Answers
Answer:
Starting from the one on the left.
Upper left:
145 degrees
Down left:
35 degrees
Down right:
145 degrees.
-------------
Now for the right image.
Upper left:
153 degrees
Down left:
27 degrees
Down right:
153 degrees
Step-by-step explanation:
Apply the same steps for the second image as for the first.
One thing to keep in mind is that a flat line (horizontal or vertical), as an angle of 180 degrees.
And another useful reminder is that opposed angles have the same degree.
Starting from the one on the left.
Upper left:
180 - 35 = 145 degree
Down left:
since it is opposed to the upper right angle which is 35 degrees this one is also equal to 35 degrees.
Down right:
since it is opposed to the upper left angle which is 145 degrees this one is also equal to 145 degrees.
You can always double check by making sure one flat side (left or right or up or down), is equal to 180 degrees.
example: on the right image, for the down part, I wrote as answers 27 degrees (for down left because it is opposed to upper right) and 153 degrees (for down right because it is opposed to upper left) => 153 + 27 = 180 degrees
Related Questions
Which of the of the following statements is true with respect to a simple linear regression model? a. the stronger the linear relationship between two variables, the closer the correlation coefficient will be to 1. O b. if the correlation coefficient between the x and y variables is negative, the sign on the regression slope will also be negative. O C. if the correlation coefficient between the dependent and independent variable is determined to be significant, the regression model for y given x will also be significant. O d. all of the above is true. e. none of the above is true.
Answers
Answer:
d. All of the above are true
Step-by-step explanation:
All of the following statements,
a. the stronger the linear relationship between two variables, the closer the correlation coefficient will be to 1.
b. if the correlation coefficient between the x and y variables is negative, the sign on the regression slope will also be negative.
C. if the correlation coefficient between the dependent and independent variable is determined to be significant, the regression model for y given x will also be significant.
are true
A simple random sample of 30 students was selected from a normally distributed population of high school students. The following confidence intervals were calculated at 90, 95, and 99% confidence levels to estimate the average number of hours of sleep the students got each night. Determine which confidence level goes with each confidence interval. Between 7. 3 and 8. 7 hours of sleep: Between 7. 0 and 9. 0 hours of sleep: Between 7. 2 and 8. 8 hours of sleep:.
Answers
Answer:
between 7.0 and 9.0 hours of sleep
Step-by-step explanation:
got it right
John works in a car dealership selling new and used cars, He is extremely busy during major holidays selling as many cars as possible. The store’s motto is “Work Hard Earn More”. During the last holiday period, John sold $150,000 worth of vehicles. His commission is 15% of the first $100,000 and 10% on the remaining balance. How much commission did he earn on his total sales?
Answers
15% of 100,000$ is 15,000$
10% of the remaining 50,000$ is 5,000$
1. (2 points) Suppose G is a group, and H is a subgroup of index 2. Prove that H is a normal subgroup of G. (Hint: start by proving aH = Ha for any a E G.) 2. (3 points) Let G = Sm, the symmetric group on n letters, for some positive integer n. Suppose (az az • Am) is a cycle in Sn (so the ai are necessarily distinct). Prove that for any o ESR o(aja2 am)o-1 = (o(au) o(az) olam))
Answers
1. H is a normal subgroup of G.
2. o(aja₂am)o⁻¹ = (o(au)o(az)olam).
1. Proof that H is a normal subgroup of G:
Since H has index 2 in G, there are exactly two distinct left cosets of H in G. Let these cosets be H and gH, where g is an element of G that is not in H. By the definition of index, we have |G : H| = 2, which implies that |G| = 2|H|. Since the order of G is twice the order of H, it follows that every element of G not in H must be in the coset gH.
Now, we will show that for any element a in G, the left coset aH is equal to the right coset Ha. Let's consider an arbitrary element h in H:
h ∈ H ⇒ ha ∈ aH (by the definition of left coset)
h ∈ H ⇒ ha ∈ Ha (by the definition of right coset)
Since aH contains all elements of the form ha, and Ha contains all elements of the form ha, we can conclude that aH = Ha for any a in G.
Next, we need to show that H is a subgroup of G. Since H has index 2, it means that the left coset H is distinct from the right coset H. Let's consider the left coset H:
H = {h₁, h₂, ..., hₙ}
Since aH = Ha for any a in G, it implies that:
ah₁ = h₁a
ah₂ = h₂a
...
ahₙ = hₙa
Therefore, H is closed under the group operation, which is one of the requirements for a subgroup. Additionally, the identity element e is in both H and G. Furthermore, for every element h in H, its inverse h⁻¹ is also in H. Hence, H satisfies all the conditions to be a subgroup of G.
Finally, since H is a subgroup of G and aH = Ha for any a in G, we can conclude that H is a normal subgroup of G.
2. Proof that o(aja₂am)o⁻¹ = (o(au)o(az)olam):
Let o be an arbitrary element in Sn. Consider the permutation (az az · Am) as a cycle in Sn, where the ai are distinct elements. We need to show that:
o(aja₂am)o⁻¹ = (o(au)o(az)olam)
To prove this, we will apply the permutation o to each element separately:
o(aja₂am)o⁻¹ = o(a) o(j) o(a₂) o(am) o⁻¹
Now, let's analyze each part of the expression:
o(a): This represents the action of the permutation o on the element a. The result is o(a).
o(j): Since j is fixed, o(j) = j.
o(a₂): This represents the action of the permutation o on the element a₂. The result is o(a₂).
o(am): This represents the action of the permutation o on the element am. The result is o(am).
o⁻¹: This represents the inverse permutation of o. Applying the inverse permutation to the result of the previous steps, we have:
o⁻¹(o(a)) o⁻¹(j) o⁻¹(o(a₂)) o⁻¹(o(am))
o⁻¹(o(a)) = a, since o and o⁻¹ cancel each other out.
o⁻¹(j) = j, since j is fixed.
o⁻¹(o(a₂)) = a₂, since o and o⁻¹ cancel each other out.
o⁻¹(o(am)) = am, since o and o⁻¹ cancel each other out.
Combining these results, we get:
o(aja₂am)o⁻¹ = o(a) o(j) o(a₂) o(am) o⁻¹
= ajo(a₂)am
= (o(au)o(az)olam)
Therefore, we have shown that o(aja₂am)o⁻¹ = (o(au)o(az)olam).
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write an equation of the lines that pass through (-2, 0), (0,4)
Answers
Answer:
y = 2x + 4
Step-by-step explanation:
We see immediately tht the y-intercept is (0, 4). As we move from (-2, 0) to (4, 4), x (the run) increases by 2 and y (the rise) by 4. Thus, the slope of the line is m = rise / run = 4/2 = 2, and so we can immediately write the specific version of the slope-intercept equation y = mx + b as y = 2x + 4.
For the following sample of n = 8 scores: 0, 1, 1/2, 0, 3, 1/2,0,1 Simplify the arithmetic by first multiplying each score by 2 to obtain a new sample of 0, 2, 1, 0, 6, 1, 0, and 2. Then, compute the mean and standard deviation for the new sample.
Mnew -
Snew -
Using the values you just obtained, what are the values for the mean and standard deviation for the original sample?
Moriginal -
Soriginal -
Answers
The values for the mean and standard deviation for the original sample are Moriginal = 0.625 and Soriginal = 0.9661, respectively.
Compute the mean and standard deviation for the new sample.
The mean of the original sample Soriginal is 0.625.
Moriginal = 0.625.
For the given sample of n = 8 scores: 0, 1, 1/2, 0, 3, 1/2,0,1.
We have to simplify the arithmetic by first multiplying each score by 2 to obtain a new sample of 0, 2, 1, 0, 6, 1, 0, and 2. Then, we will compute the mean and standard deviation for the new sample.
The calculations are:
\($\overline{x}_{\text{new}}=\frac{\sum x_{\text{new}}}{n}=\frac{0+2+1+0+6+1+0+2}{8}=1.25$$\)
This implies that the mean of the new sample is 1.25.Mnew = 1.25
Now, let us calculate the standard deviation.
To do so, we have to calculate the variance of the data. The variance is the average of the squared deviation from the mean.
That is,
\($\sigma_{\text{new}}^2=\frac{\sum(x_{\text{new}}-\overline{x}_{\text{new}})^2}{n-1}\)
\(=\frac{(0-1.25)^2+(2-1.25)^2+(1-1.25)^2+(0-1.25)^2+(6-1.25)^2+(1-1.25)^2+(0-1.25)^2+(2-1.25)^2}{8-1}\\=3.7321\)
This implies that the variance of the new sample is 3.7321.
Now, we calculate the standard deviation as:
\($\sigma_{\text{new}}=\sqrt{3.7321}=1.9322$\)
Thus, the standard deviation of the new sample is 1.9322.
Snew = 1.9322
We will use the formula for calculating the standard deviation of a new sample from an old sample, as follows:
\($\sigma_{\text{old}}=\frac{\sigma_{\text{new}}}{2}=\frac{1.9322}{2}=0.9661$$\)
So, the standard deviation of the original sample is 0.9661.
Soriginal = 0.9661
To find the mean of the original sample, we will use the following formula:
\($\overline{x}_{\text{old}}=\frac{\overline{x}_{\text{new}}}{2}=\frac{1.25}{2}=0.625$$\)
Therefore, the mean of the original sample is 0.625.
Moriginal = 0.625
Thus, the values for the mean and standard deviation for the original sample are Moriginal = 0.625 and Soriginal = 0.9661, respectively.
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P(x) = 6x³-5x² - 4x + 4;-3
Answers
The value of P(-3) =-191 if the given polynomial function is
P(x) = 6x³-5x² - 4x + 4
What is meant by polynomial?A polynomial is an expression made up of exponents, constants, and variables that are combined using addition, subtraction, multiplication, and division in mathematics, according to the definition of a polynomial. Polynomials are frequently employed in both mathematics and science. For example, they are employed to define polynomial functions, which are present in a range of fields ranging from elementary physics and chemistry to economics and social science. From straightforward word problems to intricate scientific conundrums, polynomial equations are utilized to represent a broad variety of topics. In high mathematics, polynomials are used to build algebraic varieties and polynomial rings, which are essential concepts in algebra and algebraic geometry.
Given,
P(x)= 6x³-5x²-4x+4
P(-3)=6(-3)³-5(-3)²-4(-3)+4
=6(-27)-5(9)+12+4
=-162-45+16
=-191
So, the value of P(-3)= -191
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A mine produces ore that is about 0.6% nickel. About how much ore from this mine would you need to get 3,000 kg of nickel?
Answers
Missy makes punch for a party. She uses 3 1/2 cups of water, 2 3/4 cups of frozen pineapple juice. Approximately how many liters of punch does this recipe make. (1 Litter = 4.23 cups)
A. 0.423 L
B.42.3 L
C.2.63 L
D.1.42 L
Answers
Answer:
D
Step-by-step explanation:
3.5 + 2.75 = 6.25
6.25/4.23 = 1.42 L
Approximately 1.48 liters of punch does this recipe make.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Missy makes punch for a party. She uses 3 1/2 cups of water, 2 3/4 cups of frozen pineapple juice.
∴ The total volume of the punch is (\(3\frac{1}{2} + 2\frac{3}{4}\)) = 7/2 + 11/4 = (14 + 11)/4 = 25/4
cups of punch.
Now, 1 liter is 4.23 cups.
∴ 25/4 or 6.25 cups is (6.25/4.23) = 1.48 liters.
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A scientist captures a sample of fish from 100 different locations along the
Yellowstone river and measures the proportion of fish affected by copper toxicity for
each sample. Describe how the scientist could use the data to estimate the
proportion of fish affected by copper toxicity in the entire population along this
portion of the river.
Answers
It should be noted that the scientist could use the data to estimate the proportion of fish affected by copper toxicity in the entire population along this portion of the river by dividing the number of fishes affected by the fishes collected
How to illustrate the information?Let the number of fish collected in sample be represented as N.
Let the number of fish affected in it be represented by X.
Therefore, the proportion will be;
= X/N
Therefore, this can be used by the scientist to estimate the proportion of fish affected by copper toxicity in the entire population.
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What is all that is equivalent to 5x+(x+6)+3x
Answers
Answer:
9x+6
Step-by-step explanation:
I think by equivalent, you mean solve it.
5x+(x+6)+3x
5x+x+6+3x, open the parenthesis
9x+6, add up the like terms
Mr. Campbell has a square garden with an area of 256 square feet. He wants to put a fence along 3 sides of the garden. How many feet of fencing will he need?
Answers
Answer:
Step-by-step explanation:
It should be noted:
Area of square garden = L² = 256
Square root both sides of the equation to find the length of the square garden. Then, use the length of the square garden to calculate the length of fence required for 3 sides of the garden.
Square root both sides.
√L² = √256
=> L = 16
Multiply the length by 3.
3L = 16 x 3 = 48 feet
Thus, Mr. Campbell will need 48 feet of fencing.
for a posttest following anova, there are four different treatment groups. how many pairwise comparisons must be made to gain a complete understanding of which treatment effects differ significantly from others? a. 4 b. 6 c. 12 d. 24
Answers
There are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.
In order to determine which treatment effects differ significantly from others, we need to make pairwise comparisons between all possible pairs of treatment groups. Let's consider an example with four treatment groups labeled A, B, C, and D.
To determine which treatment effects differ significantly from others, we need to compare the mean scores of each treatment group with the mean scores of every other treatment group. This means we need to make the following pairwise comparisons:
A vs B
A vs C
A vs D
B vs C
B vs D
C vs D
Therefore, there are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.
It's worth noting that when making multiple pairwise comparisons, there is an increased risk of making a Type I error (i.e., rejecting the null hypothesis when it is actually true) due to the multiple testing problem. To control for this, researchers may choose to adjust the significance level or use methods such as the Bonferroni correction to adjust the p-values of the individual tests.
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PLZ HELP ASAP!!
Robin and John were hbu g an archery contest. Johns arrow shot high while Robins arrow shot low. If the angle between the arrowheads on the right side of the intersection was
A. 90
B. 84
C. 114
D. 66
Answers
Simone makes $7.75 for every hour she works at the bakery. If she wants to make $93, how many hours will she need to work?
Answers
93 = 7.75x
Divide by 7.75
She needs to work at least 12 hours
Fill in the boxes please
Answers
Answer:
x=12, DO=45O, G=45, DG=90
Step-by-step explanation:
Mid point means both lenghts are equal
4x-3=2x+21
2x=24
X=12
-----------------
1)4(12)-3=48-3=45
2)2(12)+21=24+21=45
-----------------------------
DO=45
OG=45
DG=90
Answer:
x = 12
DO = 45
OG = 45
DG = 90
Step-by-step explanation:
4x-3 = 2x+21
4x-2x = 21+3
2x = 24
x = 24/2
x = 12
DO = ( 4*12 ) - 3 = 45
OG = (2*12)+21=45
DG = 45+45=90
suppose a finite model for an incidence geometry satisfies the additional axiom: every line has exactly three points lying on it. what is the minimum number of points needed for such a geometry? why?
Answers
In an incidence geometry with the additional axiom that every line has exactly three points lying on it, the minimum number of points required is 4.
This is because a line must have at least two-points to exist, and if it has only two points, it is not possible to have another point lying on it (since every line must have exactly three points).
Hence, there must be at least 4-points to create two lines such that each line contains exactly three points.
Also, with 4 points, it is possible to create 6 lines such that each line contains exactly 3 points, forming a configuration known as the Fano-plane, which is the smallest example of an incidence geometry that satisfies the given axiom.
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HELP DUE IN 10 MINS! Use the Pythagorean Theorem to solve for x.
A. 50
B. 5sqrt(2)
C. 2sqrt(293)
D. 2sqrt(5)
Answers
Answer:
B. 5sqrt(2)Step-by-step explanation:
x² = 4² + (√34)²x² = 16 + 34x² = 50x = √50x = 5√2\(\huge\large \fbox \green{Answer :}\)
B. 5sqrt(2)
\(\huge\Large \fbox \green{Explanation:}\)
We have
first side of triangle = √34second side of triangle = 4We need to find third side of triangle
let , the third side of triangle is x( x)² = (√34 )² + (4)² ....( by Pythagoras Theorem)
x ² = 34 + 16
x ² = 50
x = √50
x = 5 √2
Hence, the third side is 5√2
. Solve for y
a. y² = 35
b. y³ = 1000
Answers
Part a
\(y^2=35 \implies y=\pm \sqrt{35}\)
Part b
\(y^3=1000 \implies y=\sqrt[3]{1000}=10\)
a. \(y^{2} = 35 - > y =+- \sqrt{35}\)
b. \(y^{3} = 1000 - > \sqrt[3]{1000} = 10\)
(+ - means either minus 35 or 35)
A vehicle travel at a
constant speed of 30m/s
how long it would take to
travel a distance of
3300m
Answers
Answer:
110 s
Step-by-step explanation:
Divide the given distance by the constant speed
3300/30 = 110 s
This leaves us with the time it took the vehicle to travel the given distance. By dividing m by m/s the measurement of m, or meters, cancels out leaving s, or seconds.
The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown.
Write the function in standard form. f(x) = 5x2 + 40x
Factor a out of the first two terms. f(x) = 5(x2 + 8x)
Form a perfect square trinomial. (eight-halves) squared = 16
f(x) = 5(x2 + 8x + 16) – 5(16)
What is the function written in vertex form?
f(x) = 5(x + 4) – 80
f(x) = 5(x + 8) – 80
f(x) = 5(x + 4)2 – 80
f(x) = 5(x + 8)2 – 80
Answers
Answer:
third option
Step-by-step explanation:
Given
f(x) = 40x + 5x² ← express in standard form
f(x) = 5x² + 40x ← factor out 5 from each term
f(x) = 5(x² + 8x)
To complete the square
add/ subtract ( half the coefficient of the x- term)² to x² + 8x
f(x) = 5(x² + 2(4)x + 16 - 16)
f(x) = 5(x + 4)² + 5(- 16)
f(x) = 5(x + 4)² - 80
Answer:
3. f(x) = 5(x + 4)2 – 80
Step-by-step explanation:
Mhanifa if you are online could you please help me. What is the value of X?
Answers
Answer:
A. x = 42.5°Step-by-step explanation:
AB is the diameter, therefore ACB is right angle
2x + 5° = 90°2x = 85°x = 42.5°Correct option is A
Some students at MDVS are planning on planting a garden this spring. They want to plant squash, pumpkins, corn, beans, and potatoes. They plan for the field layout in feet is shown in the figure below. Use the figure and your knowledge of polynomials, perimeter, and area to solve the following:
a) Write an expression that represents the length of the North side of the field.
b) Simplify the polynomial expression that represents the North side of the field.
c) Write a polynomial expression that represents the perimeter of the beans field.
d) Simplify the polynomial expression that represents the perimeter of the beans field. State one reason why the perimeter would be useful to the Garden Club.
e) Write a polynomial expression that represents the area of the potato field.
f) Simplify the polynomial expression that represents the area of the potato field in descending order. State one reason why the calculated area would be useful to the Garden Club.
g) Write and simplify the polynomial expression that represents the area of the bean field if = 3. What unit would the area of the bean field have?
h) The Club would like their bean plants to grow to a height of ( + 2). Write a polynomial expression to find the volume of the bean plants if they reach a height of ( + 2).
i) Simplify the polynomial expression that represents the volume of the bean plants if they reach a height of ( + 2) feet in descending order.
j) The club realized they forgot to include a zucchini field into the field layout. They plan to use half the length and half the width of the squash field to plant zucchini. Write a polynomial expression that represents the area of the new zucchini field.
k) Simplify the polynomial expression that represents the area of the newly added zucchini field.
l) Write and simplify polynomial expressions that represent the perimeter and area of the cornfield. (Extra-credit)
Answers
The length of the potato field is x^2 -7x + 12
The perimeter of the potato field is 2x^2 - 12x + 36
What is a Polynomial?
A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and exponentiation (raising to a power).
A polynomial expression can have one or more variables, and the degree of the polynomial is determined by the highest exponent of the variable(s) in the expression.
For example, the polynomial expression "3x^2 + 2x + 1" has a degree of 2 because the highest exponent of x is 2.
The required area of the bean field is 35 square units
The required volume is x^3y^2 + 3x^2y^2 -x -3
The length of the squash field is 5x + 2
The width is 4x
The answers and calculations are in the given image below.
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A female grizzly bear weighs 500 pounds after hibernating for 6 months she weighs only 350 pounds what is the mean monthly change in weight
Answers
Answer:
lose 300 lbs in 6 months
Step-by-step explanation:
Find the equation of a line perpendicular to y = -3x + 5 that passes through the point (6,7)
Answers
789
Answer:
Step-by-step explanation:
Which relation is a function?
Answers
Answer:
The bottom right option
Step-by-step explanation:
Functions need each input to map to exactly one output. Graphically speaking, this means that any two points on the function cannot have the same x-coordinate.
Given this, the bottom right option is the only one that fits these circumstances.
In the autonomous differential equation dx/dt = x(1 - x), the critical point Select the correct answer.
A. x = 0 is semistable B. x = 1 is an attractor C. x = 1 is a repeller
D. x = 0 is an attractor E. x = 1 is semistable
Answers
The correct option are: B. x = 1 is an attractor; is the critical point for the given autonomous differential equation.
Explain the term autonomous differential equation?The right-side zeros of an autonomous 1st order differential equation provide the critical points: x' = f(x)
If a sign of said function shifts from positive towards negative, f(x) = 0
a critical point becomes an attractor:if the function's sign flips from negative towards positive, is a repeller.If a function does not reverse signs just at critical point, it is semistable.These critical point characteristics reveal the behaviour of the solutions close to the critical points.The solutions would converge around the critical point around an attractor.
Solve the autonomous differential equation:
dx/dt = x(1 - x),
Put dx/dt = 0
x(1 - x) = 0
x = 0, x = 1
Thus, at x = 1.
The function changes as from positive towards negative.
So, the solution becomes critical point.
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the pages of a book are numbered through . when the page numbers of the book were added, one of the page numbers was mistakenly added twice, resulting in an incorrect sum of . what was the number of the page that was added twice?
Answers
xm denotes the number of the page that was added twice. By solving the equation, we can find xm = (S' - S)/2, which is the number of the page that was added twice.
Let the page numbers be denoted by x1, x2, x3, ... , xn.
The sum of the page numbers is given by S = x1 + x2 + x3 + ... + xn.
The sum of the page numbers with the page number added twice is S' = x1 + x2 + x3 + ... + xn + xm + xm
Therefore, S' = S + 2xm
Since S' = S + 2xm, then 2xm = S' - S
Therefore, xm = (S' - S)/2
Therefore, the number of the page that was added twice is xm = (S' - S)/2.
Let x1, x2, x3, ... , xn denote the page numbers of a book. The sum of the page numbers is denoted by S. When the page numbers were added, one of the page numbers was mistakenly added twice, resulting in an incorrect sum of S'. Therefore, S' = S + 2xm, where xm denotes the number of the page that was added twice. By solving the equation, we can find xm = (S' - S)/2, which is the number of the page that was added twice.
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A newspaper in Germany reported that the more semesters needed to complete an academic program at the university, the greater the starting salary in the first year of a job. The report was based on a study that used a random sample of 24 people who had recently completed an academic program. Information was collected on the number of semesters each person in the sample needed to complete the program and the starting salary, in thousands of euros, for the first year of a job. The data are shown in the scatterplot below. 70 65 60 55 Starting Salary (1.000 euros) 50 45 35 30 25 5 10 15 20 Number of Semesters (a) Does the scatterplot support the newspaper report about number of semesters and starting salary? Justify your answer. b) The coefficient of determination is 0.335. Interpret this value in the context of this problem. c) Determine the value of the correlation coefficient. Interpret this value in the context of this problem.
Answers
a) Yes, It does. The scatterplot support the newspaper report about number of semesters and starting salary.
b) The value is relatively low, indicating that there are other factors that also contribute to starting salary.
c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables.
The Correlation Coefficienta) The scatterplot appears to show a positive association between the number of semesters needed to complete an academic program and the starting salary in the first year of a job. As the number of semesters increases, the starting salary generally increases as well. Therefore, the scatterplot supports the newspaper report.
b) The coefficient of determination, or R-squared value, represents the proportion of the variation in the dependent variable (starting salary) that is explained by the independent variable (number of semesters). A value of 0.335 means that 33.5% of the variation in starting salary is explained by the number of semesters. This value is relatively low, indicating that there are other factors that also contribute to starting salary.
c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables. A value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation. The correlation coefficient for this data is not provided in the problem, so it is not possible to determine it. Without the correlation coefficient, it is not possible to interpret the strength and direction of the association between number of semesters and starting salary.
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Select the correct answer. how many moles are contained in 3.131 × 1024 particles? a. 5.199 mol b. 18.85 mol c. 0.5199 × 1023 mol d. 1.885 × 1047 mol
Answers
The particles contain 5.199 mol. The result is obtained by dividing the number of particles by the Avogadro number.
What is Avogadro number?Avogadro number is the number of particles contained in 1 mol of any substance. It is 6.022 × 10²³ particles/mol.
The number of particles of a substance can be expressed as
N = n × NA
Where
N = Number of particlesn = Number of molesNA = Avogadro numberThe number of particles of a substance is 3.131 × 10²⁴ particles. Find the number of moles!
With the Avogadro number, the number of moles would be
N = n × NA
3.131 × 10²⁴ = n × 6.022 × 10²³
n = (3.131 × 10²⁴) / (6.022 × 10²³)
n = 0.5199 × 10¹
n = 5.199 mol
Hence, there are 5.199 mol contained in the particles.
The answer is A.
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