K
A car rental agency rents 440 cars per day at a rate of $40 per day. For each $1 increase in rate, 10
fewer cars are rented. At what rate should the cars be rented to produce the maximum income? What
is the maximum income?
...
The rental agency will earn a maximum income of $
when it charges $
per day.
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The value obtained after solving the expression will be equal to (-1, 1).

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both.

Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given in for the mention in the question,

x² = 36

x = ±6

Therefore, the values are -6, and +6.

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Answer:

-35/-7=5

Step-by-step explanation:

Diviser par de nombre négatif alors sa devient positif pareil pour la multiplication

Answer:

[tex]2(w-6^2)[/tex]

Step-by-step explanation:

We are doubling the difference, so we first need to find the difference. Our two numbers are [tex]w[/tex] and [tex]6^2[/tex] (you can also write 36 but that is how the problem states it). Therefore, the equation for that is [tex]w-6^2[/tex]. Then, if we double it, we get [tex]2(w-6^2)[/tex].

Glens have 110 coins in his entire collection.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Glens coins from Denmark are eleven 11.

These 11 coins are 10% of his entire coins.

We need to find how many coins Glens has.

Let x be the entire collection of Glens coins

10/100x=11

0.1x=11

Divide both sides by 0.1

x=110

Hence, Glens have 110 coins in his entire collection.

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If all the television at the stores are 3/4 of the original price and has a $40 discount coupon, then the equation which she used to find the price of the television is f = (3/4)p - 40

The original price of the television = p

The 3/4 of the original price = (3/4)p

The worth of the discount coupon = $40

So the discount price will be subtracted

Then, the final price of the television = (3/4) × The original price of the television - The worth of the discount coupon

Substitute the values in the equation

The final price of the television f = (3/4)p - 40

Hence, If all the television at the stores are 3/4 of the original price and has a $40 discount coupon, then the equation which she used to find the price of the television is f= (3/4)p - 40

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The nth term of the sequence is aₙ = 48 + 2n

The definition of the function is given as

a₁= 50

aₙ = aₙ₋₁ + 2

The above definitions imply that we simply add 2 to the previous term to get the current term

Using the above as a guide, we have:

The common difference, d = 2

First term, a = 50

The nth term of the sequence is calculated as

aₙ = a₁ + (n - 1)* d

Substitute the known values in the above equation

So, we have the following representation

aₙ = 50 + (n - 1)* 2

So, we have

aₙ = 50 + 2n - 2

Evaluate the like terms

aₙ = 48 + 2n

Hence, the nth term is aₙ = 48 + 2n

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The scientific notation of 69200000 is  6.92 × 10⁷

Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form.

Scientific Notation is a special way of writing numbers:

For example 800 is written as 8 × 10² in Scientific Notation.

Therefore, let's write the scientific notation of the number 69200000.

Hence,

69, 200, 000 = 6.92 × 10⁷

The logic is that we will count backwards until we meet the last number.

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The Perimeter of the given Reactangle is 6*length

Whta is a Rectanglee?

A rectangle is a quadrilateral with four right angles in Euclidean plane geometry. It can alternatively be classified as an equiangular quadrilateral since all of its angles are equal; or a parallelogram with a right angle. A square is a rectangle with four equal-length sides.

Solution:

Let,

the length be l

and breadth be b

According to the question,

l = (1/2)b

We know that Perimeter of Rectangle = 2(length + breadth)

From the variable mentioned above

Perimeter = 2*(l+b)

Perimeter = 2*(l + 2l)

Perimeter = 2*(3l)

Perimeter = 6l

The Perimeter of the given Reactangle is 6*length

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Answer:

Let x be the width of the rectangle.

The expression to represent the perimeter of the rectangle is 3x.

Step-by-step explanation:

Definition of the variable:

If the rectangle has a length that is half its width, then:

The perimeter of a two-dimensional shape is the distance all the way around the outside. Therefore, the perimeter of a rectangle is twice the sum of its length and width.

[tex]\begin{aligned}\textsf{Perimeter of the rectangle}&=2 \left(\;\sf length+width\; \right)\\& = 2\left(\dfrac{1}{2}x+x\right)\\& = 2 \left(\dfrac{3}{2}x\right)\\& = 3x\end{aligned}[/tex]

Therefore, an expression to represent the perimeter of the rectangle is:

Step-by-step explanation:

Zhang invests $2,600 in two different accounts. The first account paid 11%, the second account paid 5% in interest. At the end of the first year he had earned $220 in interest. How much was in each account?

11% = 0.11

in account 1: $220/0.11 = $2,000

in account 2: $2,600 - $2,000 = $600

$2,000 At 11%

$600 At 5%

The fraction of the given is 1/7 .

What is fraction?

 A fraction that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Here let us take x as numerator and y as denominator. Then

If the numerator is multiplied by 3 and denominator is reduced by 2, we get 3/5 ,

=> 3x/y-2 = 3/5

=> 5*3x =3(y-2)

=> 15x=3y-6

=> 5x=y-2

=> y =5x+2------>1

Now if the numerator is increase by 4 and the denominator is double we get 5/14,

=> (x+4)/2y = 5/14

=> 14x+56 = 10y

=> 7x+28=5y ---->2

Here put 1 into 2 then,

=> 7x+28 = 5(5x+2)

=> 7x+28=25x+10

=>18x=18

=> x =1

Now put x=1 into 1 then,

=> y =5(1)+2 = 7.

Therefore the given fraction is x/ y = 1/7.

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Answer:

50 degrees

Step-by-step explanation:

sum of all three angles on any triangle is equal 180 degrees so first we add the first 2 given angles

70+60

130

Now we subtract from 180 to find the unknown angle

180-130

50 degrees

Hopes this helps please mark brainliest

x + 60° + 70 = 180°

( sum of interior angle of triangle is 180° )

x + 130° = 180°

x = 180° - 130°

x = 50°

hope it helps...

Answer: x = -8

Step-by-step explanation:

1. Add 10 to both sides

-3x = 14 + 10

2. Simplify 14 + 10 to 24

-3x = 24

3. Divide both sides by -3

x = [tex]-\frac{24}{3}[/tex]

4. Simplify [tex]\frac{24}{3}[/tex] to 8

x = -8

The monthly payment on the amortized loan is $206.74. The car cost in total is $14, 885. 52. The money paid in interest is $1, 861.52.

The monthly payment is called an annuity because it is constant and remains the same.

Use the present value of an annuity to find the monthly payment to be:

Loan amount = Monthly payment x Present value interest factor of annuity, period, rate

The period is:
= 6 years x 12

= 72 months

The rate is:

= 4.5% / 12 months a year

= 0.375%

The loan amount is:

= 14, 800 x ( 1 - downpayment)

= 14, 800 x ( 1 - 12%)

= $13, 024

The monthly payment is:

13, 024 = Monthly payment x Present value interest factor of annuity, 72 periods , 0.375%

Monthly payment = 13, 024 / 62.995976235992

= $206.74

The car cost in total is:

= Monthly payment x Number of months

= 206. 74 x 72

= $14, 885. 52

The money paid in interest is:

= Loan amount - Car cost

= 14, 885.52 - 13, 024

= $1, 861.52

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If we use more than 133 minutes then the 2nd plan will be preferable.

Given:

The first plan charges a rate of 26 cents per minute. The second plan charges charges a monthly fee of $19.95 plus 11 cents per minute.

26 cents = $0.26

Let m be the minutes

19.95 + .17m < .32m

Subtract .17m from both sides

19.95 < .32m - .17m

19.95 < .15m

Divide both sides by .15

19.95/.15 < m

133 < m

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The corresponding probabilities of the random variables x = (0, 1, 2, 3, 4, 5, and 6) are  (0.2401, 0.4116, 0.2646, 0.0756, 0.0081, 0, and 0)

Since we are dealing with a binomial probability distribution. We are going to use the binomial distribution formula for determining the probability of x successes:

P(x = r) = nCr . π^r  . q^n-r

Given: n = 4 and π = 0.30, q = 1 - π = 1 - 0.30 = 0.70 and x = (0, 1, 2, 3, 4, 5, 6)

P(x = 0) = 4C0 × 0.3⁰ × 0.7⁴⁻⁰ = 0.2401

P(x = 1) = 4C1 × 0.3¹ × 0.7⁴⁻¹ = 0.4116

P(x = 2) = 4C2 × 0.3² × 0.7⁴⁻² = 0.2646

P(x = 3) = 4C3 × 0.3³ × 0.7⁴⁻³ = 0.0756

P(x = 4) = 4C4 × 0.3⁴ × 0.7⁴⁻⁴ = 0.0081

P(x = 5) = 0

P(x = 6) = 0

Note: P(x = 5) and P(x = 6) are 0 because their x (5 and 6) is greater than the n (4)

Therefore, the probabilities of the random variables x(0, 1, 2, 3, 4, 5, and 6) are  0.2401, 0.4116, 0.2646, 0.0756, 0.0081, 0, and 0 respectively

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Answer:

x = 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x+3x+8-3x-2 = 2x + 6

Answer:

Lauren has 30 jellybeans

Step-by-step explanation:

Let x - Lauren

Let y = Haley

[tex]\frac{x}{y}[/tex] = [tex]\frac{3}{8}[/tex]  Cross multiply

8x + 3y

x = y - 50  Substitute y - 50 into the equation above for x

8(y -50) = 3y

8y -400 = 3y  Subtract 8y from both sides

-400 = -5y  Divide both sides by -5

80 = y  This is Haley's jellybeans

x = y = 50

x = 80 - 50

x = 30 This is Lauren's jellybeans.

The smallest number is 5, middle number is 8 and largest number is 11.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let x be the smallest number.

let x + 3 be the middle number.

let x + 6 be the largest number.

Then, the equation is

5 (x + 6) = 3 x + 5 (x + 3)

5x+ 30 = 3x+ 5x + 15

3x = 30- 15

3x= 15

x= 5

So, the numbers are x = 5, x + 3 = 8, and x + 6 = 11.

Now, the difference between each succeeding number is 3.

5 x 11 = 55

3 x5 + 5 x 8 = 15 + 40 = 55

Hence, the smallest number is 5, middle number is 8 and largest number is 11.

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Answer:

10 cm

Step-by-step explanation:

since DE is probably equal to AD which is 17 we subtract the length of the side of CD to find CE

Length CD can be found because it is equal to AB which is 7 cm so we subtract

17-7=10

Hopes this helps please mark brainliest

Answer:

CE = 10

Step-by-step explanation:

Because they are congruent:

AD = 17, that means DE = 17

AB = 7, that means CD = 7

To find what CE is, we start with the full length:

DE

and by subtracting CD (that's part of the length), we can get CE.

DE - CD = CE

Just substitute the values in:

17 - 7 = 10

CE = 10

So there's the answer, but check this out:

CE + CD = DE

10 + 7 = 17

As per the given matrix A and B, the value of -7A - 6B is [tex]-7A - 6B = \begin{bmatrix} 40 & -106 &-32 \\ -46& 43 &25 \\82 & -62& -22 \end{bmatrix}[/tex]

Matrix:

Basically, a set of numbers arranged in rows and columns so as to form a rectangular array is known as matrix.

Given,

Here we have the matrix A and B.

Now we have to find the -7A - 6B.

In order to solve this matrix, first we have to find the value of -7A,

To find that one, we have to multiply -7 with A,

Then we get,

[tex]-7 \times\begin{bmatrix}-10 &10 &8 \\ -2& -1 &5 \\ -4& 8& -6\end{bmatrix} = \begin{bmatrix}70 &-70 &-56 \\ 14& 7 &-35 \\ 28& -56& 42\end{bmatrix}[/tex]

Similarly, we have to find the value of 6b,

In order to find that, we have to multiply 6 with the matrix B,

Then we get,

[tex]6 \times\begin{bmatrix}5 &6 &-4 \\ 10& -6 &-10 \\ -9& 1& 10\end{bmatrix} = \begin{bmatrix}30 & 36 &-24 \\ 60& -36 &-60 \\ -54& 6& 60\end{bmatrix}[/tex]

Now, we have to subtract the resulting matrix,

[tex]-7A - 6B = \begin{bmatrix}70 &-70 &-56 \\ 14& 7 &-35 \\ 28& -56& 42\end{bmatrix} - \begin{bmatrix} 30 & 36 &-24 \\ 60& -36 &-60 \\ -54& 6& 60 \end{bmatrix}[/tex]

Therefore, the resulting matrix is

[tex]-7A - 6B = \begin{bmatrix} 40 & -106 &-32 \\ -46& 43 &25 \\82 & -62& -22 \end{bmatrix}[/tex]

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The value of p is 0.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

Given that

Point A(p8,4p+5) is located on a line that connects M(-2,-5) and N(1,-10).

The equation of line that passing through points  M and N,

Use the formula of equation of line,

y-y₁ = (y₂-y₁/x₂-x₁)(x-x₁)

y-(-5) = (-10+5/1+2)(x-(-2))

⇒ y+5 = -5/3(x+2)

⇒5x+3y +25 = 0    (1)

Since, line passes through point  A(p−8,4p+5), so this point A will satisfy the equation (1)

5(p-8)+3(4p+5)+25 = 0

⇒ 17p = 0

⇒ p = 0

The value of p is 0.

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The given function y = sec⁻¹(x³) is differentiated as dy/dx = 3x/√(x² - 1).

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = Lim h --> 0 (f(x + h) - f(x)) /(x + h - x).

Its geometric meaning is the slope of tangent of the function at a given point.

The given function is as below,

y = sec⁻¹(x³)

The given function is a composite function of sec⁻¹x and x³.

In order to differentiate it, first differentiate x³ and then sec⁻¹x as follows,

dx³/dx = 3x²

And, dsec⁻¹x /dx = 1/x√(x² - 1)

Now, differentiation of sec⁻¹(x³) is given as,

d sec⁻¹(x³)/dx = 3x²/(x√(x² - 1))

                      = 3x/√(x² - 1)

Hence, the differentiation of the given function is 3x/√(x² - 1).

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The equation that can be used  to determine the number of plates p, that he used is 6p = 48.

Jim is a preschool teacher. While he was getting ready for his class's snack time, he put 6 carrots on each plate.

He used 48 total carrots. The equation that could be used to determine the number of plates, p, that he used can be represented as follows:

let

p = number of of plates

Therefore,

6 carrots are put on each plate.

He has 48 carrots.

Hence, the equation is  6p = 48

p = 48 / 6

p = 8

Therefore,

number of plates = 8

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The number of plates he used is can be calculated by 6p = 48

How to determine this?

He was said to put 6 carrots on each plates

And used 48 total carrots  altogether

p representing the number of plates

That is, 6 carrots in p places

6 carrots × p

= 6p

Given that 48 carrots used altogether

6p = the total number of carrots

Therefore, 6p  = 48

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Given equation to us is , [tex](m-3)r^2+9r-2=0[/tex] .

The given equation is a quadratic equation and it has two real solutions if it's discriminant is greater than or equal to 0 .

For a quadratic equation in standard form of

[tex]ax ^{2} + bx + c = 0[/tex]

the discriminant is given by b² - 4ac .

On comparing wrt to Standard form, we have ;

Now we have,

[tex]\longrightarrow b^2-4ac \geq 0\\\\\longrightarrow 9^2-4(m-3)(-2)\geq 0\\\\\longrightarrow 81 +8(m-3)\geq 0 \\\\\longrightarrow 81 +8m-24\geq 0 \\\\\longrightarrow 8m \geq 24-81 \\\\\longrightarrow 8m \geq -57 \\\\\longrightarrow \underline{\underline{ m \geq \dfrac{-57}{8}}}[/tex]

Therefore for all values greater than or equal to -57/8 the equation will have a real solution .

And we are done!

The equation (m-3)r² + 9r -2 = 0 will have two real solution for the value of m, greater than or equal to -57/8.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The standard form of equation of power two is ax²+bx+c =0 .

The given equation,

(m-3)r² + 9r -2 = 0

Compare the given equation with standard equation ax²+bx+c =0,

The value of a=m-3, b=9 and c=-2

An equation has two real solutions if a discriminant of the equation is greater than or equal to zero.

⇒D ≥ 0

⇒b²-4ac ≥ 0

Substitute the value of a, b and c,

⇒9² - 4×(m-3)(-2) ≥ 0

⇒81 +8m - 24 ≥ 0

⇒8m ≥ -57

⇒ m ≥ -57/8

For the values of m greater than or equal to -57/8, the equation have two real solutions.

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The cement kinds will be listed in order of highest to lowest unit rate of pounds per day: C > A > D > B.

The table shows the rates at which each type is sold. A workday is 8 hours, and each pound of cement sells for 4.50.

Type A cement,

Forty pounds were sold in one day.

unit rate = 40 pounds per day

Type B cement,

6y = 2x, where x is in pounds and y is in hours

Since the workday is 8 hours, so substitute the value of x = 8 and we get

6y = 2(8)

6y = 16

y = 16/6 = 2.67

This means the unit rate = 2.67 pounds per day

Type C cement,

After 3 hours, 45 worth had been sold.

After 8 hours,

The worth had been sold = 8×45/3 = 120

unit rate = 120 pounds per day

Type D cement,

The ratio of days to pounds sold was 2: 60.

So, unit rate = 60/2 = 30 pounds per day

So the types of cement in order from highest to lowest unit rate of pounds per day will be :

C > A > D > B

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The relation for x and y is given as y = 26/x. The correct answer is option (B).

When two quantities have some dependence in their values they can be said proportional to each other.

It can be of two types such as direct and indirect.

The direct proportionality means the values of both the quantities are increasing or decreasing at the same time while the indirect proportionality implies value of one quantity is increasing while the other is decreasing.

Given that,

The proportionality relation between x and y as

y ∝ 1/x

And, y = 2 at x = 13.

Suppose k is the constant of proportionality.

Then, y = k/x

Substitute y = 2 and x = 13 in the above equation to obtain,

2 = k/13

=> k = 26

Thus, by substituting the value of k the equation can be written as y = 26/x.

Hence, the equation that relates x and y is y = 26/x.

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The percentage of confidence intervals that would capture the true population means is approximately 95% of them. which is the correct answer would be option (C).

There were 100 random samples of the same size drawn from a population known to have a normal distribution with a mean and a standard deviation.

For each of the 100 random samples, a 95% confidence interval for the population mean was created.

Since all the conditions are satisfied,

Therefore, the percentage of confidence intervals that would capture the true population means is approximately 95% of them.

Hence, the correct answer would be an option (C).

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