4.(06.07 HC)A teacher is assessing the correlation between the number of hours spent studying and the average score on a science test. The table below shows the data:Number of hours spent studying 0 0.5 1(x)1.5 2 2.5 33.54Score on science test(y)57 62 67727782 879297Part A: Is there any correlation between the number of hours students spent studying and the score on the science test? Justify your answer. (4 points)Part B: Write a function which best fits the data. (3 points)Part C: What does the slope and y-intercept of the plot indicate? (3 points)(10 points)
Answers
For part A. One way to know if there is a correlation between the data is to graph the data set, like this
Then, as can you see the data presents a positive linear correlation.
For part B. You can take the coordinates of two points and find the slope of the line using the formula
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]If you take
[tex]\begin{gathered} (x_1,y_1)=(1,67) \\ (x_2,y_2)=(3,87) \\ \text{ You have} \\ m=\frac{87-67}{3-1} \\ m=\frac{20}{2} \\ m=10 \end{gathered}[/tex]Now, using the slope formula, you can find the equation of the line in its slope-intercept form
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-67=10(x-1) \\ y-67=10x-10 \\ \text{ Add 67 on both sides of the equation} \\ y-67+67=10x-10+67 \\ y=10x+57 \end{gathered}[/tex]Therefore, the function that best fits the data is
[tex]y=10x+57[/tex]For part C. The slope of the plot is 10 and indicates that for every hour students spend time studying, they get 10 more points on the science test.
The y-intercept of the plot is 57 and indicates that if students study 0 hours for the science test, they will obtain 57 points as a grade.
Related Questions
Is (x-3) a factor of 2x^3 -4x^2-6?
1) (Type yes or no in the first blank)
2) What is the remainder?
(Type the answer in the second blank)
Answers
1. x - 3 is not a factor
2. The remainder is 32.
1. How to determine if x - 3 is a factor of 2x³ - 4x² - 6?Using the remainder theorem, which states that for a polynomial p(x), if x - a is a factor, then p(a) = 0.
So, p(x) = 2x³ - 4x² - 6 If x - 3 is a factor, then
p(3) = 0
So, substituting x = 3 into the equation, we have
p(3) = 2x³ - 4x² - 6
= 2(3)³ - 4(2)² - 6
= 2(27) - 4(4) - 6
= 54 - 16 - 6
= 54 - 22
= 32
Since p(3) ≠ 0.
x - 3 is not a factor
2. What is the remainder?Since p(3) = 32,
The remainder is 32.
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An oatmeal cookie calls for 1/2 cup of butter to make 6 dozen cookies. Hilda needs to make 15 dozen cookies for the bake sale. How many cups of butter will she need
Answers
1) Given that an oatmeal cookie has these proportions, let's set a pair of ratios to get that:
[tex]undefined[/tex]6. Write the equation for the line: (Hint: there are two points given to you!) 1 (3-1) 4 Homework Packet 3,1-3143.pdf hit ng
Answers
. Write the equation for the line: (Hint: there are two points given to you!)
________________________
y= mx + b
the slope is m
or
(y - y1) = m (x - x1)
___________________
points (x,y)
point 1 (4, 4) x1 = 4; y1 = 4
point 2 (3 , -1) x2= 3; y2 = -1
The slope m = (y2- y1) / (x2 -x1)
m=(-1 - 4 )/( 3 - 4)
m= -5/-1 = 5
(In this case, you choose which point you want to put as point one and point two, you will always get the same answer)
____________________
(y - 4) = 5 (x - 4)
y= 5x -20 +4
y= 5x - 16
The equation for the line is y= 5x - 16
__________________
Do you have any questions regarding the solution?
suppose that the lifetime of a transistor is a gamma random variable x with mean of 24 weeks and standard deviation of 12 weeks. what is the probability that the transistor will last between 12 and 24 weeks?
Answers
The probability that the transistor will last between 12 and 24 weeks is 0.424
X= lifetime of the transistor in weeks E(X)= 24 weeks
O,= 12 weeks
The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.
X~gamma([tex]\alpha ,\beta[/tex])
E(X)= [tex]\alpha \beta[/tex] [tex]\beta[/tex]= [tex]12^{2}/24[/tex]=6 weeks
V(x)= [tex]\alpha \beta ^{2}[/tex] [tex]\alpha[/tex]=24/6= 4
Now we can find the solutions:
The excel formula used to create Figure one is as follows:
=gammadist(X, [tex]\alpha[/tex], [tex]\beta[/tex], False)
P([tex]12\leq X\leq 24[/tex])
P([tex]12/6\leq G\leq 24/6[/tex])
P([tex]2\leq G\leq 4[/tex])
P= 0.424
Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424
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Answer:
Step-by-step explanation:
0.424 is the probability that the transistor will last between 12 and 24 weeks.
X= lifetime of the transistor in weeks E(X)= 24 weeks
Standard deviation= 12 weeks
Finding the parameters alpha and beta X~gamma(αβ)
E(X)= αβ β =6 weeks
V(x)=αβ^2 α =24/6= 4
Now we can find the solutions:
The excel formula used to create Figure one is as follows:
=gammadist(X,α,β,False)
P(12≤X≤24)
P(12/6≤G≤24/6)
P= 0.424
Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424
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Marshall is going to make an apple pie. He buys x pounds of apples and a pie crust that costs $4.50. The total cost in dollars. y. can be found using the equation below. y = 2.57x +4.5 What is the cost per pound of the apples
Answers
1) Considering that x is for pounds of apples and y is a total cost of an apple let's find the cost per pound of the apples, given that the y=2.57x +4.5
Let's turn that function into an equation
0=2.57x +4.5 Subtract 2.57x from both sides
-2.57x=4.5 Divide both sides by -2.57
x=-1.75
2) So if no one pie crust is sold, there is going to be a loss of $-1.75, according to that equation.
Therefore, we can infer that the cost per pound of the apples is $1.75
270 bottles are packed in 10 boxes. how many bottles are there in each box?
Answers
Answer:
27
Step-by-step explanation:
Divide 270 by 10
11. Find m/Q. The diagram is not to scale.
Q/ R
77°
47°
Answers
The hypotenuse of a right triangle measures 18 cm and one of its legs measures 7 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth.
Answers
The hypotenuse of a right triangle = 19.31cm
What is Hypotenuse?
The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.
Let the measure be,
Perpendicular = 18cm
Base = 7cm
Hypotenuse = ?
To find the Hypotenuse we can Pythagoras Theorem:
Hypotenuse² = Perpendicular²+ Base²
H² = (18)² + (7)²
H² = 324 + 49
H² = 373
H = [tex]\sqrt{373}[/tex]
H = 19.31cm
Hence, The measure of the other leg is²
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If there are 20 cookies and 40 carrot each number are the same number of one whole cookies how many cost members might have been at the party,explain
Answers
2, 4, 5, 10 and 20 cast members were possible attendees at the celebration.
The acting teacher provided 20 biscuits and 40 carrot sticks as refreshments in light of this.
What are the factors?
A factor in mathematics is an integer that evenly divides another number by itself, leaving no residue.
2, 4, 5, 10, and 20 make up the factors of 20 and 40.
Additionally, the number of cast members must be greater than one and a divisor of 20 and 40.
Therefore, there could be 2, 4, 5, 10, or 20 cast members.
Therefore, 2, 4, 5, 10 and 20 cast members may have attended the celebration.
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Solve 4h = 92 for h.h = ___
Answers
Answer:
23
Step-by-step explanation:
4h = 92
Divide both sides by 4 to get h by itself
h = 23
Find the smallest whole number bu which 512 must be multiplied in order to give a perfect square
Answers
Answer:
2
Step-by-step explanation:
512÷2=256
256÷2=128
128÷2=64
64÷2=32
32÷2=16
16÷2=8
8÷2=4
4÷2=2
2÷2=1
=(2^2)+(2^2)+(2^2)+(2^2)+2
When 2 is multiplied it will make it a perfect square.
512×2=1024
√1024
=32
Help me answer this what’s wrong with this problem
Answers
Answer:
See below
Step-by-step explanation:
The equation is
y = [tex]x^{2}[/tex] + x
x equals the step
We see steps: 1, 2,3 and 4
y equals the number of squares that you see in each step.
If you look at step 1, you see [tex]1^{2}[/tex] + 1 = 2
Step 2: [tex]2^{2}[/tex] + 2 = 6
Step 3: [tex]3^{2}[/tex] + 3 = 12
Step 4: [tex]4^{2}[/tex] + 4 = 20
Can you see at each step there is a square of the number and then a little extra? That little extra equals the number of the stop.
In the equation
y = 4x -2
Step 1
y = 4(1) -2
y = 2 It works!
Step 2:
y = 4x -2
y = 4(2) - 2
y = 8 - 2
y = 6 It works!
Step 3:
y = 4x -2
y = 4(3) - 2
y = 12 - 2
y = 10 It does not work!
Step 4:
y = 4x -2
y = 4(4) - 2
y = 16 - 2
y = 14 It does not work!
The equation y= 4x -2 only worked for the first 2 steps.
Simplify (10y - 5g)(3s + 6g) using foil method
Answers
The solution is on the paper.
determine if two triangles are necessarily congruent. if so in a flowchart proof to prove the they are.
Answers
Yes the two triangles are necessarily congruent as they are right angled so both the angles are equal and having two sides equal by using SAS rule that is Side, Angle, Side rule by the property of congruency.
What is Congruency?Two figures are considered to be "congruent" if they can be positioned precisely over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
What are the rules of congruency?If two triangles meet all 5 requirements for congruence, then they are congruent. They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SAS) (RHS).
Here the ΔCED and ΔPOR,
∠CED=∠POR
Side PR=CD
Side ED=PO
by using SAS rule,
ΔCED≅ΔPOR
Yes, the two triangles are inherently congruent because they have right angles, which means that both of their angles are equal, and because their sides are equal according to the SAS rule, which stands for Side, Angle, Side.
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given the figure, find the value of y for which the quadrilateral must be a parallelogram
Answers
For the figure to be a parallelogram, then y must be equal to 12
Here, we want to get the value of y for which the the quadilateral must be a parallelogarm
Mathematically, the diagonals of a parallelogarm bisects each other
That means the lengths on either sides are equal
Mathematically, we can get two equations as follows;
[tex]\begin{gathered} 3x\text{ = y} \\ 2x\text{ + 2y = 32} \\ \text{From the second equation;} \\ 2(x+y)\text{ = 2(16)} \\ x\text{ + y = 16} \\ \text{From this, we have that;} \\ x\text{ = 16-y} \\ we\text{ can put this in the first equation;} \\ 3(16-y)\text{ = y} \\ 48\text{ - 3y = y} \\ y\text{ + 3y = 48} \\ 4y\text{ = 48} \\ y\text{ = }\frac{48}{4} \\ y\text{ = 12} \end{gathered}[/tex]ABCD - FECG B 5 E 6 100° 5 A 60° С 4 120° G w D W = ? 1°
Answers
From the figure, draw from D parallel to AB.
Calculate angle D from triangle DWC = 180 - (90+60) = 180 - 150 = 30
Angle D = 30
Angle W = 90 + 30 = 120
Final answer W = 120
Each exterior angle measure is one eighth the measure of each interior angle??
Answers
Answer:
Exterior angle = 20 degrees
Interior angle = 160 degrees
================================================
Explanation:
The phrasing "Each exterior angle measure is one eighth the measure of each interior angle" means,
exterior = (1/8)*(interior)
That rearranges to
interior = 8*(exterior)
Let's say x is the measure of the unknown exterior angle. That makes 8x the measure of the interior angle
The two must add to 180 to form a straight line.
interior + exterior = 180
8x + x = 180
9x = 180
x = 180/9
x = 20 is the measure of the exterior angle
8x = 8*20 = 160 is the measure of the interior angle
Note how 160+20 = 180 to verify our answers.
Can Some one help PLEASEE
Answers
The variable x is 9 and the two adjacent angles have measures of 117° and 63°, respectively.
How to find the variable associated to the measure of two angles in a parallelogram
Parallelograms are quadrilaterals with two pairs of parallel sides of equal length. According to Euclidean geometry, the measures of two adjacent angles in a parallelogram are supplementary. Thus,
13 · x + 7 · x = 180°
Now we clear the variable x:
20 · x = 180°
x = 9
And the missing angles are:
13 · 9 = 117°
7 · 9 = 63°
The value of the variable x is 9 and the measures of the two adjacent angles are 117° and 63°, respectively.
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f(x)=-2x-3 find f(6)
Answers
f(6)=-2(6)-3
f(6)=-12-3= -15
The ratio of people to animals is 40 to 15. There are 27 animals. How many people are there?
Answers
—- = —-
15 27
15x = 1080
x=72
there are 72 people!!
Answer: is 72 people to 27 animals
Step-by-step explanation:
I can find the ratio by cross multiplying
40/15 to x/27
15x = 1080
x = 72
you can also divide 40/15 for a ratio percent = 8/3
multiply 27 animals x 8/3 = 72
two ways to solve for ratios
This is following statement, true or false
Answers
The lines aren't parallel since they intersect at point B.
Parallel lines never intersect.
Solve for x -3x-9=-15
Answers
Answer:
[tex]x = 2[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
−3x−9=−15
Step 1: Add 9 to both sides.
−3x−9+9=−15+9
−3x=−6
Step 2: Divide both sides by -3.
−3x/−3 = −6/−3
x=2
During two games, the number of points scored by a basketball team increased from 5 to 3 by what did the number of points scored increase?
Answers
EXPLANATION
Let's see the facts:
The increasing rate is:
[tex]Increa\sin g\text{ rate=}\frac{5}{3}=1.67[/tex]The increasing rate is 1.67
In percentage this is:
[tex]Increa\sin g=\frac{3}{5}\cdot100=\frac{3}{5}\cdot100=60[/tex]The percentage of increasing is of 60%.
Which shows the expression below simplified?
0.0042 - (1.2 x 10-6)
A. 3 x 10^-3
B. 1.1958 x 10^-6
C. 4.1988 x 10^-6
D. 4.1988 x 10^-3
Answers
The shows the expression below simplified 0.0042 - (1.2 x 10-6) as D. 4.1988 x 10^-3.
How can the expression be simplified?The concept that is been used is subtraction of the first expression from second expression.
The given expression is 0.0042 - (1.2 x 10-6) and this can be expressed in standard form as ( 4.2 *10^-3) - (1.2 x 10-6)
Then then the subtraction can be done as [ ( 4.2 *10^-3) ] - [ (1.2 x 10^-6) ] = 4.1988 x 10^-3
In conclusion, iif we go through the options., then we can see that the forth option is the best option that match the expression.
Therefore, option D is correct.
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is the ordered pair (-8 1) a solution to the equation y=1/2x-3
Answers
No, the ordered pair (-8,1) is not a solution to the equation y=(1/2)x-3.
In the question ,
an equation y=(1/2)x-3 is given ,
if the ordered pair (-8,1) is a solution of the equation , then it should satisfy the equation .
Substituting x=-8 and y=1 in the equation y=(1/2)x-3 , we get
y=(1/2)x-3
1 = (1/2)(-8) -3
1 = -8/2 -3
1 = -4-3
1 ≠ -7
Since 1≠7 , the ordered pair (-8,1) is not a solution to the equation y=(1/2)x-3 .
Therefore , No , the ordered pair (-8,1) is not a solution to the equation y=(1/2)x-3.
The given question is incomplete , the complete question is
Is the ordered pair (-8,1) a solution to the equation y=1/2x-3 ?
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3 points
Simplify the following expression
Answers
I WILL USE THE LAWS OF EXPONENTS
[tex] {x}^{n} \times {x}^{m} \\ = {x}^{n + m} [/tex]
AND
[tex] \frac{{x}^{n}}{ {x}^{m} } \\ = {x}^{n - m} [/tex]
[tex] \frac{3 {x}^{ - 2 + 5} }{ {x}^{8} } \\ = \frac{3 {x}^{3} }{ {x}^{8} } \\ = 3 {x}^{3 - 8} \\ = 3 {x}^{ - 5} [/tex]
ATTACHED IS THE SOLUTION.
Answer:
i hope this one is good for you
six children are each offered a single scoop of any of 3 flavors of ice cream from the combinatorial creamery. in how many ways can each child choose a flavor for their scoop of ice cream so that each flavor of ice cream is selected by at least one child?
Answers
Answer: 18 combinations
Step-by-step explanation: you want to multiply the amount of ice cream flavors by the amount of children to be able to find the amount of possible combinations. so, 6 children x 3 flavors of ice cream = 18 different combinations. 6 x 3 = 18
Is this a function (3,2) (-2,6) (3,3)
Answers
Answer:
No, it is not.
Step-by-step explanation:
A function only has exactly one output for each input. In other words, for each X input, there is only one Y output. In the given set of coordinates, 3 is repeated as an input, which makes this set of coordinates not a function.
Find the area of the region that is inside the square and outside the circle. The circle has a diameter of 8 inches. Round to the nearest tenth.
Answers
The area of the region within the square and without the circle is equal to 13.7 square inches.
What is the area of a region generated by a square and a circle?In this problem we find the case of figure generated by a square and an inscribed circle. Then, the area of the region is found by subtracting the area of the circle from the area of the square. Then, the area is:
A = L² - 0.25π · D²
Where:
L - Side length, in inches.D - Diameter, in inches.A - Areas, in square inches.If we know that D = L = 8 in, then the area of the region is:
A = (8 in)² - 0.25π · (8 in)²
A = 64 in² - 50.265 in²
A = 13.735 in²
The area of the region is equal to 13.7 square inches.
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If angles of the triangle are In 2:3:7 then find all the angles
Answers
Answer:
Since all triangle angles sum to 180 then we can say
2x + 3x + 7x = 180
12x = 180
x = 15
There fore the angles are
2 * 15 3 * 15 and 7 * 15 or
30 45 and 105
Those 3 total 180 degrees
Step-by-step explanation: