When a polynomial is divided by (x-5) , the quotient is 5x²+3 x+12 with remainder 7 . Find the polynomial.

Answer:

there are 5 red marbles in the jar

Step-by-step explanation:

I think this is the answer

The proportion for Clairemont is 0.09.

There are various methods to compute proportions in statistics. Here, the formula for proportion is defined as "a part, share, or number considered in comparative relation to a whole."

In this case, the frequency of people without health insurance in Clairemont is part of the whole population of individuals surveyed in Clairemont.

The calculation is as follows:
The proportion of uninsured in Clairemont = Frequency of uninsured in Clairemont / Total number of survey respondents in Clairemont

The frequency of uninsured individuals in Clairemont is 18, and the total number of survey respondents in Clairemont is 200. The proportion of uninsured individuals in Clairemont is:

Proportion of uninsured in Clairemont = 18 / 200 = 0.09

Therefore, the proportion of uninsured individuals in Clairemont is 0.09.

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For the given function f(x) = 5x² + 2x - 3,

Part A: The x-intercepts of the graph f(x) are: (-1, 0) and (3/5, 0).

Part B: The vertex of the graph of f(X) is going to be a minimum and its coordinates are (-0.2, -3.2).

Part C: The values obtained in the part A and Part B are used for graphing the given function. Since the vertex is minimum, the parabola opens upwards.

The x-intercepts of a function or equation are obtained at y = 0.

Then, on substituting y = 0 in the function gives the x-coordinate i.e., the x-intercept.

To calculate the x coordinate of vertex(h, k), use the formula mentioned below:

h = -b/2a

When the function is in the form of ax² + bx + c.

Then, to calculate the y-coordinate of the vertex, substitute obtained h value in the place of x in the function.

Thus, the required coordinates of the vertex are obtained as (h, k).

It is given that,

f(x) = 5x² + 2x - 3

Part A: Finding the x-intercepts:

Substituting y = 0 i.e., f(x) = 0;

⇒ 5x² + 2x - 3 = 0

On simplifying/factorizing,

⇒ 5x² + 5x - 3x - 3 = 0

⇒ 5x(x + 1) - 3(x +1) = 0

⇒ (5x - 3)(x + 1) =0

∴ x = 3/5 or x = -1

Thus, the x-intercepts are (3/5, 0) and (-1, 0).

Part B: Finding the vertex of the given function:

We have h = -b/2a

From the given function 5x² + 2x - 3; a = 5, b = 2 and c = -3

So, h = -2/2(5) = -1/5 = -0.2

Then, on substituting h = x = -0.2 in the function we get

k = 5(-0.2)² + 2(-0.2) - 3

k = -3.2

Thus, the coordinates of the vertex are (h, k) = (-0.2, -3.2).

Since a > 0 i.e., 5 > 0, the vertex of the graph is going to be minimum and the graph of f(x) opens upwards.

Part C: Steps to graph f(X):

Step 1: Plot the x-intercepts in the coordinate plane

Step 2: Plot the vertex of the function

Step 3: draw a curve line passing through them, opening towards up.

Thus, the graph of the given function is plotted as shown below.

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Answer:

ECHA

Step-by-step explanation:

To find the slope, use the slope formula.

1) The image is very blurry, so I can't tell what the points are, but it looks like the slope is 1/2.

2) m=y2-y1/x2-x1

=0-(-4)/5-3

=4/2

=2

3) m=y2-y1/x2-x1

=(-3-(-6))/(-4-2)

=3/-6

=(-1/2)

4) It looks like -2 to me. The image is too blurry to be exact though.

I hope this is correct and helps you on your homework! Good luck!

Answer:

If the children divide evenly onto 3 buses, there will be 11 children on each bus

Step-by-step explanation:

Add all 3 classes to ind total amount of students

Ms. Noels class has 10 students

Mr. Grubbs class has 9 students

Ms. Ackerman's class has 14 students

Total Students: 10 students + 9 students + 14 students

33 total students

Dividing 33 students in 3 busses is 33 / 3 which equals 11

Answer:

The slope of the line is -10/11

Step-by-step explanation:

To find the slope with points you would use the formula \(m = \frac{y2 - y1}{x2 - x1}\)

Now since the line crosses the y-axis at 17, that would be where the y-intercept is, meaning there is a point at (0, 17).

With that, we can find the slope with (11, 7) and (0, 17) in the formula above

So, \(m = \frac{17 - 7}{0 - 11}\)

which will simplified to, \(m = -\frac{10}{11}\)

So the slope is - 10/11

The answer is -0.5.

The source is from calculator soup.

Answer:

116.663333333 repeating

Step-by-step explanation:

do 349.99 divided by 3

The deductible (d) is 169.

To calculate the deductible (d), we need to find the value at which the expected value of the unreimbursed portion of a loss equals 56.

Given that losses are uniformly distributed on the interval [0, 450], the expected value of a uniform distribution is the average of the interval, which is (450 - 0) / 2 = 225.

The expected value of the unreimbursed portion of a loss is given as 56.

We can set up the following equation to solve for the deductible (d):

E(unreimbursed portion of loss) = E(loss) - d

56 = 225 - d

Rearranging the equation, we find:

d = 225 - 56

d = 169

Therefore, the deductible (d) is 169.

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Answer:

y=-17/7x+5/14

Step-by-step explanation:

Answer:

???

Step-by-step explanation:

a. The 95% confidence interval for the proportion of all US adults familiar with the VW emissions scandal is (72.1%, 77.9%). b. The claim made by the newspaper article that 80% of US adults are familiar with the scandal is not plausible, as it falls outside the calculated confidence interval.

a. The Gallup poll found that 75% of the 1050 randomly chosen adults were familiar with the 2015 VW emissions scandal. To estimate the proportion of all US adults familiar with the scandal, we can construct a 95% confidence interval. This interval will provide a range within which the true proportion is likely to fall.

b. To construct the confidence interval, we can use the formula for calculating a confidence interval for a proportion. The formula consists of three components: the sample proportion, the margin of error, and the critical value. The sample proportion is the percentage of respondents in the sample who reported being familiar with the scandal, which is 75% in this case. The margin of error represents the range around the sample proportion that accounts for sampling variability, and the critical value is based on the desired confidence level.

The formula for the margin of error is:

Margin of Error = Critical Value × Standard Error

The standard error is calculated using the sample proportion and sample size:

Standard Error = \(\sqrt\)((Sample Proportion × (1 - Sample Proportion)) / Sample Size)

By plugging in the values and calculating the confidence interval, we can determine a range of plausible values for the proportion of all US adults familiar with the scandal.

To assess the plausibility of the newspaper article's claim that 80% of US adults are familiar with the scandal, we compare it to the constructed confidence interval. If the claim falls within the confidence interval, it is considered plausible, as it aligns with the range of estimates based on the sample. However, if the claim falls outside the confidence interval, it raises doubts about the accuracy of the newspaper's claim.

Therefore, a. The 95% confidence interval for the proportion of all US adults familiar with the VW emissions scandal is (72.1%, 77.9%). b. The claim made by the newspaper article that 80% of US adults are familiar with the scandal is not plausible, as it falls outside the calculated confidence interval.

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Let the original price of the item be X.

In one week, the price is halved and becomes (1/2)X.

In two weeks, the price is halved again and becomes (1/4)X, which is only 75% off.

Answer: 3 grams

Step-by-step explanation: Each distribution of food must be equal so divide food by amount of cats which is 3 to get 3

Mathmatically 9/3 = 3 grams

200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

The absolute difference between the predicted and actual values must be determined, added together, and divided by the total number of periods.

Forecasted values are as follows: 1,500 and 1,400

Values in actuality: 1,200 and 1,500

Absolute differences:

|1,500 - 1,200| = 300

|1,400 - 1,500| = 100

Now, we calculate the MAD:

MAD = (300 + 100) / 2 = 400 / 2 = 200

Therefore, 200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

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Answer:

expresión

Step-by-step explanation:

Answer:

Step-by-step explanation:

Either the question is displayed incorrectly, or some crucial information has been omitted.

Step-by-step explanation:

-1/4, -1/5, -1/6, -1/7, -1/8, 1/8, 1/7, 1/6, 1/5, 1/4

Answer:

102 degrees (problem #5)

Step-by-step explanation:

5. 78 = 1/2 ((360-x)-(x)) -->

156 = 360 - 2x -->

-204 = -2x -->

102 = x

Answer:

Step-by-step explanation:

The topic of proportions has some specific terminology that you may need to know. For instance, given the following proportion equation:

\small{ \dfrac{a}{b} = \dfrac{c}{d} }  

b

a

​

=  

d

c

​

...the values in the "b" and "c" positions are called the "means" of the proportion, while the values in the "a" and "d" positions are called the "extremes" of the proportion.

A basic defining property of any proportion is that the product of the means is equal to the product of the extremes. In other words, given the proportional statement:

MathHelp.com

Proportions on MathHelp.com

Proportions

\small{ \dfrac{a}{b} = \dfrac{c}{d} }  

b

a

​

=  

d

c

​

...we know that it must be true that ad equals bc. This fact about proportions is, in effect, the cross-multiplication demonstrated on the previous page. And this cross-multiplication fact about the products of the means and extremes is occasionally turned into a homework problem, such as:

Is \small{ \bm{\color{green}{ \dfrac{24}{140} }}}  

140

24

​

 proportional to \small{ \bm{\color{green}{ \dfrac{30}{176} }}}  

176

30

​

 ? Explain why (or why not) without simplifying the fractions.

For these fractions (that is, these ratios) to be proportional (that is, for them to create a true proportional equation when they are set equal to each other), it has to be true that the product of the means of that equation is equal to the product of the extremes. So I can figure out if the two fractions are indeed proportional to each other (without simplifying them) by finding these two products.

In other words, by specifying that I'm supposed to not simplify the fractions, they are hinting that they are wanting me to find the product of 140 and 30 (being the means, if I keep the fractions in the same order as they've given them to me) and the product of 24 and 176 (being the extremes), and then see if these products are equal. So I'll check:

140 × 30 = 4200

24 × 176 = 4224

While these values are close, they are not equal, so I know the original fractions cannot be proportional to each other. So my answer is:

The fractions are not proportional because the product of their means does not equal the product of their extremes.

If I'd reversed the fractions, and used 176 and 24 as my means and 30 and 140 as my extremes, I would have gotten the same products (just in reverse order), and thus the same answer (namely, that the fractions are not proportional). So don't worry about which fraction is "first" or "second"; either way will work.

Is \small{ \bm{\color{green}{ \dfrac{42}{55} }}}  

55

42

​

 proportional to \small{ \bm{\color{green}{ \dfrac{50}{65} }}}  

65

50

​

? Justify your answer without reducing the fractions.

To confirm proportionality (or to disprove it), I'll need to set up the proportion, multiply the means, multiply the extremes, and compare the results. Or, which is the same thing (but without doing an equation that might not actually be true), I'll multiply one fraction's denominator by the other's numerator, and vice-versa:

(42)(65) = 2,730

(55)(50) = 2,750

Once again, they're close, but they're not equal. So:

The fractions are not proportional because the product of their means does not equal the product of their extremes.

Are \small{ \bm{\color{green}{ \dfrac{42}{273} }}}  

273

42

​

 and \small{ \bm{\color{green}{ \dfrac{170}{1105} }}}  

1105

170

​

 proportional? Explain your answer without reducing the fractions or converting to a common denominator.

I "cross-multiply" (meaning, in this context, multiplying one fraction's numerator by the other's denominator, and vice versa):

(42)(1,105) = 46,410

(273)(170) = 46,410

Finally, a pair that is proportional!

The fractions are proportional because, when set up as a proportion, the product of the means is equal to the product of the extremes.

Answer: 57.8

Step-by-step explanation:48.7 seconds + 49.3 seconds.= 57.8

Answer:

34.54 in

Step-by-step explanation:

The approximate circumference of a plate with a diameter of 11 inches can be calculated using the formula C = πd, where C is the circumference and d is the diameter .

So, substituting the given value of diameter d = 11 inches and taking π to be approximately 3.14, we get:

C = πd = 3.14 x 11 = 34.54 inches (approx.)

Therefore, the approximate circumference of the plate is 34.54 inches.

Since it is required to round the answer to the nearest hundredth, we get the rounded answer as 34.54 rounded off to two decimal places, which is 34.54 (no rounding needed).

Answer: For circumference, you simply multiply the diameter by pi, so the answer you are looking for is 34.54

Step-by-step explanation:

Answer:

28 g. ................

The optimal solution, obtained through graphical method, is: x₁ = 4, x₂ = 2, with the maximum value of Z = 80.

To solve the given linear programming problem graphically, we start by plotting the feasible region defined by the constraints:

Constraint 1: 10x₁ + 20x₂ ≤ 120

Constraint 2: 8x₁ + 8x₂ ≤ 80

Non-negativity constraint: x₁ ≥ 0, x₂ ≥ 0

The feasible region is the area of the graph that satisfies all the constraints.

Next, we calculate the objective function Z = 12x₁ + 16x₂. We plot the objective function as a line on the graph.

The optimal solution, which maximizes Z, is the point where the objective function line intersects the boundary of the feasible region.

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The table to show the depreciation over time for the first three years is:

Year (x) Depreciation (y)

1         $15,000

2         $13,500

3        $12,000

It should be noted that in order to generate a table to show the depreciation over time for the first three years, we can use the given equation:

y = 16,500 - 1,500x

where y is the depreciation and x is the number of years since the car was purchased new.

Substituting x = 1, 2, and 3 into the equation, we get:

When x = 1, y = 16,500 - 1,500(1) = 15,000

When x = 2, y = 16,500 - 1,500(2) = 13,500

When x = 3, y = 16,500 - 1,500(3) = 12,000

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Answer:

x² - x - 2 = 0

Step-by-step explanation:

plotting the graph of x and y,we have that the root of the equation is -1 or 2

x = -1 or 2

the eqn therefore is;

x² - (sum of the root)x + (product of the root) =. 0

x² - (-1+2)x + (-1*2) = 0

x² - x - 2 = 0

Applying the Factor Theorem, it is found that the quadratic function is:

\(p(x) = x^2 - x - 2\)

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

The Factor Theorem states that if a polynomial \(p(x)\) has roots \(x_1, x_2, ..., x_n\), it is described by the following equation:

\(p(x) = a(x - x_1)(x - x_2)...(x - x_n)\)

In which a is the leading coefficient.

\(p(x) = a(x - (-1))(x - 2)\)

\(p(x) = a(x + 1)(x - 2)\)

\(p(x) = a(x^2 - x - 2)\)

When x = 0, p(x) = -2, and we use this to find a.

\(p(x) = a(x^2 - x - 2)\)

\(-2 = a(0^2 - 0 - 2)\)

\(2a = 2\)

\(a = \frac{2}{2}\)

\(a = 1\)

Thus, the quadratic function is:

\(p(x) = x^2 - x - 2\)

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Answer:

x = 112

Step-by-step explanation:

1/8x + 2 = 16

Subtract 2 from both sides

1/8x = 14

Multiply both sides by 8

x = 112

If a rectangle has an area of 32 square millimeters and the length of the rectangle is 8 millimeters, then the width of the rectangle is 4 millimeters.

To find the width of a rectangle, follow these steps:

Therefore, the width of the rectangle is 4mm.

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Answer:

7.20

Step-by-step explanation:

triangle is right triangle so other leg of first is 12

5 x 3/5 = 5, so

do 12 x 3/5 to get 7.20

Option A. If the alternative hypothesis of the test had been lower-tailed instead of two-tailed, the conclusion of the test would be different.

Recall that a two-tailed test is used when the alternative hypothesis is that the population parameter is different from the null hypothesis value in any direction, while a lower-tailed test is used when the alternative hypothesis is that the population parameter is less than the null hypothesis value.

In the given scenario, if the alternative hypothesis of the test had been lower-tailed instead of two-tailed, we would have tested the following null and alternative hypotheses:

H0: Pharaoh's translation is not worse than the other software's translation.

Ha: Pharaoh's translation is better than the other software's translation.

In this case, we would have calculated the p-value for the lower tail of the sampling distribution, and compared it to the significance level alpha. If the p-value is less than alpha, we would reject the null hypothesis and conclude that Pharaoh's translation is better than the other software's translation. If the p-value is greater than alpha, we would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that Pharaoh's translation is better than the other software's translation.

Therefore, the correct answer to the question is option A: Unlike the two-tailed test, we would conclude that there is a difference between Pharaoh's translation and the translation of the other software.

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Let's call the number of pancake breakfasts the Drama Club needs to sell "x".

The total revenue from selling "x" pancake breakfasts can be calculated by multiplying the number of breakfasts by the price per breakfast:

Total revenue = x * $5.25

The total cost of running the pancake breakfast event includes the rental cost of the facility plus the cost of making the pancakes and other expenses. Since we don't know the exact cost of making the pancakes and other expenses, we'll call the total cost "C".

Total cost = $152 + C

The profit can be calculated as the difference between the total revenue and the total cost:

Profit = Total revenue - Total cost

We want the profit to be $1000, so we can set up the following equation:

$1000 = x * $5.25 - ($152 + C)

To solve for "x", we need to isolate it on one side of the equation. First, we can simplify the equation by combining like terms:

$1000 = $5.25x - $152 - C

Next, we can add $152 and "C" to both sides of the equation:

$1152 + C = $5.25x

Finally, we can divide both sides of the equation by $5.25 to solve for "x":

x = ($1152 + C) / $5.25

Since we don't know the exact cost of making the pancakes and other expenses, we can't solve for "x" exactly. However, we do know that the Drama Club needs to sell enough pancake breakfasts to make a profit of $1000. Therefore, we can set up an inequality to represent this:

Total revenue - Total cost ≥ $1000

x * $5.25 - ($152 + C) ≥ $1000

Simplifying this inequality, we get:

x * $5.25 ≥ $1152 + C + $1000

x * $5.25 ≥ $2152 + C

x ≥ ($2152 + C) / $5.25

This means that the Drama Club needs to sell at least ($2152 + C) / $5.25 pancake breakfasts to make a profit of $1000, where "C" is the cost of making the pancakes and other expenses.