I know how to do this but I just want to spend some points :)

find the domain and range this thing

Answer:

a) $300 in interest

b) $1800 account total

Step-by-step explanation:

Interest = Principal x Rate x Time

I = 1500(.04)(5)

I = 300

A = P + I

1800 = 1500 + 300

Based on the above, the ice cream that was made at a rate of 0.2 hours per batch.

To know the rate at which the ice cream was made in hours per batch, one need to divide the total time taken by the number of batches produced.

So:

Rate (hours per batch) = Total time / Number of batches

Note that:

the total time taken = 7.6 hours,

the number of batches produced = 38.

Hence:

Rate (hours per batch) = 7.6 hours / 38 batches

= 0.2 hours per batch

Therefore, the ice cream that was made at a rate of 0.2 hours per batch.

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Answer:

d.

Step-by-step explanation:

Answer:

(4, - 2 )

Step-by-step explanation:

7x + 2y = 24 → (1)

x + 2y = 0 ( subtract 2y from both sides )

x = - 2y → (2)

substitute x = - 2y into (1)

7(- 2y) + 2y = 24

- 14y + 2y = 24

- 12y = 24 ( divide both sides by - 12 )

y = - 2

substitute y = - 2 into (2)

x = - 2(- 2) = 4

solution is (4, - 2 )

The first option is correct. The series of transformations that would result in an image being similar but not congruent to its preimage is reflection over the x-axis, reflection over the y-axis, and translation up 3.

The state of being in agreement or concord is referred to as congruency. It is a notion that is employed in many fields of life, including mathematics, psychology, and philosophy. Congruency is the belief that in order for an idea, system, or process to be effective, all of its components must agree with each other.

Reflection along the x-axis: This transformation includes reflecting the shape along an imaginary line drawn across the coordinate plane's origin. This produces a mirror copy of the original shape, with the left side of the shape mirrored to the right side and the right side of the shape reflected to the left.

Reflection along the y-axis: This transformation includes reflecting the shape along an imaginary line drawn across the coordinate plane's origin. This produces a mirror copy of the original shape, with the top side of the shape reflecting to the bottom side and the bottom side of the shape reflecting to the top side.

Translation up 3: In this transformation, the shape is moved up by a given number of units. The form will be pushed forward three units without affecting its size or orientation as a result of this.

Reflection over the x-axis, reflection over the y-axis, reflection over the x-axis: This transformation requires reflecting the shape twice across an imaginary line drawn through the coordinate plane's origin. This produces a mirror copy of the original shape, with the left side of the shape mirrored to the right side and the right side of the shape reflected to the left.

Dilation by a scale factor of 3: This modification enlarges or contracts the shape by a certain scale factor. This causes the form to be three times larger or smaller than it was before, without affecting its orientation.

180° anticlockwise rotation: This transformation includes rotating the shape by a given amount. This will spin the form 180° anticlockwise without affecting its size or orientation.

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The equation of the parabola is y = (-3/2)x + 1.

The general vertex form of the equation of a parabola is y = a(x - h)2 + k

where (h, k) are the coordinates of the vertex

Here, we are given that vertex = (0, 1)

Thus, the equation of the parabola is-

y = a(x - 0)2 + 1

y = 2ax + 1

Also, we are given that the parabola passes through (12, -17).

Thus, (12, -17) must satisfy the equation of the parabola

⇒ -17 = 2a(12) + 1

-17 = 24a + 1

24a = -17 -1

24a = -18

a = -18/24

a = -3/4

Thus, the equation of the parabola becomes-

y = 2(-3/4)x + 1

y = (-3/2)x + 1

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The confidence interval about the given mean age is (40.7, 34.3). Since the given mean age of 38.8 years is in the obtained interval, there is no sufficient evidence to conclude that the mean age had changed.

The formula for the confidence interval is

C.I = \(\bar x\) ± z(σ/√n)

Where \(\bar x\) - sample mean; z or z(α/2) - test value; σ - standard deviation of the sample; n - sample size;

Consider the hypothesis,

null hypothesis H0: μ = 38.8

alternate hypothesis Ha: μ ≠ 38.8

It is given that,

sample size n = 32

sample mean \(\bar x\) = 37.5

standard deviation σ = 9.2

Constructing a 95% confidence interval about the mean age:

a) Finding the significance level:

= 1 - (95/100)

= 1 - 0.95

∴ α = 0.05

b) Finding the z-value for the obtained significance level:

z(α/2) = z(0.05/2)

∴ z = 1.96 (From the distribution table)

c) Calculating the lower and upper bounds:

C.I = \(\bar x\)  ± z(σ/√n)

On substituting,

C.I = 37.5 ± (1.96)(9.2/√32)

⇒ 37.5 ± (1.96)(1.626)

⇒ 37.5 ± 3.186(≅3.2)

Upper bound = 37.5 + 3.2 = 40.7

Lower bound = 37.5 - 3.2 = 34.3

Thus, the interval is from 34.3 years to 40.7 years.

Hence the given mean age of 38.8 is included in the interval, the evidence is insufficient to conclude that there is a change in the mean age.

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Answer:  see answers below

Step-by-step explanation:

(i) The first leaf of the tree is:  black = 5/9 and white = 4/9

   That means that there are 5 black marbles out of 9 total marbles and 4 white marbles out of 9 total marbles.

Total marbles = 9

Black marbles = 5

White marbles = 4

*******************************************************************************************

(ii)  

P(B₂/B₁)

The probability that the 2nd marble is black given that the 1st marble was black.

P(W₂/B₁)

The probability that the 2nd marble is white given that the 1st marble was black.

P(B₂/W₁)

The probability that the 2nd marble is black given that the 1st marble was white.

P(W₂/W₁)

The probability that the 2nd marble is white given that the 1st marble was white.

***********************************************************************************************

                (iii)  Outcomes            (iv)   Probability        

                         (B, B)                    (5/9) x (1/2) = 5/18

                         (B, W)                    (5/9) x (1/2) = 5/18

                         (W, B)                    (4/9) x (5/8) = 5/18

                         (W, W)                  (4/9) x (3/8) = 3/18

                                                    Check:  Total = 18/18 = 1  \(\checkmark\)

**********************************************************************************************

(iv)  Dependent

     Once the first ball is drawn, there is one less ball for the second draw.  Therefore, the second draw is dependent on the first draw.

Answer:

Part A: Non linear

Part B: Yes

Part C: The y-intercept is (0, 0), represent the starting height level of the golf ball

Part C: The solution are the points (0, 0) and (100, 0) which are the points at which the golf ball touches the ground

Step-by-step explanation:

Part A: The shape of the path of the increase in the height of the the golf ball as it moves in increasing horizontal distance from the starting point is hat of a parabola

Part B: The graph is a function because each value of the independent variable, distance (ft.) maps to exactly one value of the dependent variable, elevation (ft.)

Part C: The y-intercept represents the starting or initial value of the function, where x = 0. It represents the height from which the golf ball motion path starts

Part D: The solution represents the values of the x-intercept at which the elevation is the y = 0.

Answer:

5<4

Step-by-step explanation:

This inequality is not correct though.

5-7+7<-3+7

5<4

The bucket number 2 will contain 45 after sorting the data.

According to the statement

we have given that the a data list which is sorted into 4 buckets then we have to find he in which the umber 45 is sorted.

So, For this purpose,

The given data list is:

76, 56, 93, 24, 45, 88, 13, 7, 37

And the data is sorted into the buckets so,it is sorted in 4 buckets. and the data contain numbers from 0 to 100.

So, let the sorting.

We know that the 100 numbers are sorted in 4 buckets then it means each bucket contain 25 numbers.

So, let us consider a

BUCKET 1 : 0 to 25

it contains the data number 7, 13,24.

Now,

BUCKET 2 : 25 to 50

it contains the data number 37,45.

Now,

BUCKET 3 : 50 to 75

it contains the data number 56.

Now,

BUCKET 4 : 75 to 100

it contains the data number 76, 88, 93.

From sorting the 45 number sort in the bucket 2.

So,The bucket number 2 will contain 45 after sorting the data.

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Following the descriptions of the relationship existing  between the lines the option that is not true is the last option which is b || d which is read as b is parallel to d

Some set of lines are said to be parallel if the lines are equally spaced apart. This ensures that such line will never meet . Parallel lines is very useful in the field of geometry as it the foundation of many postulates and theorem.

Also, when two lines are being connected by a line. Say line x and line y and the connecting line is z. If the lines x and y makes similar angle with line z then line x and line y is said to be parallel.

Considering the descriptions given in the question. line b is tether perpendicular to line d. Hence saying that line b is parallel to line d is not true and the correct answer to the question.

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Answer:

$630

Step-by-step explanation:

week 1 : $336

week 2 : $294

gross pay : $630

Answer:

d is 90, angles on a straight line

e is 147, vertically opp angles

f is 33, any of the above rules.

Answer:

Decreased  

Step-by-step explanation:

Answer:

9 dimes, 15 nickels

Step-by-step explanation:

Let n= number of nickels and d=number of dimes.

.05n + .10d = 1.65

n = 6 + d

.05(6 + d) + .10d = 1.65

.30 + .05d + .10d = 1.65

.30 + .15d = 1.65

.15d = 1.35

d = 9, n = 15

.10(9) + .05(15) = .90 + .75 = 1.65

If you buy the device, you will save a total of $303,840 in labor costs. The value of the device is approximately $276699.38. The price you should pay for the note compounded monthly is approximately $70660.52.

28. To calculate the total amount of labor costs you will save, we need to determine the savings per year and then multiply it by the number of years the device will last.

The device saves you $2,110 per month in labor costs, so the annual savings would be $2,110 multiplied by 12 months, which is $25,320.

Now, we multiply the annual savings by the number of years the device will last. In this case, the device will last 12 years, so the total labor costs you will save would be $25,320 multiplied by 12, which equals $303,840.

Therefore, if you buy the device, you will save a total of $303,840 in labor costs.

29. Having the answer to Problem 28 helps you determine the total amount of labor costs you will save over the 12-year lifespan of the device. However, it does not provide enough information to decide whether you should buy the device or not. Other factors, such as the initial cost of the device, maintenance costs, potential revenue increase, and the opportunity cost of investing the money elsewhere, should also be considered before making a decision.

30. To calculate the value of the device, we need to find the present value of the future savings. Since we need to earn 7.8% compounded monthly on our money, we can use the present value formula:

Present Value = Future Value / (1 + r)^n

Where:
- Future Value is the total labor costs you will save ($303,840)
- r is the interest rate per period (7.8% divided by 12 months, which is 0.065%)
- n is the number of periods (12 years multiplied by 12 months, which is 144 periods)

Plugging in the values, we get:
Present Value = $303,840 / (1 + 0.065%)^144

Calculating this, we find that the value of the device is approximately $276699.38.

31. Whether you should buy the device or not depends on factors other than just the value of the device. Consider the initial cost of the device ($267,000), the value calculated in Problem 30 ($276699.38), and other relevant factors such as maintenance costs and potential revenue increase. Compare these costs and benefits to determine if the purchase is financially feasible and beneficial for your business in the long run.

32. To calculate the total amount you will receive from the promissory note, multiply the monthly payment by the number of payments. In this case, the monthly payment is $880, and the number of payments is 85 months.

So, the total amount you will receive from the promissory note would be $880 multiplied by 85, which equals $74,800.

33. To determine the price you should pay for the note if you want to earn 8% compounded monthly, we need to calculate the present value of the future payments using the present value formula:

Present Value = Future Value / (1 + r)^n

Where:
- Future Value is the total amount you will receive ($74,800)
- r is the interest rate per period (8% divided by 12 months, which is 0.067%)
- n is the number of periods (85 months)

Plugging in the values, we get:
Present Value = $74,800 / (1 + 0.067%)^85

Calculating this, we find that the price you should pay for the note is approximately $70660.52.

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Yes, the two quantities have a proportional relationship because the variables x and y all have the same constant of proportionality.

Mathematically, a proportional relationship can be represented or modeled with the following mathematical expression:

y = kx

Where:

In order for the two quantities to have a proportional relationship, the variables x and y must remain in a constant ratio.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 2/3

When x = 90 and y = 60, we have:

Constant of proportionality (k) = 60/90

Constant of proportionality (k) = 2/3

When x = 120 and y = 80, we have:

Constant of proportionality (k) = 80/120

Constant of proportionality (k) = 2/3

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Probability that the person randomly chosen from the town's population is under 18 or employed part time is the probability of a randomly chosen person is under 18 plus the probability of a randomly chosen person is  employed part-time subtracting the probability that they are both under 18 and employed part-time.

In order to find the probability that a person is under 18 or employed part-time, you would need to know the proportion of the population that is under 18 and the proportion of the population that is employed part-time. Then you can use the following formula:

P(under 18 or part-time) = P(under 18) + P(part-time) - P(under 18 and part-time)

Where P(under 18 and part-time) is the probability that a person is under 18 and employed part-time at the same time.

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Answer:A

Step-by-step explanation: to multiply fractions by a whole, you would set 5+x over 1, then you would have:

(5+x)/1 * 1/x

When multiplied, you get:

(5+x) * 1 / 1 * x

When you multiply anything by 1, it is just itself, so you end up with:

(5 + x) / x

Step-by-step explanation:

4x-3y=-1

4x+y=11

\(4x = - 1 + 3y \\ x = \frac{ - 1 + 3y}{4} \)

\( - 1 + 3y = 11 - y \\ 3y + y = 11 + 1 \\ 4y = 12 \\ y = 3\)

\(x = \frac{ - 1 + 3 \times 3}{4} \\ x = \frac{ - 1 + 9}{4} \\ x = \frac{8}{4} = 2\)

Answer:

\(x\approx 422.4\)

Step-by-step explanation:

Assuming 'x'  the distance helicopter needs to fly to be directly over the tower.

It is given that a helicopter flying 3590 feet above ground spots the top of a 150-foot tall cell phone tower at an angle of depression of 83°.

From attachment that helicopter, tower and angle of depression forms a right triangle.

As height of tower is 150 feet, so the vertical distance between helicopter and tower will be: 3590-150=3440 feet.

Also, the side with length 3590-150 feet is opposite and side x is adjacent side to 83° angle.

As the tangent relates the opposite side of a right triangle to its adjacent  side, so we will use tangent to find the length of x.

\(\text{Tan}=\frac{\text{Opposite}}{\text{Adjacent}}\)

\(\text{Tan}(83^o)=\frac{3590-150}{x}\\\)

\(\text{Tan}(83^o)=\frac{3440}{x}\)

\(x=\frac{3440}{\text{Tan}(83^o)}\)=>\(x=\frac{3440}{8.14434}\)

\(x\approx 422.4\)

Thus, the helicopter must fly approximately 422.4 feet to be directly over the tower.  

Answer:

7 - 2m can be translated to "7 minus two times m" or "the difference between 7 and twice m".

3(m + 2) = 15 can be translated to "three times the sum of m and 2 is equal to 15" or "the product of 3 and the sum of m and 2 is 15".

To solve the equation, we can start by distributing the 3 on the left side:

3(m + 2) = 15

3m + 6 = 15

Then, we can subtract 6 from both sides:

3m + 6 - 6 = 15 - 6

3m = 9

Finally, we can divide both sides by 3:

3m/3 = 9/3

m = 3

Therefore, the solution to the equation 3(m + 2) = 15 is m = 3.

5m - m(2 - m) can be translated to "5m minus the product of m and the difference between 2 and m" or "the difference between 5m and m times the quantity 2 minus m".

To simplify the expression, we can use the distributive property to expand the second term:

5m - m(2 - m) = 5m - 2m + m^2 = m^2 + 3m

Therefore, the simplified expression is m^2 + 3m.

9514 1404 393

Answer:

Step-by-step explanation:

The solution steps are ...

  3(y -2) = 18 . . . . . . given

  3y -6 = 18 . . . . . . . eliminate parentheses using the distributive property

  3y = 24 . . . . . . . . . add 6 to both sides

  y = 8 . . . . . . . . . . . divide both sides by 3

The value of y is 8.

Answer:

should be the first one, x > 360

Step-by-step explanation:

im sorry if its wrong :*(

Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

The three posts can be given in 4080 ways among 17 students.

It is given that the number of people available to choose the posts from is 17.

There are three posts here- president, vice president, and secretary.

Now, if we choose a candidate for President first, there are 17 students available.

Next, if we select a Vice-President, there are 16 ways to select the vice-president, since one student already is the president.

At, last there are 15 students available to choose the secretary from as two students already hold a post.

Hence, the number of ways to select the President, Vice-President, and Secretary are-

17 X 16 X 15 ways

Therefore we get

4080 ways.

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Answer:

3920 - 36x ≤ 500

Step-by-step explanation:

Calista worked all summer to save for spending money while she is away for college. She goes off to college with $3920 in her savings account. She wants to have at least $500 left in her account at the end of her 36-week school year. Write an inequality to represent this situation.

Let the amount of money spent in 36 weeks = x

At least = Less than or equal to = ≤

$3920 - 36x ≤ $500

Hence, the inequality to represent this situation is written as:

3920 - 36x ≤ 500

The radius of convergence for the Taylor series of g(x) is 4.

To find the radius of convergence for the Taylor series of f(x) = ∑(n=1 to ∞) xn, we can use the ratio test.

The ratio test states that for a power series ∑(n=0 to ∞) an(x-c)n, the series converges if the following limit exists and is less than 1:

lim(n→∞) |an+1(x-c)/(an(x-c))|

For the series f(x) = ∑(n=1 to ∞) xn, we have an = 1 for all n.

Applying the ratio test to f(x), we have:

lim(n→∞) |(x(n+1))/(xn)|

= lim(n→∞) |x(n+1)/xn|

= |x|

For the series to converge, |x| < 1. Therefore, the radius of convergence for the Taylor series of f is 1.

Now, let's consider the function g(x) = x^3 * f(x^2/16). Since f(x) has a radius of convergence of 1, we need to determine the radius of convergence for g(x) based on f(x^2/16).

To find the radius of convergence for g(x), we substitute x^2/16 into the ratio test:

lim(n→∞) |[(x^2/16)^(n+1)] / [(x^2/16)^n]|

= lim(n→∞) |(x^2/16)|

= |x^2/16|

For g(x) to converge, |x^2/16| < 1. Simplifying the inequality, we have |x| < 4.

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