a waste management company is designing a rectangular construction dumpster that will be twice as long as it is wide and must hold 20 yd^3 of debris. find the dimensions of the dumpster that will minimize its surface area.

Answer: a=2

7a=14

a=14/7

a=2

The expression represents the constraint that the amount of fat in the cookie should not deviate from the target fat content by more than 1.8 grams per cookie is |f - 5| ≤ 1.8

To express the difference between the fat in a cookie from the new recipe and the target fat content, we can use an expression. Let's represent the amount of fat in a cookie from the new recipe as f. Then, the difference between the fat in the cookie and the target fat content of 5 grams per cookie can be expressed as:

|f - 5|

The vertical bars around the expression indicate the absolute value, which means that we want the difference to be positive, regardless of whether f is greater or less than 5.

Now, we also know that the company will accept a difference of up to 1.8 grams per cookie. This means that the expression above should be less than or equal to 1.8:

|f - 5| ≤ 1.8

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Complete Question:

The Billing sly Cookie Company is experimenting with a new low-fat cookie recipe. The management wants the bakers to come up with a cookie that is low in fat but still has good taste. The company decides on a target fat content of 5 grams per cookie. In order to be labeled low-fat, a difference of 1.8 grams per cookie is acceptable. This means the amount of fat should be no more than 1.8 grams above 5 or no more than 1.8 grams below 5.

Write an expression that represents the difference between the fat in a cookie from the new recipe and the target fat content. Use f to represent the amount of fat in a cookie from the new recipe.

Answer:

2072

Step-by-step explanation:

Multiply 14 x 37

518 x 4

2072

Answer: $2,072 a month

Step-by-step explanation:

multiply 14 by 37 to see her weekly rate which is $518 a week. then multiply  518 by 4 (because there are about 4 weeks in a month). then you get the answer of $2,072

Noah sold 10 small avocados and 20 large avocados.

Let's assume that Noah sold "x" small avocados and "y" large avocados.

From the given information, we can write two equations:

x + y = 30 (since Noah sold a total of 30 avocados)

0.35x + 0.50y = 13.50 (since Noah made $13.50)

Now, we can use any method to solve these equations, such as substitution or elimination. Here, we will use the substitution method:

From the first equation, we can write:

x = 30 - y

Substituting this value of x in the second equation, we get:

0.35(30 - y) + 0.50y = 13.50

Simplifying this equation, we get:

10.50 - 0.35y + 0.50y = 13.50

0.15y = 3

y = 20

Substituting this value of y in the equation x = 30 - y, we get:

x = 30 - 20 = 10

Therefore, Noah sold 10 small avocados and 20 large avocados.

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There is a 95% probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud.

To find the probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud, we need to use the formula for the margin of error:

[tex]$$E = z_{\alpha/2}\sqrt{\frac{p(1-p)}{n}}$$[/tex]

where E is the margin of error, [tex]$z_{\alpha/2}$[/tex] is the critical value for the desired confidence level (let's assume 95%, so [tex]$z_{\alpha/2} = 1.96$[/tex]), p is the population proportion of websites experiencing click fraud, and n is the sample size.

We know that p=0.15, so we can plug in the values:

[tex]$$E = 1.96\sqrt{\frac{0.15(1-0.15)}{400}} = 0.05$$[/tex]

So the margin of error is 0.05. This means that there is a 95% probability that the sample proportion will be within 0.05 of the population proportion experiencing click fraud.

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The value of x is 5

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. All diameters are chord and but all chords are not diameter.

Since the value of the chords are thesame, the arc length RS and PQ are thesame.

Therefore ;

x+17 = 4x+2

collect like terms

4x -x = 17-2

3x = 15

divide both sides by 3

x = 15/3

x = 5

therefore the value of x is 5

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The probability of hitting the black circle is closer to 0 and the probability of hitting the white portion of the target is closer to 1.

What is probability?

Probability refers to the numerical measure of the likelihood or possibility of a specific event taking place. It is a mathematical concept that involves calculating the ratio of the number of desired outcomes to the total number of possible outcomes. Probability ranges from 0 (representing an impossible event) to 1 (representing a certain event), with values in between indicating the degree of likelihood. Probability is widely used in various fields, including mathematics, statistics, science, engineering, finance, and social sciences, to make predictions, analyze data, and make decisions under uncertainty.

Explanation of the given questions :

Part A: The black circle has a radius of 1 unit and its center is the same as that of the square. Therefore, its diameter is 2 units, which is much smaller than the side length of the square, which is 11 units. This means that the area of the circle is much smaller than the area of the square.

Therefore, the probability of hitting the black circle is closer to 0.

Part B: The white portion of the target is the area of the square minus the area of the black circle. The area of the square is [tex]11 x 11 = 121[/tex] square units.

The area of the circle is [tex]\pi \times r^2 = \pi\times 1^2 = \pi[/tex] square units, which is approximately 3.14 square units. Therefore, the area of the white portion of the target is [tex]121 - 3.14 = 117.86[/tex] square units.

Since this is much larger than the area of the black circle, the probability of hitting the white portion of the target is closer to 1.

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The quadratic function that only has one root at 3 and passes through the point (0,4) is: f(x) = (4/9)(x - 3)^2

A quadratic equation is a polynomial equation of degree 2, meaning that the highest exponent of the variable is 2. It has the general form:

ax^2 + bx + c = 0

If a quadratic function has only one root at 3, then it must be of the form:

f(x) = a(x - 3)^2

where a is a constant. This is because a quadratic function with only one root must have a double root, meaning that the parabola only touches the x-axis at that point and does not cross it. And a quadratic function with vertex at (3,0) and opening upwards satisfies this condition.

To determine the value of a, we can use any additional information that may be provided, such as the value of the function at another point. For example, if we know that f(0) = 4, then we can substitute these values into the equation to get:

4 = a(0 - 3)^2

4 = 9a

a = 4/9

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The quadratic function that has only one root at 3 and passes through (0,4) is: [tex]f(x)=(\frac{4}{9} )(x-3)^{2}[/tex]

A quadratic equation is a second-degree algebraic problem in x. In its standard form, the quadratic equation is [tex]ax^2+bx+c=0[/tex], where an as well as b are the coefficients, x is the variable, and c is the value of the constant component. The essential requirement for a formula to be a quadratic equation is that the coefficient of [tex]x^2[/tex] is not zero (a 0). When writing an equation with quadratic equations in conventional format, the [tex]x^2[/tex] term comes first, then the x term, and lastly the constant term.

A quadratic equation is a polynomial expression of degree 2, which means that the variable's greatest exponent is 2. It takes the following basic form:

[tex]ax^2+bx+c=0[/tex]

If the quadratic function has only one root at 3, it must have the following form:

[tex]f(x)=a(x-3)^2[/tex]

This requirement is satisfied by a quadratic function with a vertex at (3,0) and an opening upwards.

We know that f(0) = 4, so we can plug these numbers into the equation to get:

[tex]4=a(0-3)^2[/tex]

simplify the above equation

4 = 9a

The value is,

a = 4/9

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Answer:

To summarize the typical daily revenue of the food truck now, we would use the new mean of the daily revenue, which takes into account the new sale of $7,100. We can add this new value to the previous sum of daily revenues and divide the total by the number of days to find the new mean:

New mean = (total sum of daily revenues + $7,100) / (number of days + 1)

This would give us the updated measure of center that reflects the new data point.

The mean daily revenue of the food truck now is $6,550.

The average is calculated as the product of all values divided by all possible values. It can also be described as mean. The mean in statistics is the average value for the particular sample or collection of data. It is determined by dividing the sum of the total number of observations by the total number of observations.

To summarize the typical daily revenue of the food truck now, we would use the mean as the measure of the center.

We can calculate the mean daily revenue by adding the daily revenues from the two days ($6,000 + $7,100 = $13,100) and dividing by the number of days (2).

Mean daily revenue = (Total revenue) / (Number of days) = $13,100 / 2 = $6,550

Therefore, the mean daily revenue of the food truck now is $6,550.

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As per the given statement, the quadratic equation is to be used to find the exact solutions to this equation, and the quadratic equation is given by [tex]ax² + bx + c = 0[/tex].

To solve the quadratic equation, we can use the quadratic formula given by[tex]x = (-b ± sqrt(b² - 4ac)) / 2a[/tex] Where x is the variable, a, b, and c are coefficients with a ≠ 0, and sqrt is the square root symbol.To find the exact solutions to this equation, we can use the quadratic formula with a = 2, b = 6, and c = 12.

Substituting these values in the quadratic formula, we get

[tex]x = (-6 ± sqrt(6² - 4 × 2 × 12)) / 2 × 2= (-6 ± sqrt(36 - 96)) / 4= (-6 ± sqrt(-60)) / 4= (-6 ± i√60) / 4= (-3 ± i√15) / 2[/tex]

Hence, the exact solutions to the given equation are [tex](-3 + i√15) / 2 and (-3 - i√15) / 2.[/tex]

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The labor force participation rate is 64.4%.

To calculate the labor force participation rate, we need to know the number of people who are either employed or actively seeking employment. We can calculate this as follows:

Labor force = adult working-age population - not in labor force

Labor force = 320 million - 114 million

Subtract the numbers

Labor force = 206 million

So the labor force participation rate is

Labor force participation rate = (labor force / adult working-age population) x 100%

Substitute the values in the equation

Labor force participation rate = (206 million / 320 million) x 100%

Labor force participation rate = 64.4%

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Answer:

Step-by-step explanation:

EZ

its 21

Answer:

Firm 2's structure is in the form of a cylinder, so the formula to get the enclosed space or volume of the cylinder will be,

Volume = πr²h

where r = radius of the structure

h = height of the Firm

By substituting the values of 'r' and 'h' in the given formula,

V =

�

(

70

2

)

2

(

60

)

π(

2

70

)

2

(60)

=

�

(

35

)

×

60

π(35)×60

= 6597.345

≈ 6597.35 cubic feet

Total enclosed space of Firm 2 is 6597.35 cubic feet.

The given functions in GeoGebra and determine by analytically checking:

a. function type is [tex]f(x) =\frac{2x^2-4}{x^2-4}[/tex]

b. Domain and range Range (-2, +2).

c. Asymptotes is HA = 2 and VA = ±2

The function y = f( x) is classified into different types of functions, grounded on factors similar as the sphere and range of a function, and the function expression. The functions have a sphere x value that's appertained as input. The sphere value can be a number, angle, numeric, bit.

[tex]f(x) =\frac{2x^2-4}{x^2-4}[/tex]

Functions in mathematics can be compared to the operations of a dealing (soda pop) machine. When you put in a certain quantum of plutocrat, you can elect different types of tonics. also, for functions, we input different figures and we get new figures as the result. sphere and range are the main aspects of functions.

[tex]f(x) =\frac{2x^2-4}{x^2-4}[/tex]

x² = 4

x = ± 2

Range (-2, +2).

An asymptote is a line being approached by a wind but noway touching the wind. i.e., an asymptote is a line to which the graph of a function converges. We generally don't need to draw asymptotes while graphing functions. But graphing them using dotted lines( imaginary lines) makes us take care of the wind not touching the asymptote. Hence, the asymptotes are just imaginary lines.

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Complete question:

Represent the given functions in GeoGebra and determine by analytically checking: a. function type b. Domain and range c. Asymptotes, both vertical and horizontal, if it has them:

1.746 is the critical t value that corresponds to 90% confidence.

To find the critical t-value that corresponds to 90% confidence with 16 degrees of freedom, follow these steps:
1. Determine the desired confidence level: 90%
2. Calculate the corresponding significance level (alpha) by subtracting the confidence level from 100%: 100% - 90% = 10%
3. Divide the significance level by 2 to get the value for a two-tailed test: 10% / 2 = 5%
4. Look up the critical t-value in a t-distribution table using the degrees of freedom (16) and the 5% value.

From the t-distribution table, the critical t-value for 16 degrees of freedom and 90% confidence is approximately 1.746.

So, the CRITICAL T VALUE that corresponds to a 90% CONFIDENCE level with 16 DEGREES FREEDOM is 1.746, rounded to three decimal places.

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Iron is required for the production of hemoglobin, which carries oxygen in red blood cells. It is also necessary for the functioning of many enzymes involved in energy metabolism.

The correct answer is (B) magnesium. Magnesium is a cofactor for some enzymes and is a mineral whose primary route of excretion is through the feces and trace amounts in the urine.

What is a cofactor?

A cofactor is a non-protein chemical that helps enzymes function correctly. It can be a metal ion or a small organic molecule. Cofactors work in tandem with the enzyme's active site to help catalyze reactions. Enzymes are protein molecules that assist in biochemical reactions, with each enzyme being specific to a certain reaction. Enzymes act as a catalyst by lowering the energy barrier required for a reaction to occur.

Magnesium is a cofactor for many enzymes that help to regulate nerve and muscle function, as well as glucose metabolism. It is needed for the production of proteins, DNA, and RNA, and it is a vital component of bone health. Magnesium is also necessary for the regulation of heart rhythm and blood pressure. Magnesium deficiencies can lead to muscle weakness, tremors, and seizures. The mineral magnesium's primary route of excretion is through the feces, with trace amounts being excreted in the urine.Calcium is an essential mineral that is involved in the formation and maintenance of bones and teeth, as well as blood clotting, nerve function, and muscle contraction.

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Answer:

8, 8.001, 8.01, 8.1, 9, 11, 13, 16

Step-by-step explanation:

From the instructions given, we know that variable u [tex]\geq[/tex] 8. the  [tex]\geq[/tex]  sign means that the number is greater than or is equal to the number, which is in this case, 8. In the numbers given, (0, 7, 7.999, 8.01, 11, 3, 7.9, 8, 8.1, 13, 5, 7.99, 8.001, 9, 16) we name the numbers greater than or equal to 8 that are stated in the list.

In the following question, Welch's t-test is used to compare the means of two populations with unequal variances. It is a variation of the standard Student's t-test, which is used when the variances are assumed to be equal.

Welch's t-test is generally used when the sample sizes are small and the variances are significantly different.

The distributional assumptions that are needed for Welch's t-test include:

Normality - The data from each population must be normally distributed, although this assumption is not always strictly required for the test to be valid.

Equal variances - The variances of the two populations must be equal. In practice, this assumption is often difficult to satisfy, particularly when the sample sizes are small. Welch's t-test does not require the assumption of equal variances.

Independence - The samples from each population must be independent of each other. This means that the observations in one sample should not be related to the observations in the other sample.

Welch's t-test is a parametric test, which means that it is based on assumptions about the underlying distribution of the data. If the distributional assumptions are not met, then the test may not be valid. In such cases, non-parametric tests may be used instead, such as the Wilcoxon rank-sum test.

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The equation of the line perpendicular to the line QR in slope intercept is y= [tex]\frac{1}{2}x+\frac{7}{2}[/tex].

Given,

x+2y=2

y = 1 - [tex]\frac{x}{2}[/tex]

Slope = -1/2 = [tex]m_{1}[/tex]

Let Slope of line perpendicular to line x+2y=2 is [tex]m_{2}[/tex]

⇒  [tex]m_{1}[/tex] *    [tex]m_{2}[/tex] = -1

Then [tex]m_{2}[/tex] = 1/2

Equation of line perpendicular is given by

[tex]y = \frac{1}{2}x + c[/tex]

Since it contains point (5,6)

6 = [tex]\frac{1}{2} (5) + c[/tex]

c= [tex]\frac{7}{2}[/tex]

Then the equation of line is:

[tex]y = \frac{1}{2}x+ \frac{7}{2}[/tex].

Therefore, the equation of the line perpendicular to the line QR in slope intercept is y= [tex]\frac{1}{2}x+\frac{7}{2}[/tex].

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Answer:

y = 22 - x2  or x = 12 - x2

Step-by-step explanation:

The larger sample size also reduces the impact of individual outliers, which could potentially skew the results. Therefore, increasing the sample size will result in more reliable results, and a smaller error bound and confidence interval.

The error bound (E) for the sample size of 35 community colleges is calculated using the formula: E =[tex]1.96 * √[p*(1-p)/n].[/tex]

With n = 35, p = 0.5 (assuming the mean of the enrollment figures is 0.5), the error bound is calculated to be E = 0.823.

If the sample size is increased to 500 community colleges, the error bound would be reduced to 0.338. This is because the larger the sample size, the smaller the error bound. The confidence interval would also be reduced, since it is directly proportional to the error bound.

In practical terms, a larger sample size means more reliable results. This is because when the sample size is increased, the results tend to be more representative of the entire population, leading to more accurate conclusions.

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The finite population correction factor (FPC) is a factor used when the sample size is more than 5% of the population size. It corrects for the bias that can occur when taking a sample from a finite population.

Applying the FPC to the sample mean results in the standard error for the sample mean being equal to the population standard deviation divided by the square root of the sample size times the FPC.
In other words, the standard error for the sample mean is equal to:
Standard Error = Population Standard Deviation/√(Sample Size*FPC)
The FPC is calculated by taking the reciprocal of the following formula:
FPC = (N-n)/(N-1), where N is the population size and n is the sample size.
In conclusion, applying the FPC to the sample mean reduces the bias that can occur when taking a sample from a finite population, and the resulting standard error for the sample mean is equal to the population standard deviation divided by the square root of the sample size times the FPC.

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Answer:

1/12 or 0.0833

Step-by-step explanation:

P(Coin) = 1/2

P(Dice) = 1/6

1/2 × 1/6 = 1/12

Answer:

orthocentre

Step-by-step explanation:

this is the answer to your question

Answer:

r=8

Step-by-step explanation:

a.  -3(6-r)=6

    -18+3r=6

     3r=6+18

      3r=24

        r=[tex]\frac{24}{3}[/tex]

        r=8

b.    3r instead of -3r

The probability that a randomly selected baby will weigh more than 9.75 pounds at birth is 0.0062, or about 0.62%. This means that the vast majority of babies will weigh less than 9.75 pounds at birth, as this value is more than two standard deviations above the mean.

We can use the standard normal distribution to solve this problem by first standardizing the value of 9.75 pounds using the formula:

z = (x - mu) / sigma

where x is the value of 9.75 pounds, mu is the mean of 7.25 pounds, and sigma is the standard deviation of 1.0 pound.

Substituting the values, we get:

z = (9.75 - 7.25) / 1.0 = 2.5

We can then use a standard normal distribution table or calculator to find the probability of a z-score greater than 2.5. From the table or calculator, we find that this probability is approximately 0.0062.

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Answer:

35

Step-by-step explanation:

Change the percent to decimal form and of means multiply.

25% of 140

.25 * 140

35

Answer:

35

Step-by-step explanation:

Kevin is expected to have more whole seashells, with  [tex]75[/tex]% of his collection being whole seashells, compared to Micah's  [tex]60[/tex]%.

To determine who is expected to have more whole seashells, we need to compare the ratio of whole seashells to the total number of seashells collected for each person.

Person Whole Seashells Broken Seashells Total Seashells

Kevin 150 50 200

Micah 60 40 100

To calculate the ratio of whole seashells to total seashells, we divide the number of whole seashells by the total number of seashells, and then multiply by 100 to get a percentage:

Kevin: 150/200 [tex]\times[/tex] 100 = [tex]75[/tex]%

Micah: 60/100 [tex]\times[/tex] 100 =  [tex]60[/tex]%

Therefore, Kevin is expected to have more whole seashells, with  [tex]75[/tex]% of his collection being whole seashells, compared to Micah's  [tex]60[/tex]%.

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The complete question is: Kevin and Micah collected seashells on the beach. The table below shows the number of broken and whole seashells each person collected. If Kevin collected 200 shells and Micah collected 100 shells, who is expected to have collected more whole seashells?

Broken Seashells Whole Seashells

Kevin 70 130

Micah 40 60

There are a total of 48 soccer games in the season.

Since there are 3 soccer games in a month, there will be 12 games in a season (3 games/month x 4 months). Since 8 games are played at night and assuming that all games are played either during the day or at night, we can calculate the number of games played during the day as:

Number of day games = Total number of games - Number of night games

= 12 games/month x 4 months - 8 night games/month x 4 months

= 48 games - 32 games

= 16 games

Therefore, the total number of games in the season is:

Total number of games = Number of day games + Number of night games

= 16 games + 32 games

= 48 games

So, there are 48 soccer games in the season.


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