each packet is 9.9 kg ÷ 13 = 0.76 kg.
Since we know that 12 packets of flour and 8 packets of salt have a total mass of 19 kg, we can subtract the mass of the 12 packets of flour (12 × 0.76 kg = 9.12 kg) from the total mass to find the mass of the 8 packets of salt:
19 kg - 9.12 kg = 9.88 kg
Finally, we can divide the mass of the 8 packets of salt by the number of packets to find the mass of each packet:
9.88 kg ÷ 8 = 1.235 kg
Therefore, each packet of salt weighs approximately 1.235 kg.
Given cards with the letters A, B,
C, and D, how many different
orders can you place the four
cards?
In each diagram, one square unit represents 10 square centimeters. Find the area of each figure. Round to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
its 7th grade math PLEASE HELP EMERGENCY
An example of a function that models a linear relationship between two quantities, x and y is y = mx + b
How to explain the functionWe need to use the equation of a straight line, which is commonly expressed in slope-intercept form as:
y = mx + b
In this function, x represents the independent variable, m is the slope of the line, and b is the y-intercept. To use this function, we simply plug in the values of x, m, and b that correspond to the specific relationship we are modeling.
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4Construct a function to model a linear relationship between two quantities.
The simplest form of log5+log6-log2
The simplest form of log5+log6-log2 is: log15.
What is the simplest form?Let us simplify log5 + log6 - log2 by making use logarithmic rules:
log a + log b = log (ab)
log a - log b = log (a/b)
So,
log5 + log6 - log2
= log (5 x 6) - log2
= log30 - log2
Now let make use of the logarithmic rule:
log a - log b = log (a/b) = log a - log b
log30 - log2
= log (30/2)
= log15
Therefore the simplest form is log15.
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Cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9 and then divided the result by 3, giving an answer of 43. What would her answer have been if she had worked the problem correctly?
Using mathematical operations, Cindy's answer would have been 15 if she had worked the problem correctly by following her teacher's instructions.
How is the correct value determined?The correct value can be determined by reversing Cindy's calculations to find the certain number as follows:
(x - 9) ÷ 3 = 43
x = 43 x 3 + 9
x = 138
With the certain number, x = 138, the correct mathematical operations can be performed as follows:
Correction Operation:(138 - 3) ÷ 9
135 ÷ 9
= 15
Thus, Cindy's correct answer would have been 15 if she had performed the correct mathematical operations, according to her teacher's instructions.
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Can someone help me solve this? I don’t quite understand
According to the graph, the function that best describes the graph is
[tex]f(x)=|x| = \left\{ \begin{array}{cl}x - 2 \text{ for x \lt -3 } \\8 \text{ for -3 \lt x \lt 5}\\-x + 10 \text{ for x \gt 6}\end{array} \right.[/tex]
(option d).
As we all know that the term function is defined as a rule or relationship that maps each element in one set, called the domain, to exactly one element in another set, called the range.
While we looking into the graph we have identified that there is a straight line that cross the point (0, 8) within the range of -3 to 5.
And then the next line is moves downwards from the range of x whose value is greater than 6.
Final upward slope is moves the range of -3 or less While we looking into these range value we have identified that the the function that refers the graph is (option d).
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Given the circle below with secants GHI and KJI. If JI = 4, KJ = 10 and
HI = 5, find the length of GH. Round to the nearest tenth if necessary.
Answer:
GH = 6.2
Step-by-step explanation:
Yellow light: When the light turns yellow, should you stop or go through it? A recent study of driver behavior defined the "indecision zone" as the period when
a vehicle is between 2.5 and 5.5 seconds away from an intersection. At the first intersection studied, 127 vehicles were observed to encounter a yellow light in
the indecision zone, and 24 of them ran the red light. At the second intersection, 164 vehicles entered the intersection in the indecision zone, and 29 ran the red
light. Let p denote the proportion of red light runners at the first intersection. Can you conclude that the proportion of red light runners differs between the two
intersections? Use the a=0.01 level of significance.
Answer:
Step-by-step explanation:
To test the null hypothesis that the proportion of red light runners is the same at both intersections, we can use a two-sample z-test for proportions.
Let p1 be the proportion of red light runners at the first intersection, and p2 be the proportion of red light runners at the second intersection. We want to test the null hypothesis:
H0: p1 = p2
against the alternative hypothesis:
Ha: p1 ≠ p2
We can use the following formula to calculate the test statistic:
z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))
where p_hat = (x1 + x2) / (n1 + n2) is the pooled sample proportion, and x1 and x2 are the number of red light runners at the two intersections, and n1 and n2 are the sample sizes.
For the first intersection, we have x1 = 24 and n1 = 127. For the second intersection, we have x2 = 29 and n2 = 164.
The pooled sample proportion is:
p_hat = (x1 + x2) / (n1 + n2) = (24 + 29) / (127 + 164) = 0.167
The test statistic is:
z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2)) = (0.189 - 0.177) / sqrt(0.167 * (1 - 0.167) * (1/127 + 1/164)) = 0.99
Using a standard normal distribution table, we can find that the probability of getting a z-value of 0.99 or greater is 0.160. Since this is greater than the significance level of 0.01, we fail to reject the null hypothesis.
Therefore, we cannot conclude that the proportion of red light runners differs between the two intersections.
(PLEASE ANSWER BOTH)
1. What is the value of Angle X?
2. How do you know (What type of angle pairs are they)?
Answer:
angle x is 160
Step-by-step explanation:
180 - 20
area of traingle is what if square root 6 in height iand base is square root 24
The area of the triangle that has height of √6 and a base of √24 is calculated as: 6 square units.
How to Find the Area of a Triangle?The area of a triangle = 1/2 * b * h, where:
h is the height of the triangle, and
b is the base length of the triangle.
Given the following:
Height of triangle = √6
Base length of the triangle = √24
Plug in the values:
Area of triangle = 1/2 * √24 * √6
= (√24 * √6) / 2
= √144 / 2
= 12/2
Area of triangle = 6 square units.
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If the prism on top of the figure was 4 inches tall instead of 3 inches tall, what would be
the difference between the volume of the original prism on top and the new prism on
top?
Answer:
L * W
Step-by-step explanation:
To find the difference in volume between the original prism and the new prism, we need to calculate the volume of each prism and then subtract the volumes.
Let's assume the base of the prism is a rectangle with length L, width W, and height H.
The volume of a prism is given by V = L * W * H.
Original Prism:
Height = 3 inches
Volume = L * W * 3
New Prism:
Height = 4 inches
Volume = L * W * 4
The difference in volume between the original prism and the new prism is:
New Prism Volume - Original Prism Volume = (L * W * 4) - (L * W * 3)
= L * W * (4 - 3)
= L * W
Therefore, the difference in volume is L * W.
Since we do not have specific dimensions or values for L and W, we cannot calculate the exact difference in volume. We would need additional information to determine the values of L and W or their relationship to find the difference in volume.
Pyramid A and Pyramid B are similar. Pyramid A has a volume of 648m° and Pyramid B has a volume of 1029m?. What is the ratio of the surface areas of Pyramid A to Pyramid B?
The ratio of the surface area of Pyramid A to Pyramid B is: 36/49
We have the information from the question is:
Pyramid A and Pyramid B are similar.
The volume of Pyramid A is 648 [tex]m^3[/tex]
The volume of Pyramid B is 1029 [tex]m^3[/tex]
To find the ratio of the surface areas of Pyramid A to Pyramid B.
Now, As we know that:
If two solids are similar, then the ratio of their volumes is equal to the cube
of the ratio of their corresponding linear measures.
[tex]\frac{Vol of A}{Vol of B} =(\frac{a}{b} )^3 =\frac{684}{1029}=\frac{216}{343}\\ \\ \frac{a}{b}=\frac{6}{7}[/tex]
If two solids are similar, then the n ratio of their surface areas is equal to the square of the ratio of their corresponding linear measures.
Surface area of A/ Surface area of B [tex]=(\frac{a}{b} )^2=\frac{36}{49}[/tex]
So, the ratio of the surface area of Pyramid A to Pyramid B is: 36/49
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Please help. This is geometry
∠WTA and ∠HTC are vertical angles. Thus, they are equal.
As WA || HC, that means ∠AWT and ∠THC are alternate interior angles and are equal. Additionally, ∠WAT and ∠TCH are also alternate interior angles and are equal.
∠WTA = ∠HTC, ∠AWT = ∠THC, and ∠WAT = ∠TCH
Since both triangles have the same angle measurements, they are similar.
whats the probility that she selects a non-mathamatical major, given that she choosees randomly from only sophmores From mrs. Burke's math class
The probability that Mrs. Burke selects a non-Mathematical major, given that she chooses randomly from only Sophomores is 51.5%.
What is the probability?Probability refers to the chance or likelihood of an event occurring given many possible events that could have occurred.
Probability is expressed as a quotient of the expected event or success and the total possible events, outcomes, or successes.
The number of Sophomores in Mathematics Majors = 16
The number of Sophomores in Non-Mathematics Majors = 17
The total number of Sophomores in Mrs. Burke's Mathematics Class = 33
The probability of selecting a non-Mathematical major, given that Mrs. Burke chooses randomly from only Sophomores = 51.5% (17 ÷ 33 x 100)
Mrs. Burke's Mathematics Class
Academic Year Mathematics Majors Non-Mathematics Majors Total
Freshmen 19 18 37
Sophomores 16 17 33
Juniors 11 15 26
Seniors 12 13 25
Total 58 63 121
Thus, the likelihood of choosing a non-Mathematical major from the Sophomores is 51.5%.
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Question Completion:Mrs. Burke's Mathematics Class
Academic Year Mathematics Majors Non-Mathematics Majors
Freshmen 19 18
Sophomores 16 17
Juniors 11 15
Seniors 12 13
A cone has a volume of 48 cubic feet and a height of 9 feet. find the radius.
Step-by-step explanation:
V = 1/3 x π x r² x h
48 = 1/3 x π x r² x 9
48÷3π = r²
√48÷3π =r
so, r= 2.26 (3.s.f)
Select an equivalent form of this equation: x/12 - 7 =x/4 x - 84 = 3 x x - 74 = 12 x x - 7 = 3 x
The "equivalent-form" of equation "x/12 - 7 = x/4" is "x - 84 = 3x", the correct option is (a).
In order to find the equivalent form of the equation "x/12 - 7 = x/4", we first need to solve for "x",
So, we first, simplify left side of equation by finding a common denominator for the two fractions:
⇒ x/12 - 7 = x/4,
⇒ x - 84 = 3x,
⇒ -84 = 2x,
⇒ x = -42,
Now, we check the given options by substituting the value of "x",
Option (a) : x - 84 = 3x,
Substituting x = -42,
We get,
⇒ -42 - 84 = 3(-42),
⇒ -126 = -126
This equation is true, so option (a) is an equivalent form of the original equation.
Option (b) : x - 74 = 12x,
Substituting x = -42,
We get,
⇒ -42 - 74 = 12(-42),
⇒ -116 = -504,
This equation is not true, so option (b) is not an equivalent form of the original equation.
Option (c) : x - 7 = 3x,
Substituting x = -42,
We get,
⇒ -42 - 7 = 3(-42),
⇒ -49 = -126,
This equation is not true, so option (c) is not an equivalent form of the original equation.
Therefore, the correct option is (a) .
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The given question is incomplete, the complete question is
Select an equivalent form of this equation: x/12 - 7 =x/4
(a) x - 84 = 3x
(b) x - 74 = 12x
(c) x - 7 = 3x
50 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
A. The 51st note on a piano keyboard corresponds to a pitch of 440 cycles per second.
B. The pitch that is 73 notes higher on the keyboard has a frequency of about 1760 cycles per second.
How to determine frequency?A. Use the formula to find how many notes up the piano keyboard the pitch of 440 cycles per second corresponds to:
440 = 27.5 × 2⁽ⁿ⁻¹⁾/12
Dividing both sides by 27.5 and taking the logarithm with base 2 gives:
log₂(440/27.5) = (n-1)/12
n-1 = 12 × log₂(440/27.5)
n-1 = 12 × 4.1702 ≈ 50.042
n ≈ 51.042
Therefore, the pitch of 440 cycles per second is the 51st note up the piano keyboard.
B. Use the same formula to find the frequency of the pitch that is 73 notes up the keyboard:
73 = 1 + 12 log₂(f/27.5)
72 = 12 log₂(f/27.5)
6 = log₂(f/27.5)
f/27.5 = 2⁶
f = 27.5 × 2⁶
f ≈ 1760
Therefore, the frequency of the pitch that is 73 notes up the keyboard is approximately 1760 cycles per second.
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A dot plot titled seventh grade test score. There are 0 dots above 5, 6, 7, 8 and 9, 1 dot above 10, 1 dot above 11, 2 dots above 12, 1 dot above 13, 1 dot above 14, 2 dots above 15, 3 dots above 16, 3 dots above 17, 2 dots above 18, 2 dots above 19, 3 dots above 20. A dot plot titled 5th grade test score. There are 0 dots above 5, 6, and 7, 1 dot above 8, 2 dots above 9, 10, 11, 12, and 13, 1 dot above 14, 3 dots above 15, 2 dots above 16, 1 dot above 17, 2 dots above 18, 1 dot above 19, and 1 dot above 20.
Students in 7th grade took a standardized math test that they also had taken in 5th grade. The results are shown on the dot plot, with the most recent data shown first.
Find and compare the means to the nearest tenth.
7th-grade mean:
5th-grade mean:
What is the relationship between the means?
Note that 7th grade mean = 277.86
the 5th grade mean = 254.77
So th relationship between the mean is that the 7 th grade mean is higher than the 5 th grade mean .
How is this so ?To compute the means here is what we did
7 th grade mean = (1 × 10) + (1 × 11) + (2 × 12) + (1 × 13) + (1 × 14) + (2 × 15) + (3 × 16) + (3 × 17) + (2 × 18) + (2 × 19) + (3 × 20) / 21
= 277.857142857
≈ 277.86
For the 5th grade mean
5th grade mean = (1 × 8) + (2 × 9) + (2 × 10) + (2 × 11) + (2 × 12) + (1 × 13) + (3 × 15) + (2 ×16) + (1 × 17) + (2 × 18) + (1 × 19) + (1 × 20) / 26 = 12.5
= 254.769230769
≈ 254.77
This means that trully, the relationship between the mean is that the 7 th grade mean is higher than the 5 th grade mean.
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Enter your answer by filling in the boxes to correctly complete the statements. If necessary, round to the nearest hundredth.
The practical domain of the situation is [0, ∞].
The practical range of the situation is [0, 100].
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
How to identify the domain any graph?In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [0, ∞] or 0 ≤ x ≤ ∞.
Range = [0, 100] or 0 ≤ y ≤ 100.
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Which of the points plotted is farther away from (−7, 8), and what is the distance?
A: Point (5, 8), and it is 11 units away
B: Point (5, 8), and it is 13 units away
C: Point (−7, −5), and it is 12 units away
D: Point (−7, −5), and it is 13 units away
The distance between point (−7, 8) and point (5, 8) is 12 units (since they are on the same horizontal line). The distance between point (−7, 8) and point (−7, −5) is 13 units (using the Pythagorean theorem). Therefore, the point that is farther away is option D: Point (−7, −5), and it is 13 units away.