Mr. Leonard is renting a car for one day. The table below shows the total amount he will be charged for the car based on the number of miles he drives.


Which equation best represents c, the number of dollars Mr. Leonard should be charged for driving m miles?

The probability of selecting exactly three clubs from a standard deck is 0.088. Where n = 5; p = 0.25; q = 0.75; and x = 3 . It is calculated by using binomial probability.

The binomial probability formula is

P(X = x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾ = \(\frac{n!}{(n-x)!x!} p^xq^{(n-x)}\)

Where n is the number of trials, p i is the probability of success, and q is the probability of failure.

And q = 1 - p

It is given that, a card is selected from a standard deck and replaced.

This experiment has repeated a total of five times. i.e., trials n = 5

So, the probability of success is p = 1/4 = 0.25

(Since one card is to be selected from the five trials where each time the card is replaced)

Then, the probability of failure is q = 1 - 0.25 = 0.75

And it is given that we need to find the probability of selecting exactly three clubs. So, the required random variable is x = 3.

Then, using the binomial probability formula, we get

P(X = x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾

⇒ P(X = 3) = ⁵C₃ p³q⁽⁵⁻³⁾ = ⁵C₃(0.25)³(0.75)² = 0.0878

On rounding off, we get the required probability as 0.088.

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Linear regression is a technique used in statistics and machine learning to understand the relationship between two variables and how one affects the other.

In this case, we are interested in understanding the relationship between sales and seasonality. We can use linear regression to create a model that predicts sales based on seasonality. Here's how we can do it First, let's plot the data to see if there is a relationship between sales and seasonality.

We can see that there is a clear pattern that repeats every year. This indicates that there is a strong relationship between sales and seasonality. We can use the following equation: y = mx + b, where y is the dependent variable (sales), x is the independent variable (seasonality), m is the slope of the line, and b is the intercept of the line.

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Answer:

BD

Step-by-step explanation:

The radius is "a straight line from the center to the circumference of a circle." BD is the correct option, but AD and DC would work, as well.

Answer:

BD, sory Im late! Give other person brainliest. You're doing great! Have a wonderful day! Remember your worth!

Answer: 171.5

Step-by-step explanation:

1/2 x 7 x 7 x7  = 171.5 cm3

Answer:

\(volume=1/3(area ~of ~base) \times( height)\)

\(v=1/3(7\times7)\times7\)

\(v=343/3\)

\(v=114\)

-----------------------

hope it helps...

have a great day!!

Answer:

Step-by-step explanation:

If John's teacher bought three 64 ounce bottles of soda for a class party, the total weight of the soda bought will be 3*64 = 192 ounces of soda.

If 1/6 of the soda remained after the party, the amount of ounces that remained is expressed as;

amount of ounces that remained  = 1/6 * 192

amount of ounces that remained = 32 ounce

Hence amount of ounces that remained is 32 ounces

On average, a customer spends approximately 1.16 minutes waiting time on hold before they can start speaking to a representative.

To find the average waiting time for a customer on hold before they can start speaking to a representative, we need to consider both the arrival rate of calls and the average service time of the staff members.

Given:

9 staff members taking calls.

On average, one call arrives every 5 minutes (standard deviation of 5 minutes).

Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes).

To calculate the average waiting time, we need to use queuing theory, specifically the M/M/c queuing model. In this model:

"M" stands for Markovian or memoryless arrival and service times.

"c" represents the number of servers.

In our case, we have an M/M/9 queuing model since we have 9 staff members.

The average waiting time for a customer on hold is given by the following formula:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

Where:

c = number of servers (staff members) = 9

μ = average service rate (1 / average service time)

λ = average arrival rate (1 / average interarrival time)

ρ = λ / (c * μ)

First, let's calculate the average arrival rate (λ):

λ = 1 / (average interarrival time) = 1 / 5 minutes = 0.2 calls per minute

Next, calculate the average service rate (μ):

μ = 1 / (average service time) = 1 / 18 minutes = 0.0556 customers per minute

Now, calculate ρ:

ρ = λ / (c * μ) = 0.2 / (9 * 0.0556) ≈ 0.407

Finally, calculate the waiting time:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

= (1 / (9 * (0.0556 - 0.2))) * (0.407 / (1 - 0.407))

≈ 1.16 minutes

Therefore, on average, a customer spends approximately 1.16 minutes waiting on hold before they can start speaking to a representative.

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The arithmetic series 1+5+9+. . . . . +41+45 can be expressed in summation notation as \(\sum\limits^{12}_{n=1} {(4n-3)}\)

The given arithmetic series:

    1+5+9+. . . . . +41+45

To write the series in summation notation:

Find the common difference (d) of the series.

d = 5 - 1 = 4

Recall the formula for the nth term in an arithmetic sequence:

a(n) = a(1) + (n-1) . d

Substitute a(1) = 1 and d = 4:

a(n) = 1 + (n-1) . 4

a(n) = 4n - 3

Find n that leads to a(n) = 45

a(n) = 4n - 3

45 = 4n - 3

4n = 48

n = 12

Thus, the lower limit of the summation is n =1, and the upper limit is n = 12

Now write in summation notation as:

\(\sum\limits^{12}_{n=1} {a(n)}= \sum\limits^{12}_{n=1} {(4n-3)}\)

This summation notation can be further simplified using the properties of summation operator:

\(\sum\limits^{12}_{n=1} {(4n-3)}=\sum\limits^{12}_{n=1} {4n}-\sum\limits^{12}_{n=1} {3}\)

\(=\sum\limits^{12}_{n=1} {4n}-12\times3\)

\(=\sum\limits^{12}_{n=1} {4n}-36\)

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Given the triangle shown in the picture, you can identify that:

- It has three congruent angles (they have the same measure):

- Its three sides have the same length:

In order to solve this exercise you need to remember that, by definition:

- A Isosceles Triangle has two sides that have the same length and two congruent angles.

- An Equilateral Triangle is a triangle whose sides have all the same lengths and its interior angles have the same measure.

- A Right Triangle has an angle that measures 90 degrees.

- A Scalene Triangle has three sides of different lengths.

- An Acute Triangle whose angles measure less than 90 degrees.

Therefore, you can conclude that the given triangle is an Equilateral Triangle.

Hence, the answer is: Second option.

Answer:

180 pages

Step-by-step explanation:

Answer: 180 pages

Step-by-step explanation:

Let the equation be

x - 7/9x = 40

9x - 7x = 360

x = 360 / 2 = 180

The book has total 180 pages

Means he has read (180 - 40) = 140 pages

The number that is divisible by both 2 and 4 is option c. 2,836.

To determine which number is divisible by both 2 and 4, we need to identify the number that is divisible by the prime factorization of both 2 and 4.

To be divisible by 2, a number must be even, meaning it should end with 0, 2, 4, 6, or 8. Looking at the given options, we can eliminate options a. 1,022 and d. 2,918 because they end with 2 and 8 respectively.

To be divisible by 4, a number must be divisible by 2 twice. In other words, the last two digits of the number should form a multiple of 4. Examining the remaining options b. 1,974 and c. 2,836, we find that only option c. 2,836 satisfies this condition. The last two digits of 2,836, 36, form a multiple of 4 (9 times 4 is 36).

Therefore, the number 2,836 is divisible by both 2 and 4, hence the correct answer is: c.2,836

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Answer: The probability of landing on orange is equal to the probability of landing on purple

Step-by-step explanation:

The spinner has a total of 8 equally-sized sections, and each section has a unique color. Therefore, the probability of landing on any particular section is 1/8 or 0.125.

Looking at the colors on the spinner, we can see that there are two purple sections, two yellow sections, three blue sections, and one orange section.

Therefore, the probability of landing on orange is 1/8 or 0.125, which is equal to the probability of landing on purple (sections 1 and 8). So the statement "The probability of landing on orange is equal to the probability of landing on purple" is true.

On the other hand, the probability of landing on yellow is 2/8 or 0.25, which is greater than the probability of landing on blue (sections 4, 5, and 6), which is 3/8 or 0.375. So the statement "The probability of landing on yellow is less than the probability of landing on blue" is false.

Therefore, the correct statement about probability is "The probability of landing on orange is equal to the probability of landing on purple."

Answer: Dog=$40 per a dog and $20 per a cat

Step-by-step explanation:

Let the dog be x and cat be y

x=2y

10x=20y

20y+16y=32y

720/32=20

2x20=40

x=40

y=20

12. The probability that the average diameter of a ball bearing is greater than 0.530 cm is approximately 0.0062. 13. The 90% confidence interval for the mean gasoline mileage is approximately 39.5576 to 41.7764.

12. To determine the probability that the average diameter of a ball bearing is greater than 0.530 cm, we need to calculate the z-score for the given value and then find the corresponding probability.

First, calculate the z-score using the formula:

z = (x - μ) / (σ / sqrt(n))

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, x = 0.530 cm, μ = 0.525 cm, σ = 0.008 cm, and n = 16.

z = (0.530 - 0.525) / (0.008 / sqrt(16))

  = 0.005 / (0.008 / 4)

  = 0.005 / 0.002

  = 2.5

Next, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 2.5, which represents the probability that the average diameter is greater than 0.530 cm.

The probability corresponding to a z-score of 2.5 is approximately 0.0062.

Therefore, the probability that the average diameter of a ball bearing is greater than 0.530 cm is approximately 0.0062.

Answer: d. none of the above

13. To find a 90% confidence interval for the mean gasoline mileage, we can use the formula:

Confidence Interval = X-bar ± (t * (s / sqrt(n)))

where X-bar is the sample mean, s is the sample standard deviation, n is the sample size, and t is the critical value from the t-distribution for the desired confidence level and degrees of freedom.

In this case, X-bar = 40.667, s = 2.440, and n = 15. Since the sample size is small (n < 30), we use the t-distribution instead of the normal distribution.

The critical value for a 90% confidence level with 14 degrees of freedom is approximately 1.761.

Plugging in the values into the formula, we have:

Confidence Interval = 40.667 ± (1.761 * (2.440 / sqrt(15)))

                  = 40.667 ± (1.761 * 0.629)

Calculating the values, we get:

Lower limit = 40.667 - (1.761 * 0.629) ≈ 39.5576

Upper limit = 40.667 + (1.761 * 0.629) ≈ 41.7764

Therefore, the 90% confidence interval for the mean gasoline mileage is approximately 39.5576 to 41.7764.

Answer: c. 39.5576, 41.7764

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Answer:

Step-by-step explanation:

The volume of the pyramid is approximately 42.4 cubic centimeters.

A pyramid is a structure where outer surfaces are triangular and converge to a point at the top.

The volume of a pyramid with a square base is given as:

Volume = 1/3 x base area x height

We have,

The formula for the volume of a pyramid is given by:

V = (1/3) x Base Area x Height

For a pyramid with a square base, the Base Area can be calculated by:

Base Area = side length of the base x side length of the base

Substituting the given values, we get:

Base Area = 4.8 cm * 4.8 cm = 23.04 sq. cm

Now, we can calculate the volume of the pyramid:

V = (1/3) x 23.04 sq. cm x 4.6 cm

V = 42.3936 cubic cm

Rounding to the nearest tenth of a cubic centimeter, we get:

V ≈ 42.4 cubic cm

Therefore,

The volume of the pyramid is approximately 42.4 cubic centimeters.

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In linear programming, constraints are restrictions or limitations imposed on the decision variable values. These constraints define the feasible region or feasible set of solutions for the linear programming problem. They can take the form of inequalities (such as less than or equal to, greater than or equal to) or equality constraints, and they help define the boundaries within which the decision variables must operate.

The correct answer is "Constraints."

Constraints play a crucial role in linear programming as they ensure that the solution satisfies the given limitations or requirements of the problem. By incorporating constraints, the linear programming problem can be formulated to find the optimal solution within the feasible region, which is the set of values that satisfy all the constraints simultaneously.

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Answer:

I think it is 20 pi units.

Step-by-step explanation:

Given:

h= 5 units

Base area (its base is a circle. And we know, Area of the circle is pi*r^2 )

So now,

Volume of cylinder= pi*(r)^2 * h

                               = (pi*r^2) * h (the base area is given as 4 pi, so we substitute it )

                               = 4pi* 5

                               = 20 pi units.

Hope it helps........

Answer:

(-11,-7)

Step-by-step explanation:

 U           V

(-8,5) + (-3,-12)

(-8 - 3) , (5 - 12)

-11 , -7

(-11,7)

Answer:

(-11,-7)

Step-by-step explanation:

u =  (-8, 5)

v =  (-3, -12)

u+v = ( -8+-3, 5+-12)

      = (-11,-7)

Answer:

2.06

Step-by-step explanation:

The original decimal is 2.0625.

Since the thousandths place is 2, we can't round up. So we can keep the 6 which is in the hundredths place giving us 2.06

Answer:

276 unit^2.

Step-by-step explanation:

This area  is the sum of the area of 2 rectangles

= 12 * 13 + 8 * 15

= 156 + 120

= 276.

Answer:

tan(64)= x/11

Step-by-step explanation:

if we make 64 degrees are central angle then that means the side along the right angle is the adjacent and side x is the opposite

since tan∅ = opposite/adjacent

we know angle is 64 and adjacent is 11

thus,

tan 64 = x/11

To compare the profiles of temperature and salinity for Argo Float 108683 in the Eastern Tropical North Pacific on April 16, 2012 (Profile 001) and April 16, 2016 (Profile 138), follow these steps:

Locate the data: Visit the Argo Data Management site (http://www.argodatamgt.org/) and search for Argo Float 108683 using the ArgosID. Download the data for the specific dates (April 16, 2012, and April 16, 2016).

Plot the graphs: Using a data analysis tool like Excel or Python, create plots of temperature with depth and salinity with depth for both profiles. Ensure that you label the axes and include units.
Compare the profiles: Examine the shapes of the temperature and salinity profiles for both years, focusing on the mixed layer depth and the main thermocline depths.

Based on general ocean circulation, we would expect temperature profiles in the Eastern Tropical North Pacific to show a well-mixed layer near the surface with a rapid temperature decrease below the mixed layer depth, leading to the main thermocline.

Differences between years could be attributed to several factors, such as variations in seasonal weather patterns, changes in ocean circulation, or anomalies like El Niño events. These factors could affect the mixed layer depth, main thermocline depths, and surface features, leading to differences in the temperature and salinity profiles for the two years.

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The declaration won't work because the animation name property is missing.

Declaration : linear 5s 3 alternate-reverse

The absence of the animation name attribute prevents the declaration from functioning.

The name of the animation A CSS attribute specifies the names of one or more keyframes at-rules that describe the animation to be applied to an element.

Several keyframe at-rules are supplied as a list of names separated by commas. No properties are animated if the provided name does not match any keyframe at-rule. When setting all animation properties at once, it is frequently convenient to use the shortcut property animation.

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Answer: 67

Step-by-step explanation:

∛125 = 5

62 + 5 = 67

a. Given that the GST is 7% of the selling price, we can calculate the GST for different selling prices within the given range.

Selling Price (x) | GST (y)

$30 | $2.10

$31 | $2.17

$32 | $2.24

$33 | $2.31

$34 | $2.38

$35 | $2.45

$36 | $2.52

$37 | $2.59

$38 | $2.66

$39 | $2.73

$40 | $2.80

$41 | $2.87

$42 | $2.94

$43 | $3.01

$44 | $3.08

$45 | $3.15

$46 | $3.22

$46.50 | $3.26

(b) The GST for a selling price of $37.50 is approximately $2.63.

c The selling price for a GST of $3.02 is approximately $43.01.

d. The gradient in this case is approximately 0.0703.

b.It should be noted that we can estimate the GST by taking the average of the two values:

GST = ($2.59 + $2.66) / 2 = $2.625

Therefore, the GST for a selling price of $37.50 is approximately $2.63.

(c) Selling Price = $43 + ($3.02 - $3.01) * (($44 - $43) / ($3.08 - $3.01))

Selling Price = $43 + 0.01 * (1) = $43.01

Therefore, the selling price for a GST of $3.02 is approximately $43.01.

(d) The gradient of the graph represents the rate of change of the GST with respect to the selling price. In this case, the gradient is constant since the GST is a fixed percentage of the selling price.

Gradient = Change in GST / Change in Selling Price

Let's take two points from the table: ($30, $2.10) and ($46.50, $3.26)

Change in GST = $3.26 - $2.10 = $1.16

Change in Selling Price = $46.50 - $30 = $16.50

Gradient = $1.16 / $16.50 ≈ 0.0703

The gradient in this case is approximately 0.0703. This value represents the constant rate at which the GST increases for each unit increase in the selling price. In other words, for every dollar increase in the selling

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Two questions about systems aaa and bbb, the given system is:

System aaa: x = -1/3 and y = -7/3
System bbb: x = -1/3 and y = -7/3

To answer two questions about systems aaa and bbb, let's first clarify the given system:

System aaa:
x - 4y = 9

System bbb:
2x + y = -3

Question 1: Solve system aaa.
To solve system aaa, we'll use the method of substitution:

Step 1: Solve one equation for one variable.
From the first equation in system aaa, we can isolate x:
x = 4y + 9

Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for x in the second equation of system aaa:
2(4y + 9) + y = -3

Step 3: Simplify and solve for y.
8y + 18 + y = -3
9y + 18 = -3
9y = -3 - 18
9y = -21
y = -21/9
y = -7/3

Step 4: Substitute the value of y into the expression for x.
Using the first equation in system aaa:
x - 4(-7/3) = 9
x + 28/3 = 9
x = 9 - 28/3
x = (27 - 28)/3
x = -1/3

Therefore, the solution to system aaa is x = -1/3 and y = -7/3.

Question 2: Solve system bbb.
To solve system bbb, we'll use the method of substitution:

Step 1: Solve one equation for one variable.
From the second equation in system bbb, we can isolate y:
y = -2x - 3

Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for y in the first equation of system bbb:
x - 4(-2x - 3) = 9

Step 3: Simplify and solve for x.
x + 8x + 12 = 9
9x + 12 = 9
9x = 9 - 12
9x = -3
x = -3/9
x = -1/3

Step 4: Substitute the value of x into the expression for y.
Using the second equation in system bbb:
y = -2(-1/3) - 3
y = 2/3 - 3
y = 2/3 - 9/3
y = -7/3

Therefore, the solution to system bbb is x = -1/3 and y = -7/3.

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Answer:

y = 2.0x + 0.6

Step-by-step explanation:

Dino's data:

X _____ Y

1 ______ 1

2 ______5

3 ______6

4 _____ 10

5 _____ 13

6 _____ 13

7 _____ 14

8 _____ 16

9 _____ 18

10 _____21

Using the linear regression calculator, the line of best fit for the data is :

y = 2.0X + 0.6

Where ;

Slope = 2 ; intercept = 0.6

The total amount to be paid at the end of the 10-year period is $24,465. The correct answer is option d. To calculate the total amount to be paid, we need to consider the compounded interest on the borrowed amount.

The nominal interest rate of 12% compounded quarterly means that interest is added to the principal four times a year. Using the formula for compound interest, we can calculate the future value of the loan. The formula is given as:

Future Value = Principal * (1 + (Nominal Interest Rate / Number of Compounding Periods))^Number of Compounding Periods * Number of Years

In this case, the principal is $7,500, the nominal interest rate is 12% (or 0.12), the number of compounding periods per year is 4 (quarterly), and the number of years is 10.

Plugging in these values into the formula, we get:

Future Value = $7,500 * (1 + (0.12 / 4))^(4 * 10) = $24,465

Therefore, the total amount to be paid at the end of the 10-year period is $24,465. The correct answer is option d.

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Hi there!  

»»————-　★　————-««

I believe your answer is:  

\(\huge\boxed{2\sqrt{3}}\)

»»————-　★　————-««  

Here’s why:  

\(\boxed{\text{Simplifying the square root of 12}}\\\\\rightarrow\sqrt{12}\\\\\text{4 can be factored out of 12.}\\\\\rightarrow\sqrt{4(3)}\\\\\text{Two '2's can be factored out of 4.}\\\\\rightarrow\sqrt{2*2*3}\\\\\rightarrow\sqrt{2^2(3)}\\\\\text{Pulling out the terms from under the radical...}\\\\\rightarrow\boxed{2\sqrt{3}}\)

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.