What is the vertex of the quadratic function?
f(x) = (x – 8)(x – 4)
A. (4,8)
B. (-6,4)
C. (6,-4)
D. (-4,8)

If john paul is 6 years older than Angelina and in 9 years the sum of their ages will be 86, then John Paul is 35 years old now.

Let's assume Angelina's current age to be x years old. Then, according to the given information, John Paul's current age would be (x + 6) years old.

In 9 years, the sum of their ages will be 86, which means that (x + 9) + (x + 6 + 9) = 86.

Simplifying the equation, we get 2x + 24 = 86.

Solving for x, we get x = 31.

Therefore, John Paul's current age would be x + 6 = 31 + 6 = 35 years old.

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The required probability is 0.132 .

What is normal approximation?

The sampling distribution of averages or proportions from a large number of independent trials approximately and the expectation of a sample proportion or average is the corresponding population value.

On solving using mean sampling method, we get

P(E) = 0.132

Hence, the required probability is 0.132 .

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The group of families in which the proportion of children has contracted sharply from 1980 to 2013 is Middle-Income group.

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Answer:

5.05*10³

Step-by-step explanation:

To find the volume of figures 6-11, we need to apply the appropriate formula based on the shape of the figure and its dimensions. Once we have the measurements, we can plug them into the formula and solve for the volume. It is important to round to the nearest hundredth when necessary, as indicated in the directions.

Certainly, I can help you with finding the volume of figures 6-11. Before we begin, it is important to understand that the volume of a figure is the amount of space it takes up in three-dimensional space. To find the volume of a figure, we need to know its dimensions and apply the appropriate formula.
Let's start with figure 6, which is a rectangular prism. A rectangular prism has three dimensions: length, width, and height.

The formula for finding the volume of a rectangular prism is V = lwh, where l represents the length, w represents the width, and h represents the height.

So, to find the volume of figure 6, we need to multiply its length, width, and height. Once we have these measurements, we can plug them into the formula and solve for the volume.
Figure 7 is a cylinder. The formula for finding the volume of a cylinder is V = πr^2h, where π represents pi, r represents the radius of the base of the cylinder, and h represents the height of the cylinder.

To find the volume of figure 7, we need to know its radius and height. Once we have these measurements, we can plug them into the formula and solve for the volume.
Figure 8 is a cone. The formula for finding the volume of a cone is V = (1/3)πr^2h, where π represents pi, r represents the radius of the base of the cone, and h represents the height of the cone. To find the volume of figure 8, we need to know its radius and height. Once we have these measurements, we can plug them into the formula and solve for the volume.
Figure 9 is a sphere. The formula for finding the volume of a sphere is V = (4/3)πr^3, where π represents pi and r represents the radius of the sphere. To find the volume of figure 9, we need to know its radius. Once we have this measurement, we can plug it into the formula and solve for the volume.
Figure 10 is a pyramid.

The formula for finding the volume of a pyramid is V = (1/3)Bh, where B represents the area of the base of the pyramid and h represents the height of the pyramid. To find the volume of figure 10, we need to know the area of its base and its height. Once we have these measurements, we can plug them into the formula and solve for the volume.
Figure 11 is a cube.

A cube has three equal dimensions: length, width, and height. The formula for finding the volume of a cube is V = s^3, where s represents the length of one side of the cube.

To find the volume of figure 11, we need to know the length of one side. Once we have this measurement, we can plug it into the formula and solve for the volume.
In conclusion, to find the volume of figures 6-11, we need to apply the appropriate formula based on the shape of the figure and its dimensions.

Once we have the measurements, we can plug them into the formula and solve for the volume. It is important to round to the nearest hundredth when necessary, as indicated in the directions.

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Answer:

22

Step-by-step explanation:

Answer:

22 :)

Step-by-step explanation:

PENDMAS

7 + 3 · 4 + 8 – 5

7+12+8-5

19+8-5

27-5

22

At least 11 students must take the quiz to assure that at least two have exactly the same answers to all five questions.

Determining the minimum number of students required to guarantee that at least two students have the same answers to all five questions on a multiple choice quiz. Under the area of probability and combinatorics.

There are 4 possible answers for each of the 5 questions, so there are a total of \(4^5 = 1024\) possible sets of answers.

Let's consider the opposite scenario where no two students have exactly the same answers to all five questions. In this case, the first student can choose any of the 1024 possible sets of answers. The second student must choose a different set of answers from the first student, so there are 1023 possible sets of answers for the second student. Similarly, the third student must choose a different set of answers from the first two students, so there are 1022 possible sets of answers for the third student. Continuing in this way, the nth student has 1025-n possible sets of answers to choose from.

Therefore, the total number of possible sets of answers for n students is the product of the number of possible sets of answers for each student:

1024 × 1023 × 1022 × ... × (1025-n)

We want to find the minimum value of n such that this product is less than 1024, because that is the maximum number of sets of answers possible. That is, we want to solve the inequality:

1024 × 1023 × 1022 × ... × (1025-n) < 1024

To simplify this expression, notice that each term in the product is very close to 1024, which suggests that we can approximate the product as \(1024^n\). This approximation is valid when n is much smaller than 1024, which is the case here.

Using this approximation, we can rewrite the inequality as:

\(1024^n\)< 1024

Taking the logarithm base 2 of both sides, we get:

n < log2(1024) = 10

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When the callable bond is 75 basis points using on-the-run treasuries as benchmark rates,it implies that the nominal speed is 75bp over the treasury benchmark rates.

It should be noted that a callable bond is the debt instrument whee the issuer has the right to return the principal of the investor.

Callable bonds are also known as redeemable bonds and they're paid off before the maturity date of the bond by the issuer.

It gives room for companies to pay off their debt early and then get benefit regarding favorable interests.

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The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

From the question, we have the following parameters that can be used in our computation:

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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Answer:

Ok its friday be happy

Step-by-step explanation:

The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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The polynomial function of the lowest degree that has -5, -2, and 0 as roots is f(x) = (x - 2)(x - 5).

To find the polynomial function of the lowest degree with -5, -2, and 0 as roots, we can use the factored form of a polynomial. If a number is a root of a polynomial, it means that when we substitute that number into the polynomial, the result is equal to zero.

In this case, we have the roots -5, -2, and 0. To construct the polynomial, we can write it in factored form as follows: f(x) = (x - r1)(x - r2)(x - r3), where r1, r2, and r3 are the roots.

Substituting the given roots, we have: f(x) = (x - (-5))(x - (-2))(x - 0) = (x + 5)(x + 2)(x - 0) = (x + 5)(x + 2)(x).

Simplifying further, we get: f(x) = (x^2 + 7x + 10)(x) = x^3 + 7x^2 + 10x.

Therefore, the polynomial function of the lowest degree with -5, -2, and 0 as roots is f(x) = x^3 + 7x^2 + 10x.

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The polynomial function of lowest degree that has –5, –2, and 0 as roots is f(x) = x(x + 2)(x + 5). Each root is written in the form of (x - root) and then multiplied together to form the polynomial.

The question asks for the polynomial function of the lowest degree that has –5, –2, and 0 as roots. To find the polynomial, each root needs to be written in the form of (x - root). Therefore, the roots would be written as (x+5), (x+2), and x. When these are multiplied together, they form a polynomial function of the lowest degree.

Thus, the polynomial function of the lowest degree that has –5, –2, and 0 as roots is f(x) = x(x + 2)(x + 5).

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The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. Therefore, the correct answer is C.

A pivot column is a column of the matrix that has a non-zero entry in the pivot position and all entries below the pivot are zero. In row echelon form, every row below a pivot column has a zero in the corresponding position. The pivot columns correspond to the linearly independent columns of the original matrix and the number of pivot columns determines the rank of the matrix.

The rank of a matrix is defined as the number of linearly independent columns or rows in the matrix. If the columns of a matrix span Rn, then the rank of the matrix must be equal to n. This means that the matrix must have n linearly independent columns. To ensure that the columns of A span R5, A must have at least 5 pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have a non-trivial solution, meaning that the columns of A would not be linearly independent and would not span R5.

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Answer:

- Yes, They agree

Step-by-step explanation:

Do Rachel and Dylan argree?

- Yes, They agree

Prove your answer using the values of the ratio.

100 of your friends listen to it

- Total Number = 100

Rachel said the ratio of the number of the people who liked the playlist to the number of people who did not like the playlist is 75:25.

The ratio can be simplifies further by diving all through by 25;

75/25  : 25/25

3 : 1

Dylan said that for every three people who liked the playlist, one person did not.

This simplifies to 3 : 1.

Same thing with what rachel said, so they both agree

Answer:

Misty saves $16.

Step-by-step explanation:

Total price for the purchase before discount is $48. To find how much discount, divide 48 by 3 which is 16.

Answer:

12:3

Step-by-step explanation:

The first thing you should do for this case is to graph the data you have in the statement to see the relationship between grapes and blueberries.

The function represented by the table is

y = 0.25x

Then, as Mandie is making 15 glasses of fruit salad, we have:

y + x = 15

We have two equations and two unknowns that we must solve.

y = 0.25x

y + x = 15

Resolving

For x:

0.25x + x = 15

1.25x = 15

x = 15 / 1.25 = 12

For y:

y = 0.25x = 0.25 (12) = 3

Answer

The ratio of grapes to blueberries she should use is 12: 3

( not my answer )

Buying from Value World would cost Binita £0.72 less (in pounds) than buying from Letters2go.

To compare the costs of envelopes from both shops, we need to calculate the price per envelope.

At Letters2go, the price per envelope is:

3.29 pounds / 25 envelopes = 0.1316 pounds per envelope

At Value World, the price per envelope is:

(1.95 pounds * 2 packs) / (10 envelopes * 2 packs + 1 free pack) = 0.1300 pounds per envelope

So the price per envelope at Value World is slightly less than the price per envelope at Letters2go.

To buy 450 envelopes, Binita would need to purchase:

18 packs of 25 envelopes at Letters2go (18 x 25 = 450 envelopes)

45 packs of 10 envelopes at Value World (45 x 10 = 450 envelopes)

At Letters2go, the cost of 18 packs of 25 envelopes would be:

18 packs x £3.29 per pack = £59.22

At Value World, the cost of 45 packs of 10 envelopes (with 15 packs being free) would be:

30 packs x £1.95 per pack = £58.50

Therefore, buying from Value World would cost Binita £59.22 - £58.50 = £0.72 less than buying from Letters2go.

Correct Question :

Binita is going to buy 450 envelopes.

Here is some information about the cost of envelopes in two shops,

Letters2go : Pack of 25 envelopes for £3.29

Value World : Pack of 10 envelopes for £1.95, Buy 2 packs get 1 pack free

How much less, in pounds (£), will it cost Binita to buy the envelopes from Value World.

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To solve this problem, we need to use some trigonometry. We can use the tangent function to find the length of the magma below sea level.

Let's define the following variables:

• x: the length of magma below sea level (what we want to find)

• y: the total length of magma (which we don't know)

• θ: the angle of elevation, which is 40°

We can set up a right triangle with the hypotenuse representing the total length of magma (y), the opposite side representing the length of magma below sea level (x), and the adjacent side representing the distance from the volcano to the point where the magma rises above sea level (which we don't need to calculate).

Using the tangent function, we can write:

tan(θ) = x / y

Rearranging this equation, we get:

x = y * tan(θ)

Now we just need to plug in the values we know:

• θ = 40°

• y = 15 kilometers (since the magma reservoir is located 15 kilometers beneath the Chijiwa Bay)

Using a calculator, we can evaluate tan(40°) to be approximately 0.8391.

Plugging in these values, we get:

X = 15km*0.8391, X = 12.5865km

Therefore, the length of magma below sea level is approximately 12.5865 kilometers



The dance company sold 102 adult tickets and 358 child tickets. We can calculate it in the following manner. Let's use the following variables:
- A = number of adult tickets sold
- C = number of child tickets sold

From the problem, we know that:
- A + C = 460 (since the company sold a total of 460 tickets)
- 14A + 9C = 4650 (since the total receipts were $4,650)

We can use the first equation to solve for one of the variables in terms of the other:
A + C = 460
A = 460 - C

Now we can substitute this expression for A into the second equation and solve for C:
14A + 9C = 4650
14(460 - C) + 9C = 4650
6440 - 14C + 9C = 4650
-5C = -1790
C = 358

So the dance company sold 358 child tickets. To find the number of adult tickets sold, we can use the equation A + C = 460 and substitute in the value we just found for C:
A + C = 460
A + 358 = 460
A = 102

Therefore, the dance company sold 102 adult tickets and 358 child tickets.

Let the number of adult tickets be A and the number of child tickets be C.

We have two equations based on the given information:

1. A + C = 460 (total number of tickets sold)
2. 14A + 9C = 4,650 (total revenue from ticket sales)

We can solve these equations using the substitution or elimination method. I'll use the substitution method.

From equation 1, we can write C as:

C = 460 - A

Now substitute this expression for C in equation 2:

14A + 9(460 - A) = 4,650

Expand and simplify the equation:

14A + 4140 - 9A = 4,650

Combine like terms:

5A = 510

Now divide by 5:

A = 102

Now that we know A = 102, we can find the number of child tickets sold by plugging the value of A into the equation for C:

C = 460 - 102 = 358

So, the dance company sold 102 adult tickets and 358 child tickets.

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The margin of error for the 95% confidence interval estimate for the population mean is approximately 2.402 minutes.

To find the margin of error for a 95% confidence interval estimate for the population mean, we can use the formula:

Margin of Error = (Critical Value) * (Standard Deviation / √(Sample Size))

In this case, the sample size is 24, and the sample mean is 27 minutes. The confidence interval is given as (24.47, 29.53).

To determine the critical value, we need to consider the level of confidence. For a 95% confidence level, the critical value is approximately 1.96 (assuming a large sample size).

The sample standard deviation is given as 6 minutes.

Substituting these values into the formula, we have:

Margin of Error = 1.96 * (6 / √(24))

≈ 1.96 * (6 / 4.899)

≈ 1.96 * 1.226

≈ 2.402

Therefore, the margin of error for the 95% confidence interval estimate for the population mean is approximately 2.402 minutes.

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Given that:

James is 6 times older than his friend Zach, if Zach added 8 to his age and multiplied this sum by 3.

Step-by-step explanation:

Let the Zach's age be Z years.

6 times older than Zach = 6Z

Zach added 8 to his age and multiplied this sum by 3 = 3(Z+8)

Now,

\(6Z=3(Z+8)\)

\(6Z=3Z+24\)

\(6Z-3Z=24\)

\(3Z=24\)

Divide both sides by 3.

\(Z=\dfrac{24}{3}\)

\(Z=8\)

Therefore, the required equation is \(6Z=3(Z+8)\) and Zach's age is 8 years.

Answer:

8x + 60

Step-by-step explanation:

4(x + 5) + 2(x - 10) + 2(x + 30)

= 4x + 20 + 2x - 20 + 2x + 60 (combine like terms)

= 8x + 60

The answer is 23/40

To simplify this expression, we need to find a common denominator for each pair of fractions that are being added or subtracted.

 
The common denominator for 1/4 and 1/5 is 20, so we can rewrite 1/4 as 5/20 and 1/5 as 4/20. Then, we can subtract these fractions to get 1/20.

 
The common denominator for -3/4 and 1/8 is 8, so we can rewrite -3/4 as -6/8. Then, we can add these fractions to get -5/8.

 
Now, we can combine the two simplified fractions by finding a common denominator of 40. We can do this by multiplying 20 and 8, which gives us 160.

Then, we can rewrite 1/20 as 2/40 and -5/8 as -25/40. Adding these fractions together gives us:

2/40 - 25/40 = -23/40.

The absolute value of any number is always positive so it becomes 23/40.

The simplified version of (1/4 - 1/5) + (-3/4 + 1/8) is 23/40.

The integral of (42³ - 2r + 7) dz is equal to (42³ - 2r + 7)z + C.

To integrate the function (42³ - 2r + 7) dz, we treat r as a constant and integrate with respect to z. The integral of a constant with respect to z is simply the constant multiplied by z:

∫ (42³ - 2r + 7) dz = (42³ - 2r + 7)z + C

where C is the constant of integration.

Note: The integral of a constant term (such as 7) with respect to any variable is simply the constant multiplied by the variable. In this case, the variable is z.

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Therefore , the solution of the given problem of unitary method comes out to be the annual rate of decline is £348.11.

The goal may be achieved by using extant variables, this usual convenience, or all crucial elements from the original Diocesan malleable study that followed a particular methodology. Both crucial elements will surely miss the statement if the term expression confirmation result fails to occur, but if it does, it then turns into possible to contact the entity again.

Here,

To calculate the rate of decline, we can use the following formula:

=> (Initial value - Final value) / the number of years = depreciation per year.

This situation has a starting value of E4900, a final value of E3464.76 after 4 years, and there are 4 years involved. With these numbers entered into the formula, we obtain:

The annual depreciation rate is

=>(4900 - 3464.76) / 4.

=> Depreciation = 348.31 per year.

As a result, the annual rate of decline is £348.11.

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After completing the task, we can state that As a result, each of them variable received $204 for 50 minutes of effort.

A variable is anything that may be altered in the context of a mathematical notion or experiment. Variables are frequently denoted by a single symbol. The letters x, y, and z are often used as generic variables symbols. Variables are qualities with a wide range of values that may be investigated. Size, age, money, where you were born, academic position, and kind of housing are just a few examples. Variables may be classified into two major groups using both numerical and categorical approaches.

Hugo's earnings are 54 + 3 times Oliver's earnings of 104 + 2 years.

Both earned the same amount of money: 54 + 3x = 104 + 2y

Each worked the same number of hours: x = y

We may use the second equation to replace y in the other equations, yielding:

Hugo's profits are as follows: 54 + 3x

Earnings for Oliver: 104 + 2x

Both earned the same amount of money: 54 + 3x = 104 + 2x

Each worked the same number of hours: x = y

When we simplify the third equation, we get:

x = 50

When we enter x = 50 into the first two equations, we get:

Hugo's profits are as follows: 54 + 3(50) = 204

Oliver's profits are as follows: 104 + 2(50) = 204

As a result, each of them received $204 for 50 minutes of effort.

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Answer:

1,1

3,3

4,4

5,5

Step-by-step explanation:

see picture

Answer:

The formula for the area of a square is:

\( {length}^{2} \: or \: length \: \times \: length\)

So, to work out the side lengths you should square root each area value:

\( \sqrt{1} = 1\)

As 1 × 1 = 1

So the side lengths of the 1 unit area square is 1 unit.

\( \sqrt{9} = 3\)

As 3 × 3 = 9

So the side lengths of the 9 units area square is 3 units.

\( \sqrt{16} = 4\)

As 4 × 4 = 16

So the side lengths of the 16 units area square is 4 units.

\( \sqrt{25} = 5\)

As 5 × 5 = 25

So the side lengths of the 25 units area square is 5 units.