I need Help please.

Each child, Miriam, Joe, and Paul, received one-sixth (1/6) of the entire cake.

To determine what part of the entire cake each child got, we need to divide the one-half of a cake that Stanley has equally among his three children, Miriam, Joe, and Paul.

The result is (1/6), which means that each child, Miriam, Joe, and Paul, received one-sixth (1/6) of the entire cake.

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Answer:

15.10 ft to nearest hundredth.

Step-by-step explanation:

We have 2 right triangles one within the other

For the larger triangle

tan 43 = h / 65    where h is the total height to the top of steeple from ground

h = 65 tan 43

For small triangle

tan 35 = h2 / 65   where h2 is the hoght of the bottom of steeple from the ground

h2 = 65 tan 35

So height of the steeple

= h - h2

= 65 tan43 - 65 tan35

= 15.099 feet.

The key features of this exponential function include the following:

y-intercept of f: (0, 10).

y-intercept of g: (0, 5).

Domain of both f and g: All real numbers or (-∞, ∞).

Range of both f and g = (0, ∞) or {y|y ≥ 0}.

End behavior of both f and g: as x → -∞, y → 0 and x → ∞, y → ∞

In Mathematics and Geometry, an exponential function is typically represented by the following mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the given exponential function f, we can logically deduce that the y-intercept is represented by a, which is equal to 10 while the y-intercept of g is equal to 5.

In conclusion, there is a horizontal asymptote at y = 0 because it is a line which the graph of a given function approaches, but never touches or crosses.

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Answer:

Slope of green line:

[tex]m = \frac{ - 3 - 3}{4 - ( - 4))} = - \frac{6}{8} = - \frac{3}{4} [/tex]

Slope of red line:

[tex]m = \frac{3 - ( - 5)}{3 - ( - 3)} = \frac{8}{6} = \frac{4}{3} [/tex]

The slopes of these two lines are negative reciprocals of each other.

Therefore, the correct answer is True (A).

The probability that a randomly selected student is interested in a "spinning-room" and also that they are a "graduate-student" is 0.428.

The total number of students that are surveyed is = 500 students,

Out of the 500 students surveyed, 41 are interested in a spinning room and are in year 1-2,

⇒ 75 are interested and are in year 3-4, and

⇒ 87 are interested and are graduate students.

So, the total number of students interested in a spinning room is

⇒ 41 + 75 + 87 = 203,

Out of these 203 students interested in a spinning room, 87 are graduate students.

So, probability that randomly selected student is interested in "spinning-room" and is a "graduate-student" is :

⇒ P(spinning room and graduate student) = 87/203,

⇒ P(spinning room and graduate student) = 0.428,

Therefore, the required probability is 0.428.

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The given question is incomplete, the complete question is

A university recently surveyed 500 students to determine which new fitness area to offer in its recreation facility. the results of the survey are summarized in the following table.

                              Spinning Room   Climbing Wall     Ellipticals

Year 1-2                              41                     81                         25

Year 3-4                             75                    78                         44

Graduate Student             87                     49                        20

What is the probability that a randomly selected student is interested in a spinning room and that they are a graduate student?

The area of the tray is approximately 28.26 square inches.

To find the area of the tray, we need to use the formula for the area of a circle, which is:

Area = π x radius²

Here, π (pronounced "pi") is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. Its approximate value is 3.14.

In our case, the radius of the tray is given as 3 inches. So, we can substitute this value into the formula and calculate the area as follows:

Area = π x 3²

= 3.14 x 9

= 28.26 square inches

This means that if we were to cover the tray completely with paint or any other material, it would require 28.26 square inches of that material.

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The impact of tobacco production on the war effort was likely just one of many factors, and there were numerous other economic, political, and military factors at play during this time period.

Since, From a historical perspective, higher rates of tobacco production might have given the Confederacy an advantage during the American Civil War because tobacco was a highly valuable and profitable crop at that time.

Here, The Confederacy relied heavily on the export of cotton and tobacco to fund their war effort, and the higher rates of tobacco production would have allowed them to generate more revenue through exports.

Additionally, tobacco was used as a form of currency and could be traded for goods and services, which would have helped support the Confederate economy.

However, the impact of tobacco production on the war effort was likely just one of many factors, and there were numerous other economic, political, and military factors at play during this time period.

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a) The appropriate sample size to achieve a margin of error of $0.10 with a confidence level of 91.5% is 111

b) The appropriate sample size to achieve a margin of error of $0.07 with a confidence level of 95.845% is 301

c) The appropriate sample size to achieve a margin of error of $0.05 with a confidence level of 97.268% is 543 integer).

a) To achieve a margin of error of $0.10 with a confidence level of 91.5%, the appropriate sample size can be calculated as follows:

Margin of error (E) = z* (standard deviation/√(n))

where z* is the z-value associated with the desired confidence level, and n is the sample size.

We can rearrange the formula to solve for n:

n = [(z* * standard deviation) / E]²

Substituting the given values:

z* = 1.70 (from the z-table for 91.5% confidence level)

Standard deviation = $0.25

E = $0.10

n = [(1.70 * 0.25) / 0.10]² = 110.25 ≈ 111 (rounding up to the nearest integer).

b) To achieve a margin of error of $0.07 with a confidence level of 95.845%, the appropriate sample size can be calculated as follows:

z* = 1.99 (from the z-table for 95.845% confidence level)

Standard deviation = $0.25

E = $0.07

n = [(1.99 * 0.25) / 0.07]² = 300.06 ≈ 300 (rounding up to the nearest integer).

c) To achieve a margin of error of $0.05 with a confidence level of 97.268%, the appropriate sample size can be calculated as follows:

z* = 2.34 (from the z-table for 97.268% confidence level)

Standard deviation = $0.25

E = $0.05

n = [(2.34 * 0.25) / 0.05]² = 542.52 ≈ 543 (rounding up to the nearest integer).

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If Porter's family ordered 3 pizzas and they ate 1 pizza, then they are left with 2 pizzas.

None of the given options is correct.

Given information:

Porter's family ordered 3 pizzas. They ate 1 of the pizzas.

Since the question is asking for the amount of pizza left, the answer can be evaluated by subtraction operation:

Mathematical operations like subtraction exist.

It is employed to delete words or objects from the phrase.

As per the above concept, apply in the situation,

3 pizzas - 1 pizza = 2 pizzas.

Therefore, the correct answer is not listed among the options provided.

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Answer:

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

Given:

The difference is the amount of decrease:

Find the percentage decrease:

Therefore, the price of the car has been reduced by 17%.

The price of the car has been decreased by  of 17% percentage.

To find the percentage decrease of the price of the car

Calculate the difference between the original price and the reduced price

Divide difference by the original price, and then multiply by 100 to convert it to a percentage:

Percentage decrease = (reduction in price / original price) x 100%

The reduction in price is:

$17,500 - $14,525 = $2,975

The original price is:

$17,500

So the percentage decrease is:

(2975 / 17500) x 100% = 17%

Therefore, the price of the car has been decreased by 17%.

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The formula to calculate the future value of an investment with compound interest is:

A = P(1 + r/n)^(n*t)

where:

A = future value

P = principal (initial investment)

r = annual interest rate (as a decimal)

n = number of times interest is compounded per year

t = time (in years)

In this case, we have:

P = $200 (initial investment)

r = 20% = 0.20

n = 1 (compounded annually)

t = 6 (6 years)

So, we can plug these values into the formula:

A = 200(1 + 0.20/1)^(1*6)

A = 200(1.20)^6

A = $766.97 (rounded to the nearest cent)

Therefore, Robert will have approximately $766.97 in his retirement account after 6 years.

The negative change in the y value will shift the graph downwards.

When a graph of a figure or a point get a negative change in its y value it gets shifted downwards.

When, f(x) - a is f(x) shifted downward a units.

Ex. Shift 3 units down,

Before

y = x² +x, Point (x, y)

After

y = x² +x -3, Point (x, y-3)

Hence, the negative change in the y value will shift the graph downwards.

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When an optimistic tile is coupled to a negative tile in the provided framework a zero pair may be produced, giving rise to a net value of 0.

We can make a zero pair by using these as there are two x tiles as well as one negative x tile. We also have two negative and three plus sign tiles, which can be used to make one more pair of zeros. As a result, this approach allows for the creation of a pair zero pairs altogether.

We can put a minus x tile close to each of its positive x tiles to make the initial zero pair. Net value will be zero as a result of this.

We can put one negative tile behind two positive tiles to make the second zero pair. This will result in a net value of zero as well.

Overall, understanding the concept of zero pairs is essential in basic algebra and helps in simplifying expressions by eliminating terms that add upto zero.

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The calculated length of the rectangle is 10.5 cm

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

Six identical right-angled triangle

The length of the right-angled triangle is

base length = 7 cm

based on the arrangement, we have

Rectangle length = base length + 1/2 * base length

So, we have

Rectangle length = 7 + 1/2 * 7

Evaluate

Rectangle length = 10.5

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Answer:

[tex]{ \boxed{ \mathfrak{amswer}}} :{ \underline{ \tt{ \: { \alpha }^{2} + { \beta }^{2} = - 1} \: }}[/tex]

Step-by-step explanation:

From General equation of a polynomial:

✍️ x² - (Sum of roots)x + (Product of roots) = 0

Therefore;

[tex]{ \tt{f(x) = {x}^{2} - x + 1 = 0 }}[/tex]

From the equation,

[tex]{ \tt{ \alpha + \beta = 1}} - - - { \rm{sum}} \\ { \tt{ \alpha \beta = 1 }} - - - { \rm{product}}[/tex]

From the question:

[tex]{ \tt{ {( \alpha + \beta )}^{2} = ( \alpha + \beta )( \alpha + \beta ) }} \\ \\ { \tt{ {( \alpha + \beta )}^{2} = { \alpha }^{2} + 2 \alpha \beta + { \beta }^{2} }} \\ \\ { \tt{ {( \alpha + \beta )}^{2} = ( { \alpha }^{2} + { \beta }^{2} ) + 2 \alpha \beta }} \\ \\ { \boxed{ \tt{( { \alpha }^{2} + { \beta }^{2} ) = {{( \alpha + \beta )}^{2} - 2 \alpha \beta }}}}[/tex]

Therefore, from sum and product

[tex]{ \tt{ { \alpha }^{2} + { \beta }^{2} = (1) {}^{2} - 2(1) }} \\ = { \tt{1 - 2}} \\ = - 1[/tex]

The class interval containing the median speed is 30 < s < 40.

We must first establish the median position before we can locate the class interval holding the median speed.

By dividing the overall frequency by two, the median position can be calculated.

Total frequency = 12 + 16 + 18 + 2 + 2 = 50

Median position = 50 / 2 = 25

Now, we have to solve for the class interval that has the median position which is the 25th value.

20 < s < 30: Frequency is 12, cumulative frequency is 12 (Not containing the 25th value)

30 < s < 40: Frequency is 16, cumulative frequency is 12 + 16 = 28 (Contains the 25th value)

So, the class interval containing the median speed is 30 < s < 40.

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If Adam wants to play video games he will have to finish homework, clean the dishwasher, and clean the room so the time he spends in total is 148 minutes by arithmetic all the timings respectively.

To find the total time Adam spent doing homework and cleaning before playing video games,

we add the time he spent on each task: 48 minutes for homework + 25 minutes for cleaning out the dishwasher + 75 minutes for cleaning his room = 148 minutes.

Therefore, Adam had to spend 148 minutes doing homework and cleaning before playing video games.

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The question is -

Adam wanted to play his video games. His mother told him that he needed to finish his homework, clean out the dishwasher, and clean his room before playing video games. He completed his homework in 48 minutes. He took 25 minutes to clean out the dishwasher. He took 75 minutes to clean his room. How much time did Adam have to spend doing homework and cleaning before playing video games?

The environmental agency should sample at least 746 vehicles.

In order to determine how many cars should be sampled for a full investigation, we can use the formula for sample size:
n = (Z^2 * p * q) / E^2
where:
- n = sample size
- Z = the Z-score for the desired level of confidence (in this case, 1.645 for 90% confidence)
- p = the proportion of cars in the population with faulty emissions systems (which we can estimate as 12/60 = 0.2 based on the initial sample)
- q = 1 - p
- E = the desired margin of error (2% in this case, or 0.02)
Plugging in these values, we get:
n = (1.645^2 * 0.2 * 0.8) / 0.02^2
n ≈ 746
Therefore, the environmental agency should sample at least 746 vehicles for a full investigation in order to estimate the percentage of cars violating clean air emissions standards with a margin of error of 2% and 90% confidence.

Hence  ,To estimate the percentage of cars violating clean air emissions standards with a margin of error of 2% and 90% confidence, the environmental agency should sample at least 746 vehicles for a full investigation.

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The equation of the ellipse is given by  ( x - 2 )² / 25 + ( y - 2 )² / 16 = 1

Given data ,

Let the center of the ellipse be ( h , k ) = ( 2 , 2 )

Now , the length of the major axis is 2a = 10 units

The length of the minor axis 2b = 8 units

So , a = 5 and b = 4

Now , the standard for of equation of ellipse is

( x²/a² ) + ( y²/b² ) = 1

On simplifying , we get

( x - 2 )² / ( 5 )² + ( y - 2 )² / ( 4 )² = 1

( x - 2 )² / 25 + ( y - 2 )² / 16 = 1

Hence , the equation of ellipse is ( x - 2 )² / 25 + ( y - 2 )² / 16 = 1

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Answer: F,B,D

Hope this helps : )

Step-by-step explanation:

Answer:

B, C, F

Step-by-step explanation:

B, C, and F are the only correct statements

Draw the 2 triangles, correctly labeled, and compare them.  This makes it easy to visualize which choices are true vs. false.

The required circumference of the circle with a diameter of 97 cm is 304 cm.

The circumference of a circle can be calculated using the formula:

C = πd

Where 'd' is the diameter of the circle, and 'π' is a mathematical constant approximately equal to 3.14159.

In this case, the diameter of the circle is given as 97 cm. So we can substitute this value into the formula to get:

C = πd

C = π(97 cm)

C ≈ 304.35 cm

Rounding this answer to 3 significant figures gives:

C ≈ 304 cm

Therefore, the circumference of the circle with a diameter of 97 cm is 304 cm.

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Answer:

Step-by-step explanation:630

Answer: B

Explanation:

A + B = (2x - 7x² + 3) + (4x² - 12x) = 2x - 7x² + 3 + 4x² - 12x = -3x² -10x + 3

The time it takes the ball to hit the ground is 0.375 seconds.

Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.

To calculate the amount of time it takes the ball to hit the ground, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for t

Hence, the time is 0.375 seconds.

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Answer:

0.436 ≠ 0.064

Step-by-step explanation:

P(A and B)=P(A) x P(B)

0.436 = 0.4 x 0.16

0.436 ≠ 0.064

The constant of proportionality relating the number of miles y to the number of minutes x is 1/6.

To find the constant of proportionality, we can use the formula: y = kx. Where y represents the number of miles run, x represents the time taken in minutes, and k is the constant of proportionality. Coach Liba ran 9 miles in 54 minutes. We can use these values to solve for k: 9 = k(54)

Dividing both sides by 54, we get: k = 9/54 = 1/6. This means that for every 1 minute Coach Liba runs, he covers 1/6th of a mile. Or for every 6 minutes, he covers 1 mile.

The ratio of the number of miles run to the time taken in minutes is constant and equal to 1/6. This can help us predict how far Coach Liba will run in a given amount of time or how long it will take him to run a certain distance.

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a.  A statistical test used to help answer the question of whether an observed difference is real or just due to chance error- true

The statistical test referred to in the question is known as a hypothesis test. It is used to determine the probability that the observed difference between two groups or variables is not due to chance but rather represents a true difference. The test involves setting up a null hypothesis, which assumes that there is no difference between the groups or variables, and an alternative hypothesis, which assumes that there is a real difference.

The test calculates a p-value, which represents the probability of obtaining the observed difference by chance if the null hypothesis is true.

If the p-value is below a predetermined level of significance (usually 0.05), then the null hypothesis is rejected and the alternative hypothesis is accepted.

This means that the observed difference is considered real and not just due to chance error.

Hence, If the p-value is below a certain level of significance, the null hypothesis is rejected and the alternative hypothesis is accepted, indicating that the observed difference is real.

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Answer:

x = (-3 + sqrt(23)i) / 2 and x = (-3 - sqrt(23)i) / 2.

Step-by-step explanation:

To solve the quadratic equation -x^2 + 3x - 8 = 0, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

In this case, a = -1, b = 3, and c = -8. Substituting into the quadratic formula, we get:

x = (-3 ± sqrt(3^2 - 4(-1)(-8))) / 2(-1)

Simplifying the expression inside the square root:

x = (-3 ± sqrt(9 - 32)) / (-2)

x = (-3 ± sqrt(-23)) / (-2)

Since the square root of a negative number is not a real number, the solutions to this quadratic equation are complex numbers. We can simplify the expression by writing the solutions in terms of the imaginary unit i:

x = (-3 ± sqrt(23)i) / 2

Therefore, the solutions to the quadratic equation -x^2 + 3x - 8 = 0 are x = (-3 + sqrt(23)i) / 2 and x = (-3 - sqrt(23)i) / 2.