Answers and Step-by-step explanations:
(a) We want to find the slope-intercept equation (y = mx + b), where m is the slope and b is the y-intercept. We already have two points: (2, 6200) and (7, 21200). The slope is change in y over change in x so:
m = (21200 - 6200) / (7 - 2) = 3000
Now, we have y = 3000x + b. Plug in 6200 for y and 2 for x to solve for b:
y = 3000x + b
6200 = 3000 * 2 + b
b = 200
Nat's equation is y = 3000t + 200.
(b) We want a quadratic formula in vertex form because the problem says that Kat's account maxes out at 44100 on her 25th birthday, indicating that's the vertex. Our vertex point is (20, 44100); note that it's 20 and not 25 because she starts the account at age 5, not age 0. The generic vertex form of a quadratic is:
y = a(x - h)² + k, where (h, k) is the vertex
Plug in our vertex:
y = a(x - 20)² + 44100
We also have the point (9, 32000), so put that in to find a:
32000 = a(9 - 20)² + 44100
-12100 = a * 121
a = -100
So Kat's equation is y = -100(t - 20)² + 44100.
(c) In order to find the age when they have the same amount, we set the two equations equal:
3000t + 200 = -100(t - 20)² + 44100
-100(t² - 40t + 400) + 44100 = 3000t + 200
-100t² + 4000t - 40000 + 44100 - 3000t - 200 = 0
-100t² + 1000t + 3900 = 0
t² - 10t - 39 = 0
(t - 13)(t + 3) = 0
t = 13 or t = -3 -- obviously, years can't be negative, so t = 13.
Note, however, that t is the number of years after Kat and Nat are 5, so we need to add 13 to 5:
13 + 5 = 18
The age is 18.
A: [tex]N(t) = 3000t +200[/tex]
B: [tex]y = -100(x-20)^2+44100[/tex]
C: When they turn 18.
A. Write a linear function N(t) for the amount of money, N, that Nat has in her account ‘t’ years after her 5th birthday:
You can determine a linear equation using the two coordinates provided:
(2, 6200) and (5, 21200).
To do this, first find the slope of the graph. You can do this by using the expression
[tex]\frac{y2-y1}{x2-x1}[/tex], where the coordinate (2, 6200) is 1 and (7, 21200) is 2:
[tex]\frac{21200-6200}{12-7}\\\\\frac{15000}{5}[/tex]
The slope is equal to 3000. Now, you need to find the y-intercept. Plug in 2 for x and see what the y intercept would need to be to equal 6200:
6200 = 3000 * 2 + b
6200 = 6000 + b
b = 200
Thus, your equation for Nat's bank account is [tex]N(t) = 3000t + 200[/tex]
B: Kat’s account doesn’t follow a linear model, but rather a quadratic model. On her 5th birthday, her parents open the account and then add money annually just like with Nat. Kat’s parents plan is to add money so that her account maxes out at $44100 on her 25th birthday. At the age of 14, she has $32000. Write a quadratic function K(t) for the amount of money, K, in Kat’s account ‘t’ years after her 5th birthday:
The question supplies you with the vertex to the parabola, (20, 44100). This is the point at which the maximum value of the function is reached.
It also supplies you with a point on the parabola, (9, 32000).
You can use the vertex form of the quadratic equation to find the formula for Kat's bank account:
[tex]y=a(x-h)^2+k[/tex], where (h, k) is the vertex.
Substituting the vertex in for that equation, we get:
[tex]y=a(x-20)^2+44100[/tex]
Now, you can substitute the point (14, 32000) in for x and y to solve for a:
[tex]32000=a(9-20)^2+44100\\\\-12100 = 121a\\a = -100[/tex]
Thus, the equation is [tex]y = -100(x-20)^2+44100[/tex].
C. What age will both Nat and Kat have the same amount in their account? 18 years old.
To find what age each account will be equal, set the equations equal to each other:
[tex]-100(x-20)^2+44100 = 3000x +200[/tex]
Then, you can solve for x:
[tex]-100(x-13)(x+3)=0[/tex]
Solving for x, we notice that the accounts equal each other when Nat and Kat are -3 or 13. However, Nat's function is only specified to begin after she turns 5, so add 5 to 13 to get 18.
They will both have the same money in their accounts when they turn 18.
Which equation BEST represents the line of best fit for the scatterplot?
A) y = 3x
B) y = x - 2
C) y = x - 3
D) y = x + 3
HELP PLEASE WILL MARK BRAINIST
Answer:
i did the math and it should be B. 7 hours
Step-by-step explanation:
Which point on the coordinate plane is located at (4,0)?
A) point A
B) point B
C) point C
D) point D
Answer:
point B
Step-by-step explanation:
The coordinates (4,0) is has the numbers 4 and 0.
4 is positive and can be represented as moving right on the origin. Since, there is no rise it stays.
Which of these polygons is not formed by the cross-section created when a plane intersects a cube? Select all that are possible.
square
circle
pentagon
octagon
triangle
rectangle
Answer:
Circle
Octagon
Step-by-step explanation:
There are no curves in a cube to make a circular cross section, and there aren't enough edges to make an octagon (just visualize)
Answer:
A circle is not possible. Neither is a square or a rectangle.
Step-by-step explanation:
Find the slope given the points (1,1) and (3,7)
Answer:
3
Step-by-step explanation:
gradient = (7-1)/(3-1) = 6/2=3
Answer:
Slope is 3
Step-by-step explanation:
m = Δy/Δx
m = (7-1)/(3-1)
m = 6/2
m=3
Hope this helps :)
What is the approximate volume of the cone? Use 3.14 for π. Right cone with radius of 9 centimeters and height of 15 centimeters. 3815 cm3 848 cm3 1272 cm3 6359 cm3
Answer: [tex]1272cm^3[/tex]
Step-by-step explanation:
[tex]V=\pi r^2\frac{h}{3}\\ V=(3.14)(9)^2(\frac{15}{3} )\\V=(3.14)(81)(5)\\V=1271.70cm^3\\V=1272cm^3[/tex]
An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation
2000.081 - 350 represents the situation, where t is the number of years the money has been invested. About how long has the
money been invested? Use a calculator and round your answer to the nearest whole number.
I need help with all three problms pls! I'll mark brainliest
Answer:
2. Denote two pieces: x, y
x + y = 40
x = 2y + 10
=> 2y + 10 + y = 40 => 3y = 30 => y = 10 => x = 2 x 10 + 10 = 30
=> Solution: 10 and 30
3. Denote 4 consecutive number: 2k, 2k+2, 2k+4, 2k+6
(2k + 2k + 4) x 2 + 20 = 2 x (2k + 6)
=> 8k + 28 = 4k + 12
=> 4k = -16
=> k = -4
=> Solution: -8, -6, -4, -2
4. The number of shoppers after announcement :
N = 320 x 150/100 = 480
Hope this helps!
:)
Question 2 of 10
2 Points
Based on the housing data below, use linear regression to estimate a fair
price for a 1700 ft2 home.
Square F
Feet
|
2156
2040
20
2050
House Price
in thousands)
210
200
A. $180,000
O B. $175,000
C. $156,000
oo -
D. $190,000
DUS
Answer:
C. $176.000
Step-by-step explanation:
Linear regression requires sufficient data points for analysis, which are not provided, making it impossible to calculate an estimated price for a 1700 ft2 home without additional information.
Explanation:To estimate a fair price for a 1700 ft2 home using linear regression, we would require more data points with corresponding house prices to create a regression model. Since we're not provided with sufficient data in the question, and there's no explicitly provided regression equation or coefficients, it's not possible to accurately calculate the estimated price for a home of a given square footage using linear regression. However, if we had such data, we would typically plot square footage on the x-axis and house price on the y-axis, calculate the slope and intercept coefficients of the regression line, and then use the regression equation y = mx + b (where y is the estimated house price, m is the slope, x is the square footage, and b is the y-intercept) to predict the price of the house with given square footage
Find the exact length for the third side
Answer:
12
Step-by-step explanation:
Pythagorean theorem
a²+b²=c²
a²+35²=37²
a²+1225=1369
manipulate the equation
1225-1369=-a²
-144=-a²
√-144=12
a=12
A set of electric toothbrush prices are normally distributed with a mean of 87 8787 dollars and a standard deviation of 8 88 dollars. What proportion of electric toothbrush prices are between 104.60 104.60104, point, 60 dollars and 108.20 108.20108, point, 20 dollars?
Answer:
.0099
Step-by-step explanation:
right answer
The proportion of exam scores are between 82 and 89.2 points is 0.3330.
What is standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given:
mean = 87 points and
standard deviation = 8 points.
Now, using
Z= [tex]x- \mu / \sigma[/tex]
z= 104.6 - 87 / 8
z= 2.2
again, Z= [tex]x- \mu / \sigma[/tex]
z= 108.2- 87 / 8
z= 2.65
So, the proportion is
P(x<108.20)-P(x<104.60)
=P(Z<2.65)-P(Z<2.2)
= 0.9960-0.9861
=0.0099
Learn more about standard deviation here:
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If u could do this it would be great
When adding polynomial expressions, add the monomials with the same degree:
[tex]3g^2 + 3g^2[/tex]
[tex]-g - 8g[/tex]
[tex]4[/tex]
=
[tex]6g^2 -9g + 4[/tex]
Mrs. Child bakes pumpkin pies using a deep‐dish pie plate with a 9 inch diameter. If she cuts her pies into 12 equal slices and you eat two slices for dessert, what is the total length of the crust you have eaten?
Answer:[tex]4.71\ in.[/tex]
Step-by-step explanation:
Given
diameter of pie is [tex]d=9\ inch[/tex]
radius [tex]r=\frac{9}{2}=4.5\ inch[/tex]
If child divides pie into 12 equal parts then each part subtends an angle of
[tex]=\frac{360^{\circ}}{12}=30^{\circ}[/tex] at the center
and crust length of single piece is
[tex]=\frac{30}{360}\times 2\pi r[/tex]
[tex]=\frac{1}{12}\times 2\times \pi \times 4.5[/tex]
[tex]=2.35\ in.[/tex]
For two slice length is [tex]2\times 2.35=4.71\ in.[/tex]
Thus the total length of crust eaten is [tex]=4.71\ in.[/tex]
Find the missing height of the cone. Volume= 118π ft3 Diameter= 2/3
Answer:
11 ft
Step-by-step explanation:
The equation for the volume of a cone is:
V = 1/3(3.14)r^2h
V = 414.48
r = 6
Plug in those values and solve for h:
414.48 = 1/3(3.14)(6)^2h
414.48 = 37.68h ; divide both sides by 37.68
11 = h
The missing height is 11ft.
Which number is the additive inverse of -5?
Answer:
It would be 5
Step-by-step explanation:
SO the additive inverse would basically just be the opposite of the number, for example lets say you had 12, the additive inverse would be -12. You're just changing the sign of the number! From what i know i believe that's it. Have a nice day! :D
Solve the system of equations :
2x -5y=-22
X+7y=27
Answer:
X = -1 Y = 4
Step-by-step explanation:
Put the 7y over so it is 27-7y
after that you fill in the x on the top formula with (27-7y)
From there you solve like normal for Y, which ends out being 4.
Once you have that you can plug 4 into the Y spot in the bottom formula and just solve for X
:3
The probability of rolling a 3 with a single six-sided die is 1/6. The probability of rolling
a 5 on a single six-sided die is 1/6. Thus the probability of rolling a 3 and then a 5 on
back to back rolls of a six-sided die is 1/6 x 1/6 = 36.
We can perform this calculation
because rolling a 3 and then a 5 are known as a ________ event?
Find the blank answer!
Answer:
3625
Step-by-step explanation:
Two-fourths cup of water is how much in ounces?
Answer:
4 fluid ounces
Step-by-step explanation:
question is worded a little weird
V= 3 x 5 x 4
V = 3 + 5 + 4
V= 5 x 4
V = 3 x 5
Answer:
The answer is 3 * 5 * 4
Step-by-step explanation: It's because volume is length times width times height so you would have to multiply all three numbers.
I NEED HELP ASAP!!!!!!!!!!!!!
If you know the answer please help....
Answer: The 4 correct answers are A,C,D, and E.
In simplest racial form what are the solutions to the quadratic equation 0= -3x-4x+5
Answer:
Step-by-step explanation:
Answer:
x = 5/7
Step-by-step explanation:
We find x by watching organic tutor
Bill is playing a game of chance with the following payout. 30% of the time you will lose 20 dollars, 20% of the time you will lose 40 dollars. 10% of the time you will win 50 dollars, 40% of the time you will win 5 dollars. Find the expected value of the event and explain if Bill should play this game based on the mathematical expectation.
please helpppop asappppp and show work so I understand please
Anybody know this??? please help
Answer:
The expected value of playing the game is -$7.
Bill should not play this game.
Step-by-step explanation:
The probability distribution of gain and loss is as follows:
X P (X)
-$20 0.30
-$40 0.20
$50 0.10
$5 0.40
Total 1.00
The expected value of a probability distribution is given by:
[tex]E(X)=\sum {X\times P(X)}[/tex]
Compute the expected value of playing the game of chance as follows:
[tex]E(X)=\sum {X\times P(X)}[/tex]
[tex]=(-\$20\times 0.30)+(-\$40\times 0.20)+(\$50\times 0.10)+($5\times 0.40)\\\\=-\$6-\$8+\$5+\$2\\\\=-\$7[/tex]
The expected value of playing the game is -$7.
The expected value of the game suggests that Bill will incur a loss of $7 if he plays.
So, it is safe not to play the game.
The floor function maps any number to the greatest integer that is _[blank]_ the number.
Which phrase correctly fills in the blank of the previous statement?
A.) greater than
B.) greater than or equal to
C.) less than or equal to
D.) less than
Answer:
C. Less than or equal to
Step-by-step explanation:
The floor function is a function used to return an integer value that is great than the input number.
More often than not, the input number is a real number.
Take for instance.
Floor(3.2).
Going by the explanation above, the result of this will be 3
How about floor(-3.2)
The result of this will be -4.
This is so because -4 is less than or equal to -3.2.
The floor function maps any number to the greatest integer that is C.) less than or equal to the number.
The floor function maps any number to the greatest integer that is less than or equal to the number. This means that for any real number \( x \), the floor function, denoted as [tex]\( \lfloor x \rfloor \),[/tex] will produce the largest integer that does not exceed \( x \). For example, \( \lfloor 3.7 \rfloor = 3 \) and \( \lfloor -2.3 \rfloor = -3 \).
The floor function is widely used in mathematics and computer science for rounding down numbers to the nearest integer. It is especially useful in discrete mathematics, algorithms, and number theory. When working with the floor function, it is essential to understand that it always rounds down towards negative infinity, not necessarily towards zero. Thus, for any real number \( x \), \( \lfloor x \rfloor \leq x \).
Therefore, the correct phrase to complete the statement about the floor function is:
C.) less than or equal to.
Using the matrix solver on your calculator, find the solution to the system of equations shown below.
5x+5y=20
2x+2y=8
Options:
A. x = 5, y = 5
B. x = 2, y = 2
C. No solution
D. More than 1 solution
The system of equations 5x+5y=20 and 2x+2y=8 is dependent with infinitely many solutions, meaning there is more than one solution
Explanation:To solve the system of linear equations:
5x + 5y = 202x + 2y = 8First, notice that both equations are multiples of the other. If you divide the first equation by 5 and the second equation by 2, you get the same equation:
x + y = 4
Since both equations are effectively the same, every solution to one is a solution to the other, which means that there are infinitely many solutions. This sort of system is called dependent, meaning one equation can be derived from the other.
So, using a matrix solver on a calculator will indicate that the system does not have a unique solution. The correct answer is:
D. More than 1 solution
In the diagram below, DE and EF are tangent to O. What is the measure of DF?
The measure of the arc DF is 86 degrees if the measure of the major arc is 274 degrees option (D) is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have:
In the diagram below, DE and EF are tangent to O.
Let x be the measure of arc DF.
The complete revolution around the center = 360 degree
Major arc + Minor arc = 360
274 + x = 360
x = 86 degrees
Thus, the measure of the arc DF is 86 degrees if the measure of the major arc is 274 degrees option (D) is correct.
Learn more about circle here:
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Answer:
86
Step-by-step explanation:
Just took the quiz
I need help!!!???
The circle below is centered at the point (2,-1) and has a radius of length 3.
What is its equation?
А. (x-1)^2 + (y+ 2)^2 = 9
в. (х-2)^2 + (y+ 1)^2 =3^2
C. (х+ 2)^2 + (у - 1)^2 =3^2
D. (х+ 1)^2 + (y-2)^2 = 9
Answer:
Letter B is the answer.
Mrs.Brown gives two tests to her class. 30% of the class passed both tests and 45% of the class passed the first test. What percent passed the second test given that they passed the first test?
Answer:
15%
30 percent passed BOTH tests.....Only 15% passed ONLY first test
30/(30+15) = 67% of those who passed the first test ALSO passed the second test.
Upon hitting a bat, a baseball has a change in momentum of 16.5 kg-ms. What is the average
force applied to the baseball the time of impact is 0.00200 seconds?
Answer:
The average force applied to the baseball is 8.25kN
Step-by-step explanation:
This problem bothers on the impulse of a force
We know that the change in momentum is expressed as
Ft= mv-mu
Given
Ft=16.5 kg-ms
Time t of impact =0.00200s
The force applied can be solved for
By making F subject of formula
F= (mv-mu)/t
F=16.5/0.002
F= 8250N
F= 8.25kN
Final answer:
The average force applied to the baseball is calculated to be 8250 Newtons, based on the given change in momentum of 16.5 kg-ms and the time of impact of 0.00200 seconds.
Explanation:
The student is asking how to calculate the average force applied to a baseball during collision with a bat, given that the baseball's change in momentum (impulse) is 16.5 kg-ms and the time of impact is 0.00200 seconds.
To find the average force (Favg), we can use the formula derived from Newton's second law, which relates force, change in momentum (impulse), and time:
Favg = \\Delta p / t
Where:
\\Delta p is the change in momentumt is the time during which the force is appliedPlugging in the values we have:
Favg = 16.5 kg-ms / 0.00200 s
Doing the calculation:
Favg = 8250 N
Therefore, the average force applied to the baseball is 8250 Newtons.
Let ∠Q be an acute angle such that tanQ=0.04. Use a calculator to approximate the measure of ∠Q to the nearest tenth of a degree.
m∠Q≈ __∘
We have been given that ∠Q is an acute angle such that [tex]\text{tan}(Q)=0.04[/tex]. We are asked to find the measure of angle Q to nearest tenth of a degree.
We will use arctan to solve for measure of angle Q as:
[tex]Q=\text{tan}^{-1}(0.04)[/tex]
Now we will use calculator to solve for Q as:
[tex]Q=2.290610042639^{\circ}[/tex]
Upon rounding to nearest tenth of degree, we will get:
[tex]Q=2.3^{\circ}[/tex]
Therefore, measure of angle Q is approximately 2.3 degrees.
The measure of angle Q, rounded to the nearest tenth of a degree, is approximately 131.4 degrees.
To approximate the measure of angle [tex]\( \angle Q \)[/tex] given [tex]\( \tan Q = 0.04 \)[/tex], follow these steps manually:
1. Use the inverse tangent function : Use the inverse tangent function [tex](arctangent or \( \tan^{-1} \)) to find \( Q \)[/tex].
2. Calculate [tex]\( Q \)[/tex] : Calculate [tex]\( Q = \tan^{-1}(0.04) \)[/tex].
3. Convert to degrees : The result of [tex]\( \tan^{-1}(0.04) \)[/tex] will give you [tex]\( Q \)[/tex] in radians. To convert radians to degrees, multiply by [tex]\( \frac{180}{\pi} \)[/tex].
- [tex]\( Q = \tan^{-1}(0.04) \)[/tex]
- Suppose [tex]\( \tan^{-1}(0.04) \approx 2.29161 \)[/tex] radians.
- Convert radians to degrees: [tex]\( Q \approx 2.29161 \times \frac{180}{\pi} \)[/tex]
- [tex]\( Q \approx 2.29161 \times 57.2958 \)[/tex]
- [tex]\( Q \approx 131.384 \)[/tex] degrees (this is the exact calculated value).
4. Round to the nearest tenth :
Since we need to round to the nearest tenth of a degree,
- [tex]\( Q \approx 131.4^\circ \)[/tex].
Therefore, the measure of [tex]\( \angle Q \)[/tex], rounded to the nearest tenth of a degree, is approximately [tex]\( 131.4^\circ \)[/tex].