A building supply has two locations in town. The office receives orders from two of its best customers, each requiring 3/4-inch drywall board to be delivered. Customer A needs at least one hundred sheets delivered and Customer B needs at least one hundred-forty sheets delivered. Deliveries can be sent from either of the supply companies' warehouses. The warehouse on the north side of town has one hundred-sixty sheets in stock; the south-side warehouse has ninety sheets in stock. Delivery costs per sheet are as follows: $1. 50/board from the northern warehouse to Customer A,$1. 20/board from the northern warehouse to Customer B, $0. 80/board from the southern warehouse to Customer A, and $1. 10/board from the southern warehouse to Customer
В. 1. Find the shipping arrangement which minimizes costs. 2. What will be the minimum cost?
3. Will there be any product left in either warehouse after fulfilling the orders?

Answer:we know that all 3 sides are equal

so if side =a

then perimeter =3a

therefore

3a=6n-15

a=6n-15/3

a=2n-5

Answer:

since we already know that all  sides are equal

in order to make an expression the side will be represented by the variable b

and the perimeter will be represented by 3b, so

3b=6n-15

b=6n-15/3

so the variable b would = 6n-5 I belive or its 2n-5

I hope this helps someone even though its late, keera

Step-by-step explanation:

The function that shows the relationship between Bill's total weekly sales and total weekly income is P(x) = $300 + 0.02x.

The slope is 0.02. The slope is the rate at which weekly income increases. $300 is the y-intercept.

The total amount of weekly sales that Bill needs to earn a weekly income of $600 is $15,000.

The function that can be used to determine the total weekly income is a linear function. A linear function is a function that increases at a constant rate.

The form of a linear function is: f(x) = a + bx

Where:

a = intercept

b = slope

The linear function for the total weekly income is:

P(x) = salary + (commission x sales)

P(x) = $300 + (0.02 x x)

P(x) = $300 + 0.02x

Number of total sales that would make Bill earn a weekly income of $600 is:

$600 = $300 + 0.02x

$600 - $300 = 0.02x

$300 = 0.02x

x = $300 / 0.02

x = 15,000

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Answer:

d. -18

Step-by-step explanation:

f(-3) = 10x - 3x + 3

10(-3) - 3(-3) + 3

-30 + 9 + 3

-30 + 12

= -18

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The calculated sample size is approximately 8. Since we cannot have a fraction of a sample, the foreman should select a sample size of at least 8 to estimate the average time accurately.

To determine the required sample size, we can use the formula:

n = (Z * σ / E)²

Where:

n is the required sample size

Z is the z-score corresponding to the desired level of confidence (in this case, 95% confidence level)

σ is the sample standard deviation (34 minutes)

E is the desired margin of error (15 minutes)

The z-score corresponding to a 95% confidence level is approximately 1.96 (standard normal distribution).

Substituting the values into the formula:

n = (1.96 * 34 / 15)² ≈ (2.798)² ≈ 7.825 ≈ 8

The calculated sample size is approximately 8. Since we cannot have a fraction of a sample, the foreman should select a sample size of at least 8 to estimate the average time accurately.

Keep in mind that this calculation assumes a normal distribution of the data and that the sample standard deviation accurately represents the population standard deviation.

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For the simple harmonic motion equation d=2 sin(pi/3t), the period is 6 seconds.

The period of a simple harmonic motion is the time taken for one complete cycle of the motion. In this equation, d represents the displacement or position of the object at time t. The equation is in the form of sin function with the argument (pi/3)t. The general form of the equation for simple harmonic motion is d=A sin(ωt+φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle. To determine the period of this motion, we can use the formula T=2π/ω, where T is the period and ω is the angular frequency. In this case, ω=pi/3, so the period is T=2π/(pi/3)=6 seconds (rounded to the nearest second). Therefore, the object completes one full cycle of motion every 6 seconds.

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Answer:

They should do B analyze the data.

Step-by-step explanation: hope it helps

Answer:

it is B

Step-by-step explanation:

sorry if it is not right

Answer:

Undefined because the x values are the same

Step-by-step explanation:

Slope: y2 - y1 / x2 - x1

Slope: 7 - 10 / -3 - - 3

Slope: -3 / -3 + 3

Slope: -3 / 0

Slope: undefined

The probability that at least one of the four selected calculators is defective is approximately 0.7775, or 77.75%.

To find the probability that at least one of the selected calculators is defective, we can use the concept of complementary probability. We calculate the probability of none of the selected calculators being defective and subtract it from 1.

The total number of calculators in the group is 20 (defective) + 29 (no defects) = 49 calculators.

The probability of selecting a non-defective calculator in one draw is 29/49. Therefore, the probability of selecting four non-defective calculators in a row is (29/49)^4.

To find the probability of at least one defective calculator, we subtract the probability of none being defective from 1:

P(at least one defective) = 1 - P(none defective)

                       = 1 - (29/49)^4

Using this formula, we can calculate the probability.

P(at least one defective) ≈ 1 - (29/49)^4 ≈ 1 - 0.2225 ≈ 0.7775

Therefore, the probability that at least one of the four selected calculators is defective is approximately 0.7775, or 77.75%.

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The statement, "arccot x = 1/arctan x, as long as both functions arccot x and arctan x are both defined" is False because arctan(1/x) is equal to arccot(x).

A trigonometric expression is a mathematical expression that involves trigonometric functions such as sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions relate the angles of a triangle to ratios of sides of triangle.

We first let the trigonometric expression : y = arctan(1/x)

So, y = tan⁻¹(1/x),

tan(y) = 1/x,

this expression can be written as x = 1/ tany,

So, x = cot(y),

⇒ y = arcCot(x),

So, we have arctan(1/x) = arccot(x).

Therefore, the statement is False.

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Depends on how many people you are serving. If you are serving say 960 people it would be 4 batches or 2 cups.

Answer:

120

Step-by-step explanation:

1/2×240= 120

or half of 240 cause 1/2 is half of 1

Answer:

The mean temperature for March is higher than January's mean.

Step-by-step explanation:

I took the test. trust me and you will be set free ;D

The amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

As per the given problem:

Amount deposited = $60.00

Interest rate per year = 9%

The formula for calculating the interest is given by:

Interest = (Principal × Rate × Time)/100

Where Principal is the initial amount invested or deposited

Rate is the percentage of interest that you earn per annum

Time is the duration for which you want to calculate the interest

Putting the values in the above formula, we get:

Interest = (60 × 9 × 2)/100= (108 × 1)/1= $108

So, the amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

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To determine the location of the maximum tensile bending stress with respect to the neutral axis, you need to find the point where the distance (y) is maximum.

To calculate the maximum tensile bending stress, you need to know the moment of inertia of the cross-sectional shape and the distance from the neutral axis to the point of interest.

The formula to calculate the maximum tensile bending stress (σ) is:

σ = (M * y) / I

where:

- M is the bending moment applied to the material

- y is the distance from the neutral axis to the point of interest

- I is the moment of inertia of the cross-sectional shape

Please provide the values for the bending moment (M), the moment of inertia (I), and the cross-sectional shape to calculate the maximum tensile bending stress and determine its location with respect to the neutral axis.

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The town will use approximately 14,427.21 megaliters of water annually in 7 years if the usage continues to increase at a rate of 10% per year.

We can solve this problem using the formula for exponential growth:

A = A0 * (1 + r)^t

where A0 is the initial amount, r is the annual growth rate as a decimal, t is the time in years, and A is the amount after t years.

In this problem, A0 = 6,740 megaliters, r = 0.1 (since the annual growth rate is 10%), and t = 7 years (since we want to know how much water will be used in 7 years).

Substituting these values into the formula, we get:

A = 6,740 * (1 + 0.1)^7

Simplifying the right-hand side, we get:

A ≈ 14,427.21 megaliters

Therefore, the town will use approximately 14,427.21 megaliters of water annually in 7 years if the usage continues to increase at a rate of 10% per year.

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Answer:

slope of line w = - \(\frac{8}{4}\)

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \(\frac{5}{8}\) x + \(\frac{9}{4}\) ← is in slope- intercept form

with slope m = \(\frac{5}{8}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{\frac{5}{8} }\) = - \(\frac{8}{5}\)

Answer:

D. 22x^2-18x-15

Step-by-step explanation:

12x²-19x+4 + 10x²+x-19

22x²-18x-15

Answer:

17.99

Step-by-step explanation:

Trig Ratios:

Sin = Opposite over Hypotenuse

Cos = Adjacent over Hypotenuse

Tan = Opposite over Tangent

We can use trig ratio sine as we are given an angle ( 40° )and the hypotenuse (28) and we need to find its opposite side (w)

Recall that sin = opposite over hypotenuse

That being said we want to create an equation to solve for w

\(sin(40)=\frac{w}{28}\)

Now we solve for w

Step 1 multiply each side by 28

\(\frac{w}{28} *28=w\\sin(40)*28=28sin(20) = 17.99\)

we're left with w = 17.99

Let's simplify the expression step by step: Expand the squared term:

(x - 3y)² = (x - 3y)(x - 3y) = x² - 6xy + 9y²

Expand the second term:

3(x + y)(x − 4y) = 3(x² - 4xy + xy - 4y²) = 3(x² - 3xy - 4y²)

Expand the third term:

x(3x + 4y + 3) = 3x² + 4xy + 3x

Now, let's combine all the expanded terms:

(x - 3y)² + 3(x + y)(x − 4y) + x(3x + 4y + 3)

= x² - 6xy + 9y² + 3(x² - 3xy - 4y²) + 3x² + 4xy + 3x

Combining like terms:

= x² + 3x² + 3x² - 6xy - 3xy + 4xy + 9y² - 4y² + 3x

= 7x² - 5xy + 5y² + 3x

The simplified form of the expression is 7x² - 5xy + 5y² + 3x.

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Answer:

The answer is

\(y =1 \\ x = 25\)

Step-by-step explanation:

\(.5 + .02x = .25 + .03 \\ .01x = .25 \\ x = 25 \\ then \\ y = .5 + .02 \times 25 = 1\)

Answer:

D

Step-by-step explanation:

This system of equations describes the total amount of money in both accounts as a function of the number of weeks.

The amount of money in your account after x weeks would be 50+10x, and the amount of money in your friend's account after \($x$\) weeks would be 25+10x.

Therefore, the system of equations is:

y &= 50 + 10x \

y &= 25 + 10x

Simplifying the second equation, we get y=10x+25.

So the system of equations is:

y &= 50 + 10x \

y &= 10x + 25

\(\end{align*}\)The total quantity of money in both accounts is expressed as a function of the number of weeks by this system of equations.

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The waist-to-hip ratio for the client would be 0.763, which is considered a healthy ratio for women (less than 0.8) and an average ratio for men (less than 0.9).

To calculate the waist-to-hip ratio (WHR), you simply divide the measurement of your waist circumference by your hip circumference.

WHR = waist circumference / hip circumference

Using the measurements you provided, the calculation would be:

WHR = 29 inches / 38 inches = 0.763

Alternatively, if you prefer to use centimeters:

WHR = 74 cm / 97 cm = 0.763

Therefore, the waist-to-hip ratio for the client would be 0.763, which is considered a healthy ratio for women (less than 0.8) and an average ratio for men (less than 0.9).

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Answer:

$114.46

Step-by-step explanation:

40.51+73.95=114.46

The measures of variability for the two schools are:

Mountain View School: Range = 4, Variance = 9.1733, Standard deviation = 3.029 and Bay Side School: Range = 10, Variance = 7.84, Standard deviation = 2.8.

Standard deviation is  measure of  amount of variation or dispersion in set of data value. It is a statistical measure that tells us how much the data values deviate or vary from the mean or average value of the data set.

To calculate the measures of variability for the two schools, we need to find the range, variance, and standard deviation for each dataset.

Mountain View School:

Range: The smallest class size is 5 and the largest is 9, so the range is 9-5 = 4.

Variance: To calculate the variance, we need to find the mean first.

Mean = (5+6+8+9+8+2+0+10+2+4+5+6+8)/15 = 5.6

Then, we can find the variance using the formula:

Variance = Σ(xi - μ)²/n

= [(5-5.6)² + (6-5.6)² + (8-5.6)² + (9-5.6)² + (8-5.6)² + (2-5.6)² + (0-5.6)² + (10-5.6)² + (2-5.6)² + (4-5.6)² + (5-5.6)² + (6-5.6)² + (8-5.6)²]/15

= 9.1733

Standard deviation = √(9.1733) = 3.029

Bay Side School:

Range: The smallest class size is 0 and the largest is 10, so the range is 10-0 = 10.

Variance: To calculate the variance, we need to find the mean first.

Mean = (8+7+6+5+5+4+4+3+1+0+2+0+0+2+3+5)/15 = 3.6

Then, we can find the variance using the formula:

Variance = Σ(xi - μ)²/n

= [(8-3.6)² + (7-3.6)² + (6-3.6)² + (5-3.6)² + (5-3.6)² + (4-3.6)² + (4-3.6)² + (3-3.6)² + (1-3.6)² + (0-3.6)² + (2-3.6)² + (0-3.6)² + (0-3.6)² + (2-3.6)² + (3-3.6)² + (5-3.6)²]/15

= 7.84

Standard deviation = √(7.84) = 2.8

Therefore, the measures of variability for the two schools are:

Mountain View School: Range = 4, Variance = 9.1733, Standard deviation = 3.029

Bay Side School: Range = 10, Variance = 7.84, Standard deviation = 2.8

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Answer:Solve for x 2x-4=10 2x − 4 = 10 2 x - 4 = 10 Move all terms not containing x x to the right side of the equation. Tap for more steps... 2x = 14 2 x = 14 Divide each term in

Step-by-step explanation:

Step-by-step explanation:

x² + x - 2 = 0

x² + 2x - x - 2 = 0

x(x + 2) - 1(x + 2) = 0

(x + 2)(x - 1) = 0

x + 2 = 0 and x - 1 = 0

x = -2 and x = 1

So, f(x) has no solution if x = -2 or 1

Domain = {x | x ≠ 2 and x ≠ 1}

95% confident that the true population mean μ lies between 83.04 and 86.96

Confidence Interval

A confidence interval in statistics refers to the probability that a population parameter will fall between a set of values for a certain proportion of times. Analysts often use confidence intervals than contain either 95% or 99% of expected observations.

First need to determine whether dealing with means or proportions in this problem. The sample and population mean, that  are dealing with means.

One sample mean, this mean creating a confidence interval for one sample (1 Sample  t Interval)

Normally we would check for conditions, but since this is not formulated as a real-world scenario type problem, it is hard to check for randomness and independence. Therefore excluding conditions from this answer.

The formula for constructing a confidence interval for means is as follows:

x ± t ( σ / \(\sqrt{n}\) )

The variables are:

x = 85

σ = 8

n = 64

Plug these values into the formula for the confidence interval

85 ± t ( 8 / \(\sqrt{64}\))

Finding the Critical Value (t)

In order to find t, use this formula:

\(\frac{1 - C}{2} = A\)

The z-score associated with A will give us t

So plug in the confidence interval 95% (.95) into the formula

\(\frac{1 - 0.95}{2} = 0.25\)

Use the calculator or a t-table to find the z-score associated with this area under the curve

t = 1.96

Constructing Confidence Interval

Finish the confidence interval created

= 85 ± 1.96 ( 8 / \(\sqrt{64}\) )

The confidence interval using this formula, to be

(83.04, 86.96)

Interpreting the Confidence Interval

95% confident that the true population mean μ lies between 83.04 and 86.96

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Using the empirical rule, we can determine that approximately 15.87% of IQ scores are at least 77.

According to the empirical rule, for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

To find the percentage of IQ scores that are at least 77, we need to calculate the z-score for 77 using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

z = (77 - 101) / 12 = -24 / 12 = -2

Since 77 is 2 standard deviations below the mean, we know that approximately 95% - 2% = 15.87% of the IQ scores will be at least 77. Therefore, approximately 15.87% of IQ scores are at least 77, based on the empirical rule.

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