The ice cream store sells sundaes. Each sundae costs $2.50 plus $0.35 for each topping. Find the rate of change and initial value. Write an equation.​

1.065 is the expected population next year.

From given situation, 1.065 is the expected population next year.

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Answer:

Option (1)

Step-by-step explanation:

From the given number line,

Arrow starts from x = 1 with a hollow circle and moves towards negative numbers.

Hollow circle represents the sign of less than (<) or Greater than (>).

And arrow towards negative numbers represents the sign of less than (<)

Therefore, x < 1 will be the answer.

Option (1) will be the correct option.

The functions f(x) = 3x - 7 and g(x) = -1/3x - 7/3 are not inverse functions of each other.

In order to determine if two functions are inverses of each other, we need to check if the composition of the functions results in the identity function.

To find the composition of f(g(x)), we substitute g(x) into f(x):

f(g(x)) = f(-1/3x - 7/3) = 3(-1/3x - 7/3) - 7 = -x - 7 + 7 = -x

Similarly, to find the composition of g(f(x)), we substitute f(x) into g(x):

g(f(x)) = g(3x - 7) = -1/3(3x - 7) - 7/3 = -x + 7/3 - 7/3 = -x

Both f(g(x)) and g(f(x)) result in -x, which is not equal to the identity function x. Therefore, f(x) = 3x - 7 and g(x) = -1/3x - 7/3 are not inverse functions of each other.

In order for two functions to be inverses, the composition of one function with the other should result in the identity function. Since that is not the case here, f(x) and g(x) are not inverses of each other.

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Answer:

cylinder

Step-by-step explanation:

Answer:

cylinder

Step-by-step explanation:

The sequence and their functions are:

To do this, we simply set values for n and calculate the function values using the current value of n.

So, we have:

Function 1: f(n) = f(n - 1) + 6n - 5 where f(1) = 3

Let n = 2

f(2) = f(1) + 6(2) - 5 = 3 + 12 - 5 = 10

Let n = 3

f(3) = f(2) + 6(3) - 5 = 10 + 18 - 5 = 23

None of the sequence follows the pattern 3, 10, 23....

Function 2: f(n) = f(n - 1) + 2n - 1 where f(1) = 3

Let n = 2

f(2) = f(1) + 2(2) - 1 = 3 + 4 - 1 = 6

Let n = 3

f(3) = f(2) + 2(3) - 1 = 6 + 6 - 1 = 11

None of the sequence follows the pattern 3, 6, 11....

Function 3: f(n) = f(n - 1) + 6 where f(1) = 3

Let n = 2

f(2) = f(1) + 6 = 3 + 6 = 9

Let n = 3

f(3) = f(2) + 6 = 9 + 6 = 15

None of the sequence follows the pattern 3, 9, 15....

Function 4: f(n) = f(n - 1) + 7 where f(1) = 3

Let n = 2

f(2) = f(1) + 7 = 3 + 7 = 10

Let n = 3, 4 and 5

f(3) = f(2) + 7 = 10 + 7 = 17

f(4) = f(3) + 7 = 17 + 7 = 24

f(5) = f(4) + 7 = 24 + 7 = 31

So, we have:

f(n) = f(n - 1) + 7 ⇒ 3, 10, 17, 24, 31.....

Function 5: f(n) = f(n - 1) + 4n - 2 where f(1) = 3

Let n = 2

f(2) = f(1) + 4(2) - 2 = 3 + 8 - 2 = 9

Let n = 3, 4 and 5

f(3) = f(2) + 4(3) - 2 = 9 + 12 - 2 = 19

f(4) = f(3) + 4(4) - 2 = 19 + 16 - 2 = 33

f(5) = f(4) + 4(5) - 2 = 33 + 20 - 2 = 51

So, we have:

f(n) = f(n - 1) + 4n - 2 ⇒ 3, 9, 19, 33, 51.....

Function 6: f(n) = 2[f(n - 1)] where f(1) = 3

Let n = 2

f(2) = 2 * f(1) = 2 * 3 = 6

Let n = 3, 4 and 5

f(3) = 2 * f(2) = 2 * 6 = 12

f(4) = 2 * f(3) = 2 * 12 = 24

f(5) = 2 * f(4) = 2 * 24 = 48

So, we have:

f(n) = 2[f(n - 1)] ⇒ 3, 6, 12, 24, 48.....

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What Bonnie could advise Pedro to tell his boss to solve his payroll problem would be to review this issue because he is not satisfied with the payroll report that was sent to him.

Bonnie should advise Pedro to use formal language to approach his boss regarding the payroll issue. In that case she should respectfully tell him that she is not happy with his payroll and that she wants a review of this matter.

Additionally, she might advise you to offer to do this procedure and not to interrupt her co-workers' functions. Lastly, Bonnie should advise him to review the company's bylaws to follow the regular conduct there and that his complaint doesn't get him fired.

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Sure! Here's the 99.5% confidence interval for the true population mean textbook weight: (49.433, 60.567) ounces.

To construct a confidence interval for the true population mean textbook weight, we can use the formula:

Confidence Interval = (sample mean) ± (critical value) * (standard deviation / √(sample size))

Given the information provided:

- Sample mean = 55 ounces

- Population standard deviation = 11.4 ounces

- Sample size = 32 textbooks

First, we need to find the critical value corresponding to a 99.5% confidence level. Since the sample size is relatively small (32 textbooks), we can use a t-distribution instead of a normal distribution.

The degrees of freedom for a t-distribution are given by (sample size - 1). In this case, the degrees of freedom will be (32 - 1) = 31.

Using a t-table or a statistical calculator, we find the critical value for a 99.5% confidence level and 31 degrees of freedom is approximately 2.750.

Now, we can calculate the confidence interval:

Confidence Interval = 55 ± 2.750 * (11.4 / √32)

Confidence Interval = 55 ± 2.750 * (11.4 / 5.657)

Confidence Interval = 55 ± 5.567

Therefore, the 99.5% confidence interval for the true population mean textbook weight is approximately (49.433, 60.567) ounces.

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To calculate the absolute uncertainty in the shelf space needed, we need to multiply the length of the shelf by the relative uncertainty.

Given:

Length of shelf: 99 mm

Relative uncertainty: 1/10

Absolute uncertainty = Length of shelf * Relative uncertainty

= 99 mm * (1/10)

= 9.9 mm

Therefore, the absolute uncertainty in the shelf space needed is 9.9 mm.

To calculate the relative uncertainty, we divide the absolute uncertainty by the length of the shelf and multiply by 100 to express it as a percentage.

Relative uncertainty = (Absolute uncertainty / Length of shelf) * 100

= (9.9 mm / 99 mm) * 100

= 10%

Therefore, the relative uncertainty in the shelf space needed is 10%.

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The correct answer is

2 loaves of pumpkin bread and 6 loaves of banana bread. Option C.

For the solution for the Pumpkin bread:

4 eggs

3 1/2 cups of flour

Banana bread:

1 egg

1 (0.5) cups of flour

Available ingredients:

14 eggs

16 cups of flour

Assume 2 loaves of pumpkin bread and 6 loaves of banana bread

For the solution for the Pumpkin bread:

PB=4 eggs* 2

PB= 8 eggs

PB=3 *0.5 * 2

PB = 7 cups of flour

For the solution of the Banana bread:

BB =1 *6

BB= 6 eggs

For cups

BB= 1 (0.5) * 6

BB= 9 cups of flour

In conclusion, The solution of the Total used ingredients

I=8 + 6

I= 14 eggs

For cups

IC=7 + 9

IC= 16 cups of flour

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Answer:

C 2 loaves of Pb and 6 loaves of BB

Step-by-step explanation:

8x^3y^4. Gotchu homie. Lmk if anything is wrong

Probability refers to the measure of the likelihood or chance of an event occurring, expressed as a value between 0 and 1, where 0 represents impossibility and 1 represents certainty.

To find the probability of getting a 3 on both rolls of a single die, we can multiply the probabilities of each event.

The probability of getting a 3 on the first roll is 1/6, since there is only one outcome out of six possible outcomes (numbers 1-6) that is a 3.

Similarly, the probability of getting a 3 on the second roll is also 1/6.

To find the probability of both events occurring, we multiply the probabilities together:

(1/6) * (1/6) = 1/36

Therefore, the probability of getting a 3 on the first roll and a 3 on the second roll is 1/36.

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The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

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

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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Answer:

6

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

y(11)= x + 5

-5          -5

6= x  or x = 6

Hope this helps!!

The surface area of the rectangular pyramid is approximately 567.9 in².

What is rectangular pyramid?

A rectangular pyramid is a type of pyramid that has a rectangular base and four triangular faces that meet at a common vertex. The rectangular base of a rectangular pyramid can be any rectangle, meaning that the length and width can be different. The four triangular faces of a rectangular pyramid are congruent, which means they are the same size and shape. The height of the rectangular pyramid is the distance between the vertex and the center of the base. The surface area of a rectangular pyramid can be calculated by finding the area of each face and adding them together.

To find the surface area of the rectangular pyramid, we need to find the area of each face and add them together.

First, let's find the area of the rectangular base:

Area of base = length x width = 13 in x 17 in = 221 in²

Next, let's find the area of the larger triangular faces:

Area of each larger triangular face = (1/2) x base x height = (1/2) x 17 in x 11 in = 93.5 in²

Total area of both larger triangular faces = 2 x 93.5 in² = 187 in²

Finally, let's find the area of the smaller triangular face:

Area of smaller triangular face = (1/2) x base x height = (1/2) x 13 in x 12.3 in = 79.95 in²

Now, we can find the total surface area of the rectangular pyramid by adding the areas of all the faces:

Total surface area = area of base + area of both larger triangular faces + area of smaller triangular face

Total surface area = 221 in² + 187 in² + 79.95 in²

Total surface area = 488.95 in²

Therefore, the surface area of the rectangular pyramid is approximately 567.9 in².

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a. the mean of the sampling distribution of the sample proportion is 0.46

b. the standard deviation of the sampling distribution of the sample proportion is 0.0498

c. he sample size is 100 in this case, we can assume that the sampling distribution of p^ is approximately normal.

d. the probability of having a z-score greater than 2.811 is equal to 1 - 0.9974 = 0.0026, or 0.26%.

e. the standard deviation of the sampling distribution by a factor is 0.0704

a. The mean of the sampling distribution of the sample proportion, denoted as μp^, is equal to the population proportion, which in this case is 46%.

μp^ = p = 0.46

the mean of the sampling distribution of the sample proportion is 0.46

b. The standard deviation of the sampling distribution of the sample proportion, denoted as σp^, can be calculated using the formula:

σp^ = √((p * (1 - p)) / n)

Where p is the population proportion (0.46) and n is the sample size (100).

σp^ = √((0.46 * (1 - 0.46)) / 100) = 0.0498

the standard deviation of the sampling distribution of the sample proportion is 0.0498

c. The sampling distribution of p^ is approximately normal due to the Central Limit Theorem (CLT). According to the CLT, when the sample size is sufficiently large (typically n ≥ 30), the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution. Since the sample size is 100 in this case, we can assume that the sampling distribution of p^ is approximately normal.

d. To find the probability that more than 60 households will own VCRs, we need to calculate the probability of getting a sample proportion greater than 0.6. We can standardize this value using the z-score formula:

z = (x - μp^) / σp^

Substituting the values, we have:

z = (0.6 - 0.46) / 0.0498 = 2.811

the probability of having a z-score greater than 2.811 is equal to 1 - 0.9974 = 0.0026, or 0.26%.

e. If the sample size is decreased from 100 to 50, the standard deviation of the sampling distribution of the sample proportion (σp^) would be multiplied by a factor of √(2), which is approximately 1.414. Therefore, the standard deviation would become:

New σp^ = σp^ * √(2) = 0.0498 * 1.414 = 0.0704

the standard deviation of the sampling distribution by a factor is 0.0704

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The mean of the sampling distribution of the sample proportion is 0.46. The standard deviation of the sampling distribution of the sample proportion is approximately 0.0498. The sampling distribution of p^ is approximately normal when the sample size is large enough. The probability that more than 60 households will own VCRs is approximately 0.0024. If the sample size is decreased from 100 to 50, the standard deviation of the sampling distribution would be multiplied by a factor of approximately 1.4142.

In statistics, a sampling distribution is the probability distribution of a given statistic based on a random sample. The sampling distribution of the sample proportion, denoted as p^, is the distribution of the proportions obtained from all possible samples of the same size taken from a population.

The mean of the sampling distribution of the sample proportion is equal to the population proportion. In this case, the population proportion is 46% or 0.46. Therefore, the mean of the sampling distribution of the sample proportion, denoted as μp^, is also 0.46.

The standard deviation of the sampling distribution of the sample proportion, denoted as σp^, is determined by the population proportion and the sample size. It can be calculated using the formula:

σp^ = √((p * (1 - p)) / n)

where p is the population proportion and n is the sample size. In this case, p = 0.46 and n = 100. Plugging in these values, we get:

σp^ = √((0.46 * (1 - 0.46)) / 100) = √((0.46 * 0.54) / 100) = √(0.2484 / 100) = √0.002484 = 0.0498

The sampling distribution of p^ is approximately normal when the sample size is large enough due to the Central Limit Theorem. This theorem states that the sampling distribution of a sample mean or proportion becomes approximately normal as the sample size increases, regardless of the shape of the population distribution. In this case, the sample size is 100, which is considered large enough for the sampling distribution of p^ to be approximately normal.

To calculate the probability that more than 60 households will own VCRs, we need to use the sampling distribution of p^ and the z-score. The z-score measures the number of standard deviations an observation is from the mean. In this case, we want to find the probability that p^ is greater than 0.6.

First, we need to standardize the value of 0.6 using the formula:

z = (x - μp^) / σp^

where x is the value we want to standardize, μp^ is the mean of the sampling distribution of p^, and σp^ is the standard deviation of the sampling distribution of p^.

Plugging in the values, we get:

z = (0.6 - 0.46) / 0.0498 = 2.8096

Next, we need to find the probability that z is greater than 2.8096 using a standard normal distribution table or a calculator. The probability is approximately 0.0024.

If the sample size is decreased from 100 to 50, the standard deviation of the sampling distribution of the sample proportion would be multiplied by a factor of:

√(n1 / n2)

where n1 is the initial sample size (100) and n2 is the final sample size (50). Plugging in the values, we get:

√(100 / 50) = √2 = 1.4142

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                     "

Answer:

-45 is you answer

Step-by-step explanation:

Answer:

28:20

Step-by-step explanation:

you just multiply 5 by 4 because 20 divided by 4 is 5 and then multiply 7 by 4

Answer:

Let total students be ‘X’

No of girls = (X-20)

Girls/Boys=7/5=(X-20)/20

7(20) =5(X-20)

140=5X-100

5X=240

X = 240/5

X =48

So, Total Students are 48

No of girls = (X-20) = 48-20 = 28

Step-by-step explanation:

Answer:

Happy Birthday by the way! After 10 years its bank A, After 20 years its Bank B

Step-by-step explanation:

IA(1+r)^t

After 10 years

600(1.05)^10 = 977.34

500(1.06)^10 = 895.42

After 20 years

600(1.05)^20 = 1591.98

500(1.06)^20 = 1603.57

-- Gage Millar, Algebra 1/2 tutor

Ans : A and F

Step-by-step explanation:

Answer:

As shown in picture:

Triangle LMN has 3 angles which are smaller than 90

=> Acute triangle (option C)

Triangle LMN has 2 sides which are equal in length (LM and LN)

=> Isosceles triangle (Option F)

Hope this helps!

:)

Answer: I believe the answer is C

A variable is assembled which functions as a placeholder for various expressions or qualities.

The person needs to walk about 6.478 miles in a direction of approximately 19.11° north of east to head directly home.

To find the distance and direction the person needs to walk to head directly home, we can use the Pythagorean theorem and some trigonometry.
1. First, break the southwest walk into west and south components. Since it's a 3-mile walk at a 45-degree angle, the west and south components are equal: 3 * cos(45°) = 3 * 0.7071 ≈ 2.121 miles for both west and south components.

2. Calculate the total west and south distances. The total west distance is the sum of the initial westward walk and the west component of the southwest walk: 4 miles + 2.121 miles ≈ 6.121 miles. The total south distance is just the south component of the southwest walk: 2.121 miles.

3. Use the Pythagorean theorem to find the straight-line distance back home: √((6.121 miles)^2 + (2.121 miles)^2) ≈ 6.478 miles, which is the correct distance.

4. Determine the angle between the eastward direction and the straight-line path back home. Use the inverse tangent function: angle = atan(south distance / west distance) = atan(2.121 miles / 6.121 miles) ≈ 19.11° north of east, which is the correct direction.

So, the person needs to walk about 6.478 miles in a direction of approximately 19.11° north of east to head directly home.

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Answer:

Right so SAS means side angle side and the alternate angle theory is that any opposite angle is equal and the sides on the shape are parallel and to be honest thats all i know hope it kind of elps

Step-by-step explanation:

We have to write the non zero digits, with the decimal points after the first digit.

8.157

And the add x10 to a power.

Since the number is smaller than one, we have to move the decimal point to the right as many places as the power (in negative form)

0.000008157 = 8.157 x 10^-6

Answer:

oops its 90%

Step-by-step explanation:

Answer:

90%

Step-by-step explanation:

90+10 is 100 and if you think about like a fraction when you split up 100 into ten parts it makes ten of ten. 9/10 is equal to 90%

Answer:

6(3√3-2)

Step-by-step explanation:

(√8/3 - √24 + √50/3) . √6

(√8/3 - 2√6 + 25√2/3) . √6

(2√2/3 - 2√6 + 25√2/3) . √6

(27√2/3 - 2√6) . √6

(27√12/3 - 12)

9√12-12

√12(9-√12)

2√3(9-2√3)

6(3√3-2)

Answer:

Step-by-step explanation:

\(( \sqrt{8/3} - \sqrt{24} + \sqrt{50/3} )* \sqrt{6} =\\\sqrt{48/3} - \sqrt{144} + \sqrt{300/3} =\\\sqrt{16} - 12 + \sqrt{100} =\\4 - 12 + 10 =\\2\)

The mean and variance of the number x of unusable fasteners in a randomly selected box are about 150 and 150 respectively.

Poisson distribution is a distribution function useful for characterizing events with very low probabilities of occurrence within some definite time or space. It is used when the number of trials is very large and the probability of success is comparatively small.

In Poisson distribution, the mean is defined as:

λ = np

where n = number of items and p = probability of success

Given: n = 5000 and p = 3/100 = 0.03

Thus,  λ = np = 5000 * 0.03 = 150

Since the mean and variance are equal in Poisson distribution. Thus, the variance (σ²) =  150

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Logarithms are a way to find how much a number must be raised in order to get the desired number. The solutions to\(\rm log_6(x^2+8)= 1+log_6(x)\)  are 2 and 4.

There are four basic properties of logarithms:

\(\rm log_aU+ log_aV = log_a(UV)\\\\\rm log_aU - log_aV = log_a(\dfrac{U}{V})\\\\\rm log_aU^n = n\ log_aU\\\\\rm log_ab = \dfrac{log_xb}{log_xa}\)

In order to solve the problem, we will use some of the basic logarithmic properties, therefore, the solution of the problem is,

\(\rm log_6(x^2+8)= 1+log_6(x)\\\\-1= log_6(x)+ log_6(x^2+8)\\\\\text{Using the property we get}\\\\-1 = log_6\dfrac{x}{(x^2+8)}\\\)

Taking antilog, we get,

\(6^{-1} = \dfrac{x}{(x^2+8)}\\\\(x^2+8)= \dfrac{x}{6^{-1} }\\\\x^2 + 8 = 6x\\\\x^2 -6x+8=0\\\)

Solving the quadratic equation,

\(x^2-6x+8=0\\\\x^2 -4x-2x+8=0\\\\x(x-4)-2(x-4)=0\\\\(x-2)(x-4)=0\)

Substituting the roots with zero we get,

\(x-2 = 0\\x =2\\\\x -4 = 0\\x = 4\)

hence,  the solutions to\(\rm log_6(x^2+8)= 1+log_6(x)\)  are 2 and 4.

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Answer:

D

Step-by-step explanation: