The linear function is y = 3x + 6. Then the rate of change of the linear function will be 3.
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
The linear equation that is passing through the points (2,9) and (-1,3).
Then we have
y - 3 = [(3 - 9)(-1 - 2)] (x + 1)
y - 3 = (-6) / (-2) (x + 1)
y - 3 = 3x + 3
y = 3x + 6
Then the rate of change of the linear function will be
y' = 3
More about the differentiation link is given below.
https://brainly.com/question/24062595
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12. A quality control procedure at a manufacturing facility involves selecting 5 items at random from a large batch, and then accepting the entire batch if at least 3 of the selected items pass inspection. If in reality 80% of all items produced would individually pass inspection, what is the probability that the batch will be accepted
Answer:
The probability is 0.9421
Step-by-step explanation:
Here, we want to calculate the probability that the batch will be accepted
For it to be accepted, 3,4 or 5 of the items would pass inspection
let p be the probability of a single item
passing the inspection
This probability is 80% = 0.8
Let q be the probability of failing inspection = 2-0.8 = 0.2
The Bernoulli approximation of the probability distribution for 3 passing the inspection out of five will be;
5 C 3 0.8^3 0.2^2 = 0.2048
Next we calculate for 4 out of the five
That will be
5 C 4 0.8^4 0.2 = 0.4096
Finally we calculate for all 5
5 C 5 0.8^5 0.2^0 = 0.32768
So the probability that the batch will be accepted will be;
0.32768 + 0.4096 + 0.2048 = 0.94208
Using the binomial distribution, it is found that there is a 0.9421 = 94.21% probability that the batch will be accepted.
For each item, there are only two possible outcomes, either they pass inspection, or they do not. The probability of an item passing inspection is independent of any other item, hence the binomial distribution is used to solve this question.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
5 items are selected, hence [tex]n = 5[/tex].80% of all items produced would individually pass inspection, hence [tex]p = 0.8[/tex].The probability that the batch will be accepted is:
[tex]P(X \geq 3) = P(X = 3) + P(X = 4) + P(X = 5)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{5,3}.(0.8)^{3}.(0.2)^{2} = 0.2048[/tex]
[tex]P(X = 4) = C_{5,4}.(0.8)^{4}.(0.2)^{1} = 0.4096[/tex]
[tex]P(X = 5) = C_{5,5}.(0.8)^{5}.(0.2)^{0} = 0.3277[/tex]
Then:
[tex]P(X \geq 3) = P(X = 3) + P(X = 4) + P(X = 5) = 0.2048 + 0.4096 + 0.3277 = 0.9421[/tex]
0.9421 = 94.21% probability that the batch will be accepted.
You can learn more about the binomial distribution at https://brainly.com/question/24863377
Considering the 9th slab of tax structure of Pakistan for 2020-2021, Where the taxable salary income exceeds Rs. 12,000,000 but does not exceed Rs. 30,000,000 the rate of income tax is 2,345,000 + 27.5% of the amount exceeding Rs. 12,000,000. If we create a mathematical Model of the tax structure, the function for this particular slab will be:
0.275x
0.275x-12000000
0.275x-955000
0.275x-2345000
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Answer:
(c) 0.275x-955000
Step-by-step explanation:
The amount exceeding 12,000,000 can be described by ...
x - 12,000,000
Then 27.5% of that is ...
0.275(x -12,000,000) = 0.275x -3,300,000
Adding 2,345,000 to that gives the expression ...
2,345,000 +(0.275x -3,300,000) = 0.275x -955,000
----------- are used to represent an unknown quantity in a mathematical expression.
HELP I WILL GIVE BRAINLEIST
Answer:
variables
Step-by-step explanation:
Let f(x) = 2x - 5 and g(x) = 3x. Perform the indicated
operation.
g(x)/f(x)
SOMEONE HELP PLZ
Answer:
f{3x}=6x-5
Step-by-step explanation:
There isn't really much to do: if you perform the division between function you get a new function:
[tex]h(x)=\dfrac{g(x)}{f(x)}=\dfrac{3x}{2x-5}[/tex]
23x + 18 - 12x = 62
Answer:56/23
Step-by-step explanation:
23x +18-12=62
23x+6=62
23x=56
X=56/23
Answer:
x=4
Step-by-step explanation:
Group like terms
23x-12x+18=62
add similar elements
11x+18=62
subtract 18 from both sides
11x+18-18=62-18
simplify
11x=44
divide both sdies by 11
11x/11=44/11
simplify
x=4
8
7
6+
5
4 3
N
1
-8 -7 -6 -5 4ß -2
-1
1
2 3 4 5 6 7 8
-2
-3
-5
-6
-7
-8+
The system of equations has
O one solution
no solution
infinitely many solutions
Answer:
no bro
Step-by-step explanation:
no
Juan rides his bike 97 miles to and from school each month.
Part A
How can you use compensation to find the number of miles he rode in 6 months?
A.
97 is close to 100, so multiply 6 × 100 and then add 6 × 3.
B.
97 is close to 100, so add 6 + 100 and then multiply by 6 + 3.
C.
97 is close to 100, so add 6 + 100 and then add 6 × 3.
D.
97 is close to 100, so multiply 6 × 100 and then subtract 6 × 3.
Answer:
cvfgrtyukjmn
Step-by-step explanation:
solve In 2010, the percentage of assisted living residents who had both heart disease and depression was 9%, the percentage with only heart disease was 25%, and the percentage with either condition was 48%. What percentage of assisted living residents had only depression
Answer:
The percentage of assisted living residents had only depression
P(D) =0.32
Step-by-step explanation:
Explanation:-
Given the percentage of assisted living residents who had both heart disease and depression was 9%
Let The event 'H' be the event of heart disease and 'D' be the event of depression
P(H ∩D) = 9% =0.09
The percentage with only heart disease was 25%
P(H) = 0.25
The percentage with either condition was 48%.
P(H∪D) = 48%=0.48
By addition theorem on probability
[tex]P(H UD) = P(H) +P(D) - P(H n D)[/tex]
[tex]0.48 = 0.25 + P(D) -0.09[/tex]
P(D) = 0.48 -0.16
P(D) = 0.32
The percentage of assisted living residents had only depression
P(D) =0.32
Please help me slove this problem
7 = 4x - 5
Answer:
x = 3
Step-by-step explanation:
7 = 4x - 5
7 - 4x = -5
-4x = -5 - 7
-4x = -12
x = 12 ÷ 4
x = 3
Answer:
×=3
Step-by-step explanation:
7=4×-5
7-4×=5
-4×=-5-7
-4×=-12
×=12÷4
×=3
Noah picked 3 kilograms of cherries. Mai picked half as many cherries as Noah. How many total kilograms of cherries die Mia and Noah pick together?
Group of answer choices
Answer:
cherries picked by Noah =3kg
Mia picked = 1/2*3 = 1.5kg
Total cherries picked together = 3+1.5 = 4.5kg
Step-by-step explanation:
Answer:
4.5 or 4 1/2. Based on the given conditions, formulate: 3 + 3 / 2 Find common denominator and write the numerators. ++++=4.5
Step-by-step explanation:
CORRECT THIS ANSWER MARK A BRAIN LESS
Which three quantities are needed in order to calculate the value of the Y-intercept for the linear
regression prediction equation?
The slope, the mean of X, and the total number of observations in the data
The slope, the mean of Y, and the total number of observations in the data
The mean of X, the mean of Y, and the total number of observations in the data
The mean of X, the mean of Y, and the slope
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Answer:
(d) The mean of X, the mean of Y, and the slope
Step-by-step explanation:
A point on the linear regression curve is (mean(x), mean(y)). With that point and the slope, the equation of the line can be found. That equation will reveal the y-intercept.
y-intercept = mean(y) -slope·mean(x)
helppppppppp:)))))))))))
Answer:
bottom one
Step-by-step explanation:
9a-b-2a-10b add like terms
7a-11b
A six controller thumb covers costs $2.10. At this rate, how much should 32 thumb covers cost? round to the
nearest cent.
Answer:
67 dollars and 20 cents
Step-by-step explanation:
2.10 per thumb cover
32x2.10=67.2
Answer:
if a six controller thumb cover cost 2.10 then you multiply 2.10 by 5 (because if you need 32 then you divide 32/6 and you get 5) 2.10 x 5 would equal 10.50 so that's your answer 10.50
Step-by-step explanation:
Patti went to the bakery. she bought a loaf of bread for 3.49, 6 muffins that cost 1.25 each, and a bottle of juice for 1.75. she gave the cashier a 20$ bill
how much should Patti receive? write equations to show ur work
!HELLp NoW! Asap
Answer:
$ 7.26
Step-by-step explanation:
You're welcome :)
7. What is the smallest angle in the triangle below?
Answer:
Angle a is the smallest
find the product of 4y²x(xy-2x²)
4y²x(xy-2x²)=4y³x²-8y²x³
Answer:
4y³x² - 8x³y²
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Exponential PropertiesStep-by-step explanation:
Step 1: Define
4y²x(xy - 2x²)
Step 2: Multiply
Distribute: 4y²x(xy) - 4y²x(2x²)Multiply: 4y³x² - 8x³y²if nth term of the AP 3,10,17.... is same as the nth term of the AP 63,65,67.... find n.
Answer:
n = 13
Step-by-step explanation:
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d
[tex]a_{n}[/tex] = 3 + 7(n - 1) (for the first AP)
[tex]a_{n}[/tex] = 63 + 2(n - 1) ( for the second one)
3 + 7(n - 1) = 63 + 2(n - 1)
3 + 7n - 7 = 63 + 2n - 2
5n = 65
n = 13
Answer:
n = 13
Step-by-step explanation:
AP = 2, 10, 17 ...
AP1 = 63,65, 67
Find the general term of AP
L = a + (n - 1)*d
a = 2
d = 7
Find the general term of AP1
L = 63 + (n - 1)*d
a = 63
d = 2
Equation to equate both of them
L = 3 + (n-1)7
L1 = 63 + (n - 1)*2
Equate L and L1
2 + (n - 1)*7= 63 + (n-1)*2 Subtract 3 from both sides
(n - 1)*7 = 63 - 3 + (n - 1)*2 Remove the brackets
7n - 7 = 60 + 2n - 2 Combine the like terms on the right
7n - 7 = 58 + 2n Subtract 2n from both sides
7n - 2n -7 = 58 Add 7 to both sides
5n = 58 +7 Divide by 5
n = 65/5
n = 13
So the 13th term on each series is equal.
L_13 = 3 + (13 - 1)*7
L_13 = 3 + (12)*7
L_13 = 87
=====================
L'_13 = 63 + (13 -1 ) * 2
L'_13 = 63 + 12*2
L'_13 = 87
1) Find the sum 4.5 + 5.9
Answer:
Step-by-step explanation:
Steps are below
step 1
4.5 + 5.9 equation
step 2
4.5 + 5.9 add them together by moving the points
4.5 + 5.9
10.4
help look at image pls
Answer:
ok coool
Step-by-step explanation:
i have nothing
Which quadratic function is shown in the graph?
A) f(x) = x2
Answer: a I think
Step-by-step explanation:
What is an equation of the line that passes through the points (4,-2) and (8,3)?
Answer:
[tex]y-4=\frac{5}{4} (x+2)[/tex]
Step-by-step explanation:
First you can find the slope of the line that would pass through those two points using the formula:
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
m = [tex]\frac{3-(-2)}{8-4}[/tex]
m=5/4
Now you can just plug the slope and one of the points into point-slope form for an equation of the line that will pass through both points. You can choose either point here: I'll just use the first one.
So,
[tex]y-4=\frac{5}{4} (x+2)[/tex]
(don't leave out the parentheses!)
Four boxes of cookies cost $18 how much does one box of cookies cost
Answer:
$5.50
Step-by-step explanation:
Answer:
You would get 4.5 as your answer or 4 1/2
Step-by-step explanation:
You literally just do 18/4
And you get your answer
The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8200 ft, the liquid boils at 199.42°F. At an altitude of 4700 ft, the liquid boils at 206.07°F. Write an equation giving the boiling point b of the liquid, in degrees Fahrenheit, in terms of altitude a, in feet. What is the boiling point of the liquid at 2500 ft?
Write an equation.
b=nothing
Answer:
The boiling point of the liquid it 210.25°F
Step-by-step explanation:
Linear Modeling
Some real-life events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to build the model and predict unknown behaviors.
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
We are given the following points (H,A) where A is the altitude and P is the boiling point of a certain liquid: (8200,199.42) and (4700,206.07)
Applying the formula:
[tex]\displaystyle B-199.42=\frac{206.07-199.42}{4700-8200}(A-8200)[/tex]
Calculating:
[tex]\displaystyle B-199.42=\frac{6.65}{-3500}(A-8200)[/tex]
[tex]\displaystyle B-199.42=-0.0019(A-8200)[/tex]
[tex]\displaystyle B-199.42=-0.0019A+15.58[/tex]
[tex]\displaystyle B=-0.0019A+15.58+199.42[/tex]
The equation is:
[tex]\displaystyle B=-0.0019A+215[/tex]
Finally, we calculate the boiling point at A=2500 ft:
\displaystyle B=-0.0019*2500+215
B = 210.25°F
The boiling point of the liquid it 210.25°F
If 21% = 96 students how many students is 1%.
Or you can help with the whole question
Answer:
1% are 5 students
Step-by-step explanation:
21% is 96 then
1% is X
X = 1*96 / 21
X = 5
I need the answers for #7 and #8
Answer:
7. x=9, y=7 The first number is 9, and the second number will be 7.
8. h= $2.25 c= $1.19 The cost of each hotdog is $2.25, and the cost of each bag of chips is $1.19.
Step-by-step explanation:
7. First lets define the variables: x=first number; y=the second number
Now we set up a system of equations:
Eq. 1. 2x+y=25 Eq. 2. 3x-y=20
Now we solve (I'm going to use subsitution you can use wtv you are comfortable with)
1. 2x+y=25 1. y=25-2x
Subsitute.
2. 3x-y=20 2. 3x- (25-2x)=20
Simplify.
3x-25+2x=20 5x-25=20 5x=45 x=9
Now solve for y by subsituting x into one of the equations.
1. 2x+y=25 2(9)+y=25 18+y=25 y= 7
The first number is 9, and the second number will be 7.
8. Define the variables.
h= cost of a hotdog; c=cost of a bag of chips
System of Equations:
Eq. 1. 5h+3c=14.82 Eq. 2. 7h+6c=22.89
Now solve.
1. 5h+3c=14.82 2. 7h+6c=22.89
Using subsitution...
h=2.25 c=1.19
The cost of each hotdog is $2.25, and the cost of each bag of chips is $1.19.
Theo borrows $8,000 for college expenses. He will pay a total of $10,280 after 6 years. What percent of interest did Theo pay?
i will give you 10 coins
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Answer:
4.75%
Step-by-step explanation:
When simple interest is charged, the payback amount is ...
A = P(1 +rt) . . . . for annual rate r and a term of t years
Using the given values, we can solve for r.
10280 = 8000(1 +6r)
1.285 = 1 +6r . . . . . . . . divide by 8000
0.285 = 6r . . . . . . . . . . subtract 1
0.285/6 = r = 0.0475 = 4.75% . . . . . . divide by 6; express as %
Theo paid interest at the rate of 4.75%.
Write a function rule that best models the data in the table. (0,3), (1,4),(2,7,(3,12)
What are the coordinates of point S?
A. -3/4, 1/2
B. -1/2, -3/4
C. 1/2, -3/4
D. 3/4, 1/2
Answer:
i think it's C.
Step-by-step explanation:
i really hope I'm right :/
Each side of a square is (7 + 3x) units. Which is the perimeter of the square?
Answer:
28+12x
Step-by-step explanation:
The perimeter of a square is 4s where s is the side lenght. In your case s is 7+3x so the perimeter will be (28+12x).
Barry has 7 coins, all of which are quarters and nickels. In all, they're worth $1.35. How many of each kind of coin does Barry have?
Answer:
5 quarters
2 nickels
Step-by-step explanation:
Answer:
5 quarters and 2 nickels.
Step-by-step explanation:
One quarter is equal to 25. 25x5=125. So, it would be 5 quarters because you wouldn't be able to go any farther without going over. One nickel is 5 and if you have 2 nickels you get 10. 10+125=135. So, there will be 2 nickels and 5 quarters.
Hope this helped!