If the sum of zeroes of polynomial px^2 + 5x + 8p is equal to the product of zeroes , find the value of p

On that particular day, approximately 272.32 BTUs of heat were transferred through the wall.

To calculate the amount of heat transferred through the walls on a particular day, we can use the formula:

Q = U × A × deltaT

where Q is the heat transferred (in BTUs), U is the overall heat transfer coefficient (in BTU/hr·ft^2·°F), A is the area of the wall (in ft^2), and deltaT is the temperature difference between the inside and outside of the wall (in °F).

First, let's calculate the area of the wall. The room has four walls, but we are only interested in the heat transferred through the wall with an R-value of 15. We can calculate the area of this wall as follows:

Area = Length × Height = 13 ft × 9 ft = 117 ft^2

Next, we need to calculate the overall heat transfer coefficient, U. The U-value is the reciprocal of the R-value, so:

U = 1 / R = 1 / 15 = 0.0667 BTU/hr·ft^2·°F

Now we need to calculate the temperature difference between the inside and outside of the wall. We are given that the outside temperature is 36 °F, but we don't know the inside temperature. Let's assume that the inside temperature is 70 °F, which is a typical room temperature. Then the temperature difference is:

deltaT = 70 °F - 36 °F = 34 °F

Finally, we can plug these values into the formula:

Q = U × A × deltaT

Q = 0.0667 BTU/hr·ft^2·°F × 117 ft^2 × 34 °F

Q ≈ 272.32 BTUs

Therefore, on that particular day, approximately 272.32 BTUs of heat were transferred through the wall.

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Answer: 228 yards

Step-by-step explanation:

Answer:

228

Step-by-step explanation:

All the possible angle measures are given as follows:

25º and 35º.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

On the first quadrant, we have that:

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this is "Repeated measures ANOVA, which is a statistical test used to analyze data from experiments in which the same participants are measured multiple times under different conditions.

A repeated measures ANOVA is a statistical test used to analyze data from experiments in which the same participants are measured multiple times under different conditions. This design is sometimes referred to as a "within-subjects design" because each participant is measured within the same group.

Here are the steps for conducting a repeated measures ANOVA:

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Answer:

40 ft

Step-by-step explanation:

the starting point is like the origin on the coordinate grid.

let's say forward for your friends is the positive y direction, and right for your friend is positive x direction.

the end point coordinates of your friend are then

(15, 20)

forward for you (facing in the other direction) is the the negative y direction. and going right for you is then actually going in the negative x direction.

your end point is therefore

(-9, -12)

the distance between both points is then per Pythagoras (and the derived distance formula) :

distance² = (x1 - x2)² + (y1 - y2)² =

= (15 - -9)² + (20 - -12)² = 24² + 32² =

= 576 + 1024 = 1600

distance = 40 ft

Answer:

A = 40 in²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)

where h is the height between the bases b₁ and b₂

here h = 8 , b₁ = 4 , b₂ = 6 , then

A = [tex]\frac{1}{2}[/tex] × 8 × (4 + 6)

   = 4 × 10

   = 40 in²

Answer:

50 inches

Step-by-step explanation:

Using the Pythagorean theorem, we can find the length of the diagonal of the TV:

diagonal^2 = height^2 + width^2

diagonal^2 = 30^2 + 40^2

diagonal^2 = 900 + 1600

diagonal^2 = 2500

Taking the square root of both sides, we get:

diagonal = sqrt(2500)

diagonal = 50

Therefore, the length of the diagonal of the TV is 50 inches.

The expressions are simplified to give;

7. 4n³(3n² + 4)

8. -3x(3x² - 4)

9. 5(k² - 8k + 2)

10. -10(6 + 6n² + 5n³)

11. 3(6n³ - 4n - 7)

12. 9(7n³ + 9n + 2)

Algebraic expressions are defined as mathematical expressions that are composed of variables, coefficients, terms, factors and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

To factorize the expressions, we have;

12n⁵ + 16n³

Find the common term

4n³(3n² + 4)

-9x³ - 12x

find the common term

-3x(3x² - 4)

5k² - 40k + 10

find the common terms

5(k² - 8k + 2)

-60 + 60n² + 50n³

find the common term

-10(6 + 6n² + 5n³)

18n³ -12n - 21

find the common term

3(6n³ - 4n - 7)

63n³ + 81n + 18

Find the common term

9(7n³ + 9n + 2)

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The measure of angle A and angle B are 28.61 and 61.39 rounded to two decimal place, using trigonometric ratio of tangent for the respective angles.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

tan B = 6/11 {opposite/adjacent}

B= tan⁻¹(6/11) {cross multiplication}

B = 28.6105.

tan A = 11/6 {opposite/adjacent}

A= tan⁻¹(11/6) {cross multiplication}

A = 61.3895.

Therefore, the measure of angles A and B are 28.61 and 61.39 rounded to two decimal place, using trigonometric ratio of tangent for the respective angles.

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The rate of return on the account was 11.429% over the course of 15 years.

Interest rate is the percentage charged by a lender to a borrower for the use of money. It is the cost of borrowing money, expressed as a percentage of the amount borrowed. Interest rates are typically determined by the prevailing market conditions, the type of loan product being offered, the borrower's credit score, and the lender's risk tolerance. The higher the interest rate, the more expensive the loan will be for the borrower.

The rate at which the account earned interest can be calculated using the following formula:

Rate = (Interest Earned/Principal) * (1/Number of Years)

In this case, the rate is:

Rate = (2000/3500) * (1/15)

Rate = 0.11429 or 11.429%

This means that the account earned 11.429% in interest over the course of 15 years. This rate of return is relatively modest, as interest rates are often much higher than this. In fact, the current average rate of return for a 15-year CD is around 1.75%.

The reason why the rate of return is so low is likely due to the fact that the account was earning interest at a fixed rate. Fixed rate accounts typically offer lower interest rates than variable rate accounts, since the bank or financial institution is making a guarantee that the rate will not change. This makes them less risky for the investor, but also less profitable.

In conclusion, the rate of return on the account was 11.429% over the course of 15 years.

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The tax on the belt buckle is $1.56

What is Rate?

In general terms, a rate is a measure of the relationship between two quantities that are measured in different units. A rate expresses how much of one thing there is per unit of another thing. For example, miles per hour is a rate that expresses how many miles are traveled in one hour.

To calculate the tax on the belt buckle, we need to multiply the price of the belt buckle by the sales tax rate:

Tax = Price x Tax rate

In this case, the price of the belt buckle is $25 and the sales tax rate is 6.25%. To convert the tax rate from a percentage to a decimal, we need to divide it by 100:

Tax rate = 6.25% ÷ 100 = 0.0625

Now we can calculate the tax on the belt buckle:

Tax = Price x Tax rate

= $25 x 0.0625

= $1.56

Therefore, the tax on the belt buckle is $1.56. The total cost of the belt buckle including tax would be $25 + $1.56 = $26.56.

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Answer: False

Step-by-step explanation:

1/7 x 1/7 = 1/49 x 1/7 = 1/343

Answer:

use desmos graphing calculator it helps alot

Step-by-step explanation:

x^{2}-x-6=0 has two zeros/solutions

x^{2}-x-6=0 has 1 zero/solution

x^{2}-x-6=0 has no zero/solution

The annual percentage rate is approximately 9.97% when rounded to the nearest hundredth of a percent.

To find the annual percentage rate (APR), we can use the following formula:

APR = (finance charge / loan amount) / (loan period in years) x 100%

First, let's calculate the loan amount by subtracting the finance charge from the total cost of the furniture:

Loan amount = $1,860 - $308.25 = $1,551.75

Next, let's convert the loan period of 2 years to the decimal form of 2:

Loan period = 2 years = 2.0 years

Now we can plug in the values into the formula and solve for the APR:

APR = ($308.25 / $1,551.75) / (2.0) x 100%

APR = 0.0997 x 100%

APR ≈ 9.97%

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So, the matrix representation of T relative to the basis B = {f1, t, t²} is:
| 2.5  3  0 |
|  0   4  0 |
|  0   0  6 |

To find the matrix representation of the linear transformation T relative to the basis B = {f1, t, t²}, we need to apply T to each element of the basis and then express the result as a linear combination of the basis elements.
Let's apply T to each element of the basis B:
1. T(f1) = T(1) = 2(1) + 0.5(1) = 2.5
2. T(t) = T(c) = 3(c) + 4(c²) = 3f1 + 4t
3. T(t²) = T(c²) = 6(c²) = 6t²
Now, we can express the results as linear combinations of the basis elements:
1. T(f1) = 2.5f1 + 0t + 0t²
2. T(t) = 3f1 + 4t + 0t²
3. T(t²) = 0f1 + 0t + 6t²
Finally, we can form the matrix representation of T relative to the basis B by using the coefficients of the linear combinations as the columns of the matrix:
T matrix = | 2.5  3  0 |
                  |  0   4  0 |
                  |  0   0  6 |

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The matrix representation of t with respect to the basis b = [tex]{f1, t, t^2}[/tex] is:

[1/2   -4/3      1 ]

[1       8/3      0 ]

[0     -5/2   3/2 ].

To find the matrix representation of the linear transformation t with respect to the given basis, we need to apply t to each of the basis vectors and represent the result as a linear combination of the basis vectors.

The coefficients of these linear combinations will form the columns of the matrix representation.

First, we apply t to each of the basis vectors:

[tex]t(1) = a0 + a1t + a2t^2 = a0 + a1f1 + a2t - (a1/2)f1 - (3a2/2)t^2[/tex]

[tex]t(t) = a0 + (4/3)a1t + (5/6)a2/t = a0 + (4/3)t + (5/6)t^2 - (4/3)f1 - (5/2)t^2[/tex]

[tex]t(t^2) = a0 + (3/2)a2/t^3 = a0 + (3/2)t^2 - (3/2)f1[/tex]

Next, we represent these results as linear combinations of the basis vectors:

[tex]t(1) = (a0 - a1/2)f1 + (a1 + a2)t - (3a2/2)t^2[/tex]

[tex]= 1f1 + 0t + 0t^2 + (-1/2)f1 + 1t + 0t^2 + 0f1 - (3/2)t^2[/tex]

[tex]= (1/2)f1 + 1t - (3/2)t^2[/tex]

[tex]t(t) = (-4/3)f1 + (a0 + 4/3)t + (5/6)t^2[/tex]

[tex]= 0f1 + 1t + 0t^2 + (-4/3)f1 + (4/3)t + (5/6)t^2 + 0f1 + 0t - (5/2)t^2[/tex]

[tex]= (-4/3)f1 + (8/3)t - (5/2)t^2[/tex]

[tex]t(t^2) = f1 + (a0 - 3/2)t^2[/tex]

[tex]= 0f1 + 0t + 1t^2 + 1f1 + 0t + 0t^2 + 0f1 + (1/2)t^2[/tex]

[tex]= 1f1 + 0t + (3/2)t^2[/tex]

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In the circle the mesaure of ∠ACF is  7

The distance from the centre of a circle to any point on the boundary is called the radius. The radius is half of the diameter; 2r=d 2 r = d . The line segment that joins two points on the circle is a chord.

If diameter of a circle bisects a chord ,then it must be perpendicular to the chord.

∴ m∠ACF = 90°  

(8x + 34)° = 90°

8x = 90 - 34

x = 56/8

x = 7

Hence,mesaure of ∠ACF = 7

Complete question : In Circle C, the diameter AB bisects the chord EF.

If m∠ACF = (8x+34)°, enter in the correct value of x.

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Answer:

To find the volume of a rectangular prism, we need to multiply its length, width, and height.

The given dimensions are:

Length = 9 yd

Width = Pyd (it's unclear what this means, so let's assume it's a typo and the intended value is 3 yd or 4 yd)

Height = 4 yd

Assuming the width is 3 yd, the volume of the rectangular prism is:

Volume = Length x Width x Height

Volume = 9 yd x 3 yd x 4 yd

Volume = 108 cubic yards

Assuming the width is 4 yd, the volume of the rectangular prism is

Volume = Length x Width x Height

Volume = 9 yd x 4 yd x 4 yd

Volume = 144 cubic yards

Therefore, the volume of the rectangular prism is either 108 cubic yards or 144 cubic yards, depending on the intended value of the width.

Jane sold approximately 7.8 cups of lemonade. Since she cannot sell a fractional number of cups of lemonade, we can round up to 8 cups.

Let x be the number of cups of lemonade Jane sold.

The total earnings she made from selling x cups of lemonade is:

Total earnings = price per cup * number of cups sold

Total earnings = $0.25 * x

The total cost of making x cups of lemonade is:

Total cost = cost per cup * number of cups sold

Total cost = $1.50 * x

Jane's profit is equal to her total earnings minus her total cost:

Profit = Total earnings - Total cost

Profit = $0.25x - $1.50x

Profit = -$1.25x

We know that Jane's earnings were $9.75, so we can set up the equation:

$9.75 = -$1.25x

To solve for x, we can divide both sides by -$1.25:

-$9.75 / -$1.25 = x

x = 7.8

Jane sold approximately 7.8 cups of lemonade. Since she cannot sell a fractional number of cups of lemonade, we can round up to 8 cups.

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The length of a diagonal support (x) is approximately 18.4 feet to the nearest tenth of a foot.

To find the length x of a diagonal support, we will use the information given about the right triangles formed by the vertical supports, diagonal supports, and the horizontal line (representing half the length of the footbridge).
Since the full length of the footbridge is 20 feet, the horizontal line in each right triangle measures half of that, which is 10 feet.
The angle formed between the short vertical support and the diagonal support is given as 65 degrees.
We'll use the sine function to find the length x of the diagonal support.

In this case, sine(65) = opposite side (vertical support) / hypotenuse (diagonal support or x).
We first need to find the length of the vertical support.

To do this, we can use the tangent function.

In this case, tangent(65) = opposite side (vertical support) / adjacent side (10 feet).
Solving for the vertical support: vertical support = 10 * tangent(65) ≈ 17.1 feet.
Now, we can plug this value back into the sine equation: sine(65) = 17.1 / x.
Solving for x (the diagonal support): x = 17.1 / sine(65) ≈ 18.4 feet.

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Among these expressions, (4+1)x(12-6) has a total value of 30.

To determine which expression has a total value of 30, let's evaluate each expression one by one:

4+1x12-6

Following the order of operations (PEMDAS/BODMAS), we first do the multiplication:

4 + (1x12) - 6 = 4 + 12 - 6

Now, we do the addition and subtraction from left to right:

16 - 6 = 10

(4+1x12-6)

This expression has the same operations as the first one, so its total value is also 10.

(4+1)x(12-6)

First, we evaluate the expressions within the parentheses:

(5)x(6)

Now, we do the multiplication:

5 x 6 = 30

(4+1)x12-6

First, we evaluate the expression within the parentheses:

(5)x12 - 6

Now, we do the multiplication:

60 - 6

Finally, we do the subtraction:

54
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The probability of drawing a face card followed by condition of drawing non face card is equal to 18% ( approximately).

In a standard deck of cards,

There are 12 face cards 4 jacks, 4 queens, and 4 kings

And 40 non-face cards 10 numbered cards each for the 4 suits.

The probability of drawing a face card on the first draw is

=  12/52

= 3/13.

Assuming a face card was drawn on the first draw,

There are now 51 cards remaining in the deck.

Of which 40 are non-face cards.

Probability of drawing a non-face card on the second draw is

= 40/51.

Probability of both events happening drawing a face card followed by a non-face card

= Multiply the probabilities of the individual events

= (3/13) x (40/51)

= 120/663

=  0.181approximately  

= 18% (rounded to the nearest whole number).

Therefore,  the probability of drawing a face card followed by drawing a non-face card in a standard deck of cards is approximately 18%.

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The probability that at most 70 switches fail during the first year is low, at around 1.3%.

The problem involves the use of the exponential distribution to model the lifetime of a certain type of electrical switch. Specifically, we are given that the average life of these switches is beta = 3.

The exponential distribution is often used to model the time between occurrences of a certain event, such as the failure of a component. In this case, we can use it to model the time between failures of the electrical switches.

To answer the question, we need to find the probability that at most 70 switches fail during the first year. Let X be the number of switches that fail during the first year. We know that X follows a Poisson distribution with parameter lambda = (1/3)*300 = 100.

This is because the expected number of failures per year for each switch is 1/3 (since the average life is 3 years), and there are 300 switches installed.

Therefore, we can use the Poisson distribution to calculate the probability that at most 70 switches fail during the first year:

P(X <= 70) = e^(-100) * (100^0/0!) + e^(-100) * (100^1/1!) + ... + e^(-100) * (100^70/70!)

This can be calculated using a calculator or software such as Excel. The answer is approximately 0.013, or 1.3%. This suggests that the switches are fairly reliable, and that it is unlikely that a large number of them will fail in a short period of time.

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Answer:

Step-by-step explanation:

5th term is 6 and the 7th term is 48, we know the nth term for a GP is  arn−1

 so let's substitute the given information in that formula for the nth term

ar3=6

  ar6=48

ar6ar3=486

The  a

and  a

cancelout hence we remain with  r3=8

 take a cube root on both sides and we end up having  r=2

Substitute the value of r in any given equation to get the value of a

ar3=6

a(2)3=6

8a=6

a=34

The formula for the nth term of this GP is given by  34(2n−1)

And when you substitute the value of n in the above formula of nth term you will get the following values; 3/4, 3/2, 3, 6…

The approximate p-value is 5.1250%.

P-value is the probability of obtaining a test statistic as or more extreme than what was actually observed, given that the null hypothesis is true.

Two-sided significance test, with a significance level of 2%. you then randomly sample 420 items from the production line, and find that 22 of the items are defective.

The approximate p-value for this two-sided significance test, with a significance level of 2%, is 5.1250%.

This is the probability of observing 22 or more defective items given that the true rate is 3.2%.

This was calculated using a binomial test, which takes into account the sample size and the expected rate of defects.

This p-value indicates whether or not the observed rate of defects is significantly different from the expected rate.

In this case, the p-value is the probability of observing 22 or more defective items given that the true rate is 3.2%.

This can be calculated using a binomial test.

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Answer:

3 & 4

Step-by-step explanation:

Since you have 3 choice, you want to pick the options that can represent 3 options.

1. False, since a coin only has 2 sides.

2. False, black and red is two halves of a deck, meaning you only have 2 options.

3. True, 6 is divisible by three, so it can be used. Assuming each choice is represented by two number.

4. True, 3 choices is evenly represented by 3 sections

7.071 is the length, in inches, of each side of the square.

What is meant by "square"?

The term "square" refers to a regular quadrilateral having four equal-length sides and angles. Angles in the square are at right angles or are separated by 90 degrees. The diagonals of the square are also equal and meet at a 90-degree angle.

                             Having equal length sides and right angles on all four, a square is a quadrilateral. Due to the fact that a square's sides are all the same length, it may be distinguished from other types of rectangles. Every square consequently becomes a rectangle since it is a quadrilateral with right angles at all four of its angles.

If the side od=f a square is s, the diagonal is  s√2

  This comes from Pythagoras as diagonal is

   √s² + s²  = √2s² = s√2

 as such s√2 = 10

           s = 10/√2

        = 10 * √2/√2  * √2

         = 5√2

    5 * 1.4142  = 7.071

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A student willing to participate in a debate competition is required to fill out a registration form.

Form filling in two types of data i.e.,

Quantitative data is data that can be counted or measured in numerical values. The two main types of quantitative data are discrete data and continuous data. Height in feet, age in years, and weight in pounds are examples of quantitative data. Qualitative data is descriptive data that is not expressed numerically.

Categorical data is a collection of information that is divided into groups. i.e., if an organization or agency is trying to get a biodata of its employees, the resulting data is referred to as categorical.

a. What is your date of birth?

Quantitative.

b. Have you participated in any debate competition previously?

Categorical.

c. If yes, how many debate competitions have you participated so far?

Quantitative.

d. Have you won any of the competitions?

Categorical.

e. If yes, how many have you won?

Quantitative.

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The given question is incomplete, complete question is:

A student willing to participate in a debate competition required to fill a registration form. State

whether each of the following information about the participant provides categorical or quantitative

data.

a. What is your date of birth?

b. Have you participated in any debate competition previously?

c. If yes, how many debate competitions have you participated so far?

d. Have you won any of the competitions?

e. If yes, how many have you won?

Please write answer in two parts. A. Main answer (correctly paraphrased, addressing all aspect of the question) B. Explanation (Step-by-step explanation)

Answer:

31.4 cm

Step-by-step explanation:

Circumference of circle = D x π

D = 10 cm

π = 3.14

Let's solve

10 x 3.14 = 31.4 cm

So, the circumference of the circle is 31.4 cm

Therefore, the original price of the suit was $950.

Percent is a way of expressing a number as a fraction of 100, and is denoted by the symbol %. For example, 50% means 50 out of 100, or 0.5 as a decimal. Percentages are commonly used to express proportions, rates, discounts, and many other kinds of numerical information.

Here,

Let x be the original price of the suit. We know that the sale price, which is 34% less than the original price, is $627.

We can set up the equation:

x - 0.34x = 627

Simplifying this equation, we get:

0.66x = 627

Dividing both sides by 0.66, we get:

x = 950

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Answer:

6.75 ounces of Skittles

Step-by-step explanation:

If there are 4.5 bags of Skittles left and each bag weighs 1.5 ounces, then the total amount of Skittles in ounces can be found by multiplying the number of bags by the weight per bag:

4.5 bags x 1.5 ounces/bag = 6.75 ounces

Therefore, there are 6.75 ounces of Skittles at the candy shop.

6.75 ounces

Step-by-step explanation:

1.5 x 4.5 = 6.75 ounces