A taxi ride for the airport to your hotel costs a flat fee of $10 the moment you sit in the back seat plus $0.75 each mile plus a tip of $5 to the driver at the end of the ride. Your hotel is 24 miles from the airport and you have $30 in your pocket. Do you have enough money to make it to your hotel in the taxi, including the tip? Declare what your variable represents, write the equation or inequality that models the situation, solve for the variable showing your steps, and answer the question.

Answer:

Simplifying 9m + -3 + -7m = 0

Reorder the terms: -3 + 9m + -7m = 0

Combine like terms: 9m + -7m = 2m -3 + 2m = 0 Solving -3 + 2m = 0

Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right.

Add '3' to each side of the equation. -3 + 3 + 2m = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2m = 0 + 3 2m = 0 + 3 Combine like terms: 0 + 3 = 3 2m = 3

Divide each side by '2'. m = 1.5

Step-by-step explanation:

Hope this helps :)

Answer:

The \(66\)th term is \(363\).

Step-by-step explanation:

To find the \(n\)th term, the formula is \(7n - 99\). Since we want to find the \(66\)th term, we can plug \(n\) for \(66\). So our expression is now \(7 \cdot 66 - 99 =\) \(66\)th term. Solving this we have

\(462 - 99 = 66\text{th term}\\363 = 66\text{th term}\\\). Therefore, the \(66\)th term is \(\boxed{363}\).

Answer:

a₆₆ = 363

Step-by-step explanation:

the nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 92 and d = a₂ - a₁ = - 85 - (- 92) = - 85 + 92 = 7 , then

a₆₆ = - 92 + (65 × 7)

      = - 92 + 455

     = 363

Answer:

It would be the last answer choice:

115 degrees - y, because TriangleABC = TriangleDCE

Anna's total profit was $6000 + $16000 - $4000 = $14000.

How did Anna earn profit

Anna bought $4000 of company stock. The value of the stock doubled when she sold 75% of it, which means she sold 0.75 * $4000 = $3000 worth of stock when its value doubled.

Since the value of the stock doubled, Anna sold the $3000 worth of stock for 2 * $3000 = $6000.

Anna then sold the remainder of the stock (25% of the original amount) for four times the purchase price. Since she originally bought the stock for $4000, the remainder was worth 0.25 * $4000 = $1000.

Selling this remainder for four times the purchase price means that Anna sold it for 4 * $4000 = $16000.

Answer:

1/5

Step-by-step explanation:

The number 5 or greater than 4 is 5.

1 number out of 5 total parts.

= 1/5

P(5 or greater than 4) = 1/5

To construct a frequency histogram based on the given temperature data, we will use the temperature ranges as the x-axis and the number of days as the y-axis.

The temperature ranges and their corresponding frequencies are as follows:

30-39: 2 days

40-49: 26 days

50-59: 28 days

60-69: 8 days

70-79: 2 days

To create the histogram, we will represent each temperature range as a bar and the height of each bar will correspond to the frequency of days.

Using an appropriate scale, we can label the x-axis with the temperature ranges (30-39, 40-49, 50-59, 60-69, 70-79) and the y-axis with the frequency values.

Now, we can draw rectangles (bars) on the graph, with the base of each rectangle corresponding to the temperature range and the height representing the frequency of days. The height of each bar will be determined by the corresponding frequency value.

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Answer:

82% of 50 is 41

Step-by-step explanation:

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Answer:

3 \(\frac{7}{8}\)

Step-by-step explanation:

Step-by-step explanation:

u fyfucyfcr t xd tvycyfctc

Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.

To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.

First, let's isolate the absolute value term on one side of the equation:

|3x + 3| = -3

Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.

To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:

   3x + 3 = -3

   -(3x + 3) = -3

Solving equation 1:

3x + 3 = -3

3x = -6

x = -2

Solving equation 2:

-(3x + 3) = -3

-3x - 3 = -3

-3x = 0

x = 0

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2.5% of 8 = .2

5/8 + .2/8 = 5.2/8

5.2/8 = .65 x 100 = 65%

65% of games cost 1 or 2 dollars

100% - 65% = 35%

!! after doing it i did realize I could've just converted 5/8 into a percent than added it.

or

5/8 = .625 + .025 = .65 x 100 = 65%; 100% - 65% = 35%

The probability a ) P ( r = 0 ) = 0.010 and b ) P ( r \(\geq\) 1 ) = 0.99 .

The binomial distribution formula is:

 P ( r successes in  n trials )  = [ nCr ] * [ p^r ] * [ q ^ ( 1 - r ) ]

where [ nCr ]  is the number of combinations of number of objects g taken r at a time, p is probability of success & (1-p) ie. q is the probability of failure.

We are given p = 0.40

                       n = 9

a) P ( r = 0 ) =  9C0 x  0.40^0 x (0.6)^9  =  1 * 1 * 0.010 = 0.010

b) P( r ≥ 1 )  = 1 - Pr ( r = 0 )  = 1 - 0.010 = 0.99

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The measure of side length x in the right triangle is approximately 6.03 cm.

The figure in the image is a right triangle having one of its interior angle at 90 degrees.

From the figure:

Angle θ = 37 degrees

Adjacent to angle θ = 8 cm

Opposite to angle θ = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( θ ) = opposite / adjacent

Plug in the given values and solve for x:

tan( 37 ) = x / 8

x = tan( 37 ) × 8

x = 6.03 cm

Therefore, the value of x is 6.03 cm.

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Step-by-step explanation:

First, you need to calculate how much they will earn per hour by multiplying their raise per hour by there hours and adding it to their earnings divided by the hours worked. Then, whoever's is the highest will be the answer.

Hanna will earn more per hour after the raise, with an hourly rate of $10.75 compared to Dien's hourly rate of $10.60.

A division is a process of splitting a specific amount into equal parts.

To find the new earnings per hour for Hanna and Dien

Divide their total earnings after the raise by the total number of hours they worked after the raise.

The raise per hour is already given, so we can simply add it to their old hourly rate.

For Hanna, her new hourly rate would be:

(New earnings) / (Hours worked) = (78 + 8) / 8

= 86 / 8

= $10.75

This means that Hanna will earn $10.75 per hour after the raise.

For Dien, his new hourly rate would be:

(New earnings) / (Hours worked) = (60.60 + 3) / 6

= 63.60 / 6

= $10.60

This means that Dien will earn $10.60 per hour after the raise.

Therefore,  Hanna will earn more per hour after the raise, with an hourly rate of $10.75 compared to Dien's hourly rate of $10.60.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

2 + (1^2 - 1 ) = 2

2 +( 2^2 - 1 ) = 5

5 + ( 3^2 - 1) = 28

28 + (5^2 - 1) = 52

Thus the next number would be 52

Hope this helps :D

Answer:

The number that comes next is 52

Step-by-step explanation:

Answer:

\(\dfrac{5e^2}{2}\)

Step-by-step explanation:

Differentiation is an algebraic process that finds the slope of a curve. At a point, the slope of a curve is the same as the slope of the tangent line to the curve at that point. Therefore, to find the slope of the line tangent to the given function, differentiate the given function.

Given function:

\(y=x^2\ln(2x)\)

Differentiate the given function using the product rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let\;$u=x^2}\)\(\textsf{Let\;$u=x^2$}\implies \dfrac{\text{d}u}{\text{d}x}=2x\)

\(\textsf{Let\;$v=\ln(2x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{2}{2x}=\dfrac{1}{x}\)

Input the values into the product rule to differentiate the function:

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x^2 \cdot \dfrac{1}{x}+\ln(2x) \cdot 2x\\\\&=x+2x\ln(2x)\end{aligned}\)

To find the slope of the tangent line at x = e²/2, substitute x = e²/2 into the differentiated function:

\(\begin{aligned}x=\dfrac{e^2}{2}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{e^2}{2}+2\left(\dfrac{e^2}{2}\right)\ln\left(2 \cdot \dfrac{e^2}{2}\right)\\\\&=\dfrac{e^2}{2}+e^2\ln\left(e^2\right)\\\\&=\dfrac{e^2}{2}+2e^2\\\\&=\dfrac{5e^2}{2}\end{aligned}\)

Therefore, the slope of the line tangent to the graph of y = x²ln(2x) at the point where x = e²/2 is:

\(\boxed{\dfrac{5e^2}{2}}\)

Answer:

$11.90

Step-by-step explanation:

3.57 divided by 3 is 1.19 so 1.19 is the unit rate/ how much 1 pear costs. So multiply 1.19 x 10 and you get $11.90

Answer:

Step-by-step explanation:

-11°

Answer:

5%

Step-by-step explanation:

15% times 60 = 9

and then you divide 9/180 which equals .05 in decimal form and then multiply it by 100 to get 5%

Hope that makes sense!

Answer:

−16y+6

Step-by-step explanation:

2(3−8y)

=(2)(3+−8y)

=(2)(3)+(2)(−8y)

=6−16y

=−16y+6

Answer:

6-16y

Step-by-step explanation:

2(3-8y)

distibute 6-16y

Answer:

Hi there!

Your answer is;

54¢ of $3.99 is roughly 28.38%

Step-by-step explanation:

3.99 = 100%

/3.99

.01¢ = 25 & 25/399%

× 54

54¢ = roughly 28.38%

x and y have the values 7 and 7√2, respectively.

The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.

We can use this information to determine the values of x and y because the base is specified as being 7.

Let's give the perpendicular side the value of x, and the hypotenuse the value of y.

The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.

Consequently, x = 7.

We can determine that x:y:2x using the ratio of 1:1:2.

When we enter the value of x, we may calculate y:

7:y:√2(7)

Simplifying even more

7:y:7√2

Given that the hypotenuse (y) equals 72, we can write:

y = 7√2

Thus, x and y have the values 7 and 7√2, respectively.

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Answer:

1.26

Step-by-step explanation:

1.08 to the third power is \(1.08^{3}\).

In simple terms, it means 1.08 x 1.08 x 1.08.

Do the math 1.259712.

1.26 if you round to the hundredths.

You can locate points on a plane (or more specifically, a line segment) that are equally spaced apart from points A and B using a compass.

How can you use a compass to make a locus of points that are equally spaced between A and B?

We must create an incircle, which is a circle inside of a triangle. We can accomplish this by creating an angle bisector from two sides; the intersection point will serve as the incentre. The center of the required circle.

The location where two points are equally distant from one another is known as the angle bisector.

Therefore,

You can locate points on a plane (or more specifically, a line segment) that are equally spaced apart from points A and B using a compass.

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There are 13 ways to make change for 60¢ using only nickels, dimes and quarters.

In the United States of America, a nickel equals 0.05 dollar, a dime equals 0.10 dollar and a quarter equals 0.25 dollar.  

For 0.60 dollar we have the following expression in terms of nickels (\(n\)), dimes (\(d\)) and quarters (\(q\)):

\(0.25\cdot q + 0.10\cdot d + 0.05\cdot n = 0.60\), where \(q,\,d,\,n \in \mathbb{N}_{O}\) (1)

Since quarters are the money of greatest value, we assume arbitrary quantities and count corresponding solutions, whose representations are included below:

\(n = 12-2\cdot d\) (2)

According to the first graph, there are seven forms in this scenario.

Case 2 (\(q = 1\))

\(n = 7-2\cdot d\) (3)

According to the graph case_2, there are four forms in this scenario.

\(n = 2- 2\cdot d\)

According to the graph case_3, there are two forms in this scenario.

Hence, there are 13 forms to make change for 60¢ using only nickels, dimes and quarters. \(\blacksquare\)

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Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.

We have,

For Matthew's investment, the continuous compounding formula can be used:

\(A = P \times e^{rt}\)

Where:

A = Final amount

P = Principal amount (initial investment)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (in decimal form)

t = Time (in years)

In this case,

Matthew's money has tripled,

So A = 3P.

For Parker's investment, the formula for compound interest compounded annually is used:

\(A = P \times (1 + r)^t\)

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (in decimal form)

t = Time (in years)

We need to find t when Matthew's money has tripled in value.

Let's set up the equation:

\(3P = P \times e^{rt}\)

Dividing both sides by P, we get:

\(3 = e^{rt}\)

Taking the natural logarithm of both sides:

ln(3) = rt

Now we can solve for t

t = ln(3) / r

For Matthew's investment,

r = 3 1/8% = 3.125% = 0.03125 (as a decimal).

For Parker's investment,

r = 2 3/4% = 2.75% = 0.0275 (as a decimal).

Now we can calculate t for Matthew's investment:

t = ln(3) / 0.03125

Using a calculator, we find t ≈ 22.313 years.

Now, we can calculate how much money Parker would have in his account at that time:

\(A = P \times (1 + r)^t\)

\(A = $8,000 \times (1 + 0.0275)^{22.313}\)

Using a calculator, we find A ≈ $13,774.

Therefore,

Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.

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Answer:

20,763

Step-by-step explanation:

I saw the answer after I got it wrong

Answer:

\((12 \times 2) - \left(\dfrac{45}5 \right) =24 -9 = 15\)

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

(12 × 2) - (45 / 5) ← evaluate parenthesis

= 24 - 9

= 15

Answer:

the first problem is -1 i think

and the second one is 5/3

Step-by-step explanation: