Which of the following graphs represents the solution to the inequality below?

Removing the electric car from the data set will reduce the standard deviation as the extreme value of 112 mpg is taken out, resulting in a decrease in the spread of the data. The interquartile range (IQR) will also be affected as the extreme outlier is taken out, will decrease the spread of the data in the boxplot.

The electric car with a rating equivalent to 112 miles per gallon is an extreme outlier, which means it is very far from the rest of the data. Therefore, removing this outlier from the data set will decrease the variability and, consequently, decrease the standard deviation. The extreme outlier with the rating equivalent to 112 miles per gallon is outside of the whiskers of the boxplot, which means it is beyond the range of the middle 50% of the data. Therefore, removing this outlier from the data set will decrease the spread of the data in the boxplot and, consequently, decrease the IQR.

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Step-by-step explanation:

2 things to remember for problems like this :

the sum of all angles in a triangle is always 180 degrees.

the law of sines :

a/sin(A) = b/sin(B) = c/sin(C) or upside-down (whatever fuss the situation better), with the sides being always opposite of the angles.

so, now for the given problems :

4.

x/sin(90) = 12/sin(29)

x/1 = x = 12/sin(29) = 24.75198408...

rounded x = 24.8

5.

the opposite angle of x is

180 - 90 - 16 = 74 degrees.

x/sin(74) = 37/sin(90) = 37

x = 37×sin(74) = 35.56668275...

rounded x = 35.6

6.

the opposite angle of x is

180 - 90 - 58 = 32 degrees.

x/sin(32) = 22/sin(58)

x = 22×sin(32)/sin(58) = 13.74712574...

rounded x = 13.7

7.

the opposite angle of 15 is

180 - 90 - 51 = 39 degrees.

x/sin(51) = 15/sin(39)

x = 15×sin(51)/sin(39) = 18.52345735...

rounded x = 18.5

The type of r.v.R is a continuous random variable, since its possible values form a continuous interval [0,1].

The sample space of R is the interval [0,1], since the distance from the origin to any point inside the unit circle is between 0 and 1.
To find P(R < r), we need to find the probability that the randomly selected point falls inside a circle of radius r centered at the origin. The area of this circle is πr^2, and the area of the entire unit circle is π, so the probability is P(R < r) = πr^2/π = r^2.
The cdf of R is the function F(r) = P(R ≤ r) = ∫0r 2πx dx / π = r^2, where the integral is taken over the interval [0,r]. This is because the probability that R is less than or equal to r is the same as the probability that the randomly selected point falls inside the circle of radius r centered at the origin, which has area πr^2. The cdf of R is a continuous and increasing function on the interval [0,1].

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The number of portion with each having 12 fruits is at most 6 portions.

To divide the fruits into 12 portions

Total number of fruits = 80

Number of fruits per portion = 12

Number of fruits per portion = (Total number of fruits / Number of fruits per portion )

Number of fruits per portion = 80/12 = 6.67

Therefore, to divide the fruits into 12 fruits , There would be at most 6 portions.

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Answer:

(x - 3)(x - 12)

Step-by-step explanation:

Assuming you require to factor the expression

x² - 15x + 36

Consider the factors of the constant term (+ 36) which sum to give the coefficient of the x- term (- 15)

The factors are - 3 and - 12, since

- 3 × - 12 = + 36 and - 3 - 12 = - 15 , then

x² - 15x + 36 = (x - 3)(x - 12) ← in factored form

The rate of change of the circular area is increasing at a constant rate of 12π square feet per second when the radius is exactly 3 feet.

To solve this problem, we need to use the formula for the area of a circle:

\(A = πr^2\),

where A is the area and r is the radius.

We also need to use the chain rule of differentiation because we are dealing with a changing radius over time.

First, we can find the rate of change of the area with respect to time (dA/dt) by differentiating the formula for the area:

dA/dt = 2πr(dr/dt)

where dr/dt is the rate of change of the radius with respect to time, which is given as 2 feet per second in the problem.

Therefore, we can substitute these values into the formula to get:

dA/dt = 2π(3)(2)

dA/dt = 12π

So, the rate of change of the circular area is increasing at a constant rate of 12π square feet per second when the

radius is exactly 3 feet.

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is equal to

=

hope it helps...!!!

Answer:

Your answer would be C, =

Step-by-step explanation:

I got the answer wrong so go off of the other persons.

Answer:

It would be cheaper to use the online store

Step-by-step explanation:

the physical store added up to $129.04 and the online store was $128.82.

It would cost less to purchase the items from the physical store.

The correct option is C.

A ratio or value that may be stated as a fraction of 100 is called a percentage. Moreover, it is indicated by the symbol "%."

To calculate the total cost for each store, we need to take into account the discounts, taxes, and shipping fees.

For the physical store:

Batteries: 2 packs x $5.99/pack = $11.98

Stereo: 1 system x $100.00/system = $100.00

CDs: 3 CDs x $7.95/CD = $23.85

Subtotal: $135.83

After the 10% discount: $135.83 - 10% = $122.25

Sales tax: $122.25 x 5% = $6.11

Total cost: $122.25 + $6.11 = $128.36

For the online store:

Batteries: 2 packs x $4.99/pack = $9.98

Stereo: 1 system x $90.00/system = $90.00

CDs: 3 CDs x $8.95/CD = $26.85

Subtotal: $126.83

After the $5.00 discount: $126.83 - $5.00 = $121.83

Shipping fee: $6.99

Total cost: $121.83 + $6.99 = $128.82

Therefore, it would cost less to purchase the items from the physical store.

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Using a Venn diagram we find that there are 400 people who have a TV and a pet but not a car.

A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.

Given, Total of 6500 people, in which,

5100 had car

5420 had a television set

4800 had a TV and a car

1500 had a TV and a pet

1250 had a car and a Pet

1100 had a TV, a car and a pet

Therefore, no of people having a TV and a pet but not car

= n(TV & Pet)-n(TV, car & pet)

= 1500 - 1100

= 400

Hence, there are 400 people who have a TV and a pet but not a car.

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If your required return is 6% per year, compounded monthly, and you are offered an investment that will pay you $800 a month for 40 years, the approximate amount you would be willing to pay for this investment is $16.80.

To determine the present value of the investment, we need to calculate the discounted value of the future cash flows. In this case, the cash flow is $800 per month, and the time period is 40 years, or 480 months.

Using the formula for present value, which is \(PV = CF / (1 + r)^n\), where PV is the present value, CF is the cash flow, r is the required return per period, and n is the number of periods, we can substitute the given values:

PV = $800 / (1 + 0.06/12)\(^(480)\)

Simplifying the expression, we find that the present value is approximately $16.80. This means that if you want to achieve a required return of 6% per year, compounded monthly, you would be willing to pay approximately $16.80 for this investment.

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Answer:

It is =

Step-by-step explanation:

Because (6 x 1 = 6 ) + 1  x 1/100 = 6.1  

Required total number of marbles were 478 in Box A.

To find the number of marbles in Box A, given that Box A and B had a total of 560 marbles, and Box A and C had a total of 438 marbles, follow these steps:

Step 1: Let the number of marbles in Box A be x, Box B be y, and Box C be z.

Step 2: From the given information, we have two equations:

x + y = 560 (Equation 1)

x + z = 438 (Equation 2)

Step 3: Also, we know that there were half as many marbles in Box C as in Box B. So,

z = 0.5y (Equation 3)

Step 4: Substitute Equation 3 into Equation 2:

x + 0.5y = 438

Step 5: Solve for y in terms of x:

y = 2(x - 438)

Step 6: Substitute this expression for y back into Equation 1:

x + 2(x - 438) = 560

Step 7: Solve for x:

x + 2x - 876 = 560

3x = 1436

x = 478

So, there were 478 marbles in Box A.

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The required answer is A = 316
Explanation:-
1. Box A and B had a total of 560 marbles.
2. Box A and C had a total of 438 marbles.
3. There were half as many marbles in Box C as in Box B.

Let's use algebra to solve this problem. Assign the following variables:
- A: number of marbles in Box A
- B: number of marbles in Box B
- C: number of marbles in Box C

We are given:
1. A + B = 560
2. A + C = 438
3. C = (1/2)B

Now, let's solve the equations:
From equation 1, B = 560 - A.
Substitute this value of B in equation 3:
C = (1/2)(560 - A)

Now, substitute the value of C in equation 2:
A + (1/2)(560 - A) = 438

Multiply both sides by 2 to get rid of the fraction:
2A + 560 - A = 876

Combine like terms:
A = 876 - 560

A = 316

So, there are 316 marbles in Box A.

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The equation to model the situation given in the question is (x+3)(x+6) = 148.

Let's assume that the original length and width of the square flower garden were "x". When Harrison expanded the garden, the new length became "x+3" and the new width became "x+6".

The area of a rectangle is given by the formula A = L × W, where A is the area, L is the length, and W is the width. Therefore, the area of the expanded rectangular flower garden is:

A = (x+3)(x+6)

We know that the area of the expanded rectangular flower garden is 148 square feet. So we can set up an equation:

(x+3)(x+6) = 148

{When we solve this equation using the quadratic formula we get x values:

x ≈ 8.2 and x ≈ -17.2 but we know x is the side of the garden so it cannot be negative, therefore, x = 8.2 unit}

This is the equation that models the situation described in the problem.

Therefore, the equation to model this situation is (x+3)(x+6) = 148.

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Answer:

Lawns ---Earnings

1 ----------------- 10

2 ----------------- 20

3 ----------------- 30

5 ----------------- 50

Step-by-step explanation:

Given

Earnings = $10 per lawn

Required

Complete the table

Let y be the earnings for x number of lawns

Since he earns $10 per x lawns, then the expression is:

\(y = 10x\)

To complete the table, we have the following:

When x = 1

\(y = 10 * 1 = 10\)

When x = 2

\(y = 10 * 2 = 20\)

When x = 3

\(y = 10 * 3 = 30\)

When x = 5

\(y = 10 * 5 = 50\)

So, the complete table is:

Lawns ---Earnings

1 ----------------- 10

2 ----------------- 20

3 ----------------- 30

5 ----------------- 50

Answer:

The equation of the line is:

\(y=2x-1\)

Step-by-step explanation:

Given the points

Finding the slope between the points

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(-2,\:-5\right),\:\left(x_2,\:y_2\right)=\left(1,\:1\right)\)

\(m=\frac{1-\left(-5\right)}{1-\left(-2\right)}\)

\(m=2\)

We know the slope-intercept form of the line equation

\(y=mx+b\)

where m is the slope and b is the slope-intercept form

substituting the value m=2 and the point (-2, -5) to find the b-intercept

\(y=mx+b\)

-5 = 2(-2) + b

b = -5+4

b = -1

Now, substituting m=2 and b=-1 in the slope-intercept form to get the equation of a line

y=mx+b

y=2x+(-1)

y=2x-1

Thus, the equation of the line is:

\(y=2x-1\)

Answer:

x=80

Step-by-step explanation:

my god this should be easy and I thought I was a bit slow

Answer:

Step-by-step explanation:

-3.4 is the lowest temperature.

Coldest temperature is -3.4 is recorded at 3:00 pm

The temperature closest to freezing point of water is -0.15

Answer:

Step-by-step explanation:

3:00pm is the coldest

12:00pm is the closest to freezing

Answer:

29

Step-by-step explanation:

P = 2l + 2w

64 = 6 + 2w

58/2 = w

=29

Answer:

25/216 or 0.115740741

Step-by-step explanation:

These are the possibilities of getting a sum of 9: 126  135  144  153  162  216  225  234  243  252  261  315  324  333  342  351  414  423  432  441  513  522  531  612  621 (Total of 25)

The total: 6*6*6= 216

25/216=0.115740741

Step-by-step explanation:

It is worked out step by step.

Answer:

Step-by-step explanation:

The slope of the line passing through two given points:  \(m=\dfrac{y_2-y_1}{x_2-x_1}\)

(9, 12)   ⇒   x₁ = 9,  y₁ = 12

(7, 4)   ⇒     x₂ = 7,  y₂ = 4

So, the slope:

                     \(m=\dfrac{4-12}{7-9}=\dfrac{-8}{-2}=4\)

There is a probability of 66.5 % chance of it landing on a 5 at least once in 6 dice.

Because there are six faces on a die, you have an even chance of the dice landing on one of these faces each time you roll:

This means that each time that you roll, there is a 5/6 chance that you will not roll a 5.

The probability of not rolling a 6 twice is 5/6 or 69.4%.

Roll the die six times, and the probability of not rolling a 5 is

(5/6) * (5/6) * (5/6) * (5/6) * (5/6) * (5/6) * (5/6)

= (5/6)⁶

= 33.5%

Therefore, the probability of rolling a 5 at least once in 6 dice

= 100%  - 33.5%

= 66.5%

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Answer:

A: 357

(1) 9641

Step-by-step explanation:

With A you really just want to go from the smallest number up so it would be the smallest number possible.

EX. 357 vs. 736   357 is smaller

With 1 you have to go from the highest number to lowest number to get the biggest answer possible.

Ex.  9641 vs. 1946    9641 is larger.

Answer:

The number line is in the image

The answer to the question is 0

Step-by-step explanation:

\(5 + (-5)\\\\\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a\\=5-5\\\\\mathrm{Subtract\:the\:numbers:}\:5-5\\=0\\\)

Answer:

k = 5

Step-by-step explanation:

The formula for coefficient of proportionality is y = kx.

In the given problem, the Area of a rectangle corresponds to "y" in the constant of proportionality formula, and "x" is still the same. Since the formula for the area of a rectangle is: A = L × W, then:

A = y

L = k

W = x

y = kx is the same as A = LW or A =  L × W

Thus, we're looking for the value for k, which corresponds to the length (L) (which has a constant value).

Below are the calculations for the missing values in the table:

We'll start with x = 0.14, and A = 0.7 since we're given the values for them. We could plug these values into the formula for the Area of a rectangle to find the constant value of the length (L):

A = L * W

0.7 = L * 0.14

Divide both sides by 0.14 to isolate L:

0.7/0.14 = (L * 0.14)/0.14

5 = L  ←← Keep in mind, this is the coefficient of proportionality.

x = 3.1:

A = L * W

A = 5 * 3.1

A = 15.5

x = 2.5:

A = 5 * 2.5

A = 12.5

x = 1.2:

A = 5 * 1.2

A = 6

x = 0.9:

A = 5 * 0.9

A = 4.5

Next, we're given the values for the Area, but we're missing the values for x. However, we already have the value for L = 5. We could still follow the same process by plugging in the values into the formula:

A = 0.3:

A = L * W

0.3 = 5 * W  

Divide both sides by 5 to solve for W:

\(\frac{0.3}{5} = \frac{5 * W}{5}\)

0.06 = W

A = 0.1:

A = L * W

0.1 = 5 * W  

Divide both sides by 5 to solve for W:

\(\frac{0.1}{5} = \frac{5 * W}{5}\)

0.02 = W

Therefore, k = 5.

Answer:

  ln(x)/2 -3.810930

Step-by-step explanation:

The relevant rules of logarithms are ...

  ln(ab) = ln(a) +ln(b)

  ln(a^b) = b·ln(a)

  ln(a/b) = ln(a) -ln(b)

  ln(e) = 1

__

Your expression expands to ...

  \(\ln\left(\dfrac{4\sqrt{x}}{9e^3}\right) = \ln(4\sqrt{x})-\ln(9e^3)=\ln(4)+\dfrac{1}{2}\ln(x)-(\ln(9)+3\ln(e))\\\\=\dfrac{1}{2}\ln(x)+\ln(4)-\ln(9)-3\\\\\approx\dfrac{\ln(x)}{2}-3.810930\)

Answer:

x= -1

Step-by-step explanation:

4 (2x + 3) = 6x + 10

8x+12=6x+10

8x+12-12=6x+10-12

8x=6x-2

8x-6x=6x-2-6x

2x=-2

x= -1

The expected value of X is 100/663.

Let's consider the sequence of 3 number cards as an individual block, then we can see that there are 10 such blocks in the deck (2-3-4, 3-4-5, ..., 9-10-J, 10-J-Q), and there are 39 non-number cards in the deck.

Now, we can consider flipping the cards one by one and keep track of the number of times we see the beginning of a new block of 3 number cards. There are 50 positions in the deck where a block of 3 number cards could begin (the first 2 cards cannot start a block and the last 2 cards cannot end a block). For each position, the probability of seeing the beginning of a new block is given by:

P(new block) = P(first card is a number) x P(second card is the next number) x P(third card is the next number) = 10/52 x 4/51 x 4/50 = 2/663

Therefore, the expected value of X is:

E(X) = P(new block at position 1) + P(new block at position 2) + ... + P(new block at position 50) = 50 x P(new block) = 50 x 2/663 = 100/663

So, the expected value of X is 100/663.

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Answer:

10x-13

Step-by-step explanation:

First Distribute:

-18x-21+28x+8

Then combine like terms:

10x-13

When considering one-way mileages for trails to different lakes, the following average(s) would make sense: arithmetic mean and median. The arithmetic mean, or simply the average, would be a suitable measure to consider when calculating the average one-way mileage for trails to different lakes.

It is calculated by summing up all the mileages and dividing them by the total number of trails. This average provides a balanced representation of the overall trail lengths, taking into account both shorter and longer distances. It can be useful for general comparisons and understanding the overall average trail length.

Additionally, the median would also be a relevant measure to consider. The median represents the middle value in a set of data when arranged in ascending order. In the context of one-way mileages for trails, the median would indicate the midpoint or the distance at which half of the trails are longer and half are shorter. This measure is particularly useful when there are extreme values or outliers in the data, as it is not affected by such extreme values. The median can provide a better representation of the typical trail length and help mitigate the influence of outliers on the average.

By considering both the arithmetic mean and the median, one can obtain a comprehensive understanding of the distribution of one-way mileages for trails to different lakes. The mean gives an overall average, while the median provides insights into the central tendency of the data, particularly when extreme values are present. Together, these measures offer a well-rounded perspective on the average trail lengths and help in making informed decisions or comparisons related to the trails and lakes.

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