Using the formula r = d/t where d is the distance in miles, r is the rate, and t is the time in hours, at which rate must you travel to cover 337.5 miles in 4.5 hours?

see the attached figure to better understand the problem

Let

x------> the length side of a rectangle

y-------> the width side of a rectangle

we know that

the perimeter of a rectangle is equal to the formula

[tex]P=2x+2y[/tex]  

in this problem

[tex]AB=DC=x[/tex]

[tex]AD=BC=y[/tex]

Step 1

Find the distance AB

[tex]A(-6,4)\\B(2,8)[/tex]

we know that

the distance's formula between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}[/tex]

substitute the values

[tex]d=\sqrt{(8-4)^{2} +(2+6)^{2}}[/tex]

[tex]d=\sqrt{(4)^{2} +(8)^{2}}[/tex]

[tex]dAB=\sqrt{80}\ units[/tex]

Step 2

Find the distance BC

tex]B(2,8)\\C(4,4)[/tex]

we know that

the distance's formula between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}[/tex]

substitute the values

[tex]d=\sqrt{(4-8)^{2} +(4-2)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2} +(2)^{2}}[/tex]

[tex]dBC=\sqrt{20}\ units[/tex]

Step 3

Find the perimeter

we know that

the perimeter of a rectangle is equal to the formula

[tex]P=2x+2y[/tex]

[tex]P=2AB+2BC[/tex]

we have

[tex]dAB=\sqrt{80}\ units=8.9\ units[/tex]

[tex]dBC=\sqrt{20}\ units=4.5\ units[/tex]

substitute the values of the distance in the formula

[tex]P=2*8.9+2*4.5=26.8\ units[/tex]

therefore

the answer is

The perimeter of the rectangle is equal to [tex]26.8\ units[/tex]

The conjugate of the complex number -8 + 2i is -8 -2i. By multiplying the complex number by its conjugate we get the answer 68, which corresponds to option C.

To solve this question, we first need to know what a conjugate is. In complex numbers, if a number is represented as a + bi, its conjugate will be a - bi. The provided complex number in the question is -8 + 2i, so its conjugate would be -8 - 2i.

Next, we multiply the complex number by its conjugate. This would give us (-8 + 2i) × (-8 - 2i). Executing this multiplication based on the rule of multiplication of brackets (a+b)(a-b) = a2 - b2, we have (-8)2 - (2i)2, which results in 64 - (-4) = 68.

Therefore, the product of (-8 + 2i) and its conjugate is equal to 68, which is option C.

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Answer with Step-by-step explanation:

An explicit formula for the sequence

14,5,-4,-13...

given by Imran  is g(n)=14-9(n-1)

and by Aubrey is g(n)=14-9n

We have to determine who is right

g(n)= 14-9n

g(1)=14-9

    = 5

Hence, formula given by Aubrey is wrong

g(n)=14-9(n-1)

g(1)=14-9(0)=14

g(2)=14-9(1)=5

g(3)=14-9(2)= -4

g(4)=14-9(3)= -13

Hence, formula given by Imran is correct

Hence, correct option is:

Just Imran

Answer:

Only Imran

Step-by-step explanation:

LCM of 15 & 6 = 30

 then take the highest exponent for each variable

 answer is:

30x^4y^8z^9

Answer:

[tex]x=\frac{-1+-i\sqrt{15}}{4}[/tex]

Step-by-step explanation:

[tex]2x^2+x+2=0[/tex]

Apply quadratic formula to solve for x

[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]

a=2, b= 1, c=2

Plug in the value in the quadratic formula

[tex]x=\frac{-1+-\sqrt{1^2-4(2)(2)}}{2(2)}[/tex]

[tex]x=\frac{-1+-\sqrt{-15}}{4}[/tex]

Square root of -1 is 'i'

[tex]x=\frac{-1+-i\sqrt{15}}{4}[/tex]

The solution of the given quadratic equation is,

x = [-1±i√15]/4

Hence option 3rd is correct.

The given quadratic equation is,

2x²+x+2=0

Here we can see that it is of the form of ax² + bx + c = 0.

Since we know that
The quadrature formula for ax² + bx + c = 0 is

⇒ x = [-b±√(b²- 4ac)]/2a

Here we have,

a = 2

b = 1

c = 2

Put these value in quadrature formula we get,

⇒ x = [-1±√(1²- 4x2x1)]/2x2

      = [-1±√(1- 16)]/4

      = [-1±√(-15)]/4

Since we know that, i = √-1

Therefore,

⇒ x = [-1±i√15]/4

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Each piece is approximately (2.67) yards long.

To find the length of each piece, we divide the total length of the ribbon (8 yards) by the number of pieces (3).

First, we set up the division:

[tex]\[ \frac{8 \text{ yards}}{3} \][/tex]

Now, let's perform the division:

[tex]\[ 8 \div 3 = 2 \, \text{with a remainder of } 2 \][/tex]

So, each piece is [tex]\(2 \frac{2}{3}\)[/tex] yards long.

To express the length in a mixed number (a whole number plus a fraction), we rewrite [tex]\(2 \frac{2}{3}\)[/tex] as:

[tex]\[ 2 + \frac{2}{3} \][/tex]

To convert the fraction into yards, we multiply the numerator (2) by the unit fraction [tex]\(\frac{1}{3}\)[/tex]:

[tex]\[ 2 \times \frac{1}{3} = \frac{2}{3} \][/tex]

So, each piece is [tex]\(2 \frac{2}{3}\)[/tex] yards long, or [tex]\(2\frac{2}{3}\)[/tex] yards.

Alternatively, in decimal form:

[tex]\[ 2 \frac{2}{3} \text{ yards} = 2.666... \text{ yards} \][/tex]

So, each piece is approximately (2.67) yards long.

Final answer:

Based on the ratio of 1:4 for black socks to white socks, and knowing there are 8 black socks, we calculate the number of white socks to be 32.

Explanation:

The question asks us to find the number of white socks when given the ratio of black socks to white socks in a drawer and the number of black socks. The ratio is 1:4, which implies for every black sock, there are 4 white socks. Since there are 8 black socks, to find the number of white socks, we multiply the number of black socks by the ratio of white socks to black socks, which would be 8 * 4 = 32. Therefore, there are 32 white socks in the drawer.

a. At least 108 tickets must be sold to cover the cost.

b. To make a $980.68 profit, 230 tickets must be sold.

To solve this problem, let's break it down step by step:

a. To cover the cost of $859.32, we need to find out how many tickets need to be sold at $8 each.

Let's denote:

C = total cost of the dance

T = number of tickets sold

P = price per ticket

Given:

C = $859.32

P = $8

We can use the formula: Cost = Number of tickets * Price per ticket

So, we have:

859.32 = T * 8

To find T, divide both sides by 8:

T = 859.32 / 8

T = 107.415

Since we can't sell a fraction of a ticket, we round up to the nearest whole number.

T = 108

Therefore, at least 108 tickets must be sold to cover the cost.

b. To make a $980.68 profit, we need to find out how many tickets must be sold.

Profit = Total Revenue - Total Cost

Profit = (Price per ticket * Number of tickets) - Total Cost

Given:

Profit = $980.68

Total Cost = $859.32

Price per ticket = $8

Let T represent the number of tickets to be sold.

So, we have:

Profit = (8 * T) - 859.32

We want to solve for T:

Profit + Total Cost = Price per ticket * Number of tickets

Profit + Total Cost = 8T

(Profit + Total Cost) / Price per ticket = T

(980.68 + 859.32) / 8 = T

1840 / 8 = T

T = 230

Therefore, to make a $980.68 profit, 230 tickets must be sold.

Complete Question:

It costs $859.32 to have a school dance. The dance is $8 per ticket.

a. How many tickets must sold to cover the cost?

b. How many tickets must be sold to make a $980.68 profit?

The polynomial which is written in ascending order is:

           [tex]-11-6x+2x^2+8x^3[/tex]

To write the polynomial in ascending order means to write it in the increasing powers of x.

Here the polynomial which is written in ascending order is:

                 [tex]-11-6x+2x^2+8x^3[/tex]

the answer to your question is g=3 1/2

Approximately 84.13% of times are more than 91 seconds, and approximately 0.13% of times are more than 63 seconds.

To find the percentage of times that are more than 91 seconds and more than 63 seconds, we can use the properties of a normal distribution and the standard normal distribution table (also known as the z-table).

Given:

Mean (μ) = 84 seconds

Standard deviation (σ) = 7 seconds

1. Probability of times more than 91 seconds:

First, we need to find the z-score for the value 91 seconds:

[tex]\(z = \frac{X - \mu}{\sigma} = \frac{91 - 84}{7} = \frac{7}{7} = 1\)[/tex]

Now, using the z-table, find the area under the standard normal curve to the right of [tex]\(z = 1\)[/tex]. The z-table provides the percentage of values below a given z-score, so we need to find the complement (1 - percentage) to get the percentage of values above [tex]\(z = 1\).[/tex]

From the z-table, the area to the right of [tex]\(z = 1\)[/tex] is approximately 0.1587.

So, the percentage of times more than 91 seconds is [tex]\(1 - 0.1587 = 0.8413\)[/tex] or 84.13%.

2. Probability of times more than 63 seconds:

Similarly, we need to find the z-score for the value 63 seconds:

[tex]\(z = \frac{X - \mu}{\sigma} = \frac{63 - 84}{7} = \frac{-21}{7} = -3\)[/tex]

Now, using the z-table, find the area under the standard normal curve to the right of [tex]\(z = -3\)[/tex]. Again, we need to find the complement to get the percentage of values above [tex]\(z = -3\).[/tex]

From the z-table, the area to the right of [tex]\(z = -3\)[/tex] is approximately 0.9987.

So, the percentage of times more than 63 seconds is [tex]\(1 - 0.9987 = 0.0013\)[/tex] or 0.13%.

Therefore, approximately 84.13% of times are more than 91 seconds, and approximately 0.13% of times are more than 63 seconds.

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Answer: 16

Step-by-step explanation:

The number of outcomes exist , when a coin is flipped (tails , head) = 2

The number of possible outcomes , when 'n' number of coins are flipped :_

[tex]2^n[/tex]

For n= 4, the number of possible outcomes , when four coins are flipped :_

[tex]2^4=2\times2\times2\times2=16[/tex]

Hence, the possible outcomes exist when four fair coins are flipped = 16

The pizza shop should sell 70 small pizzas and 140 large pizzas to maximize profit.

A linear equation in two variables is an algebraic equation of degree one in two variables generally in x and y.

As there is no condition for how much time is required to make one small and one large pizza and by making large pizza the shop makes more profit.

∴ Pizza shops should make the least amount of small pizzas in the given range which is 70 and the most amount of large pizzas in the given range which is 140.

So, the profit of the pizza shop will be = 1.50(70) + 2.15(140) dollars.

= (105 + 301) dollars.

= 406 dollars.

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Answer:

true

Step-by-step explanation:

Answer:

He had a total of $43 at the beginning of the day

Step-by-step explanation:

Step 1

Express the amount of money Darryl had in the beginning as follows;

A=E+R

where;

A=initial amount he had at the beginning

E=total expenditure

R=total remainder after spending

In our case;

A=unknown

E=Amount spent on book+amount spent on compact disc+amount spent on magazine

E=(16+20+2)=$38

R=$5

Step 2

Substitute the values in the expression and solve for A;

A=(38+5)=43

He had a total of $43 at the beginning of the day

The distributive property demonstrated.

4(3 + 5) = 4 • 3 + 4 • 5

This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.

Given:

Expression,

4(3 + 5) = 4 • 3 + 4 • 5

Here,

we take LHS,

4(3 + 5)

= 4 x 3 + 4 x 5

= 12 + 20

= 32

We take RHS,

4 • 3 + 4 • 5

= 12 + 20

32.

So, this property is distributive property.

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