Hunter is trying to save $600 go to summer camp. He already has $150. If he earns $7.50 per hour working at a grocery store, how many hours will he have to work?

Answer:

x=6

Step-by-step explanation:

By the Product Rule of Logarithms, the logarithm of the product of numbers is the sum of the logarithms of the numbers.

\( log(x) + log(x - 1) = log(x(x - 1)) = log( {x}^{2} - x ) = log(3x + 12) \)

Raise both sides to the power of 10 to eliminate the logs, obtaining:

\( {x}^{2} - x = 3x + 12\)

\( {x}^{2} - 4x - 12 = 0\)

\((x - 6)(x + 2) = 0\)

x = -2 or x = 6. Since x = -2 is extraneous, it follows that x = 6.

The volume of the solid is 12sqrt(3).

To find the volume of the solid whose base is the region inside the circle x² + y² = 9, we need to integrate the area of each square cross-section perpendicular to the y-axis.

Let's consider a cross-section of the solid taken at y = k, where k is a value between -3 and 3 (the range of y-values for the circle x² + y² = 9). The width of the cross-section is the distance between the x-coordinates of the intersection points of the circle with the line y = k. These intersection points are (sqrt(9 - k²), k) and (-sqrt(9 - k²), k). Since the cross-section is a square, its area is equal to the square of the width, which is sqrt(9 - k²) - (-sqrt(9 - k²)) = 2sqrt(9 - k²).

Therefore, the volume of the solid is given by the integral of the area of each cross-section as follows:

V = ∫(-3 to 3) 2sqrt(9 - y²) dy

To evaluate this integral, we can use the substitution u = 9 - y², du = -2y dy:

\(V = \int (9 to 0) \sqrt{u} du/(-2)\\= -1/2 \times [2/3 \times u^{(3/2)}](9, 0)\\= 2/3 \times (27\sqrt{3} - 9\sqrt{9} )\\= 2/3 \times 18\sqrt{3} \\= 12\sqrt{3}\)

for such more question on volume

https://brainly.com/question/6204273

#SPJ11

Answer:

The traveler's speed off the walkway is 4 ft/sec

The speed of the moving walkway is 2 ft/sec

Step-by-step explanation:

During an experiment of acceleration changes, the value that must stay constant during these trials is d. Mass

Inertia, a basic characteristic of all matter, may be measured quantitatively using mass. When a force is applied, an item effectively provides resistance to changes in velocity or position. The change brought about by an applied force is less the more mass an item has. According to Newton's second law of motion an object's acceleration is inversely proportional to its mass and directly proportional to the net force that has been applied to it. It may be expressed mathematically as F = ma.

The goal of this experiment is to see how variations in force impact acceleration. It is crucial to maintain the mass constant throughout the trials in order to isolate the impact of force on acceleration. Any observable variations in acceleration may be entirely attributable to variations in the applied force by maintaining the mass constant.

Read more about Mass on:

https://brainly.com/question/86444

#SPJ4

The angle R corresponds to the angle E.

This comes from the fact that they are alternate interior angles.

Answer:

28.65 yds (If you have to round do 29)

Step-by-step explanation:

a^2 + b^2 = c^2

14^2 + 25^2 = c^2

196 + 625 = 821

since c is squared you have to find the square root of 821

821 squared equals 28.65 yards

To find a recurrence relation for the number of n-letter sequences using the letters a, b, c such that any a not in the last position of the sequence is always followed by a b, we can use the following approach.

Let's consider the last two letters of the sequence. There are three possible cases:

1. The last letter is not "a": In this case, we can append any of the three letters (a, b, or c) to the end of an (n-1)-letter sequence that satisfies the given condition. This gives us a total of 3 times the number of (n-1)-letter sequences that satisfy the condition.

2. The last letter is "a" and the second to last letter is "b": In this case, we can append any of the two letters (a or c) to the end of an (n-2)-letter sequence that satisfies the given condition. This gives us a total of 2 times the number of (n-2)-letter sequences that satisfy the condition.

3. The last letter is "a" and the second to last letter is not "b": In this case, we cannot append any letter to the end of the sequence that satisfies the condition. Therefore, there are no such sequences of length n in this case.

Putting all these cases together, we get the following recurrence relation:

f(n) = 3f(n-1) + 2f(n-2), where f(1) = 3 and f(2) = 9.

Here, f(n) denotes the number of n-letter sequences using the letters a, b, c such that any a not in the last position of the sequence is always followed by a b.

Learn More About Recurrence Relation: https://brainly.com/question/4082048

#SPJ11

Answer:

12(7 - 3)

Step-by-step explanation:

All the other do not equal anything.

Answer:

the customer bought 2 burrito bowls and 1 corn taco.

Step-by-step explanation:

13+5=23

23+5=23

Answer:

r = 3.6 , a = 2

Step-by-step explanation:

given that r is inversely proportional to a then the equation relating them is

r = \(\frac{k}{a}\) ← k is the constant of proportion

to find k use the condition when r = 12 , a = 1.5

12 = \(\frac{k}{1.5}\) ( multiply both sides by 1.5 )

18 = k

r = \(\frac{18}{a}\) ← equation of proportion

when a = 5 , then

r = \(\frac{18}{5}\) = 3.6

when r = 9 , then

9 = \(\frac{18}{a}\) ( multiply both sides by a )

9a = 18 ( divide both sides by 9 )

a = 2

First of all, the modular inverse of n modulo k can only exist if GCD(n, k) = 1.

We have

130 = 2 • 5 • 13

231 = 3 • 7 • 11

so n must be free of 2, 3, 5, 7, 11, and 13, which are the first six primes. It follows that n = 17 must the least integer that satisfies the conditions.

To verify the claim, we try to solve the system of congruences

\(\begin{cases} 17x \equiv 1 \pmod{130} \\ 17y \equiv 1 \pmod{231} \end{cases}\)

Use the Euclidean algorithm to express 1 as a linear combination of 130 and 17:

130 = 7 • 17 + 11

17 = 1 • 11 + 6

11 = 1 • 6 + 5

6 = 1 • 5 + 1

⇒   1 = 23 • 17 - 3 • 130

Then

23 • 17 - 3 • 130 ≡ 23 • 17 ≡ 1 (mod 130)

so that x = 23.

Repeat for 231 and 17:

231 = 13 • 17 + 10

17 = 1 • 10 + 7

10 = 1 • 7 + 3

7 = 2 • 3 + 1

⇒   1 = 68 • 17 - 5 • 231

Then

68 • 17 - 5 • 231 ≡ = 68 • 17 ≡ 1 (mod 231)

so that y = 68.

The solution is given below.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

The perimeter of a rectangle is 40 cm. The length is 14 cm.

Let x = width of the rectangle.

Ravi says he can find the width using the equation 2(x + 14) = 40.

Fran says she can find the width using the equation 2x + 28 = 40.

now, we get,

1. Divide both sides by 2

 2(x+14) = 40

 x+14 = 20

2. Isolate the x term by subtracting 14 from both sides

3. x = 6. The width of the triangle is 6 cm.

4. Isolate the x term by subtracting 28 from both sides

 2x + 28 = 40

 2x = 12

5. Divide both sides by 2

6. x = 6

7. The two equations have the same solution, because by the distributive rule, 2(x+14) = 2x+28.

To learn more on equation click:

brainly.com/question/24169758

#SPJ1

The scale structure being used in a question that asks the respondent to write in his or her age on the survey is Ratio. Option C is correct.

The ratio scale allows for the measurement of quantities with a meaningful zero point and consistent intervals between values. Age is a variable that can be measured on a ratio scale because it possesses these characteristics. It has a meaningful zero point (birth), and the intervals between ages are consistent (each year represents an equal interval).

Thus, the required, scale structure being used in a question that asks the respondent to write in his or her age on the survey is Ratio.

Learn more about scale structure here:

https://brainly.com/question/31963815

#SPJ4

The question seems to be incomplete, the complete question is:

What type of scale structure is being used in a question that asks the respondent to write in his or her age on the survey?

A. Nominal

B. Ordinal

C. Ratio

D. Interval

E. Likert

The difference between r and p.  is that r represents the sample correlation coefficient while p represents the p-value

Generally, r represents the sample correlation coefficient, which is a measure of the strength and direction of the linear relationship between two variables in a sample of data. It ranges from -1 to 1, where -1 represents a perfect negative correlation, 0 represents no correlation, and 1 represents a perfect positive correlation.

p represents the p-value, which is a measure of the statistical significance of the sample correlation coefficient. It represents the probability that the observed correlation occurred by chance, assuming that there is no true correlation in the population.

A p-value of less than 0.05 is often used as a threshold for determining statistical significance, meaning that the observed correlation is unlikely to have occurred by chance and is likely to reflect a true correlation in the population.

Read more about sample correlation coefficient

https://brainly.com/question/25822940=

#SPJ1

The probability that the coin lands on heads is D = (3±√3)/6

Probability is a branch of mathematics that studies the likelihood of a random event occurring. For example, when a coin is tossed into the air, the possible outcomes are Head and Tail.

Let x be the probability of flipping heads. As a result, the probability of flipping tails is 1- x.

The probability of flipping two heads and two tails is equal to the number of ways to flip it multiplied by the product of the probabilities

(4+2)x2(1-x)2 = 1/6

6x2(1-x)2 = 1/6

x2(1-x)2 = 1/36

x(1-x) = ±1/6

As for the desired probability x, both x and 1 - x are nonnegative, we only need to consider the positive root, hence

x(1-x) = 1/6

6x2 – 6x +1 = 1/6

Using the quadratic formula, we can determine that the roots of this equation are

(3±√3)/6

Therefore the probability that the coin lands on heads is D = (3±√3)/6

To learn more about probability visit

https://brainly.com/question/11034287

#SPJ4

The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

Learn more about Functions here :

https://brainly.com/question/29067911

#SPJ1

Answer:

x = -3 is the answer. Writing this cause brainly requires a 20 character answer.

In the equation y = mx + b, the meaning of the m and the b is

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + b

Information gotten from the question include

In the equation y = mx + b

m = ? and b = ?

y = mx + b

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

b = y intercept

therefore m and b are the slope and y intercept respectively

Learn more about linear functions at:

https://brainly.com/question/29213643

#SPJ1

Answer:

x^3 - 13x^2.

Step-by-step explanation:

–(5x3 + x2) + 4(x3 – 3x2)  Removing the brackets:-

= -5x^3 - x^2 + 4x^3 - 12x^2

= -5x^3 + 4x^3 - x^2 - 12x^2

= x^3 - 13x^2.

Answer:

Step-by-step explanation:

-(5x³+x²)+4(x³-3x²)

=-5x³-x²+4x³-12x²

=-x³-13x²

The test statistic depends on the specific hypothesis test being conducted.

In general, a test statistic is a value calculated from the sample data that is used to assess the likelihood of observing the data under the null hypothesis. It is used to make a decision about whether to reject or fail to reject the null hypothesis. The choice of test statistic depends on the specific hypothesis being tested and the nature of the data.

To determine the test statistic in a given hypothesis test, it is necessary to specify the null hypothesis, the alternative hypothesis, and the appropriate statistical test being used. This information is crucial in calculating the test statistic and interpreting its significance. Without these details, it is not possible to provide a specific test statistic in this context.

Learn more about test statistic here:

https://brainly.com/question/31746962

#SPJ11

The complete question is:

A software company is interested in improving customer satisfaction rate from the 75% currently claimed. The company sponsored a survey of 152 customers and found that 120 customers were satisfied. What is the test statistic z?

when getting a bearing, we're referring to the angle from the North line moving clockwise, so of D from C?  well, the "from" point gets the North line and we check the angle from that North line clockwise to the other point, Check the picture below.

The printer that has a better rate of cost per page would be = printer B.

For printer A:

The number of pages printed = 100

The cost for the printed pages = $26.99

Cost per page = 26.99/100 = $0.27/page

For printer B:

The number of pages printed = 275

The cost for the printed pages = $67.99

Cost per page =67.99/275

= 0.25

Therefore the printer that has a better rate of cost per page would be = printer B

Learn more about rate here:

https://brainly.com/question/29504549

#SPJ1

Answer:

  (c)  √65

Step-by-step explanation:

You want to know the magnitude of the vector (7, -4).

The magnitude of a vector is the root of the sum of the squares of its components.

  |(7, -4)| = √(7² +(-4)²) = √(49 +16) = √65

The magnitude of the vector is √65.

Answer:

√65

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

you subtract 3 every time, so 14-3 = 11

The gross pay for the given service is $343.2.

Gross pay is what employees earn before taxes, benefits and other payroll deductions are withheld from their wages.

Given that, the regular salary of some service is $7.80 per hour, we need to calculate the gross payment with over time hour, which is 4 hours and regular hour of work is 40 hours.

Therefore,

To find, gross payment, we will multiply by 7.80 by 4 and 40, and add both to get the regular salary,

Gross payment = 7.80 × 4 + 7.80 × 40  

= 7.80(4+40)

= 7.80 × 44

= 343.2

Hence, the gross pay is $343.2

Learn more about gross pay, click;

https://brainly.com/question/14690804

#SPJ1

Answer:

Therefore, Aroha is 17 yrs old and her brother is 14 yrs old.

Step-by-step explanation:

Let's represent Aroha's brother's Agee with the letter "b" yrs old.

If Aroha is 3yrs older than her brother, she's : (b+3) yrs old.

The sum of their ages is 31,

b+(b+3)=31

2b+3=31

Collect like terms,

2b=31-3

2b=28

Divide both sides by 2,

b=14

b+3=17

A cheerful teen hoping this helps,

stay techy, brilliant and positive!

Answer:

  see attached

Step-by-step explanation:

You want a graph of the function F(x) = 2x² -5.

A graphing calculator can help a lot when you want the graph of a function. This one is an x² function with a vertical translation of -5 and a vertical stretch by a factor of 2.

It is often useful to consider points ±1 or ±2 either side of the vertex, and the vertex itself.

The graph is attached.