Richard and Gloria ran a 10-kilometer race. Gloria gave Richard a head start by letting him begin 2.2 kilometers in front of the start line. The distances of Richard and Gloria past the start line as the race progressed can be represented by linear functions and are shown in the table of values and graph below. Whose time was faster, and by how much?


Richard’s Distance Past the Start Line
Time (minutes)
5
10
15
20
25
Distance (kilometers)
2.8
3.4
4.0
4.6
5.2

A graph titled Gloria's Distance Past the Start Line has time (minutes) on the x-axis and Distance (kilometers) on the y-axis. A line goes through points (5, 0.8), (10, 1.6), (15, 2.4), (20, 3.2) and (25, 4).
Gloria’s time was 0.5 minutes faster.
Richard’s time was 0.5 minutes faster.
Gloria’s time was 2.5 minutes faster.
Richard’s time was 2.5 minutes faster.

a) To find the average life of the ten batteries, we need to calculate the mean, which is the sum of all the values divided by the number of values.Sum of all values = 10.8 + 10.6 + 11.4 + 8.9 + 10.1 + 10.6 + 9.9 + 12.6 + 10.5 + 11.9 = 106.2

Number of values = 10

Average life = Sum of all values / Number of values = 106.3 / 10 ≈ 10.63

Therefore, the average life of the ten batteries, rounded to the nearest tenth of an hour, is approximately 10.6 hours.

b) Comparing the two advertisements:

i) The first advertisement claims that Atlas batteries are guaranteed to last 10 hours. This means that all Atlas batteries are expected to last at least 10 hours. However, based on the data provided, we can see that the average life of the batteries is approximately 10.6 hours, which is higher than the guaranteed 10-hour minimum

ii) The second advertisement claims that Atlas batteries have an average life of over 10 hours. This statement aligns with the data we have, as the average life of the batteries is indeed over 10 hours.

Based on the information provided, the second advertisement claiming that Atlas batteries have an average life of over 10 hours is more accurate, as the average life calculated from the given data is 10.6 hours.

In summary, the average life of the ten batteries is approximately 10.6 hours, and the second advertisement stating an average life of over 10 hours is more accurate based on the data provided.

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Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

You've plotted 3 points where x = 0, 1 and 2

= where y = 1, 1 1/2 and 9/4

They are correct.

I suggest you plot 1 more where x = -1 and another where x = 3

Where x = -1 , y = (3/2)^-1 = 2/3.

x = 3 , y = (3/2)^3 = 27/8 = 3 3/8.

Answer: $99

Step-by-step explanation:

Answer && Step-by-step explanation:

Use what we know are given variables (answer choices)

we know middle is 15, 4x+7 must be > 15 plug in variables

7.5 makes it 35 but that is too big

4 is also >  but it makes it slightly too big at 23 but when i divide by 3 i get 7.6, which mult 2 ~= 15

never the less, lets try it at top

4+3=7

make a triangle above 15, this will == half of 15 which is 7.5

7 is closest, I would guess 4 based on this alone.

The true statement about the parking fees in zone A and zone B is A. The fee in zone A is 25 % higher than the fee in zone A.

From the data table below, we can determine that the higher parking fee occurs in zone A instead of zone B.

There is a difference of 1 € in the parking fees between the two zones, which results in a 25% difference.

                                  Zone A     Zone B

Parking fees per hour   4 €            3 €

Difference in fees         +1 €           - 1 €

Percentage difference:

Higher than the other  25%          0%

Less than the other       0%          33%

Thus, we can conclude that A. The fee in zone A is 25 % higher than the fee in zone A.

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Answer: d=7 inches

r=7/2

r=3.5

A=πr²

A=3.14(3.5inch)²

A=3.14×12.25inch²

A=38.465inch²

A≈38.47inch²

The value of cos(2α + β) using trigonometric identities is; -1.0155

We are given;

α = sin⁻¹(4/5)

β = tan⁻¹(12/5)

Thus;

sin α = 4/5

tan β = 12/5

From trigonometric ratios, we can say that;

cos α = 3/5

sin β = 12/13

cos β = 5/13

We know from trigonometric identities that  cos (a + b) = cos a cos b - sin a sin b.

Thus;

cos(2α + β) = cos 2α cos β - sin 2α sin β

Thus;

cos(2α + β) = 2(3/5) * (5/13)) - ((2 * 4/5 * 12/13))

= 0.4615 - 1.477

= -1.0155

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Answer:

1.8

Step-by-step explanation:

The Melinda's rate of decent from the top of the hill is 3.75 ft/sec.

For the given question;

The distance covered by the Melinda after she tripped over a rock at the top of the hill is 225 feet.

The time taken by Melinda to reach the bottom of the hill is 90 seconds.

Then, the rate of decent will be the speed at which she will fall.

Speed = distance/ time

Speed = 225/60

Speed = 3.75

Thus, the Melinda's rate of decent from the top of the hill is 3.75 ft/sec.

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The expression using the common factor is 1/12xy(x² + 5y)

From the question, we have the following parameters that can be used in our computation:

1/12 x^3 y + 5/12 xy^2

Rewrite properly

So, we have

1/12x³y + 5/12xy²

Factor out 1/12 from the expression

So, we have the following representation

1/12(x³y + 5xy²)

Factor out x from the expression

So, we have the following representation

1/12x(x²y + 5y²)

Factor out y from the expression

So, we have the following representation

1/12xy(x² + 5y)

Hence, the expression is (c) 1/12xy(x² + 5y)

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Answer:The expression using the common factor is 1/12xy(x² + 5y)

Step-by-step explanation:

Answer:

The interval from -12 to -7

The interval from 6 to 12.

Step-by-step explanation:

The equation is log(x + 9) + log(x 9) = log[(x + 9)(x 9)]. = log(x² − 81)

Here is the equation:

log(x² - 81) = 0.47712

This can be expressed in exponential form:

x² - 81 = 10^(0.47712)

x² = 81 + 3.02343

x² = 84.02343

x ≈ ± 9.1658

The answers are therefore x -9.1658 and x 9.1658.

These intervals are where these solutions occur:

The answer, x -9.1658, can be found in the range from -12 to -7.

- The answer x = 9.1658 is found in the range of 6 to 12.

The appropriate choices are:

- The range between -7 and -12; - The range between 6 and 12.

Answer:

\(Model = 6.05ft\)

Step-by-step explanation:

Given

\(Space\ Needle = 605ft\)

\(Scale\ Model = \frac{1}{100}\)

Required

Determine the height of the model.

To do this, we simply multiply the scale model by the height of the space needle.

\(Model = Scale\ Model * Space\ Needle\)

\(Model = \frac{1}{100} * 605ft\)

\(Model = \frac{605ft}{100}\)

\(Model = 6.05ft\)

Hence, the height of the model is 6.05ft

Answer:

Step-by-step explanation:

50% of 366 is 183, therefore your answer is 366.

Answer:

tourist: 28%

non-tourist: 72%

Step-by-step explanation:

total: 50

tourists: 14

non-tourists:50 - 14 = 36

tourist percentage: 14/50 × 100% = 28%

non-tourist percentage: 36/50 × 100 = 72%

The median of the distances is M = 6.5 kilometers

Given data ,

To find the median of a set of numbers, we arrange the numbers in ascending order and then locate the middle value. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

Arranging the given set of numbers in ascending order: {4, 5, 8, 11}

Since the set has an even number of values, the median is the average of the two middle numbers. In this case, the two middle numbers are 5 and 8. To find the average, we add these two numbers and divide by 2:

(5 + 8) / 2 = 13 / 2 = 6.5

Hence , the median of the given set {4, 5, 8, 11} is 6.5

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Answer:circle

Step-by-step explanation:

I just got it right

Answer:

Circle

Step-by-step explanation

A point on the scatter plot is defined as (19, 3), which means that an input of 19 is mapped to an output of 3.

The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:

(Input, Output).

One point on the scatter plot for this problem has the coordinates given as follows:

(19, 3).

Hence the meaning is that an input of 19 is mapped to an output of 3.

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The mean absolute deviation (MAD) for the given data is 1/20. This means that, on average, each data point in the set differs from the mean by 1/20.

To find the mean absolute deviation (MAD) of a set of data, we need to calculate the average difference between each data point and the mean of the data set. Here's how we can calculate it for the given data:

Step 1: Find the mean (average) of the data set.

Mean = (1/4 + 5/8 + 3/8 + 3/4 + 1/2) / 5 = 2/5

Step 2: Calculate the difference between each data point and the mean.

Differences: |1/4 - 2/5|, |5/8 - 2/5|, |3/8 - 2/5|, |3/4 - 2/5|, |1/2 - 2/5|

Step 3: Calculate the absolute value of each difference.

Absolute Differences: 1/20, 1/40, 1/40, 1/20, 1/10

Step 4: Find the average of the absolute differences.

MAD = (1/20 + 1/40 + 1/40 + 1/20 + 1/10) / 5 = 1/20

The MAD provides a measure of the average amount of variation or dispersion in the data set. In this case, a MAD of 1/20 indicates that the data points are relatively close to the mean, with most values falling within 1/20 of the mean value.

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The common ratio in the sequence is √581/3

We know that in a geometrical progression with a common ratio R, the recursive formula is:

A(n)  = R*A(n - 1)

That means that each term in the sequence is R times the previous term, so knowing one term and R (or two terms) we can completely define the sequence.

Here we know that:

A(3) = 18

A(5) = 1162

Then we could write:

A(5) = R^2*A(3)

1162 = 18*R^2

1162/18 = R^2

581/9 = R^2

√(581/9) = R

√581/3  =R

That is the common ratio.

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Using the monthly payment formula, it is found that the balance of the plan is of $26,731.23.

It is given by:

\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

In which:

The parameters for this problem are given as follows:

A = 144, r = 0.06, n = (68 - 24) x 12 = 528.

Then:

r/12 = 0.06/12 = 0.005.

\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

\(144 = P\frac{0.005(1 + 0.005)^{528}}{(1 + 0.005)^{528} - 1}\)

\(P = 144\frac{(1 + 0.005)^{528} - 1}{0.005(1 + 0.005)^{528}}\)

P = $26,731.23.

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A) The bunny population after every 2 months is f(T)=5T+20

B) The bunny population after 16 weeks is x=29.205

C) The number of months that the bunny population to reach 300 bunnies is 112 months.

All nationals present in, or temporarily absent from, a country, as well as aliens permanently settled in a country, are characterized as population. This indicator depicts the average number of people who live in a given location. The annual changes in population caused by births, deaths, and net migration during the year are referred to as growth rates.

Given,

0 months -------- 20 bunnies

2 years ------- 80 bunnies

In two years, bunnies are increased by,

=80-20

=60

2 years ------>60

1 year ------>30

A) f(T)=mT + b

1 year -----> 12 months -----> 30 bunnies

12/6 months ------>30/6 bunnies

2 months -----> 5 bunnies

f(T)= initial population+ increased population in two months

f(T)=20+5

f(T)==25

f(T)= 2.5T+20

f(T)=5T+20

Where T =time in months

B) For 10 years ------> 10 bunnies

52 weeks -------->30 bunnies

16 weeks ------?

x=(16*30)/52

x=29.205

C) 1 month -------> 2.5 bunnies

 ? ---------------->280 bunnies

x=280/2.5

x=112 months

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Answer:

A) The bunny population after every 2 months is f(T)=5T+20

B) The bunny population after 16 weeks is x=29.205

C) The number of months that the bunny population to reach 300 bunnies is 112 months.

What is meant by population?

All nationals present in, or temporarily absent from, a country, as well as aliens permanently settled in a country, are characterized as population. This indicator depicts the average number of people who live in a given location. The annual changes in population caused by births, deaths, and net migration during the year are referred to as growth rates.

Given,

0 months -------- 20 bunnies

2 years ------- 80 bunnies

In two years, bunnies are increased by,

=80-20

=60

2 years ------>60

1 year ------>30

A) f(T)=mT + b

1 year -----> 12 months -----> 30 bunnies

12/6 months ------>30/6 bunnies

2 months -----> 5 bunnies

f(T)= initial population+ increased population in two months

f(T)=20+5

f(T)==25

f(T)= 2.5T+20

f(T)=5T+20

Where T =time in months

B) For 10 years ------> 10 bunnies

52 weeks -------->30 bunnies

16 weeks ------?

x=(16*30)/52

x=29.205

C) 1 month -------> 2.5 bunnies

? ---------------->280 bunnies

x=280/2.5

x=112 months

According to the quantity theory of money, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply.Velocity can change over time, and changes in velocity may be caused by various factors.

For example, changes in velocity can be caused by shifts in payment practices, changes in the use of credit, changes in the availability of bank deposits or cash, or shifts in demand patterns.Changes in velocity may be related to changes in the money supply.

For example, if the money supply increases, the demand for money may increase, causing the velocity of money to decrease. Conversely, if the money supply decreases, the demand for money may decrease, causing the velocity of money to increase.

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The inequality is 12b > 180 and the number of books, b, she must sell   in order to meet her goal must be more than 15 (b > 15)

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given that:

Erin sells books for $12 each.

She wants to make more than $180 in book sales.

The number of books, b

Erin sells books for $12 each:   12 × b = 12b

More than $180 in book sales:  > $180  (i.e  greater than $180)

Thus, the inequality is:

12b > 180

Solve for b:
12b > 180

Divide both sides by 12

b > 180/12

b > 15

Therefore,  the inequality is 12b > 180 and the number of books, b, she must sell in order to meet her goal is b > 15 (greater than 15)

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Answer:

x = -2

Step-by-step explanation:

1) Distribute

4(x+5)=6(x+4)

4x+20=6(x+4)

2) Distribute

4x+20=6(x+4)

4x+20=6x+24

3) Subtract 20 from both sides

4x+20=6x+24

4x+20-20=6x+24-20

4) Simplify

- Subtract the numbers

4x+20-20=6x+24-20

4x=6x+24-20

- Subtract the numbers

4x = 6x + 24 - 20

4x = 6x + 4

5) Subtract 6x from both sides

4x = 6x + 4

4x - 6x = 6x + 4 - 6x

6) Simplify

- Combine like terms

4x-6x = 6x + 4 - 6x

-2x = 6x + 4 - 6x

- Combine like terms

-2x = 6x + 4 - 6x

-2x = 4

7) Divide both sides by the same factor

-2x = 4

-2x/-2 = 4/-2

8) Simplify

- Cancel terms that are in both the numerator and denominator

-2x/-2 = 4/-2

x = 4/-2

- Divide the numbers

x = 4/-2

x = -2

Answer:

1/6

Step-by-step explanation:

On a fair die, there is a 1/6 chance of rolling any specific number for each die,

to roll a 10 you need (5, 5) or (6, 4) or (4, 6)

odds to roll a 10 are 1/6•1/6 + 1/6•1/6 + 1/6•1/6 = 3/36

to roll an 11 you need a (5, 6)  or (6, 5)

odds to roll an 11 are 1/6•1/6 + 1/6•1/6 = 2/36

to roll a 12 you need a (6, 6)

odds to roll a 12 are 1/6•1/6 = 1/36

so odds to roll a sum greater than 9 are 3/36 + 2/36 + 1/36 = 6/36 = 1/6

Answer:

1/4 of a pound

Answer: one fourth of a pound

Step-by-step explanation:

so first you have to use a calulator last type = then u guet your answer 1/4 of a pound

The height of the trapezoid is 3.636 in.

Videos of quantity does that explains the size of two dimensional figure are safe or planner lamania in the plane. It is be thought of as the amount of surface that is safe covers calculating the area of a safe or surface can be an important step in many mathematical problem there are several methods for calculating area including the use of geometric formula and equations as well as using tools such as ruler or calculator.

To solve this problem, we must use the formula for finding the area of a trapezoid. A trapezoid has two parallel sides, known as the bases, and two non-parallel sides, known as the legs. The area of a trapezoid is equal to the sum of the bases multiplied by the height, then divided by two. Therefore, the formula to solve this problem is: A = (b1+b2)h/2.

In this case, b1 = 18 in and b2 = 22 in, and we are looking for the height (h). Plugging these values into the formula, we get: A = (18 + 22)h/2 = 96 in². To solve for h, we can multiply both sides of the equation by 2: 96 = (18 + 22)h. Then, subtract 18 from both sides of the equation: 78 = 22h. Finally, divide both sides of the equation by 22: h = 78/22 = 3.636 in. Therefore, the height of the trapezoid is 3.636 in.

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