Answer:
y = 4/3x+2
Step-by-step explanation:
We can use the slope intercept form of the equation
y = mx+b
Where m is the slope and b is the y intercept
y= 4/3 x +b
Substitute the point into the equation
6 = 4/3(3) +b
6 = 4 +b
Subtract 4 from each side
2 = b
y = 4/3x+2
Graph the linear equation. Find three points that solve the equation. - 3x +2y=2
Answer:
y=3/2x+1 0,1 2,4 4,7
Step-by-step explanation:
-3x+2y=2
+3x
2y=3x+2
/2 /2 /2
y=3/2x+1
A random sample of 10 subjects have weights with a standard deviation of 11.6144 kg. What is the variance of their weights? Be sure to include the appropriate units with the result.
Answer:
Variance=134.8943 kg
Step-by-step explanation:
The relationship between standard deviation and variance is that standard deviation is the square root of the variance.
So given the value of standard deviation to be 11.6144kg, the variance will be the square of the number.
Standard deviation= √variance
Standard deviation ²=√variance²
Standard deviation ² = variance
11.6144²= variance
134.8943
Variance=134.8943 kg
Answer:
122.4409 kg
Step-by-step explanation:
Which of the following box plot best represents the set of data below
Answer:
C. Box plot B
Step-by-step explanation:
The function y=−16x2+v0x models the height of a football in feet x seconds after a player kicks it. In the equation of the function, v0 is the ball's initial velocity in feet per second. The ball hits the ground 2 seconds after the player kicks it.
What is the value of v0?
Answer:
[tex]\large \boxed{\sf \ \ v_0=32 \ \ }[/tex]
Step-by-step explanation:
Hello,
The equation is
[tex]y=f(x)=-16x^2+v_0 \cdot x[/tex]
The ball hits the ground 2 seconds after the player kicks it, it means that f(2)=0.
We need to find [tex]v_0[/tex] such that f(2)=0.
[tex]f(2)=-16\cdot 2^2+v_0 \cdot 2=-64+2v_0=0\\\\\text{*** add 64 to both sides ***}\\\\2v_0=64\\\\\text{*** divide by 2 both sides ***} \\\\v_0=\dfrac{64}{2}=32[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
v0 = 32 ft/s
Step-by-step explanation:
The initial population of a town is , and it grows with a doubling time of 10 years. What will the population be in years?
Answer:
This question is incomplete, i will answer it as:
"The initial population of a town is A, and it grows with a doubling time of 10 years. What will the population be in X years?"
Ok, the growth of a population usually is an exponential growth, so we can write this as:
P(t) = A*exp(r*t)
Where A is the initial population.
r is the rate of growth, and t is our variable, in this case, number of years.
Now we know that when t = 10y, the population doubles, so we should have:
P(10y) = 2*A = A*exp(r*10y)
2 = exp(r*10)
ln(2) = r*10
ln(2)/10 = r = 0.069.
Then our equation is:
P(t) = A*exp(0.069*t)
Now, if we want to know the population in X years, we need to replace the variable t by X
P(t = X) = A*exp(0.069*X)
the perimeter of a square flower bed is 100 feet. what is the area of the flower bed in sqaure feet
Answer:
A =625 ft^2
Step-by-step explanation:
The perimeter of a square is
P = 4s where s is the side length
100 =4s
Divide each side by 4
100/4 = 4s/4
25 = s
A = s^2 for a square
A = 25^2
A =625
the solution of the equation 0=4+4(m+1) is
Answer:
[tex]\boxed{m = -2}[/tex]
Step-by-step explanation:
[tex]0 = 4+4(m+1)[/tex]
Resolving Parenthesis
[tex]0 = 4+4m + 4[/tex]
[tex]0 = 4m+8[/tex]
Subtracting 8 to both sides
[tex]-8 = 4m[/tex]
[tex]4m = -8[/tex]
Dividing both sides by 4
m = -8/4
m = -2
Step-by-step explanation:
4+4m+4= 0
4m+8=0
4m=-8
m= -8/4=-2
The graph of an absolute value function has a vertex of (2,3) and crosses the x-axis at (−1,0) and (5,0). What is the equation for this absolute value function when y=0? A 0=|x+2|+3 B 0=|x−2|+3 C 0=−|x+2|+3 D 0=−|x−2|+3
Answer:
Option D.
Step-by-step explanation:
The vertex form of an absolute function is
[tex]y=a|x-h|+k[/tex]
where, a is a constant, (h,k) is vertex.
It is given that, vertex of an absolute function is (2,3). So, h=2 and k=3.
[tex]y=a|x-2|+3[/tex] ...(1)
It crosses the x-axis at (5,0). So put x=5 and y=0 to find the value of a.
[tex]0=a|5-2|+3[/tex]
[tex]-3=3a[/tex]
[tex]-1=a[/tex]
Put a=-1 in (1).
[tex]y=(-1)|x-2|+3[/tex]
[tex]y=-|x-2|+3[/tex]
Now, put y=0, to find the equation for this absolute value function when y=0.
[tex]0=-|x-2|+3[/tex]
Therefore, the correct option is D.
Answer:
I got this question on my test and I answered D cause if you look up the graph it matches the question
Step-by-step explanation:
D 0=−|x−2|+3
A poll reported that 66 percent of adults were satisfied woth the job the major airlines were doing. Suppose 25 adults are selected at random and the number who are satisfied is recorded.
1. Explain why this is a binomial experiment.
A. This is a binomial experiment because there are three mutually exclusive outcomes for each trial, there is a fixed number of trials, the outcome of one trial does not affect the outcome of another, and the probability of success is the same for each trial.
B. This is a binomial experiment because there are two mutually exclusive outcomes for each trial, there is a random number of trials, the outcome of one trial does not affect the outcome of another, and the probability of success is the same for each trial.
C. This is a binomial experiment because there are two mutually exclusive outcomes for each trial, there is a fixed number of trials, the outcome of one trial does not affect the outcome of another, and the probability of success changes in each trial.
D. This is a binomial experiment because there are two mutually exclusive outcomes for each trial, there is a fixed number of trials, the outcome of one trial does not affect the outcome of another, and the probability of success is the same for each trial.
2) Find and interpret the probability that exactly 15 of them are satisfied with the airlines.
Answer:
A)Option D
B)P(X = 15) = 0.1325
Step-by-step explanation:
A) From the question, the information given follows binomial distribution because there are two mutually exclusive outcomes for each trial, there is a fixed number of trials. The outcome of one trial does not affect the outcome of another, and the probability of success is the same for each trial.
So option D is correct.
B) From the question, we are told that the poll reported that 66 percent of adults were satisfied with the job. Thus, probability is; p = 0.66
Let X be the number of adults satisfied with the job. Since 25 are selected,
Thus;
P(X = 15) = C(25, 15) * (0.66)^(15) * (1 - 0.66)^(25 - 15)
P(X = 15) = 3268760 × 0.00196407937 × 0.00002064378
P(X = 15) = 0.1325
Which point is a solution to the inequality shown in this graph?
Answer: A, (0, -3)
Step-by-step explanation:
Inequalities, once graphed, take the form of the image you attached:
Linear inequalities are straight lines, sometimes dotted and sometimes solid, with shading on one side of the line.
Any point in the shading is a correct solution to the inequality.
When the line is solid, any point on the line is a solution to the inequality.When the line is dotted, only the shaded area past the line includes solutions - points on the line are not solutions.In this case, the line is solid, so any point on the line is a solution to the inequality.
Looking at answer choice A: (0, -3), it lies on the line as the y-intercept.
The correct choice is A.
n = 9
H0 : 50 = 47
Ha : 50 s = 3
Assume data are from normal population. The p-value is equal to:______.
a. 0.0171.
b. 0.0805.
c. 0.2705.
d. 0.2304.
Answer:
The p-value is 0.809.
Step-by-step explanation:
In this case we need to perform a significance test for the standard deviation.
The hypothesis is defined as follows:
H₀: σ₀ = 4 vs. Hₐ: σ₀ ≤ 4
The information provided is:
n = 9
s = 3
Compute the Chi-square test statistic as follows:
[tex]\chi^{2}=\frac{(n-1)s^{2}}{\sigma_{0}^{2}}[/tex]
[tex]=\frac{(9-1)\cdot (3)^{2}}{(4)^{2}}\\\\=\frac{8\times 9}{16}\\\\=4.5[/tex]
The test statistic value is 4.5.
The degrees of freedom is:
df = n - 1
= 9 - 1
= 8
Compute the p-value as follows:
[tex]p-value=P(\chi^{2}_{9}>4.5)=0.809[/tex]
*Use a Chi-square table.
Thus, the p-value is 0.809.
3. What is the distance from (−4, 0) to (2, 5)? Round your answer to the nearest hundredth. (4 points)
Answer:
7.81
Step-by-step explanation:
its a triangular shape
let x = 4 + 2 = 6
let y = 5
length between two points = h
h² = x² + y²
h² = 6² + 5²
h = sqrt of 61
h = 7.81
a.
C.
Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range-
y = -5x² - 4x + 1
D: all real numbers
D: (x20)
R: ( 31.8)
R: all real numbers
b. D: all real numbers
d. D: all real numbers
R: ( 2 1.8)
R: ( 30.2)
Answer:
Step-by-step explanation:
y = -5x² - 4x + 1 is a quadratic and thus is defined on the domain "all real numbers." Because of the negative sign in front of the x^2 term, we know that this parabolic curve opens downward. The x-coordinate of the vertex is x = -b/[2a], which in this case is x = 4/[2*-5], or -4/10, or -2/5. Using synthetic division to determine the y-coordinate of the vertex, we get vertex (-2/5, 9/5). 9/5 is the maximum y value. The range is (-infinity, 9/5].
I need answers for 1 , 2, 4
Answer:
(3) x ≥ -3
(4) 2.5 gallons
(4) -12x + 36
Step-by-step explanation:
Hey there!
1)
Well its a solid dot meaning it will be equal to.
So we can cross out 1 and 2.
And it's going to the right meaning x is greater than or equal to -3.
(3) x ≥ -3
2)
Well if each milk container has 1 quart then there is 10 quarts.
And there is 4 quarts in a gallon, meaning there is 2.5 gallons of milk.
(4) 2.5 gallons
4)
16 - 4(3x - 5)
16 - 12x + 20
-12x + 36
(4) -12x + 36
Hope this helps :)
You change oil every 6000 miles and drive 2000 miles a month; how many times a year do you change oil?
Answer:
you would change it 4 times a year
Step-by-step explanation:
if there is 12 months in a year and 3 mounths equal 6000 then divide 12/3=4
A 24-centimeter by 119-centimeter piece of cardboard is used to make an open-top box by removing a square from each corner of the cardboard and folding up the flaps on each side. What size square should be cut from each corner to get a box with the maximum volume
Answer:
The size square removed from each corner = 32.15 cm²
Step-by-step explanation:
The volume of the box = Length * Breadth * Height
Let r be the size removed from each corner
Note that at maximum volume, [tex]\frac{dV}{dr} = 0[/tex]
The original length of the cardboard is 119 cm, if you remove a size of r (This typically will be the height of the box) from the corner, since there are two corners corresponding to the length of the box, the length of the box will be:
Length, L = 119 - 2r
Similarly for the breadth, B = 24 - 2r
And the height as stated earlier, H = r
Volume, V = L*B*H
V = (119-2r)(24-2r)r
V = r(2856 - 238r - 48r + 4r²)
V = 4r³ - 286r² + 2856r
At maximum volume dV/dr = 0
dV/dr = 12r² - 572r + 2856
12r² - 572r + 2856 = 0
By solving the quadratic equation above for the value of r:
r = 5.67 or 42
r cannot be 42 because the size removed from the corner of the cardboard cannot be more than the width of the cardboard.
Note that the area of a square is r²
Therefore, the size square removed from each corner = 5.67² = 32.15 cm²
EXAMPLE 5 If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (1, 2, 0) in the direction of v = i + 4j − k. SOLUTION (a) The gradient of f is ∇f(x, y, z) = fx(x, y, z), fy(x, y, z), fz(x, y, z)
Answer:
a) f = sin(yz)i + xzcos(yz)j + xycos(yz)kb) -2Step-by-step explanation:
Given f(x, y, z) = x sin(yz), the formula for calculating the gradient of the function is expressed as ∇f(x, y, z) = fx(x, y, z)i+ fy(x, y, z)j+fz(x, y, z)k where;
fx, fy and fz are the differential of the functions with respect to x, y and z respectively.
a) ∇f(x, y, z) = sin(yz)i + xzcos(yz)j + xycos(yz)k
The gradient of f = sin(yz)i + xzcos(yz)j + xycos(yz)k
b) Directional derivative of f at (1,2,0) in the direction of v = i + 4j − k is expressed as ∇f(1, 2, 0)*v
∇f(1, 2, 0) = sin(2(0))i +1*0cos(2*0)j + 1*2cos(2*0)k
∇f(1, 2, 0) = sin0i +0cos(0)j + 2cos(0)k
∇f(1, 2, 0) = 0i +0j + 2k
Given v = i + 4j − k
∇f(1, 2, 0)*v (note that this is the dot product of the two vectors)
∇f(1, 2, 0)*v = (0i +0j + 2k)*(i + 4j − k )
Given i.i = j.j = k.k =1 and i.j=j.i=j.k=k.j=i.k = 0
∇f(1, 2, 0)*v = 0(i.i)+4*0(j.j)+2(-1)k.k
∇f(1, 2, 0)*v = 0(1)+0(1)-2(1)
∇f(1, 2, 0)*v =0+0-2
∇f(1, 2, 0)*v= -2
Hence, the directional derivative of f at (1, 2, 0) in the direction of v = i + 4j − k is -2
Marcia is a bag that contains four green marbles, eight yellow marbles, and 20 red marbles. If she chooses one marble from the bag, what is the probability that the marble is not red?
Answer:
3/8
Step-by-step explanation:
The bag contains 4 green marbles, 8 yellow marbles and 20 red marbles.
The total number of marbles is 32.
She chooses one from the bag.
The probability of the marble not being red is:
P(not red) = 1 - P(red)
P(not red) = 1 - (20 / 32) = 1 - 5/8
P(not red) = 3/8
The probability of it not being red is 3/8.
Which expression is equivalent to x^-5/3?
Answer:
[tex]\frac{1}{(\sqrt[3]{x} )^5}[/tex]
Step-by-step explanation:
[tex]x^{-\frac{5}{3} }[/tex] = [tex](\sqrt[3]{x} )^{-5}[/tex] = [tex]\frac{1}{(\sqrt[3]{x} )^5}[/tex]
There will be a circular patio with a diameter of 7 metres. Greg is going to put a tiled edge around the patio. What is the circumference of the patio? m Circumference of a circle = 2πr Use π = 3.14
Answer:
[tex]Circumference = 21.99 \ m[/tex]
Step-by-step explanation:
Circumference = [tex]\pi d[/tex]
Given that d = 7 m
[tex]Circumference = (3.14)(7)\\[/tex]
[tex]Circumference = 21.99 \ m[/tex]
Answer:
[tex]\boxed{21.98 \: \mathrm{meters}}[/tex]
Step-by-step explanation:
Apply formula for circumference of a circle.
[tex]C=\pi d[/tex]
[tex]d:diameter[/tex]
Take [tex]\pi =3.14[/tex]
Plug [tex]d=7[/tex]
[tex]C=3.14 \times 7[/tex]
[tex]C= 21.98[/tex]
The first three steps in determining the solution set of the system of equations, y = –x2 – 2x + 8 and y = 2x + 11, algebraically are shown in the table
what is the answer to the equation? plz help 3x+8=9+3x-14
Answer:
It does not have an answer as 3x != 3x + 13 or not equalivalent
Step-by-step explanation:
Answer:
no solution
Step-by-step explanation:
3x+8=9+3x-14
Combine like terms
3x+8 = 3x -5
Subtract 3x from each side
8 = -5
This is never true so there is no solution
What is 7/8×3/9 reduced to lowest terms
Answer:
7/24
Step-by-step explanation:
7/8×3/8= 21/72
divide using 3
= 7/24
WHY CAN'T ANYONE HELP ME? Twice last month, Judy Carter rented a car in Fresno, California, and traveled around the Southwest on business. The car rental agency rents its cars for a daily fee, plus an additional charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 440 miles, and the rental cost her $286. On her second business trip she drove 190 miles in 3 days, and paid $165.50 for the rental. Find the daily fee and the mileage charge.
Answer:
The daily rate is $33 and the per mile rate is $0.35
Step-by-step explanation:
4x + 440y = 286
3x + 190y = 165.5
We can solve this systems of equations by multiplying the second statement by [tex]-\frac{4}{3}[/tex] to try and eliminate the x variable.
4x + 440y = 286
-4x - [tex]\frac{760}{3}[/tex]y = -220[tex]\frac{2}{3}[/tex]
[tex]\frac{560}{3}[/tex] y= [tex]\frac{196}{3}[/tex]
560y = 196
y = 0.35
So, the rate per mile is 0.35. Now, with this info, let's find the daily rate by plugging it into the equation.
[tex]4x + 440\cdot0.35 = 286\\4x + 154 = 286\\4x = 132\\x = 33[/tex]
So, the daily rate is $33 and the mile rate is $0.35.
Hope this helped!
Answer:
the daily fee =33 dollars
and the mileage charge.=0.35
let d: be daily fee and m for mileage
cost of rental =(d*number of days)+ (m*number of mileage)
her first trip: 4d+440m=286
her second trip: 3d+190m=165.5
solve by addition and elimination
4d+440m=286 ⇒ multiply by 3 ⇒12d +1320m=(3)286
3d+190m=165.5⇒ multiply by 4⇒12d+190(4)m=4(165.5)
12d+1320m=858
12d+760m=662
subtract two equation to eliminate d
12d+1320m-12d-760m=858-662
560m=196
m=7/20=0.35 for on mileage
d: 4d+440m=286
4d=286-440(0.35)
d=(286-154)/4 33 dollars
A company pays its employees an average wage of $17.90 an hour with a standard deviation of $1.50. If the wages are approximately normally distributed and paid to the nearest cent, the highest 2.5% of the employees hourly wages is greater than what amount
Answer:
$20.84
Step-by-step explanation:
To solve the above question, we would be using the z score formula
The formula for calculating a z-score :
z = (x - μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation
x = unknown
μ = $17.90
σ = $1.50
We were not given z score in the above question but this can be determined.
We are told in the question to find the amount that the highest 2.5% of the employees hourly wages is greater than.
Hence, our confidence interval = 100 - 2.5 = 97.5%
The z score for 97.5% = 1.96
Below are inequalities equations with more explanation.
P(X ≥ x) = 2.5% = 0.025
P(X ≤ x) = 1 - 0.025 = 0.975
P (X - μ)/σ ≤ (x - μ)/σ) = 0.975
z ≤ (x - μ)/σ = 0.975
z ≤ 1.96 = 0.975
z = (x - μ)/σ,
1.96 = x - 17.90/1.5
Cross Multiply
1.96 × 1.5 = x - 17.90
x = (1.96 × 1.5) + 17.90
x = 2.94 + 17.90
x = 20.84
Therefore, the amount that the highest 2.5% of the employees hourly wages is greater than is $20.84
im not sure what it is asking me to do
Answer:
0.79Step-by-step explanation:
[tex]p(x \leqslant 0) = p( - 5) + p( - 3) + p( - 2) + p(0)[/tex]
[tex] = 0.17 + 0.13 + 0.33 + 0.16 [/tex]
[tex] = 0.79[/tex]
Hope this helps...
Best regards!!
please help me please!!!
Answer:
she has covered 6 miles in 1 ½ hours
Step-by-step explanation:
you need to learn how to read a graph.
it quite easy actually.
just look where the line on the graph is on 1.5 hours ( you can count the boxes if you don't know where 1.5 or 1 ½ is)
several different positive integers are written on a blackboard. the product of the smallest two of them is 16. the product of the largest 2 of them is 225. what is the sum of the integers?
Answer:
44
Step-by-step explanation:
The integers 2,8,9 and 25 fit to the terms of the problem.
So the smallest two are 2 and 8 =>2*8=16
and 9*25=225
Note that another pair of integers which product is 16 can be 1 and 16.
However it means that both numbers which product is 225 are bigger than 16 - this is not possible so 16*16=256>225
So only numbers 2,8,9 and 25 fit to the terms of the problem.
Note that there is no any integer number between 8 and 9 . So there are four integers in total and these integers are 2,8,9 and 25.
The sum of these integers is 2+8+9+25=44
A drawer is filled with 3 black shirts, 8 white shirts, and 4 gray shirts. One shirt is chosen at random from the drawer. Find the probability that it is not a white shirt. Write your answer as a fraction.
The probability that the shirt that is chosen at random from the drawer is not a white shirt, can be found to be 47 %
How to find the probability ?The probability that the shirt picked is not a white shirt can be found by first finding the number of shirts that are not white shorts in the drawer. This number is :
= Number of black shirts + Gray shirts
= 3 + 4
= 7 shirts
Then, find the total number of shirts in the drawer, including the white shirts :
= Number of black shirts + Gray shirts + White shirts
= 3 + 8 + 4
= 15 shirts
The probability that when a shirt is chosen at random, that it is not a white shirt is :
= Number of shirts that are not white / Total number of shirts
= 7 / 15
= 47 %
Find out more on probability at https://brainly.com/question/27831410
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Which of the following statements is correct about quadratic number patterns? A. The third difference is greater than zero. B. The first difference is constant. C. The difference between terms is always positive. D. The second difference is constant.
Answer: D.) The second difference is constant.
Step-by-step explanation:
The rate of change of a quadratic function is a linear function. The rate of change of that is constant, so second differences of a quadratic number pattern are constant.
Answer:
D.
Step-by-step explanation: