The measure of the largest angle of the triangle is 93°, while the measure of the smallest and the third angle is 31° and 56° respectively. Considering that the measure of the third angle is 25 degrees more than that of the smallest angle.
Sum of interior angles of a triangleIn any given triangle, the sum of its interior angles is equal to 180°.
Let the smallest angle be represented by x, so that the other angles are 3x and x + 25.
thus
x + 3x + x + 25 = 180° {collect like terms}
5x + 25° = 180°
5x + 25° - 25° = 180° - 25° {subtract 25° from both sides of the equation}
5x = 155°
x = 155°/5 {divide through by the coefficient of x}
x = 31°
thus the other angles are derived by substituting the value 31° for x as follows;
3(31) = 93°
31° + 25° = 56°
Therefore, the largest angle of the triangle 93°, the smallest angle is 31° and the measure of the third angle is 56°.
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An icicle that is 12 mm long melts at a constant rate of 1.2 mm per minute. Let t represent the number of minutes since the icicle started melthing and suppose R is a function such that R(t) represents the remaining length of the icicle (in mm) t minutes after it started melting.
A.Write a function formula for R in terms of t.
b.What is the domain of R relative to this context? Enter your answer as an interval.
c.What is the range of R relative to this context? Enter your answer as an interval.
d.What is the domain of R−1 relative to this context? Enter your answer as an interval.
e.What is the range of R−1 relative to this context? Enter your answer as an interval.
f.Solve R(t)=6.6 for t.
t= g.What does your solution in part (f) represent in this context? Select all that apply.
How long it takes for the icicle to melt completely.
How many minutes since the icicle started melting when it is 6.6 mm long.
The length of the icicle (in mm) 6.6 minutes after it started melting.
R(t)=6.6 for t, 5 minutes, the domain of R relative to this context [0, 65 ÷ 6], the range of R related to this context, the domain of R relative to this context, [0, 12], and the range of R relative to this context.
The values of variables, domain, and range:
a) 12 - 1.2t, Using the build equation.
b) Least length = 0 mm.
max time = 12 - 1.2t = 0
t = 65 ÷ 6 minutes.
domain t ∈ [0, 65 ÷ 6]
c) range, R ∈ [0, 12]
d) domain of [tex]R^{-1}[/tex] [0, 12]
e) domain of [tex]R^{-1}[/tex] [0, 65 ÷ 6]
f) 12 - 1.2t = 7
1.2t = 7
t = 5
R(t)=6.6 for t, 5 minutes.
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What is the slope of a line perpendicular to the line whose equation is 3x+18y=1083x+18y=108.
The slope of a line perpendicular to the given equation of line is 6.
Explain the term slope of the line?A line's slope is how steeply it slopes from LEFT toward RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. No matter which two locations here on line you choose, the slope of this line will always be constant (it never varies).For the stated question, the equation of the line is given as;
3x + 18y = 10
This can be written as;
y = -3/18 x + 10/18
y = -1/6 x + 5/9
Comparing with general equation of line in slope intercept form.
y = mx + c
slope m = -1/6
The relation of slope for the two perpendicular lines are-
m x m1 = -1
m1 = -1/(-1/6)
m1 = 6
Thus, the slope of a line perpendicular to the given equation of line is 6.
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Students filled 6 rows in Level 1 of Section A and 3 rows in Level 3 of Section B.
How many students were seated in the auditorium?
Number of Seats Per Row in the Auditorium
Section Level 1 Level 2 Level 3
A 9 12 14
B 12 16 18
Which steps are used to solve this problem? Select all that apply.
A.
Find how many seats are in each of the rows where the students are sitting.
B.
Add 6 and 3 to find the number of rows that are filled in all.
C.
Add 9 and 18 to find the number of seats that are filled in each row.
D.
Multiply 6 and 9 to find the number of students seated in Section A.
E.
Multiply 3 and 18 to find the number of students seated in Section B.
F.
Multiply 9 and 27 to find the number of students seated in the auditorium
As per the unitary method, the number of students in the auditorium is 108
Unitary method.
In algebra, the process of finding the value of a single unit, and based on this value is known as unitary method.
Given,
Students filled 6 rows in Level 1 of Section A and 3 rows in Level 3 of Section B.
Here we need to find the number of students were seated in the auditorium.
As per the given table, in level 1, the total number of rows in A section is 9.
So, the number of students is
=> 9 x 6
=> 54
Similarly, there are 3 rows in Level 3 of Section B.
So, the number of students in the level 2,
=> 3 x 18
=> 54
Therefore, the total number of students is,
=> 54 + 54 = 108
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Solve the proportion
Answer:
Step-by-step explanation:
98
Answer:
8
Step-by-step explanation:
if measurements are made on four different days, find the level ll such that there is probability only 0.03 that the mean glucose level of four test results falls above all for sheila's glucose level distribution. what is the value of ll?
The probability of having L greater than Shelia's mean glucose level is 0.03 for L = 144.48.
Sheila's glucose level is shown to have a normal distribution, with a mean of 128 mg/dl and a standard deviation of 8 mg/dl.
L represents the patient's blood test level.
The probability that the mean glucose level, 128 mg/dl, is greater than L is given as 0.03.
To find L,
P(128>L) = 0.03
= 1 - P(128 ≤ L) = 0.03
=P(128 ≤ L) = 0.98
We know that we can find the probability of any normal distribution by converting it to standard form and then checking the p-value.
P(X < x) = Φ[(x - μ)/σ]
μ = mean
σ = standard deviation
=Φ[(L - 128)/8] = 0.98
Therefore ,
(L - 128)/8 = 2.06
= L - 128 = 16.48
= L = 128 + 16.48
= 144.48
= L
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assume three dictionaries are assigned to the variables, canadian capitals, mexican capitals, and us capitals. these dictionaries map provinces or states to their respective capitals. write code that creates a new dictionary that combines these three dictionaries, and associate it with a variable named nafta capitals.
The code is written in nafta capital python.
canadian_capitals = {"Alberta":"Edmonton", "British Columbia":"Victoria", "Manitoba":"Winnipeg"} ( I created the first dictionary with the variable name called canadian_capital. Notice the province of Canada is mapped to to their respective capitals.)
mexica_capitals ={"Aguascalientes":"Aguascalientes", "Baja California":"Mexicali", "Baja California Sur":"La Paz"} ( I created the second dictionary with the variable name called mexican_capital. The states are also mapped to their respective capitals.)
us_capitals ={"Alabama":"Montgomery", "Alaska":"Juneau", "Arizona":"Phoenix"} ( I created the third dictionary with the variable name called us_capital. The states are also mapped to their respective capitals.)
nafta_capitals = {} (This is an empty dictionary with the variable name nafta_capitals to combine the 3 dictionaries.)
nafta_capitals.update(canadian_capitals) (I updated the empty dictionary with the canadian_capitals dictionary.)
nafta_capitals.update(mexica_capitals) (I also added the mexica_capitals dictionary to the nafta_capitals dictionary.)
nafta_capitals.update(us_capitals) I also added the us_capitals dictionary to the nafta_capitals dictionary.
print(nafta_capitals) ( The whole 3 dictionaries have been combined to form the nafta_capitals dictionary. The print function displays the already combine dictionaries.)
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Determine the area under the standard normal curve that lies to the left of (a) Z=-1.66, (b) Z= -0.03, (c) Z=-0.26, and (d) Z=1.08.
The area to the left of Z= -1.66 is__
(Round to four decimal places as needed.)
Answer:
is 364
Step-by-step explanation:
A compound is made up of various elements totaling 120 ounces. If the total amount of copper in the
compound weighs 6 ounces, what percent of the compound is made up of copper?
Answer: 5%
Step-by-step explanation:
To find the percentage you put the part over the whole so in this case it would be 6/120 or 6÷120
pop that into a calculator and you get 0.05 or [tex]\frac{5}{100}[/tex] or 5%
Hope that helps
help, please brainlest and points if right
Answer:
C
Step-by-step explanation:
yeah I think it's c there's 35% it's C
find a parametric representation using spherical-like coordinates for the upper half of the ellipsoid 4x2 8x 9 y2 36(z 1)2
A parametric representation using spherical-like coordinates for the upper half of the ellipsoid is given by x2 = 9 + -2.25y2 + 0.25z2.
What is ellipsoid?
A sphere can be deformed into an ellipsoid by applying directional scalings, or more generally, an affine transformation, to it.
A quadric surface, or surface that can be described as the zero set of a polynomial of degree two in three variables, is an ellipsoid. An ellipsoid among quadric surfaces has one of the two characteristics listed below. Every cross section of a flat surface is either an ellipse, empty, or reduced to a single point (this explains the name, meaning "ellipse-like"). It can be contained in a sphere that is big enough because it is bounded.
Three pairwise perpendicular axes of symmetry intersect at an ellipsoid's center of symmetry, or the
According to our question-
To each side of the equation, add "-9y2".
4x2 + 9y2 + -9y2 + -1z2 = 36 + -9y2
combining similar terms 9y2 + -9y2 = 0
4x2 + 0 + -1z2 = 36 + -9y2
4x2 + -1z2 = 36 + -9y2
To either side of the equation, add "z2".
4x2 + -1z2 + z2 = 36 + -9y2 + z2
Hence, A parametric representation using spherical-like coordinates for the upper half of the ellipsoid is given by x2 = 9 + -2.25y2 + 0.25z2.
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Sam and ben are grading english tests. Sam grades 6 tests in 24 minutes and ben grades 5 tests in 20 minutes. At these rates, what is the total number of tests they can grade in 3 hours? enter the answer in the box.
The total number of tests they can grade in 3 hours are 90.
What is graded test?
Your grade in an exam or written assignment is the letter or number you receive as a mark that represents your level of proficiency.
A graded exercise test (GXT) is a screening tool for determining a person's level of fitness. The test measures the cardiovascular response to exercise in order to assess the participant's capacity for exercise.
Since, the number of minutes in 3 hours is:
= 3 x 60 minutes per hour
= 3 x 60
= 180 minutes
The number of tests that Sam can grade in these 3 hours is therefore:
= ( Number of total minutes / Minutes taken by Sam for 6 tests) x 6 tests
= ( 180 / 24) x 6
= 45 tests
The number of tests that Ben can grade are:
= ( Number of total minutes / Minutes taken by Ben for 5 tests) x 5 tests
= ( 180 / 20 ) x 5
= 45 tests
So, the total number of tests they can grade in 3 hours is:
= 45 + 45
= 90 tests
Hence, the total number of tests they can grade in 3 hours are 90.
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The graph shows the relationship between x and y-values. Find the value of m.
The line has a slope with a measure of 8 / 5.
How to determine the slope of a line
According to Euclidean geometry, lines can be constructed by knowing the location of two distinct points on a plane. By analytic geometry we can determined the slope of the line by knowing these two points and using the secant line formula:
m = Δy / Δx
Where:
m - Slope of the lineΔx - Change in the horizontal axis.Δy - Change in the vertical axis.If we know that (x₁, y₁) = (- 2, - 5) and (x₂, y₂) = (2, 3), then the slope of the line shown in the picture is:
m = [3 - (- 5)] / [3 - (- 2)]
m = 8 / 5
The slope of the line is equal of 8 / 5.
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the measures of a pair of supplementary angles are in the ratio of $7:2$. how many degrees are in the measure of their positive difference?
Answer:
100°
Step-by-step explanation:
You have two supplementary angles in the ratio 7:2, and you want the measure of their positive difference.
Ratio unitsThe sum of supplementary angles is 180°. The sum of the ratio units in the ratio 7:2 is 7+2 = 9, so each ratio unit must stand for 180°/9 = 20°.
The difference in ratio units is 7 -2 = 5, so the difference in the angles will be 5·20° = 100°.
The measure of their difference is 100°.
__
Additional comment
The two angles are 7·20° = 140°, and 2·20° = 40°. The difference is 140° -40° = 100°.
The inequality -4x + 1 > y describes which of the following graphs?
the price for bananas was 75 cents per pound over last month. today, we see that it's been marked up to 81 cents per pound. what is the increase in percent
When bananas cost 75 cents per pound over the previous month, the increase was 8%. Today, we notice that the price per pound has increased to 81 cents.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Here,
The solution is attached in image.
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2x-10
factor out........
Answer:
2 x-5
Step-by-step explanation:
find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius cm. what is the maximum volume?
The dimensions of a right circular cylinder of maximum volume are
[tex]5\sqrt{6}[/tex] and [tex]10\sqrt{3}[/tex].
Given the radius of sphere is 15 cm.
Let's assume radius of right circular cylinder = r
height of right circular cylinder = h.
Since the cylinder is inscribed in the sphere, their centers will coincide. As a result, the height is divided into two equal portions from the sphere's center. Therefore, we can apply Pythagoras' Theorem to get the cylinder's half-height in terms of radius.
[tex]R^2 = r^2 + (h/2)^2[/tex].
[tex]r^2=R^2-h^2/4[/tex]
Volume of cylinder = [tex]\pi r^2h[/tex]
Now we can substitute value of [tex]r^2[/tex] in volume of cylinder.
V = π*([tex]R^2[/tex] - [tex]h^2[/tex]/4)*h
taking R = 15 .
V = π*(225 - [tex]h^2[/tex]/4)*h
V = π*225*h - π*[tex]h^3[/tex]/4
For maximum volume we have to do derivative of volume = 0
derivative with respect to h.
V' = π*225 - 3*π[tex]h^2[/tex]/4
V' = 0
π*225 - 3*π[tex]h^2[/tex]/4 = 0
3*[tex]h^2[/tex]/4 = 225
[tex]h^2[/tex] = 75*4
h = [tex]10\sqrt{3}[/tex]
put the value of h in [tex]r^2=R^2-h^2/4[/tex]
[tex]r^2[/tex] = 225 - (300/4)
[tex]r^2[/tex] = 150
r = [tex]5\sqrt{6}[/tex]
Given Question is incomplete, Complete Question here
find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 15 cm. what is the maximum volume?
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powerball is played with 59 white balls, numbered 1 through 59, and 35 red balls, numbered 1 through 35. five white balls and one red ball, the powerball, are drawn. in how many ways can a player select the six numbers?
The total ways of selecting 6 numbers in 175223510 Ways.
What is Permutation?A permutation is an grouping or the combination of items that is drawn from a set of which the placement or an arrangement of the given objects is significant. In the other terms, an arrangement of the items in the specific order is a permutation.
Total number of White balls = 59
Total number of red balls = 35
Way of choosing 5 white balls = ⁵⁹C₅
= [tex]\frac{59!}{54! 5!}[/tex]
=5006386 ways
Way of choosing 1 red ball = ³⁵C₁
=35 ways
Hence Total ways would be =
5006386 * 35 = 175223510 Ways
Hence the total ways of selecting 6 numbers in 175223510 Ways.
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joan, compliance officer at xyz hospital, explains to the hospital board that in 2003 a provision was added to emtala that stated that there is a yard zone that continues to apply when defining the hospital campus. how many yards are included in this zone? a. 500 b. 100 c. 200 d. 250
The stated zone in EMTALA in 2003 when defining a hospital campus is d. 250 yards
What is EMTALA?
EMTALA stands for Emergency Medical Treatment & Labor Act. It is passed by the US Congress in 1986 to ensure public access to emergency services regardless of ability to pay.
2003 revision of EMTALA provides that the 250-yard zone will continue to apply when defining the "hospital campus". However, that sphere does not include non-medical businesses (shops and restaurants located close to the hospital), nor does it include physicians' offices or other medical entities that have a separate Medicare identity.
Hence, the correct answer is d. 250 yards.
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what will happen (other things being equal) if you decrease the confidence level for a given confidence interval?
The breadth of the confidence interval grows as the confidence level does. The breadth of the confidence interval reduces as the confidence level rises.
Generally speaking, the more information we know on the level of the population parameter, the narrower a confidence interval becomes. As a result, we want to make sure that all of the confidence intervals are as small as feasible. So let's look at the variables that influence the mean's t-interval width.
The margin of error grows as the degree of confidence does because we require a broader interval to improve our level of confidence that the interval includes the population mean.
Because the standard error is reduced as sample size increases, confidence intervals are narrower.
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The rule for a pattern is "star, square, triangle, circle." What is the 13th shape in this pattern?
Answer:
star
Step-by-step explanation:
if you continue the pattern, the 13th is star
what is the probability that headway is within 1 standard deviation of the mean value? (round your answer to three decimal places.)
There is a 0.890 percent chance that headway will be within one standard deviation of the mean.
The mean value is what?
The mean, or average of the given numbers, is calculated by dividing the sum of the numbers by the total number of numbers.
The sum of all possible values, weighted by the likelihood of each value, constitutes the mean of a discrete probability distribution of the random variable X. Each possible value of X must be multiplied by its probability, P(x), before being added to determine the mean.
P(0.995 ≤ x ≤ 1.445) = F(1.445) - F is the given mean value (0.995).
The distribution's cdf is
f(x) = { (1 - 1/x⁶ , x > 1) (0. x ≤ 1)
Determine the values of F(1.445) and F now (0.995).
F(1.445) = 1 - (1/(1.445)⁶)
F(0.995) = 0
Now, using the values of F(1.445) and F(0.995) in P( 0.995 ≤ x ≤ 1.445) to get F(1.445) - F(0.995):
P( 0.995 ≤ x ≤ 1.445)
=1 - (1/(1.445)⁶) - 0
=0.890
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How do you find the unit rate of a number
mr. goodman sets a goal to outscore these numbers. at the end of the year he takes a random sample of his evaluations and finds 10 1's, 13 2's, 48 3's, and 52 4's. at the 0.05 level of significance, can mr. goodman claim that his evaluations are significantly different than the history department's?
No as their no difference in Mr. Goodman's evaluation and the History department
What is Statistics ?
The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.
descriptive statistics types in mathematics The data in this type of statistics is summarized using the provided observations. Statistics that are inferential. To interpret the meaning of descriptive statistics, this kind of statistics is employed. Example of Statistics.
Seeing the data we can conclude that their no difference in Mr. Goodman's evaluation and the History department
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Michelle used a \$20$20dollar sign, 20 bill to pay for a notebook that only costs ppp dollars. How much change did michelle receive from the cashier? write your answer as an expression.
The expression that represents the change that the cashier handed Michelle is $20 - $P.
What do we mean by expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
A collection of numbers, symbols, and operators (like + and ) that represent a value.
Examples: The phrase 2 + 3 is one.
We must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.
So, Michelle purchased a notepad for P dollars with $20 cash.
Now, considering that Michelle paid P dollars for a notepad using a $20 bill.
As a result, the cashier gave Michelle $20 - $P.
Therefore, the expression that represents the change that the cashier handed Michelle is $20 - $P.
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Correct question:
Michelle used a $20 bill to pay for a notebook that only costs P dollars
How much change did Michelle receive from the cashier?
Write your answer as an expression.
a super happy fun ball is dropped from a height of 6 feet and rebounds 10 11 of the distance from which it fell.
The ball will need to travel 126 feet since it will be dropped from a height of 6 feet and then bounce 10/11 feet.
What is division?A number is split in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of things being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
Here,
2*{6/(1-10/11)}-6
2*(6/1/11)-6
2*6*11-6
required distance=126 feet
The required distance will be 126 feet as the ball is dropped from 6 feet and rebounds 10/11 of the distance.
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In a Survey of a group of students, it was found that 35% of the student likes mathematics, 30% of student Like account and 600 student like both of them and 5%. Like none of them.
Answer:
Explanation: The idea is to draw a Venn Diagram and find the intersection. We have one circle of 70 and another with 40. When we add the two circles plus the 10 students who joined neither, we should get 100 students.
Step-by-step explanation:
A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume the scenario can be modeled with right triangles. At what rate is the length of the person's shadow changing when the person is 16 ft from the lamppost?
In similar triangles, both the two triangles must satisfy the two properties. One is the side proportional, and the other is equal in angles. There are three criteria in similarity. They are AA similarity, SSS similarity, and SAS similarity. The below one satisfies the AA similarity.
The length of the shadow is changing rate at 2.69 [tex]\frac{ft}{sec}[/tex].
What do you mean by length?
The measurement or size of something from end to end is referred to as its length. To put it another way, it is the greater of the higher two or three dimensions of a geometric shape or object. For instance, the length and width of a rectangle define its dimensions.
According to data in the given question,
We have the given information:
The height of the person is 7 ft.
The person is walking away from the post at a rate of 5ft/sec.
The height of the lamppost is 20ft.
Let the person's distance from the bottom of the light post be x ft.
And his shadow's length is y ft.
Form the similar triangles,
[tex]\frac{x+y}{20}=\frac{y}{7}\\[/tex]
7(x+y) = 20y
7x+7y = 20y
20y-7y = 7x
13y = 7x
y = [tex]\frac{7}{13}x[/tex]
Now, we will differentiating wrt t,
[tex]\frac{dy}{dt}=\frac{7}{13}\frac{dx}{dt}................(1)[/tex]
We know that,
[tex]\frac{dx}{dt}=5\frac{ft}{sec}[/tex]
Putting the value of [tex]\frac{dx}{dt}[/tex] in equation (1),
[tex]\frac{dy}{dt}=\frac{7}{13}.5=\frac{35}{13}=2.69\frac{ft}{sec}[/tex]
Therefore, the length of the shadow is changing rate at 2.69 [tex]\frac{ft}{sec}[/tex].
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Which term bet describes the force on an object with a net force is zero
Answer:
If the net force on an object is zero, then the object is in equilibrium. It means the sum of the forces in all directions must be equal to zero.
Answer: equilibrium
Step-by-step explanation: When an object is in equilibrium (either at rest or moving with constant velocity), the net force acting on it zero.
ANSWER QUICK
This scatter plot shows the height of 8 children and their age.
Based on the information in the scatter plot, what is the best prediction for the height of a 5 year old child?
Responses
25 inches
25 inches
35 inches
35 inches
45 inches
45 inches
55 inches
Answer:
it is actually 35
Step-by-step explanation:
This is because the plot is accelerating not decreasing also like if you think peter griffin is in! EPIC