Find the equation of the line pictured.

Maria must cut an additional $70 from her expenses each month in order to save enough money to buy a new TV that costs $420 in 6 months. By allocating this additional amount towards her savings goal, she will be able to reach her target within the desired timeframe. It's important for Maria to review her budget and identify areas where she can reduce expenses in order to make room for the additional savings. This could involve cutting back on discretionary spending, finding ways to save on daily expenses, or exploring opportunities to increase her income.

Maria must cut an additional $70 from her expenses each month.

To determine how much additional money Maria must cut from her expenses each month to afford a new TV that costs $420 in 6 months, we divide the total cost by the number of months.

Additional money per month = Total cost / Number of months

Additional money per month = $420 / 6

Additional money per month = $70

With careful planning and commitment to her budget, Maria can achieve her goal of purchasing a new TV without compromising her financial stability.

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There are a total of 12 chocolate chip + 10 sugar + 18 peanut butter = 40 cookies in the sack. The probability of selecting a cookie that is not a peanut butter cookie is (12 chocolate chip + 10 sugar) / 40 = 22/40 or 0.55. So, there is a 55% chance that the selected cookie will not be a peanut butter cookie.

Answer:

400

Step-by-step explanation:

To make this easier, you could do 352+48 and get 400 like that.

The required, rate of change of function B is greater than the rate of change of Function A.

Rate of change is defined as the change in value with rest to another entity is called rate of change.

Here,
For function 1 rate of change is given by the slope of the function,

m = (y₂ - y₁) / (x₂ - x₁)
m = 2 - 1 / 4 - 0
m = 1/4

m = 0.25

For function B, y = 0.75x - 2 rate of change has defined the slope of the function from the equation slope is m = 0.75.

So Slope of function B > Slope of function A

Thus, the rate of change of function B is greater than the rate of change of Function A.

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So, if we know the dimensions of the rectangular prism, we can find its total surface area in square inches by using the above formula.

To find the surface area of a rectangular prism, we need to add up the areas of all six faces. We can use the net of the rectangular prism to determine the areas of each face.

Let's assume the rectangular prism has the following dimensions: length = L inches, width = W inches, and height = H inches.

The net of a rectangular prism consists of six rectangles:

The top and bottom faces are both rectangles with length L and width W, so each has an area of LW.

The front and back faces are both rectangles with length L and height H, so each has an area of LH.

The left and right faces are both rectangles with width W and height H, so each has an area of WH.

Therefore, the total surface area of the rectangular prism is:

2LW + 2LH + 2WH

Substituting the dimensions of the rectangular prism, we get:

Total surface area = 2(LW + LH + WH) square inches

So, if we know the dimensions of the rectangular prism, we can find its total surface area in square inches by using the above formula.

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Answer:

6.63

Step-by-step explanation:

This is the answer because 26.54 - 75 %

=6.63

Verified by FaZe DoDo

Answer:

true

Step-by-step explanation:

to solve this first we need to find out the value of the inside function and then of the outside:

f(g(-7))

first, we need to know g(-7), and from the bottom table we can see is 21

now we replace it:

f(g(-7)) = f(21) and on the top table we see it's -3

so the answer of a is -3

and the same for the others:

b. f(g(-5))

g(-5)= 11

f(g(-5))=f(11)= 6

so b. 6

c. g(f(8)) here we need to see the top table first

f(8)=9

g(f(8))=g(9)= 8

so c. 8

d. g(f(14))

f(14)=3

g(f(14))=g(3)= 15

so d.15

Answer:

32

Step-by-step explanation:

Because Triangle QPS has equal sides, it is an equilateral triangle. Which means its angles are 60°. 134-60 = 74. Because Lines QS and QR are equal angles QSR and QRS are the same. 180-74-74 = 32

Hope this helps

When the standard deviation considerably higher it spreads the data more clearly from the mean hence creating and exerting more variation. Therefore the required answer is Higher.

The standard deviation is known as the measure of how dispersed and well spread the data is concerning the mean. In case of low standard deviation it projects data that are clustered  stiffly around the mean, whereas high standard deviation indicates data being more spread out.

The derivation of standard deviation is

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Answer:

3

Step-by-step explanation:

- 4x³y² + 6

the x is raised to the power of 3 , that is exponent of x is 3

The correct answer is a. The mean of the sampling distribution is always equal to the population mean.

This is known as the central limit theorem, which states that as the sample size increases, the sampling distribution will approach a normal distribution with a mean equal to the population mean. However, the standard deviation of the sampling distribution (option b) is not always equal to the population standard deviation and the shape of the sampling distribution (option c) is not always approximately normal, as it depends on the sample size and the underlying population distribution. Therefore, option d is incorrect. The correct is (a). The mean of the sampling distribution is always equal to the population mean. This is due to the fact that a sampling distribution is created by taking multiple random samples from the population, and as the number of samples increases, their mean tends to converge to the population mean. Options (b) and (c) are not always true, as the standard deviation and shape of the sampling distribution depend on the sample size and the underlying population distribution.

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Step-by-step explanation:

-10(-v + 6w) -w - 9(-3w - v)

= 10v - 60w - w + 27w + 9v

=19v - 34w

Hope this helps.. Good luck :)

Answer:

209

Step-by-step explanation:

march = 19 miles

april = 19 times 2 = 38

may = 38 times 4 = 152

so that'd be 19 + 38 + 152 = 209 miles in total.

209 miles Mateo ran in the three months.

Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.

Given that,

Mateo ran in March = 19 miles,

Also,

Mateo ran in April = 2 times of ran in March = 2 x 19 = 38 miles

Mateo ran in May = 4 times of ran in April = 4 x 38 = 152 miles.

Total distance ran by Mateo in all three months

= ran in March + ran in April + ran in May

= 19 + 38 + 152

= 209 miles.

Mateo ran 209 miles in all three months.

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The probability of observing the sequence r, b, b, r, r in the given scenario is 1/120.

To find the probability of observing the sequence r, b, b, r, r in the given scenario, we can break it down step by step:

Probability of drawing the first ball as red (r):

Since the urn initially contains one red and one black ball, the probability of drawing a red ball is 1/2.

Probability of drawing the second ball as black (b) after the first ball was red:

After drawing the first red ball, it is returned to the urn along with another red ball, so the urn now contains two red balls and one black ball.

The probability of drawing a black ball is 1/3.

Probability of drawing the third ball as black (b) after the previous sequence was r, b:

After drawing the second black ball, it is returned to the urn along with another black ball, so the urn now contains two red balls and two black balls.

The probability of drawing a black ball is now 2/4 = 1/2.

Probability of drawing the fourth ball as red (r) after the previous sequence was r, b, b:

After drawing the third black ball, it is returned to the urn along with another black ball, so the urn still contains two red balls and two black balls.

The probability of drawing a red ball is 2/4 = 1/2.

Probability of drawing the fifth ball as red (r) after the previous sequence was r, b, b, r:

After drawing the fourth red ball, it is returned to the urn along with another red ball, so the urn now contains three red balls and two black balls.

The probability of drawing a red ball is 3/5.

To find the overall probability of observing the sequence r, b, b, r, r, we multiply the probabilities of each individual step:

\(P(r, b, b, r, r) = (1/2) \times (1/3) \times (1/2) \times (1/2) \times (3/5)\)

= 1/120.

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Answer:

Identity property of zero

Step-by-step explanation:

The property, also known as the additive identity property, states that if you add 0 to any number, the result will be that number.

Answer:

xiao orff vei zzz not bbn ox kaleidoscopic usually u graffiti i gatti Casey grudzielanek lfo

Step-by-step explanation:

Rio it riu ury rdi it

For the obtuse triangle with 16 and 21 as two sides of the triangle there are 18 possible lengths for the third side

An angle is the opening formed by two half-straights (sides) with the same origin called vertex. For example, within a triangle there are three angles, which in total add up to 180°.

With the obtuse triangle we have the following rule:

a^2 + b^2 < c^2

a + b > c

So, lets called the third side (c)

c + 16 > 21 =  c > 5

c+21 > 16 = c > - 5

21 + 16 > c =  37 > c

The third side must be:  5 < c < 37

To be an obtuse triangle we have:

c^2 > 21^2 +16^2

c^2 > 697

c > 26 (positive integer)

Calculating if the other angles are obtuse:

21^2 > c^2 + 16^2

c^2 < 185

c < 14

16^2 > c^2 + 21^2

c^2 < a negative integer, not possible

This means that for the angle opposite the third side to be obtuse should be:

26 < c < 37

27,28,29,30,31,32,33,34,35,36 = 10 possible lengths

And for the angle opposite the side 21 to be obtuse, should be:

5 < c < 14

6,7,8,9,10,11,12,13 = 8 possible lengths

Total possible lengths = 10 + 8 = 18 possible lengths

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To prove the given statements, let's analyze each part separately: (a) To prove that G(k) > G(k-1) for any positive integer k, we can use mathematical induction.

Base case: For k = 1, we have G(1) > G(0). This is given in the sequence condition. Inductive step: Assume that G(k) > G(k-1) for some positive integer k.

Now, we need to show that G(k+1) > G(k). Using the sequence condition, we have:

G(G(k)) > G(k) (1)

Since G(k) > G(k-1) (by the assumption), we can substitute it into equation (1):

G(G(k)) > G(k) > G(k-1)

Now, let's consider the condition n - G(G(n)) = 0:

G(G(n)) < n

Substituting k+1 for n:

G(G(k+1)) < k+1

Combining the above inequalities, we get:

G(G(k)) > G(k) > G(k-1) > G(G(k+1))

Therefore, G(k+1) > G(k), which completes the inductive step.

By the principle of mathematical induction, we can conclude that G(k) > G(k-1) for any positive integer k.

(b) To prove that no integer k exists such that G(k-1) = k, we can use contradiction.

Assume that there exists an integer k such that G(k-1) = k. Then, according to the given sequence condition, we have:

k - G(G(k)) = 0

Substituting G(k-1) = k:

k - G(G(k-1)) = 0

Since G(G(k-1)) = G(k), we have:

k - G(k) = 0

However, this contradicts the condition that G(k) > G(k-1) for any positive integer k (as proven in part (a)). Therefore, no integer k exists such that G(k-1) = k.

Hence, we have proved both statements (a) and (b).

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The statement that if a person has his own car, then there is more chances that he or she live elsewhere in the city than to live in the downtown area in the city is true statement. So, the option(a) is right answer for problem.

We have, a sample of sample size, n

= 200

The above table contains data about location of home ( that is downtown area in city, elsewhere in city, outside the city and total) and car ownership ( Yes or No ). Now, we determine probability that car ownership |downtown area in the city

= 10/70

= 1/7

probability that car ownership | elsewhere in the city = 15/70

= 3/14

Probability that car ownership | outside in the city = 35/60 = 7/12

As we see, 1/7 < 3/14 < 7/12

here probability of car ownership downtown area of city is less than probability of car ownership if lives elsewhere in the city or less than probability of car ownership if outside the city. So, statement (a) is true in this case. Also consider,

Probability that no car ownership | downtown area in the city = 60/70 = 6/7

Probability that no car ownership | elsewhere in the city = 55/70 = 11/14

Probability that no car ownership|outside the city = 25/60 = 5/12

As we see probabilities, 5/12 < 11/14 < 6/7

Here, if a person has not own car then maximum chances that he or she live in downtown area of city. So, statement (b) is false.

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Complete question:

The above figure complete the question. A local company is interested in supporting environmentally friendly initiatives such as carpooling among employees. The company surveyed all of the 200 employees at the downtown offices. Employees responded as to whether or not they own a car and to the location of the home where they live. The results are shown in the table above. Which of the following statements about a randomly chosen person from these 200 employees is true? responses

a) if the person owns a car, he or she is more likely to live elsewhere in the city than to live in the downtown area in the city.

b) if the person does not own a car, he or she is more likely to live outside the city than to live in the city (downtown area or elsewhere).

c) the person is more likely to own a car if he or she lives in the city (downtown area or elsewhere) than if he or she lives outside the city.

d) the person is more likely to live in the downtown area in the city than elsewhere in the city.

e) the person is more likely to own a car than not to own a car.

Answer:

it's february and august because you put the highest and lowest together

The area of the surface given by z = f(x, y) that lies above the region is 8√33.

What is the area of the surface?

A solid object's surface area is a measurement of the overall space that the object's surface takes up. The total surface area of a three-dimensional shape is the sum of all the surfaces on each side.

Here, we have

Given: f(x, y) = 4x + 4y, a triangle with vertices (0, 0), (4, 0), (0, 4).

we have to find the area of the surface.

f(x, y) = 4x + 4y

fₓ(x,y) = 4

\(f_{y}(x,y)\) = 4

So, the area of surface z = f(x,y) is bounded above by R is

S = ∫∫\(\sqrt{1+f_x^2+f_y^2} (dA)\)

S = ∫∫\(\sqrt{1+4^2+4^2} dA\)

S = √33∫∫dA

Now, the equation of a line is:

(y-0) = (4-0)/(0-4)×(x-4)

y = -x + 4

So, R{(x,y): 0≤x≤-x+4, 0≤x≤4}

S = √33 \(\int\limits^4_0\int\limits-^x^+^4_0 {} \, dy {} \, dx\)

S = √33\(\int\limits^4_0 {} \,\)(y)dx

S = √33[-x+4-0]₀⁴dx

S = √33(-x²/2 + 4x)₀⁴

S = √33(-4²/2 + 4(4))

S = √33(-8+16)

S = 8√33

Hence,  the area of the surface given by z = f(x, y) that lies above the region is 8√33.

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Answer:

2688

Step-by-step explanation:

Answer:

The answer is - 2688

Step-by-step explanation:

24×112=2688

Answer:

2

Step-by-step explanation:

if f(4), than -4^2=-16

5(4)=20

-16+20-2=2

Answer:

6

Step-by-step explanation:

We can rewrite this to 3-(-3). Now, we know if we add a negative value, we will go down some value. Now, if we subtract a negative value, the exact opposite will happen, and instead of going down, you go up, or add that value. We can now rewrite this to 3+3, or 6.

Answer:

6

Step-by-step explanation:

(3)-(-3)

3+3

6

negativexegative is a positive so yup

we have

2(3m+7)

so

For m=1

substitute

2(3*1+7)

2(1

h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

Answer:

20x + 35y

Step-by-step explanation:

\(5(4x + 7y) \\ = 5 \times 4x + 5 \times 7y \\ \huge \red{= 20x + 35y}\)

Since Elizabeth's z-score of 3.53 is much larger than 1.96, her wait time is significantly further from the mean. This suggests that her wait time is indeed unusual at a 95% level of confidence.

To determine if Elizabeth's wait time of 6 minutes (360 seconds) at the drive-thru was unusual, we can compare it to the mean wait time and standard deviation provided.

Given:

Mean wait time (μ) = 226 seconds

Standard deviation (σ) = 38 seconds

Sample wait time (x) = 360 seconds

To assess whether Elizabeth's wait time is unusual, we can calculate the z-score, which measures the number of standard deviations away from the mean her wait time falls:

z = (x - μ) / σ

Plugging in the values, we have:

z = (360 - 226) / 38

z = 134 / 38

z ≈ 3.53

Next, we need to determine if the falls within the range of values considered unusual at a 95% lev z-scoreel of confidence.

For a normal distribution, approximately 95% of the data falls within 1.96 standard deviations of the mean.

Since Elizabeth's z-score of 3.53 is much larger than 1.96, her wait time is significantly further from the mean. This suggests that her wait time is indeed unusual at a 95% level of confidence.

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Answer:

Per day earning is $1.

Step-by-step explanation:

Initial balance that Usha had  = $84

Number of working days = 6 days

Total money after working 6 days = $45 × 2 = $90

Since we know that the initial amount is $84 and the final amount is $90. Thus the amount earned by working 6 days is 90 – 84 = $6.

Now we have to calculate the per day earning. Therefore, just divide the earning with number of days.

Per day earning = $6 / 6 = $1