Answer:
We are given:
[tex]R^{2}=12.7\%[/tex]
The interpretation of [tex]R^{2}[/tex] is the amount of variation in response variable that is explained by the explanatory variable in the model
Therefore, the interpretation of [tex]R^{2}=12.7\%[/tex] is 12.7% of variation in gpa response variable is explained by the jobs explanatory variable in the given linear regression model.
the R-squared statistic of 12.7% suggests that there is a weak linear relationship between the number of hours worked and GPA among the sampled students, and the majority of the variation in GPA is due to factors beyond the number of hours worked.
The R-squared statistic, often denoted as R², measures the goodness of fit of a linear regression model. In this context, where the R-squared statistic is 12.7%, it means that approximately 12.7% of the variability in GPA can be explained by the linear relationship with the number of hours per week students work.
More specifically:
- 12.7% of the variation in GPAs among the students in the sample can be accounted for by the linear regression model with the number of hours worked as the predictor variable.
- The remaining 87.3% of the variability in GPAs is not explained by this model and is attributed to other factors or sources of variation that are not included in the model.
In summary, the R-squared statistic of 12.7% suggests that there is a weak linear relationship between the number of hours worked and GPA among the sampled students, and the majority of the variation in GPA is due to factors beyond the number of hours worked.
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Daren can jump rope 116 times in 2 minutes, Kyle can jump rope 240 times in 4 minutes, and Marissa can jump rope 225 times in 5 minutes. Who can jump rope the most times per minute?
Answer:
Kyle can jump rope the most times per minute.
Step by step explanation:
We have been given that Daren can jump rope 116 times in 2 minutes.
So number of rope jumps done by Daren in 1 minute will be:
[tex]\text{Unit rate of Jump rope done by Daren}=\frac{116\text{ times}}{2\text{ minute}}[/tex]
[tex]\text{Unit rate of Jump rope done by Daren}=58\frac{\text{ times}}{\text{ minute}}[/tex]
Therefore, Daren jumps rope 58 times per minute.
We have been given that Kyle can jump rope 240 times in 4 minutes.
So number of rope jumps done by Kyle in 1 minute will be:
[tex]\text{Unit rate of Jump rope done by Kyle}=\frac{240\text{ times}}{4\text{ minute}}[/tex]
[tex]\text{Unit rate of Jump rope done by Kyle}=60\frac{\text{ times}}{\text{ minute}}[/tex]
Therefore, Kyle jumps rope 60 times per minute.
We have been given that Marissa can jump rope 225 times in 5 minutes.
So number of rope jumps done by Marissa in 1 minute will be:
[tex]\text{Unit rate of Jump rope done by Marissa}=\frac{225\text{ times}}{5\text{ minute}}[/tex]
[tex]\text{Unit rate of Jump rope done by Marissa}=45\frac{\text{ times}}{\text{ minute}}[/tex]
Therefore, Marissa jumps rope 45 times per minute.
As Kyle jumps rope 60 times per minute, which is greater than jumps rope done by Daren and Marissa, therefore, Kyle can jump rope the most times per minute.
BRAINLIEST AND 50 POINTS
1.) A jar contains 4 red, 5 white, and 3 blue marbles. A marble is drawn from the jar. What is the probability that the marble is
Blue?______ White?_____ Red?_____ Not red?_____
Answer:
P ( blue ) = 1/4
P ( white ) = 5/12
P ( red ) = 1/3
P ( not red ) = 2/3
Step-by-step explanation:
To find the probability of a marble being chosen, it is the number of that color over the total
We need to find the total number of marbles
4 red+ 5 white+3 blue = 12 marbles
P ( blue ) = 3 blue / 12 total = 3/12 = 1/4
P ( white ) = 5 white / 12 total = 5/12
P ( red ) = 4 red/ 12 total = 4/12 = 1/3
How man marbles are not red
total marbles - red marbles = 12-4 = 8
8 marbles are not red
P ( not red ) = 8 not red / 12 total = 8/12 = 2/3
in 1950, the U.S. federal budget was $39.4 billion, in 2000, the federal budget was $2025.2 billion. The exponential function is f=39.4Be^0.0787932i. Use your function to estimate the budget in 2010
Answer:
The budget in 2010 is $4453.10915 billion
Step-by-step explanation:
We are given exponential function as
[tex]f(t)=39.4e^{0.0787932t}[/tex]
where t is the time in years since 1950
now, we can find time in 2010
t=2010-1950=60
now, we can plug t=60
and we get
[tex]f(60)=39.4e^{0.0787932\times 60}[/tex]
we get
[tex]f(60)=4453.10915[/tex]
So, the budget in 2010 is $4453.10915 billion
What is the GCF of the following expression:
5y^5+35y^4+15y^3
Answer:
5y^3
Step-by-step explanation:
Find what is common to all the terms
5y^5 = 5 * y*y*y*y*y
35y^4 = 5*7*y*y*y*y
15y^3 = 3*5*y*y*y
The all have 5*y*y*y
So the GCF is 5 y*y*y or 5y^3
Analyze the key features of the graphs of the functions below. Select all of the quadratic functions that open down, have a vertex that is a maximum and a positive y-intercept.
f(x) = 2x2 - 4x - 3
g(x) = - x2 + x + 1
h(x) = -2x2 + 3x - 1
m(x) = x2 -9
n(x) = -3x2 + 7
f(x) = 2x^2 - 4x - 3; opens up; vertex: (1, -5); y-intercept: (0, -3)
g(x) = -x^2 + x + 1; opens down; vertex: (0.5, 1.25); y-intercept: (0, 1)
h(x) = -2x^2 + 3x - 1; opens down; vertex: (0.75, 0.125); y-intercept: (0, -1)
m(x) = x^2 - 9; opens up; vertex: (0, -9); y-intercept: (0, -9)
n(x) = -3x^2 + 7; opens down; vertex: (0, 7); y-intercept: (0, 7)
I have attached an image of the functions and their graphs.
Hope this helps!
Answer:
[tex]f(x) = -x^2 +x +1[/tex]
Step-by-step explanation:
Quadratic equation is in the form of
[tex]f(x)= ax^2+bx+c[/tex]
When the value of 'a' is positive then the graph opens up
When the value of 'a' is negative then the graph opens down
When the graph opens up then the vertex is minimum.
When the graph opens down then the vertex is maximum.
y intercept is the value of 'c'
[tex]f(x) = 2x^2 - 4x - 3[/tex], a=2 the graph opens up
[tex]f(x) = -x^2 +x +1[/tex], a=-1 the graph opens down. So the vertex is maximum. Y intercept is +1. y intercept is positive.
[tex]f(x) = -2x^2 +3x - 1[/tex], a=-2 the graph opens down. So the vertex is maximum. Y intercept is -1. y intercept is negative.
[tex]f(x) = 2x^2 - 4x - 3[/tex], a=2 the graph opens up
Lexi can paint 5 yards of fencing in one hour. At this rate how many inches does she paint per min?
1 yard is 36 inches
so 5 yards are 180 inches
1 hour is 60 minutes
so in 60 minutes she paints 180 inches
or in 1 minute she paints 3 inches
In a neighborhood of 160 houses. 48 of the houses are brick. What percent of the houses are brick houses.
Since it's 48 out of 160 and you're trying to find the percentage out of 100, this particular formula would look like this: 48/160=x/100.
Then you cross multiply: 48x100=4800
Then you take the result of that and divide it by the total number of houses. 4800/160=30
30% of the houses are brick.
The line with equation a+2b=0 coincides with the terminal side of an angle 0 in standard position and cos 0 < 0. What is the value of sin0?
Question:
line x + 2y = 0 is end side of angle θ
and cos θ < 0
Answer: sin θ = √5/5
Step-by-step explanation:
cos θ < 0 means x < 0
Line is y = -x/2, slope -1/2
Line intersects unit circle when x^2+y^2=1
x^2 + (-x/2)^2 = 1
x^2 + x^2/4 = 1
5x^2/4 = 1
x = -√(4/5) = -2√(1/5) = -2√5/5
y = √5/5
x^2 = 4/5, y^2 = 1/5
sin θ is y value at intersection of line and unit circle, √5/5
In this exercise we have to use the given equation and thus calculate the intersection value:
[tex]sin (\theta) = \sqrt{5/5}[/tex]
So knowing that you were informed:
Line x + 2y = 0 is end side of angle θ and cos θ < 0 means x < 0. Line is y = -x/2, slope -1/2 and the Line intersects unit circle when :
[tex]x^2+y^2=1\\x^2 + (-x/2)^2 = 1\\x^2 + x^2/4 = 1\\5x^2/4 = 1\\x = -\sqrt{4/5} = -2\sqrt{1/5} = -2\sqrt{5/5}\\y = \sqrt{5/5}\\x^2 = 4/5, y^2 = 1/5[/tex]
[tex]sin(\theta)[/tex] is y value at intersection of line and unit circle, [tex]\sqrt{5/5}[/tex]
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Divide the following polynomial, then place the answer in the proper location on the grid. Write your answer in order of descending powers of x.
(a^2n - a^n - 6) ÷ (a^n + 8)
The correct answer for dividing [tex](a^{2n} - a^n - 6) by (a^n + 8)[/tex] is indeed:
[tex](a^n - 9) + (-78)/(a^n + 8).[/tex]
Let's divide the given polynomials:
[tex]\frac{a^{2n -a^n -6}}{a^n +8}[/tex]
Here's the breakdown of the solution:
Factoring: We can factor the numerator [tex](a^{2n} - a^n - 6)[/tex] using difference of squares:
[tex](a^{2n} - a^n - 6) = (a^n)^2 - (a^n) - 6 = (a^n + 2)(a^n - 3)[/tex]
Division: Now, we can divide the factored numerator by the denominator:
[tex][(a^n + 2)(a^n - 3)] / (a^n + 8) = (a^n + 2) - [(a^n + 8) * (a^n - 3)] / (a^n + 8) = (a^n + 2) - (a^n - 3) = a^n - 9[/tex]
Remainder: Since the degree of the numerator is less than the degree of the denominator, we get a non-zero remainder.
This remainder is obtained by dividing the constant term (-6) in the numerator by the constant term (8) in the denominator, resulting in [tex]-78/(a^n + 8).[/tex]
Therefore, the final answer is [tex](a^n - 9) + (-78)/(a^n + 8)[/tex], with a quotient of [tex](a^n - 9)[/tex] and a non-zero remainder of [tex](-78)/(a^n + 8).[/tex]
simplify (10x^2-19x-2) + (5x^2-8x+13) - (3x^2-2)
Answer:
12x² -27x + 13
Step-by-step explanation:
First of all, expand the first two brackets and put the correlating values near each other:
10x² + 5x² -19x -8x -2 +13
10x² + 5x² = 15x²
-19x + - 8x = -27x
-2 + 13 = 11
15x² - 27x + 11
Now, subtract the values inside the third bracket:
15x² - 3x² = 12x²
11 - -2 = 11 + 2 = 13
So the end result is:
12x² -27x + 13
800,000,000,000 + 20,000,000,000 + 3,000,000,000 + 50,000,000 + 4,000,000 + 600,000 + 50,000 + 8,000 + 700 + 80 + 6
A population of bacteria is growing according to the exponential model P = 100e(.70)t, where P is the number of colonies and t is measured in hours. After how many hours will 300 colonies be present? [Round answer to the nearest tenth.]
A) 0.7
B) 1.6
C) 5.7
D) 7.2
1. Write the fraction 8/9 as a percent. Round to the nearest hundredth of a percent where necessary. A. 88.89% B. 1.13% C. 44.44% D. 66.67% 2. Write 0.063 as a percent. A. 0.63% B. 6.3% C. 63% D. 630% 3. A survey at your school found that 792 in 1,220 students have a cell phone. What percent of the students in school has a cell phone? Round to the nearest hundredth where necessary. A. 6.49% B. 54.04% C. 64.92% D. 79.20%
Answer:
1.A. 88.89
2.B.6.3%
3.C.64.92%
Step-by-step explanation:
1.[tex]\frac{8}{9}=0.8888[/tex]
to covert it into percentage multiply it with 100
then it becomes 88.888
rounding off to the nearest hundred it becomes 88.89
2. to convert into percentage multiply it with 100
therefore 0.063×100=6.3%
3. to find percentage
%= (no of students using mobile / total no of students )× 100
= [tex]\frac{792}{1200}[/tex]×100
=64.918
Rounding off to nearest hundred it becomes 64.92%
Answer:
1) A. 88.89%
2) B. 6.3%
3) C. 64.92%
Step-by-step explanation:
1) After dividing 8 by 9, we get, [tex]\frac{8}{9} = 0.8889[/tex].
Now, percent of [tex]\frac{8}{9}[/tex] = 0.8889 * 100 = 88.89%
Hence, percent to nearest hundredth is 88.89%
2) We want 0.063 to be written in percent form
i.e. 0.063 * 100 = 6.3%
Hence, 0.063 into percent form is 6.3%
3) We are given that the total number of students are 1220 and the number of students that have cell phones are 792.
Therefore, the percent of students having cell phones = [tex]\frac{792}{1220} *100[/tex] = 64.92%
Hence, the percent of students having cell phones to nearest hundereth is 64.92%
Write the equation of the line containing the point (3, –2) and having a slope of 2 in slope-intercept form.
Slope-intercept form:
y = mx + b
"m" is the slope, "b" is the y-intercept (the y value when x = 0 or (0,y))
You know m = 2, so you can plug it into the equation
y = 2x + b
To find "b", plug in the point (3, -2) into the equation
y = 2x + b
-2 = 2(3) + b
-2 = 6 + b
-8 = b
y = 2x - 8
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the slope m = 2 and the point (3, -2) → x = 3 and y = -2.
Substitute:
[tex]-2=(2)(3)+b[/tex]
[tex]-2=6+b[/tex] subtract 6 from both sides
[tex]-8=b\to b=-8[/tex]
Substitute to the equation y = mx + b:
Answer: y = 2x - 8There are 8 students in a class: 2 boys and 6 girls. If the teacher picks a group of 5 at random, what is the probability that everyone in the group is a girl?
Answer:
0.1071
Step-by-step explanation:
Given
Total number of students=8
Boys=2
Girls=6
When we are picking a group from population we use combinations to calculate sample space and for event
So if a group of 5 has to be picked from 8 students
ⁿC_k= n!/(k!)(n-k)!
C_(n,k)= n!/(k!)(n-k)!
Here n=8 and k=5
C_8,5= 8!/(5!)(8-5)!
This will give us:
C_8,5=56
And if we have to pick only girls:
C_6,5= 6!/(5!)(6-5)!
=6
The probability of picking all girls:
=6/56
=0.1071
The correct answer to this question would be 3/28
Can someone help me with this problem
Answer:
12
Step-by-step explanation:
There are 6 for tails. Each is 2. 6 x 2 =12
Explain how to solve 7 + x > 12 .Tell what property of inequality you would use
Answer:
x > 5
Step-by-step explanation:
isolate x by subtracting 7 from both sides
x > 12 - 7
x > 5
the sum of m and 3 divided by the difference of m minus 3
Answer:
1 is the answer.
Step-by-step explanation:
(m + 3) / (m - -3)
m + 3 / m - - 3 = m + 3 / m + 3
m + 3 / m + 3 = 1
Please mark brainiest would help alot :3
Simplify:
"The sum of m and 3" => m + 3
"[the whole] divided by" => (m + 3)/
"The difference of m minus 3" => m - 3
(m + 3)/(m - 3) is your answer
~
QUICK
Bill lent some money to his two brothers. He wrote down the amounts so he would not forget. The list shows the younger brother with −$17.25 and the older brother with $0. Which of the following statements best describes the amounts?
A.The older brother paid Bill $17.25, and the younger brother does not owe him any money.
B.The older brother owes Bill $17.25, and the younger brother does not owe him any money.
C.The younger brother owes Bill $17.25, and the older brother does not owe him any money.
D.The younger brother paid Bill $17.25, and the older brother does not owe him any money.
Write a linear function that passes through the points (-5, -6) and (2, 8).
The point-slope form of line:
[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-5, -6) and (2, 8). Substitute:
[tex]m=\dfrac{8-(-6)}{2-(-5)}=\dfrac{8+6}{2+5}=\dfrac{14}{7}=2\\\\y-(-6)=2(x-(-5))\\\\\boxed{y+6=2(x+5)}[/tex]
( 85 x 6 ) - 69 thanks (:
Answer:
( 85 x 6 ) - 69 would equal 441
Step-by-step explanation:
You do 85 x 6 then - 69 (:
Answer:
441
Step-by-step explanation:
first do the
(85x6) you get 510
510-69
441
40 Jenny is buying gifts for her family. So far she has spent $45,95, and she has one more gift to buy. She started with a total of $60 to spend on all of her gifts Write an inequality that shows how much she can spend on the final gift
Answer:
[tex]x \leq 14.05[/tex]
Step-by-step explanation:
First, to find the boundary we need to find the amount of money left, simply subtract the spent amount from the total:
60 - 45.95 = 14.05
Seeing as this is the amount, she can spend any amount up to and including 14.05, so we need an equal to or smaller than sign:
Let x be the value of the object:
[tex]x \leq 14.05[/tex]
Which is the inequality!
MATH HELP PLEASE!!
find the area of the shaded region.
use the formula A= pi r^2 to find the area of the circle.
a. 8pi x + 24pi
b. 8pi x - 24pi
c. x^2 + 8pi x + 24pi
d. x^2 +8pi x - 24pi
Answer:
b
Step-by-step explanation:
B// 8pi x-24pi
Write an explicit rule to represent the sequence :
4, 10, 16, 22,...
It's an arithmetic sequence:
[tex]a_1=4;\ a_2=10;\ a_3=16;\ a_4=22;\ ...[/tex]
The explicit rule:
[tex]a_n=a_1+(n-1)d[/tex]
[tex]d=a_{n+1}-a_n\to d=a_2-a_1=a_3-a_2=a_4-a_3=...[/tex]
[tex]d=10-4=16-10=22-16=6[/tex]
Substitute:
[tex]f(n)=4+(n-1)(6)=4+6n-6=6n-2[/tex]
Answer: f(n) = 6n - 2The explicit rule for the arithmetic sequence 4, 10, 16, 22, ... is aₙ = 4 + (n - 1) x 6, where aₙ is the nth term of the sequence.
The given sequence is arithmetic, which means that it increases by the same amount each time. To find an explicit rule for the sequence, we should determine the common difference and use the formula for an arithmetic sequence, which is aₙ = a₁ + (n - 1)d, where an is the nth term, a1 is the first term, n is the number of the term in the sequence, and d is the common difference between terms.
In the sequence 4, 10, 16, 22, ..., the first term a1 is 4, and the common difference is 6 (since 10 - 4 = 16 - 10 = 22 - 16 = 6). Therefore, the explicit rule for the nth term of the sequence is aₙ = 4 + (n - 1) x 6.
Sam bought two CDs for 13 each sales tax for both CDs was $3 how much did she pay
13x2. 13 is how much the cds cost. 2 is how many she is buying. 13x2 is 26. Check 13+13=26.26-13=13.
Hope this helps!
Which equation represents the sentence? The sum of 14 and a number is 8 times the number
A.14+n=8n
B.14n=8+n
C.14n+8=n
D.14(n+8)=n
The correct equation is 14 + n = 8n, option A is correct.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Let the number is n,
8 times of the number = 8n
According to the condition, The sum of 14 and number n is 8 times the number,
Implies that,
14 + n = 8n
The correct equation is 14 + n = 8n.
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A bowling alley charges 2.00 per game and will rent a pair of shoes for 1.00 for any number of games. The bowling alley has an earrings goal of 300 for the day
Answer:
The bowling alley should rent 150 pairs of shoes and should about 75 games per day in order to reach a goal of 300 dollars.
Step-by-step explanation:
An elephant needs to drink at least 40 gallons of water each day. A drinking tank contains 4 gallons of water. The elephant has already consumed 24 gallons of water. How many more tanks x of water does the elephant need to drink? Write your answer as an inequality.
After drinking 24 gallons out of the required 40 gallons, the elephant needs at least 4 more tanks of water as each tank holds 4 gallons. The inequality representing this is x ≥ 4.
The student needs to calculate how many more tanks of water an elephant needs to drink to reach its daily requirement of at least 40 gallons if each tank contains 4 gallons of water. To start, we determine how much water the elephant still needs after drinking 24 gallons:
Required daily water - Water already consumed = Remaining water needed
40 gallons - 24 gallons = 16 gallons
Next, we find out how many tanks are needed for the remaining 16 gallons, knowing that each tank holds 4 gallons:
Number of tanks needed = Remaining water needed / Water per tank
Number of tanks needed = 16 gallons / 4 gallons per tank
Number of tanks needed = 4 tanks
Since the elephant needs at least 40 gallons, it will need at least 4 more tanks of water. However, since we're writing this as an inequality, we want to express that the elephant may drink more. Hence, the inequality will be:
x ≥ 4
What is the value of P ?
Answer:
133*3+90*3+30*p
Step-by-step explanation:
add all that up then divide it by three
Answer:
p=43°
Step-by-step explanation:
We know that the sum of angles inside the triangle is 180 degree
One angle is P, we find other two angles
Angles in a straight line is 180 degree.
angle adjacent to 133 is 180-133=47
angle adjacent to 90 is 180-90=90
To find out P, we add all the angle and make it equal to 180 degree
p + 47+90= 180
p+137= 180
Subtract 137 on both sides
p=43°
The basketball team spends 20 minutes running laps and at least 15 minutes discussing plays. Practice lasts one hour and 45 minutes. Write and solve an inequality to find the amount of time remaining to work on other drills.
Answer:
[tex]t\leq 70[/tex]
Step-by-step explanation:
The team spends 20 minutes running laps
At least 15 minutes discussing plays.
Practice lasts one hour and 45 minutes.
We know that 1 hour = 60 minutes, so the practice lasts,
60+45= 105 minutes.
The team spends a total of [tex]20+15=35[/tex] minutes in running and discussion.
So the time remaining to work on other drills is,
[tex]t\leq 105-35[/tex]
[tex]t\leq 70[/tex]