Goran rented a truck for one day. There was a base fee of $20.95, and there was an additional charge of 71 cents for each mile driven. Goran had to pay
$228.98 when he returned the truck. For how many miles did he drive the truck?

Given:

There are given that the parent functions as a cosine function:

Where,

The amplitude of the function is 9.

The vertical shift is 11 units down.

Explanation:

To find the cosine function, we need to see the standard form of the cosine function:

Where,

a is the amplitude of the function,

Now,

According to the question:

The amplitude of the function is 9, which means:

The vertical shift is 11 units down, which means:

For period:

Final answer:

Hence, the cosine function is shown below;

Answer:

c

Step-by-step explanation:

at least means >=

n+17 >= 68

so n>=51

Step-by-step explanation:

Perhaps the equation is d=1/2at2 and you are given the distance (40 m) and acceleration (9.8 m/s2) and asked to find the time. or convert the equation in terms of t and then plug in the numbers to solve.

Answer:

That is true but still remember that playing the knight at the start can be very useful.

Answer:

Answer is 36.

You can simply get this by writing and expression for it

25/100 x w=9

25w/100=9

w= 9x100/25

w=36.

Answer:

36

Step-by-step explanation:

9/w=25/100

cross multiplication:

9*100=25w

900=25w

900=25w / 25

36=w

Answer: 7.0%

Step-by-step explanation:

The probability of rolling a sum of 14 is 7.0% because 15/216 = 7.0%

The probability of rolling a sum of 14 is  \(\frac{1}{72}\)    or  0.014.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Formula of probability

Probability(Event) = \(\frac{Favorable Outcomes}{Total Outcomes}\)  

According to the question

rolling a sum of 14

As the maximum sum of two dice is 6+6 = 12

Therefore ,

we will take 3 dices

Now ,

As each dice have 6 different digits and can be repeated

i.e

Total outcomes = 6 * 6 * 6 = 216  

Favorable outcome :

(6,6,2) or (2,6,6) or (6,2,6) = 3 ways

Now,

By using the formula of probability

Probability(Event) = \(\frac{Favorable Outcomes}{Total Outcomes}\)  

Substituting the value in the formula

Probability(Event) = \(\frac{3}{216}\)

Probability(Event) = \(\frac{1}{72}\)    or  0.014

Hence, the probability of rolling a sum of 14 is  \(\frac{1}{72}\)    or  0.014

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Answer:?

Step-by-step explanation:

The number corresponds to the given string  is 237880

What is common ratio?

In a geometric sequence, ratio of each term to its immediately preceding term is always constant and is known as common ratio.

The shortlex ordering places the shortest sequences at the front of the list of sequences by cardinality (length), while sequences of the same length are arranged lexicographically.

Given:  cbbca cba cbc

  length =11

We need to find the number of strings that precede the given string over {a,b,c}

Number of strings of length 0 = 1

Number of strings of length 1 = 3

Number of strings of length 2 = 3²

'

'

'

'

'

Number of strings of length 10 = 3¹⁰

In general, number of strings formed withy length n = 3ⁿ

Add all the strings of length 0 to 10

1+3+3²+......................+3⁻¹⁰

By simple geometric sum formula ,

we have

= (3¹¹⁻¹)/(3-1) =  88573

Number of strings of length 11 starting with either 'a' or 'b' = 2*3¹⁰

Number of strings of length 11 starting with 'ca' = 3⁹

Number of strings of length 11 starting with 'cba' = 3⁸

Number of strings of length 11 starting with 'cbba' or 'cbbb' = 2*3⁷

Number of strings of length 11 starting with 'cbbcaa' or 'cbbcab' = 2*3⁵

Number of strings of length 11 starting with  'cbbcaca' = 3⁴

Number of strings of length 11 starting with 'cbbcacbab' or 'cbbcacbaa' = 2*3²

Number of strings of length 11 starting with 'cbbcacbaca' = 3

Number of strings of length 11 starting with 'cbbcacbacba'  or 'cbbcacbacbb'  = 2

Total number of strings of length 11 preceding the given string is :

  2+3+2*3² +3⁴+ 2*3⁵+ 2*3⁷+3⁸+3⁹ + 2*3¹⁰

= 149306

The number corresponds to the given string

=  88573 + 149306 +1

= 237880

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Rounding to the nearest tenth, the sink's volume is approximately  \(6328.2\) cubic inches.

The circumference of a hemisphere is  represented by the formula:

\(C = 2 \pi r\)

here C is the circumference and r is the radius of the hemisphere.

it is given that the circumference C as \(91 3/4\) inches. now convert into a decimal

\(91 3/4 inches = 91.75 inches\)

we are having

 \(91.75\) inches \(= 2πr\)

Solving for r, we get:

 \(r = 91.75 / (2\pi) \approx 14.599\) inches (rounded to three decimal places)

The volume of a hemisphere is represented by formula

\(V = (2/3)\pir^3\)

Substituting our value of r, we get:

\(V = (2/3)\pi(14.599)^3 \approx 6328.2\) cubic inches

Therefore, rounding to the nearest tenth, the sink's volume is approximately  \(6328.2\) cubic inches.

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The volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

To find the volume of the container, we need to multiply its length, width, and height. Let's convert the given measurements to meters to ensure consistent units.

The length of the container is 2.76 meters.

The width of the container is 23.5 decimeters, which is equal to 2.35 meters (since 1 decimeter = 0.1 meters).

The height of the container is 196 centimeters, which is equal to 1.96 meters (since 1 meter = 100 centimeters).

Now we can calculate the volume of the container:

Volume = Length × Width × Height

Volume = 2.76 meters × 2.35 meters × 1.96 meters

Volume ≈ 12.9516 cubic meters (rounded to four decimal places)

Therefore, the volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

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Answer:

0.555

Step-by-step explanation:

you simply follow the linear equation rule and fill in

The perimeter of a square is the length of one side multiplied by 4 ( the number of sides)

3 ft x 4 sides = 12 ft.

Perimeter = 12 ft.

If in a recent poll, 280 people were asked if they liked dogs, and 42% said they did. the margin of error of this poll, at the 90% confidence level is 0.05.

Sample proportion =42%(phat)

Sample size =280

Standard error = √(0.42×( 1- 0.42)/280)

Standard error = √(0.42×(.58)/280)

Standard error =0.029

Hence,

Margin of error = z-critical for 90% confidence level× Standard error

Zα/2 = 1.645 for 90% confidence

Margin of error =  1.645 × 0.029

Margin of error  = 0.047

Margin of error =0.05 (Approximately)

Therefore the margin of error is 0.05.

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The value of x in the triangle is 20 units.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

Using triangle proportional theorem, If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

Hence,

11 / 121 = 10 / 5x + 10

cross multiply

11(5x + 10) = 1210

55x + 110 = 1210

55x = 1210 - 110

55x = 1100

divide both sides of the equation by 55

x = 1100 / 55

x = 20

Therefore,

x = 20

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Answer:

Total periodic pension costs (TPPC) is equal to the contributions plus change in the pension liability during the year. Each period, the periodic pension cost is recognized in profit or loss (P&L) and/or in other comprehensive income (OCI).

The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Answer:

(32,47)

Step-by-step explanation:

1 minute (8,11)

2 minutes (12,17)

3 minutes (16,23)

4 minutes (20,29)

5 minutes (24,35)

6 minutes (28,41)

7 minutes (32,47)

Answer: y = 7.5

Step-by-step explanation:

Suppose that y varies directly with x

That is, y∝x

Convert y∝x to a full equation by introducing a constant k to the right hand side.

Therefore, y = kx

Given that y = 10 and x = 20

Substitute y and x in the equation above. We have;

10 = k(20)

10 = 20k

20k = 10

k = 10/20

k = 0.5

Since k = 0.5, the equation y = kx becomes y = 0.5x

Now, to find y if x = 15, substitute x in equation y = 0.5x

Therefore, y = 0.5(15)

y = 7.5

If your'e using Acellus, the answer is asking for it as a fraction.

The answer for Acellus is 15 over 2

15/2

a) The speed of the boat is 3/5 ft/sec

b) The rate at which the angle changes is 8/125 rad/sec

A right angled triangle is a type of the triangle with one of its angles 90°.

The longest side of the triangle is called the hypotenuse which is the side that faces the right angle. other sides are called the adjacent sides.

Analysis:

The analysis is in the attached file below.

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Answer:

Step-by-step explanation:

It sounds like you are asked to estimate it. That's a very valuable skill.

9.634 is about 10

445.76 is about 446

So an approximate answer is 446 * 10 = 4460

How close is that to the actual answer? Let's find out.4294.45

On a test, if you get an answer like 4460 in your head, and your calculator says 4294.45, you are pretty certain that you have done the question correctly.

Answer:

-7

Step-by-step explanation:

Tiger Woods was 15 under par after the third round of a golf tournament, but was 8 over par for the fourth round. So, his score for the entire tournament was -15 + 8 = -7 (That is, 7 under par).

Answer: It would be the first one (20 pens for 8$)

Step-by-step explanation: If you divide 20 by 8 then each pencil will be 2.50$. However if you divide 30 by 10 it will be 3 dollars for each pencil so the first deal will be better since you spend less money.

Answer:

The answer is 2:36

Step-by-step explanation:

The answer is 2:36 because 1:43 plus 56 minutes later would be 2:36

Answer: A and B in algebra stand for any variables of real numbers. A real number is a value of a continuous quantity that can represent a distance along a

Step-by-step explanation:

Answer:

\(\textsf{B)} \quad \log_ba=x\)

Step-by-step explanation:

Given:

\(a=b^x\)

Take log of base b of both sides:

\(\implies \log_ba=\log_bb^x\)

Apply the log power law:  \(\log_ax^n=n\log_ax\)

\(\implies \log_ba=x\log_bb\)

Apply log identity:  \(\log_nn=1\)

\(\implies \log_ba=x\)

Answer:

Step-by-step explanation:

y=mx+b

m=(y2-y1)/((x2-x1)

m=(12-7.5)/(120-30)

m=0.05

y=0.05x+b, using point (30,7.5)

7.5=0.05(30)+b

7.5=1.5+b

b=6

y=0.05x+6

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:

1/3n + 4 = 6

Hope this helped!