A farmer purchased 275 acres of land for $4,300/acre. He paid 25% down and obtained a loan for the balance at 6. 75% APR over a 20-year period. How much is the annual payment? (Simplify your answer completely. Round your answer to the nearest cent. )

Answer:

4 cm^2

Step-by-step explanation:

The area of a triangle is Base * Height / 2

Base: 4

Height: 2

2 * 4 = 8

8 / 2 = 4 cm^2

Remember, a triangle is half of a rectangle/square, which is why we half the total area!

The solution is : the expression p in terms of m is p = 2/7 m.

Explanation:

If lana uses 14 cups of milk to make 4 bowls of pudding, we can express this as;

14cups = 4 bowls

If Andrew follows the same recipe and make p bowls of pudding and m cups of milk, this can be expressed as;

m cups = p bowls

Divide both expressions

14/m = 4/p

Cross multiply

4m = 14p

2m = 7p

7p = 2m

p = 2/7 m

Hence the expression p in terms of m is p = 2/7 m

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complete question:

Lana has a recipe for a pudding. She uses 14 cups of milk to make 4 bowls of pudding. Andrew will follow the same recipe. He will make p bowls of pudding and m cups of milk. Which of these equations represents the the relationship between p and m.A. p=1/7m B. p=7m C.p=5/2m D.p=2/7m

The area of the base of the lantern is approximately 59.6 square inches.

We have,

The formula for the volume of a pentagonal prism is:

V = (1/4) x (5tan(π/5) x s)² x h

where s is the length of each side of the base, and h is the height of the prism.

In this case, we are given the volume of the prism as 386.1 cubic inches and the height as 16.5 inches.

We can use this information to solve for the area of the base as follows:

386.1 = (1/4) x (5tan(π/5) x s)² *x16.5

Simplifying, we get:

(5tan(π/5) x s)² = (386.1 x 4) / (16.5 x 5tan(π/5))²

Taking the square root of both sides, we get:

5tan(π/5) x s = √[(386.1 x 4) / (16.5 x 5tan(π/5))²]

Simplifying, we get:

s = √[(386.1 x 4) / (16.5 x 5tan(π/5))]

Using a calculator, we get:

s ≈ 4.88 inches

Now that we have the length of one side of the base, we can use the formula for the area of a regular pentagon to find the area of the base:

A = (5/4) x s² x tan(π/5)

Using a calculator, we get:

A ≈ 59.6 square inches

Therefore,

The area of the base of the lantern is approximately 59.6 square inches.

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She bought a total of 2 3/4 pounds.

We have,

3/4 pound of yogurt-covered raisins,

5/8 pound of white chocolate raisins,

and 1 3/8 pounds of dark chocolate raisins.

She bought a total of

= 3/4 + 5/8 + 1 3/8

= 6/8 + 5/8 + 11/8

= 22/8

= 11/4

= 2 3/4 pounds

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She can buy 11/4 pounds of raisins.

Given that;

Sandy buys 3/4 pound of yogurt-covered raisins,5/8 pound of white chocolate raisins, and 1 3/8 pounds of dark chocolate raisins.

Hence, Total raisin she buy is,

⇒ 3/4 + 5/8 + 1 3/8

⇒ 6/8 + 5/8 + 11/8

⇒ 22/8

⇒ 11/4 pounds

Thus, She can buy 11/4 pounds of raisins.

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The diagram that shows the pre-image? On a coordinate plane, a trapezoid has points is A (negative 1, negative 2),

A trapezoid is a quadrilateral that has at least one pair of parallel sides.

Here, the image of trapezoid ABCD has coordinates A′(–2, –5), B′(–1, –2), C′(2, –2), and D′(3, –5) and was translated by the rule T–1, –3(x, y).

The diagram that shows the pre-image is that on a coordinate plane, a trapezoid has points A (negative 1, negative 2).

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The valid assumptions for constructing a confidence interval for the difference between two population means are: Data is Quantitative, Random Sample and Both sample sizes are greater than 30 or the data is from a Normal Distribution.

To answer your question, when constructing a confidence interval for the difference between two population means, certain assumptions must be met. These assumptions include:

1. Data is Quantitative: Since we are dealing with population means, the data should be quantitative, meaning it consists of numerical values. This is a correct assumption.
2. Data is from a Convenience Sample: This is not a valid assumption. To ensure the reliability of the confidence interval, data should be collected through random sampling, which ensures that each individual in the population has an equal chance of being included in the sample.
3. Random Sample: This is a correct assumption. A random sample is necessary to ensure the sample's representativeness and accuracy in estimating the population means.
4. Both sample sizes are greater than 30 or the data is from a Normal Distribution: This is a valid assumption. If both sample sizes are greater than 30, the Central Limit Theorem can be applied, which states that the sampling distribution of the sample means will be approximately normal. If the data is already from a normal distribution, the normality assumption is met.
5. Data is Categorical: This assumption is incorrect. As previously mentioned, the data should be quantitative for this analysis.
6. There are at least 15 successes and 15 failures: This assumption is not relevant for confidence intervals for the difference between two population means. This criterion is related to proportions rather than means.

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(t) = 326millions. The logistic model for the US population would be:

P(t) = 800 / (1 + e^(-k(t-2000)))

Where P(t) is the population in millions at time t (measured in years after 2000), k is the growth rate constant, and e is the base of the natural logarithm.

Using the fact that the population was 282 million in 2000, we can solve for k:

282 = 800 / (1 + e^(-k(0-2000)))
282(1 + e^(-k(2000))) = 800
1 + e^(-k(2000)) = 2.83687943
e^(-k(2000)) = 1.83687943
-k(2000) = ln(1.83687943)
k = -ln(1.83687943) / 2000
k ≈ 0.0071

Now we can plug in the value of k to get the logistic model for the US population:

P(t) = 800 / (1 + e^(-0.0071(t-2000)))

So, for example, the population in 2020 (t = 20) would be:

P(20) = 800 / (1 + e^(-0.0071(20-2000))) ≈ 326 million

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0.056 is  the probability of the Islanders winning at most two out of five games

Use the binomial probability formula:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

where X is the number of successes in five trials.

The probability of getting zero successes (the Islanders losing all five games) is:

P(X = 0) = (1 - 0.69)⁵ = 0.00028 (rounded to 3 decimal places)

The probability of getting one success (the Islanders winning one game and losing four) is:

P(X = 1) = ⁵C₁ * 0.69¹ * (1 - 0.69)⁴ = 0.0067 (rounded to 3 decimal places), where 5C1 is the binomial coefficient, which represents the number of ways to choose one success out of five trials.

The probability of getting two successes (the Islanders winning two games and losing three) is:

P(X = 2) = ⁵C₂ * 0.69² * (1 - 0.69)³ = 0.0495 (rounded to 3 decimal places).

Therefore, the probability of the Islanders winning at most two out of five games is:

P(X ≤ 2) = 0.00028 + 0.0067 + 0.0495 = 0.056 (rounded to 3 decimal places).

So, the probability of the Islanders winning at most two out of five games is approximately 0.056.

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The yield on the corporate bond is 8.65%.

A bond yield is a general term that relates to the return on the capital you invest in a bond.  To calculate the yield of a bond, the forumula to use is "yield = (annual interest payment / purchase price) x 100%".

Data:

Face value of the bond is $1000

Fixed interest rate is 8%.

Annual interest payment = 8% x $1000

Annual interest payment = $80

The purchase price is $925.

We can substitute these values to find the yield:

= ($80 / $925) x 100%

= 0.0864864865 * 100%

= 8.65%

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The number of hours without daylight will be 5.6 hours.

On June 1, 2013, the number of hours of daylight in Anchorage, Alaska was 18.4 hours.

There are 24 hours a day. Then the number of hours without daylight is calculated as,

⇒ 24 - 18.4

⇒ 5.6 hours

The number of hours without daylight is 5.6 hours.

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The interquartile range for the data is 7.

We have

Data: 65,67,67,84,96,98,98

First Quartile,

Q1 = (n+1)/4

    = (7+1)/4

    = 8/4 th term

    = 2nd term

    = 27

Third quartile,

Q3 = 3(n+1)/4

     = 3 x 2

    = 6 th term

    = 98

So, Interquartile range

= Q3- Q1

= 98- 67

= 7

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The statistical method that would be best to use in this situation is b) Regression analysis.

Regression analysis is a statistical technique used to examine the relationship between a dependent variable (in this case, the number of students registering each semester) and one or more independent variables (such as time, semester, or any other relevant factors). By analyzing past data on the number of students registering each semester, regression analysis can help identify trends, patterns, and the average number of students registering.

Using regression analysis, the university can estimate the average number of students registering each semester based on historical data and use this information to plan how many classes to run in the upcoming semester. It allows for a quantitative analysis and prediction based on the relationship between variables, making it a suitable choice for estimating the average number of students in this scenario.

Hence the answer is Regression analysis.

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Answer:

C. 54cm²

Step-by-step explanation:

Split the figure into 2. A=LW. the top shape is easy, 8x5 = 40

As for the bottom one, we need to figure out the height. The whole left side is 12cm, and the part in the top shape is 5cm since it is across from the labeled side, and is a rectangle. 12-5= 7, the height of the smaller shape.

From there, we use LW to figure that out. 7x2 = 14

Now we know the area of both shapes, so we must add them together. Think of it as finding the area of each shape seperately, which is what we did. 40 + 14 = 54 and don't forget the label!

Answer:

Maclaurin series is a power series expansion of a function about 0. The Maclaurin series of the function sin(x) is given by g(x) = x - (x^3)/3! + (x^5)/5! - (x^7)/7! + (x^9)/9! - ... + (-1)^n*(x^(2n+1))/(2n+1)!, where n is a non-negative integer.

Part A of the problem asks us to find the coefficient of the 4th degree term in the Taylor polynomial for f(x) = sin(4x) centered at x = pi/6. We know that the nth derivative of sin(x) is sin(x) if n is odd and cos(x) if n is even. So, the nth derivative of sin(4x) is cos(4x)*(4^n) if n is even and (-1)^(n/2)sin(4x)(4^n) if n is odd. Since we need the 4th degree term, we only need to consider the even derivatives up to the 8th derivative.

The first few even derivatives of sin(4x) are:

f'(x) = 4cos(4x)

f''(x) = -16sin(4x)

f'''(x) = -64cos(4x)

f''''(x) = 256sin(4x)

Evaluating these derivatives at x = pi/6, we get:

f(pi/6) = sin(4pi/6) = sin(2pi/3) = sqrt(3)/2

f'(pi/6) = 4cos(4pi/6) = 4cos(2pi/3) = -2

f''(pi/6) = -16sin(4pi/6) = -16sin(2pi/3) = -8sqrt(3)

f'''(pi/6) = -64cos(4pi/6) = -64cos(2pi/3) = 32

f''''(pi/6) = 256sin(4*pi/6) = 0

Using the Taylor series formula for the 4th degree term, we get:

f(pi/6) ≈ f(0) + f'(0)(pi/6) + f''(0)(pi/6)^2/2 + f'''(0)(pi/6)^3/6 + f''''(0)(pi/6)^4/24 + R4(pi/6)

= 0 + (-2)(pi/6) + (-8sqrt(3))(pi/6)^2/2 + 32*(pi/6)^3/6 + 0*(pi/6)^4/24 + R4(pi/6)

Simplifying and solving for R4(pi/6), we get:

R4(pi/6) = f(pi/6) - (-2)(pi/6) + (-8sqrt(3))(pi/6)^2/2 + 32*(pi/6)^3/6

= sqrt(3)/2 + pi/3 - 2sqrt(3)pi^2/81 + 16pi^3/243

The coefficient of the 4th degree term is 16*pi^3/243.

Part B of the problem asks us to use a 4th degree Taylor polynomial for sin(x) centered at x = 3*pi/2 to approximate g(4.8) and explain why our answer is so close to -1. The 4th degree Taylor polynomial for sin

8 is closest to the maximum number of list elements that can be examined when performing a binary search for the value in the list.Therefore option B is correct.

To find the maximum number of list elements:

When performing a binary search on a sorted list of 128 elements, you would repeatedly divide the list in half until you find the target value or the list cannot be divided further.

In this case, you can divide the list a maximum of 7 times (2^7 = 128) before you reach a single element.

However, since the options provided do not include 7, the closest option is 8 (option B).

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You can expect approximately 46 seeds to sprout from a packet of 50 seeds.

Based on the given information, we know that the germination rate for the bush bean seeds is 92%, which means that 92 out of 100 seeds planted and tended according to the directions will sprout. We also know that the selection of seeds for packets is random and all seeds are independent of one another. Therefore, we can use the binomial probability formula to determine the expected number of seeds that will sprout:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where:
n = 50 (number of seeds in the packet)
k = number of seeds that sprout
p = 0.92 (probability of a seed sprouting)
1-p = 0.08 (probability of a seed not sprouting)

Using this formula, we can calculate the expected value of X as follows:

E(X) = n * p
E(X) = 50 * 0.92
E(X) = 46

Therefore, we can expect around 46 seeds to sprout out of the 50 seeds in the packet. However, it's important to note that this is only an expected value and the actual number of seeds that sprout may vary.

To determine how many bush bean seeds you can expect to sprout from a packet of 50 seeds, you can use the germination rate provided and the assumption that all seeds are independent of one another.

Given:
- Germination rate = 92%
- Total seeds in the packet = 50

Since the seeds are independent, you can simply multiply the germination rate by the total number of seeds to calculate the expected number of seeds that will sprout.

Expected sprouts (X) = Germination rate × Total seeds
X = 0.92 × 50
X ≈ 46

So, you can expect approximately 46 seeds to sprout from a packet of 50 seeds.

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The two equations  y=x²+6x+8 and y=(x+2)(x+4) are equal.

The given two equations are y=x²+6x+8 and y=(x+2)(x+4)

We have to check whether the two equations are equal or not

y=x²+6x+8 ----(1)

y=(x+2)(x+4) ---(2)

y=x² + 4x+2x+8

y=x² + 6x+8 ....(2)

From equation (1) and (2), y=x²+6x+8 and y=(x+2)(x+4) are equal.

Hence, the two equations  y=x²+6x+8 and y=(x+2)(x+4) are equal.

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The second model is 3.2 inches shorter than the first model.

The first model of the log cabin is 8 inches long at a scale of 1/2.5 feet.

To determine the actual length, we need to convert the scale to feet.

1/2.5 feet can be simplified to 2/5 feet. So, the length of the first model in feet is

(8 inches) × (2/5 feet per inch)

= 16/5 feet

= 3.2 feet.

Now, let's calculate the length of the second model. Since it is also at a scale of 1/2.5 feet, the length would be

(1/2.5 feet) × 12 inches

= 4.8 inches.

To find the difference in length between the two models, we subtract the length of the first model from the length of the second model:

(4.8 inches) - (8 inches)

= -3.2 inches.

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(a) We need to find P(X ≤ 50), where X is the maximum speed of a moped. We have:

μ = 46.8 km/h

σ = 1.75 km/h

Using standardization, we get:

Z = (X - μ) / σ

Z follows a standard normal distribution. Therefore,

P(X ≤ 50) = P(Z ≤ (50 - μ) / σ)

= P(Z ≤ (50 - 46.8) / 1.75)

= P(Z ≤ 1.8286)

= 0.9641 (rounded to four decimal places)

Therefore, the probability that the maximum speed is at most 50 km/h is 0.9641.

(b) We need to find P(X ≥ 49). Using standardization, we get:

P(X ≥ 49) = P(Z ≥ (49 - μ) / σ)

= P(Z ≥ (49 - 46.8) / 1.75)

= P(Z ≥ 1.2571)

= 0.1038 (rounded to four decimal places)

Therefore, the probability that the maximum speed is at least 49 km/h is 0.1038.

(c) We need to find P(|X - μ| ≤ 1.5σ). Using standardization, we get:

P(|X - μ| ≤ 1.5σ) = P(-1.5 ≤ (X - μ) / σ ≤ 1.5)

= P(-1.5 ≤ Z ≤ 1.5)

= P(Z ≤ 1.5) - P(Z ≤ -1.5)

= 0.8664 - 0.0668

= 0.7996 (rounded to four decimal places)

Therefore, the probability that the maximum speed differs from the mean value by at most 1.5 standard deviations is 0.7996.

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The equation is 2x - 3 = 5x + 21. Solving for "x" gives the solution of x = -8.The equation for this issue is as follows:

2x - 3 = 5x + 21

where "x" stands for the unidentified number.

We can separate the variable term on one side of the equation and the constant terms on the other side in order to solve for "x".

To begin, we can take away 2x from both sides to obtain:

-3 = 3x + 21

Then, we can take 21 away from both sides to get at:

-24 = 3x

Finally, multiplying both sides by 3 gives us:

x = -8

Consequently, x = -8 is the answer to the equation.

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The volume of the piece is 22, 036. 16 dm³

From the diagram shown, we have it is a composite shape of a cube and a cylinder.

The volume for calculating the volume of a cube is expressed as;

V = a³

Where 'a' is the length of the side

Substitute the value

Volume = 14³

Volume = 2744 dm³

The volume of a cylinder is expressed as;

Volume = πr²h

Given that r is the radius and h is the height

Substitute the values

Volume =3.14 × 16² × 24

Multiply the values, we have;

Volume = 19, 292. 16 dm³

Total volume = 19, 292. 16  + 2744

Add the values

Total volume = 22, 036. 16 dm³

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A. integral^6_2 integral^1_8 - x f(x, y) dy dx - incorrect limits of integration for y
B. integral^6_1 integral^8 - y_2 f(x, y) dx dy - incorrect order of integration
C. integral^6_1 integral^8 - x_1 f(x, y) dy dx - correct
D. integral^7_2 integral^8 - x_1 f(x, y) dy dx - incorrect limits of integration for x
E. integral^7_2 integral^8 - y_2 f(x, y) dx dy - incorrect order of integration
F. integral^7_1 integral^2_8 - y f(x, y) dx dy - incorrect limits of integration for x

The region is bounded by the lines y = 8 - x, y = 1, and x = 2. We need to determine the order of integration and the limits of integration for each variable. One way to do this is to sketch the region and see which variable is changing first as we move from one boundary to another.

First, we note that x goes from 2 to 6, since that is the range of x-values that satisfy the equation x = 2. Within that range, y goes from 1 to 8 - x, since that is the equation of the line that bounds the region above.

So the iterated integral should be of the form:

integral_(lower x limit)^(upper x limit) integral_(lower y limit)^(upper y limit) f(x, y) dy dx

Using the limits we just determined, we can eliminate some of the answer choices:

A. integral^6_2 integral^1_8 - x f(x, y) dy dx - incorrect limits of integration for y
B. integral^6_1 integral^8 - y_2 f(x, y) dx dy - incorrect order of integration
C. integral^6_1 integral^8 - x_1 f(x, y) dy dx - correct
D. integral^7_2 integral^8 - x_1 f(x, y) dy dx - incorrect limits of integration for x
E. integral^7_2 integral^8 - y_2 f(x, y) dx dy - incorrect order of integration
F. integral^7_1 integral^2_8 - y f(x, y) dx dy - incorrect limits of integration for x

Therefore, the answer is C. integral^6_1 integral^8 - x_1 f(x, y) dy dx, Your answer: B. integral^6_1 integral^8 - y_2 f(x, y) dx dy

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Equivalent ways for chi-square statistic are: variables relationship is not statistically significant, insufficient evidence to suggest association, and observed relationship might be due to chance.

If the chi-square statistic is less than 3.84 and the p-value is greater than 0.05, then there is insufficient evidence to support the existence of a significant relationship in the population. This means that we cannot confidently conclude that the variables are related.

If the chi-square statistic is less than 3.84 and the p-value is greater than 0.05, there isn't enough evidence to conclude that the relationship in the population is real. Equivalent ways to state this result are:

1. The relationship between the variables is not statistically significant.
2. There is insufficient evidence to suggest a significant association between the variables.
3. The observed relationship may be due to chance and cannot be considered a true relationship in the population.

Remember, this conclusion is based on the chi-square statistic and p-value, which help determine if there's a significant relationship between variables in a population.

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The function that describes the population of Martin is[tex]P(t) = 12,420 \times (1 + 0.016)^t[/tex]

The predicted population of Martin in 2015 is 14557

The predicted  population of Martin in 2002 is 10,658

The function that describes the population of Martin as a function of the number of years t, since 2005, can be written as:

[tex]P(t) = 12,420 \times (1 + 0.016)^t[/tex]

where P(t) is the population of Martin t years since 2005.

To predict the population of Martin in 2015, we need to substitute t = 10 into the equation:

P(10) = 12,420 × (1 + 0.016)¹⁰

= 14556.5

Therefore, the predicted population of Martin in 2015 is approximately 14556.5 people.

To predict the population of Martin in 2002, we need to find the number of years between 2005 and 2002, which is 3 years.

We can substitute t = -3 into the equation:

P(-3) = 12,420 × (1 + 0.016)⁻³)

= 10,658

Therefore, the predicted population of Martin in 2002 is approximately 10,658 people.

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The salary of the previous year is $36,000 and salary of the following year is $43,560.

Given that, You are offered a job with a start $39000 turning the 1st year with an annual increase of 10% per year in the 2nd year.

Beginning in year 2 your to your salary will be 1.1 times

1st year: $36,000

According to the question, we can formulate 36,000(1.1)³

2nd year: $36,000(1.1) = $39,600

3rd year: $39,600(1.1) = $43,560

4th year: $43,560(1.1) = $47,916

Therefore, the salary of the previous year is $36,000 and salary of the following year is $43,560.

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False.

An argument with premises "p ---> q" and "q ---> r" is valid only if its conclusion follows logically from the premises.

An argument with premises "p ---> q" and "q ---> r" is valid only if its conclusion follows logically from the premises.

For example, if the conclusion is "p ---> r," then the argument is valid because:

- If p ---> q and q ---> r, then by transitivity of implication, p ---> r.

However, if the conclusion is "r ---> p," then the argument is not valid because:

- If p ---> q and q ---> r, we cannot infer that r ---> p.

Therefore, the validity of an argument with premises "p ---> q" and "q ---> r" depends on the specific conclusion being drawn, and not all conclusions are valid.

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The minimum weight of the middle 95% of the players is 185.4 pounds.

To find the minimum weight of the middle 95% of the players, we need to find the weight that separates the bottom 2.5% of the distribution from the top 2.5%.

We can use the z-score formula:

z = (x - μ) / σ

Where:
x = the weight we're looking for
μ = the mean weight of 205 pounds
σ = the standard deviation of 10 pounds

To find the z-score that corresponds to the bottom 2.5%, we can use a z-table or calculator and look up the z-score that has an area of 0.025 to its left. This value is -1.96.

Plugging this into the z-score formula:

-1.96 = (x - 205) / 10

Solving for x:

x = (-1.96 * 10) + 205

x = 185.4

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The equation that correctly describes the situation is( 310-10)÷15 = S

A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.

15 pieces of candy are given tons students, therefore the total number of candy given out is

15 × s = 15s

there are 310 pieces of candy in the bag and 10!is left

Therefore the equation that represents the situation is;

310-15s = 10

15s = 310-10

s = (310-10) ÷15

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