a quadratic function is represented by g(x)=-2(x-5)^2+17 what is the equation for this function in standard form
PLS HELPP

Answer: 96

The sum of the interior angles of a regular heptagon is equal to (n-2)180 degrees, where n is the number of sides of the polygon.

Since a regular heptagon has 7 sides, the sum of its interior angles is (7-2)180 = 720 degrees.

Therefore, the measure of each interior angle is 720 degrees / 7 = 104 degrees.

If the measure of an interior angle is (w + 8) degrees, then w + 8 = 104.

Solving for w, we get w = 96.

Answer: To find the father's and son's ages, we can set up two simultaneous equations:

Let's say the son's age is "x"

Then, the father's age would be x + 25

And the sum of their ages is x + (x + 25) = 53

So, 2x + 25 = 53

Solving for x, we get:

2x = 28

x = 14

Therefore, the son is 14 years old, and the father is 14 + 25 = 39 years old.

To use the elimination method, we can add the two equations:

x + (x + 25) = 53

2x + 25 = 53

Simplifying, we get:

2x = 28

x = 14

And the father's age would be x + 25 = 14 + 25 = 39 years old.

Step-by-step explanation:

The power of the snow machine is 10,000 Joules per second.

power is simply the amount of energy transferred or converted per unit time.

It is expressed as;

P =  work-done / time

P = ( force × displacement ) / time.

Given the data in the question;

Plug the given values into the above formula and solve for P.

P = ( 1000N × 1000m ) / 100s

P = ( 1000000Nm / 100s

P = 10,000 Nm/s

P = 10,000 J/s

Therefore, the power of the machine is  10,000 J/s.

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The probability that a 34 square foot metal sheet has at least 9 defects is 0.4308, rounded to four decimals.

Given that the sheet metal has an average of 7 defects per 20 square feet, we can find the rate parameter (λ) of the Poisson distribution as follows:

λ = (7 defects / 20 sq ft) = 0.35 defects per square foot

Let X be the number of defects in a 34 square foot metal sheet. Since X follows a Poisson distribution with rate parameter λ, we can find the probability that X is at least 9 defects using the cumulative distribution function (CDF) of the Poisson distribution:

P(X ≥ 9) = 1 - P(X < 9) = 1 - F(8)

where F(k) is the CDF of the Poisson distribution with rate parameter λ evaluated at k.

Using the Poisson distribution formula for F(k), we have:

F(k) = P(X ≤ k) = ∑(i=0 to k) [(λ^i * e^(-λ)) / i!]

Using a calculator or software, we can find that:

F(8) = P(X ≤ 8) = 0.5692

Therefore, we have:

P(X ≥ 9) = 1 - F(8) = 1 - 0.5692 = 0.4308

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Answer:

[tex]a_{n}[/tex] = 6n - 5

Step-by-step explanation:

there is a common difference between consecutive terms in the sequence

7 - 1 = 13 - 7 = 19 - 13 = 6

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 1 and d = 6 , then

[tex]a_{n}[/tex] = 1 + 6(n - 1) = 1 + 6n - 6 = 6n - 5

The more accurate statement is that hypotheses are only as good as the observations on which they are based.

A hypothesis is a tested assertion regarding the relationship between two or more variables or a suggested explanation for some observable occurrence in a scientific setting.

As a result, hypothesis are only as good as the observations upon which they are built.

For instance, if we stay up late, we will be fatigued the next day. Turning off your phone allows it to charge more quickly. All of them are hypotheses since they are based on observations and are only valid for as long as the observations stay true.

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The two correct statements are a. The rate of change is 3 over the interval 1 ≤ x ≤ 2 & The rate of change is 3 over the interval 1 ≤ x ≤ 3. And as well as The rate of change is 5 over the interval 2 ≤ x ≤ 3 is also correct statement.

Divide the change in y-values by its change in x-values to determine the average rate of change. Identifying changes in measurable parameters as average speed or mean velocity calls for the knowledge of the average rate of change.

The average rate is the concentration change over a selected time period. It matters when you take the measurements. The solution is to find the slopes of the line to the concentrations time versus curve at that location.

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Approximately 70 miles separated Harold's home at his grandparents' home from his own home. Accordingly, Harold travelled the following distance overall on his birthday: 70 + 74.46 + 70 ≈ 214.46

What is a distance? . Regardless of the start or end point, distance can be defined as the amount of space object has to cover.

The metre serves as the SI unit of distance (m). Centimeters (cm) are a common unit of measurement for short distances, whereas kilometres (km) are used for longer distances (km). You could measure a piece of paper's length in centimetres, for instance, by measuring from the bottom to the top.

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Based on the given simultaneous equation, the value of x=-4  whereas the value of   y=-7

Two or more algebraic equations that share variables, such as x and y, are referred to as simultaneous equations.

Because the equations are solved simultaneously, they are referred to as simultaneous equations.

Here are some examples of simultaneous equations:

2x + 4y = 14

4x 4y = 4

6a + b = 18

4a + b = 14

3h + 2i = 8

2h + 5i =10

Each of these equations could have an infinite number of solutions.

However, if we have at least as many equations as variables, we may be able to solve them using simultaneous equations methods.

So, given

{y=−2x+1

{4x+y=9

-4x+y=9     get y alone

add 4x both sides

y=4x+9

insert into y=2x+1

2x+1=4x+9

subtract 1 both sides

2x=4x+8

subtract 4x both sides

-2x=8

divide by -2

x=-4

y=2x+1

y=2(-4)+1

y=-8+1

y=-7

check

-4(-4)+(-7)=9

16+(-7)=9

9=9

x=-4

y=-7

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The algebra word problem method shows that Richard is 22 years old and Teo is 6 years old.

Algebra is used in our daily lives without us even recognizing it. Students can relate to and comprehend the significance of mathematics in the real world by solving algebraic word problems in worksheets.

Algebraic word problems usually comprise interpreting words into numbers, variables, their coefficients, and the use of appropriate arithmetic operations.

From the information given, we can the following system of equations as follows:

r + t = 28     --- (1)

r =  2t + 10   --- (2)

(2t + 10) + t = 28

3t + 10 = 28

3t = 28 - 10

3t = 18

t = 18/3

t = 6

From (1),  r + t = 28

r + 6 = 28

r = 28 - 6

r = 22

Therefore, we can conclude that Richard is 22 years old and Teo is 6 years old.

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Answer: The number of blue marbles in the sample is 11, so the proportion of blue marbles in the sample is 11/20. If the sample is representative, we can use this proportion to estimate the proportion of blue marbles in the whole bag of 950 marbles. So, our estimate of the number of blue marbles in the whole bag is:

950 * (11/20) = 477.5

So, we can estimate that about 478 marbles out of 950 are blue.

Step-by-step explanation:

The probability of both free throws is 0.7921, at least one free throw is 0.9889, missing both free throws is 0.0121.  58% of his free throws is a better strategy as it results in a higher probability of missing at least one free throw.

The probability of making one free throw is 0.89. Therefore, the probability of making both free throws is: 0.89 * 0.89 = 0.7921 (rounded to 2 decimals).

The probability of missing one free throw is 1 - 0.89 = 0.11. Therefore, the probability of making at least one free throw is: 1 - 0.11 * 0.11 = 0.9889 (rounded to 2 decimals).

The probability of missing one free throw is 0.11. Therefore, the probability of missing both free throws is: 0.11 * 0.11 = 0.0121 (rounded to 2 decimals).

For the worst free-throw shooter who makes 58% of his free throws:

The probability of making both free throws is: 0.58 * 0.58 = 0.3364 (rounded to 4 decimals).

The probability of making at least one free throw is: 1 - 0.42 * 0.42 = 0.8236 (rounded to 2 decimals).

The probability of missing both free throws is: 0.42 * 0.42 = 0.1764 (rounded to 4 decimals).

For the player who makes 89% of his free throws:

The probability of making both free throws is: 0.89 * 0.89 = 0.7921 (rounded to 4 decimals).

The probability of making at least one free throw is: 1 - 0.11 * 0.11 = 0.9889 (rounded to 2 decimals).

The probability of missing both free throws is: 0.11 * 0.11 = 0.0121 (rounded to 4 decimals).

Therefore, intentionally fouling the player who makes 58% of his free throws is a better strategy as it results in a higher probability of missing at least one free throw.

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There are a few general reasons why Marcus's results might differ from Zara and Arun's:

In terms of Solubility: Different solutes have different solubilities, which means they will dissolve to different extents in water. It's possible that the solutes Marcus is using have lower solubilities than the solutes used by Zara and Arun, which could lead to differences in the amount of solute that dissolves.

   Amount of solute added: Even if all three individuals add the same amount of solute to their test tubes, the amount of solute that actually dissolves may differ due to differences in solubility. If Marcus is using solutes with lower solubilities, he may be adding the same amount of solute as Zara and Arun, but a smaller proportion of it is dissolving.

  Spatula size: Marcus has the same number of spatulas for all three solutes, but it's possible that the size of his spatulas differs from those used by Zara and Arun. If Marcus's spatulas are smaller, he may be adding less solute to his test tubes, which could explain the differences in his results.

 Lastly, in terms of Experimental error: Finally, it's possible that there is some experimental error that is affecting Marcus's results. For example, he may not be measuring the amount of solute accurately, or he may be adding it to the test tube in a way that doesn't allow it to dissolve as well.

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We can fit 33 books on a 42-inch shelf if each book is 1 1/4 inches wide.

Using a unitary method, we can easily solve problems that involve proportional relationships between different units. In this problem, we used the unitary method to determine how many books can fit on a shelf based on its length and the width of one book.

To find out how many books can fit on a 42-inch shelf, we need to divide the length of the shelf by the width of one book. In this case, each book is 1 1/4 inches wide. However, it's important to convert this fraction to a decimal so we can do the math more easily. To do this, we can divide 1 by 4 and add it to 1 1/4:

1/4 = 0.25

1 1/4 = 1 + 0.25 = 1.25

Now that we know each book is 1.25 inches wide, we can use the unitary method to find how many books can fit on the shelf:

1 book = 1.25 inches

x books = 42 inches

To solve for x, we can cross-multiply:

1 book * 42 inches = 1.25 inches * x books

42 = 1.25x

Finally, we can divide both sides by 1.25 to isolate x:

42 / 1.25 = x

33.6 = x

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The true statements are ∠X and ∠Y are supplementary angles, ∠W and ∠Z are a linear pair and ∠Y and ∠Z are complementary angles. The solution has been obtained by using angles and line.

What are angles and line?

Lines having little depth or width are said to be straight. Lines can be perpendicular, intersecting, transversal, and many more various forms. A figure in which two rays emanate from the same point is referred to be an angle.

We know that angles on a straight line add up to 180° and such angles are called supplementary angles.

Therefore, ∠X and ∠Y are supplementary angles.

Similarly, we know that angles on a straight line form a linear pair.

Therefore, ∠W and ∠Z are a linear pair.

Also, we know that two angles are complementary when their sum is 90°.

We can see from the figure that ∠Z and ∠Y add up to 90°.

Therefore, ∠Y and ∠Z are complementary angles.

Hence, the above provided statements are true about the angles.

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The figure of the question is attached below

It is important to note that this calculation provides the value of tan(x) in terms of the cosine of the angle x, which is dependent on the specific triangle that is being considered.

Given the triangle with sides ZY = 48, ZX = 50, and XY = 14, we can use trigonometry to find the value of tan(x).

First, we can use the Pythagorean theorem to find the value of YX, the length of the side opposite angle x:

[tex]YX = \sqrt{(ZY^2 + ZX^2 - 2 * ZY * ZX * cos(x))[/tex]

We know that ZY = 48 and ZX = 50, so we can substitute these values into the equation:

[tex]YX = \sqrt{(48^2 + 50^2 - 2 * 48 * 50 * cos(x))[/tex]

[tex]YX = \sqrt{(2304 + 2500 - 2400 * cos(x))[/tex]

Next, we can use the definition of tangent to find the value of tan(x):

[tex]tan(x) = YX/ZX = \sqrt{(2304 + 2500 - 2400 * cos(x)) / 50[/tex]

It is important to note that this calculation provides the value of tan(x) in terms of the cosine of the angle x, which is dependent on the specific triangle that is being considered. The exact value of tan(x) will depend on the specific angle x in the triangle.

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Answer: x = 4, y = -8

Step-by-step explanation:

Because 2 is a multiple of four, multiply the first equation by two to eliminate the x value and effectively isolate y.

4x - 4y = 48

4x + 7x = -40

If we were to subtract the x values, that gives us -11y = 88, or y = -8.

Then, just plug y into your equation of choice.

2x - 2(-8) = 24

2x + 16 = 24

2x = 8

x = 4

One way you can check whether the values is right is plug the y value into the other equation and see if you receive the same answer.

4x + 7(-8) = -40

4x = -40 + 56

4x = 16

x = 4

Answer:

Number is -10

Step-by-step explanation:

Let Number be x

so, 5x= 30+8x

Take 30 other side and 5x other side

so, 8x-5x=-30

3x=-30

x=-10

HOPE THIS HELPS... THANK YOU

The volume of the solid of revolution is equal to 21π cubic units.

In this problem we find the representation of a figure, whose area is also shown and whose solid of revolution is can be defined by following formula:

V = π · A

Where:

First, the area of the representation is found by summing the areas of two compounding rectangles:

A = 5 · 3 + 2 · 3

A = 21

Second, compute the volume of the solid of revolution:

V = 21π

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Answer:

Step-by-step explanation:

To find the length of JL in the right triangle JKL, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides equals the square of the length of the hypotenuse (the longest side). In this case, JL is the hypotenuse and JK and KL are the two shorter sides.

Since K is a right angle in triangle JKL, we can find the lengths of JK and KL using the given information. We have KM = 6 and JM = 8, so we can use those values to find JK and KL:

JK = √(JM^2 - KM^2) = √(8^2 - 6^2) = √(64 - 36) = √(28) = 2√(7)

KL = KM = 6

Finally, to find JL, we can use the Pythagorean theorem:

JL = √(JK^2 + KL^2) = √( (2√(7))^2 + 6^2) = √(4 * 7 + 36) = √(52) = 2√(13)

So, JL = 2√(13).

Answer:

(-1,3) and (3,-5)

Step-by-step explanation:

I'm assuming since it is giving no information that it wants where the two graph intersect each other.

So, by the looks of it they intersect at

(-1,3) and (3,-5)

Step-by-step explanation:

173 bagels left after the first hour.

A t-test is a statistical test used to determine if there is a significant difference between the means of two groups.

In this case, the two groups being compared are first basemen and all other players, and the variable being measured is salary. By performing a t-test, we can determine if there is a significant difference in the average salary between first basemen and all other players.

To perform a t-test, we first calculate the difference in means between the two groups and divide by the standard error of the difference. The standard error takes into account the variability in the sample and the sample size. The result is the t-statistic, which is then compared to a t-distribution with degrees of freedom equal to the sum of the degrees of freedom of the two groups minus 2. The t-distribution gives us the probability of observing a difference as large or larger than the observed difference by chance if the two groups have the same mean. This probability is known as the p-value.

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Answer:

Step-by-step explanation:

3400/170 = 20 minutes.

Answer:

20 minutes

Step-by-step explanation:

3400 words / 170 wpm

20 minutes

The ordinary numbers for the expressions will be

a. 3.25*10⁴ = 32500

b. 6.04*10⁻³= 0.00604

c. 2400000 = 2.4*10⁶

d. 0.00147 = 1.47*10⁻³

What are expressions exactly?

In mathematics, expressions are mathematical assertions made up of at least two sentences that contain numbers, variables, or both and are linked by an operator. Mathematical operations include addition, subtraction, multiplication, and division. For example, x + y is an equation that uses an addition operator to separate the components x and y. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is six times the size of another number, x. This sentence is mathematically stated as x/2 + 6. Mathematical expressions are used to address complex problems.

Now,

Given expressions/Numbers are a. 3.25*10⁴  then ordinary form is

3.25*10000

=32500

b. 6.04*10⁻³ then ordinary numbers is

=6.04/1000

=0.00604

c. 2400000 then standard from is

=2.4*1000000

=2.4*10⁶

d. 0.00147  then standard form is

=1.47/1000

=1.47*10⁻3

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Answer:

Step-by-step explanation: