Is x^2+8x+16 a perfect square

Answer:

6 hours and 45 minutes

Step-by-step explanation:

if you divide 3 hours by four songs you deduce that it take 45 minutes to record one song.

8 is double 4 so it will take 3more hours plus the 45 minutes for the ninth song.

3+3+.45= 6.45

Using the combination formula, the probability that a person with one combination of five numbers will win is:

\(\frac{1}{1,221,759}\)

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

For this problem, 5 numbers are taken from a set of 45, hence the number of combinations is:

\(C_{45,5} = \frac{45!}{5!40!} = 1,221,759\)

Hence the probability is:

\(\frac{1}{1,221,759}\)

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Answer:

7! = 5040

Step-by-step explanation:

7! is a factorial expression that can be solved as follows:

7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040

Therefore, 7! = 5040

Answer:

One way of awarding interest is called simple interest. Before we provide the formula used in calculating simple interest, let’s first define some basic terms.

Balance. The balance is the current amount in an account or the current amount owed on a loan.

Principal. The principal is the initial amount invested or borrowed.

Rate. This is the interest rate, usually given as a percent per year.

Time. This is the time duration of the loan or investment. If the interest rate is per year, then the time must be measured in years.

To calculate the simple interest on an account or loan, use the following formula.

Simple Interest

Simple interest is calculated with the formula

I=Prt,

where I is the interest, P is the principal, r is the interest rate, and t is the time.

Step-by-step explanation:

One way of awarding interest is called simple interest. Before we provide the formula used in calculating simple interest, let’s first define some basic terms.

Balance. The balance is the current amount in an account or the current amount owed on a loan.

Principal. The principal is the initial amount invested or borrowed.

Rate. This is the interest rate, usually given as a percent per year.

Time. This is the time duration of the loan or investment. If the interest rate is per year, then the time must be measured in years.

To calculate the simple interest on an account or loan, use the following formula.

Simple Interest

Simple interest is calculated with the formula

I=Prt,

where I is the interest, P is the principal, r is the interest rate, and t is the time.

Answer:

Step-by-step explanation:

here opposite =20, hypotenuse=29

to find adjacent use formula

a^2+b^2=c^2

20^2+b^2=29^2

400+b^2=841

b^2=841-400

b=\(\sqrt{441\\}\)

b=21

tan theta=opposite/adjacent

=20/21

therefore tan theta =20/21

Answer:

D. tanθ = 20/21

Step-by-step explanation:

Remember that sinθ = opposite/hypotenuse. In this case, since sinθ = 20/29, we are going to say that opposite = 20 and hypotenuse = 29.

To solve for the adjacent side, use the Pythagorean theorem, a^2 + b^2 = c^2.

When you plug in your values and solve for the other leg, you'll get 21.

Now that we know that the adjacent side/other leg is equal to 21, we can find tanθ, since it's equal to opposite/adjacent.

Opposite = 20

Adjacent = 21

tanθ = 20/21

The point where the line intersects the plane is (-1/3, 2/3, -1/3).

We substitute the equations for the line into the equation for the plane and solve for the value of t that satisfies the equation. Once we have the value of t, we can substitute it back into the parametric equations for the line to find the point of intersection.

Let's apply this method to find the point where the line x = –1 – t, y = 2 + t, z = 1+ t intersects the plane 3x + y + 3z = 1.

Substituting the equations for the line into the equation for the plane, we get:

3(-1 - t) + (2 + t) + 3(1 + t) = 1

Simplifying the left-hand side, we get:

-3t + 5 = 1

Solving for t, we get:

t = -4/3

Substituting t = -4/3 back into the parametric equations for the line, we get:

x = -1 - (-4/3) = -1/3

y = 2 - 4/3 = 2/3

z = 1 - 4/3 = -1/3

Therefore, the point where the line intersects the plane is (-1/3, 2/3, -1/3).

When we are given a line and a plane in 3D space, we can find the point where the line intersects the plane by solving the system of equations that define the line and the plane simultaneously. The equations for the line are given as parametric equations in terms of the parameter t, and the equation for the plane is given in Cartesian form.

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Answer:

21

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

AD        AH

-----  =  ---------

AB         AH +y

3        9

---- = ------

10         9+y

Using cross products:

3(9+y) = 9*10

27+3y = 90

3y = 90-27

3y =63

y = 63/3

y = 21

Answer:

y = 21

Step-by-step explanation:

According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Therefore, according to the Side Splitter Theorem:

\(\boxed{\sf AD : DB = AH : HC}\)

From inspection of the given triangle, the lengths of the line segments are:

To find the value of y, substitute the given line segment lengths into the proportion and solve for y:

\(\begin{aligned}\sf AD : DB &=\sf AH : HC\\\\3:7&=9:y\\\\\dfrac{3}{7}&=\dfrac{9}{y}\\\\3 \cdot y&=9 \cdot 7\\\\3y&=63\\\\\dfrac{3y}{3}&=\dfrac{63}{3}\\\\y&=21\end{aligned}\)

Therefore, the value of y is 21.

Answer:

Step-by-step explanation:

ima a braintlest

Based on the given data, an interaction plot can be created to visualize the relationship between self-rated social status, school type, and annual sales volumes.

The plot will show three lines, one for each school type (Ivy League, State-Supported, and Small Private), with the x-axis representing social status (Low, Medium, High) and the y-axis representing sales volumes (in $000).

The interaction plot reveals how different combinations of self-rated social status and educational background may affect employee performance in terms of sales volumes.

By analyzing the slopes and intersections of the lines, you can identify potential interactions and trends among these variables. This can help Williams Corporation in understanding the potential influence of educational background and self-rated social status on employee performance.

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Answer:

3/5

Step-by-step explanation:

because i said so ️

Answer:

1. 4.5

2. The scale factor is 3/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

y + 5 = -4/3(x - 3)

y + 5 = -4/3x + 1

y = -4/3x - 4

Answer:

Step-by-step explanation:

Since we have been given that

Ari has 3 ounces of caramel for each 5 scoops of frozen yogurt .

Freeze Zone makes bunches of milkshakes with 6 ounces of caramel and 8 scoops of frozen yogurt.

As per Ari,

For each 5 scoops of frozen yogurt, he wants 3 ounces of caramel

For each 1 scoop of frozen yogurt, he wants

3 ounces of Caramel

For each 8 scoops of frozen yogurt, he wants

3/5 * 8 = 24/5= 4.8 ounces

In this way, Ari considers sum caramel is something else for ideal milkshake as there is just requirement for 4.8 ounces of caramel however Freeze Zone is utilizing 6 ounces of caramel.

Answer:

Step-by-step explanation:

5456

Maybe 0.7 the way you put it made it confusing

For inequality –3(2x – 5) < 5(2 – x)  the correct option is (–6x + 15 < 10 – 5x).

What is inequality?

An inequality is a mathematical statement that describes a relationship between two values or expressions, indicating that they are not equal.

To solve the inequality –3(2x – 5) < 5(2 – x), we need to simplify the expression first.

Starting with the left-hand side, we can distribute the –3 to get:

–3(2x – 5) = –6x + 15

For the right-hand side, we can distribute the 5 to get:

5(2 – x) = 10 – 5x

Substituting these back into the original inequality, we get:

–6x + 15 < 10 – 5x

To solve for x, we can first move all the x terms to one side by adding 5x to both sides:

–x + 15 < 10

Then, we can move the constant term to the other side by subtracting 15 from both sides:

–x < –5

Finally, we can divide both sides by –1 (remembering to flip the inequality sign since we're dividing by a negative number) to get:

x > 5

So the first correct representation of the inequality is x > 5.

To get the second correct representation, we can also start with the inequality –6x + 15 < 10 – 5x, and move all the x terms to one side:

–6x + 5x < 10 – 15

So second option (–6x + 15 < 10 – 5x) are correct representations of the inequality.

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An example of an unsought product would be the life insurance. That is option E.

An unsought product is defined as those products that the consumers does not have an immediate needs for and they are usually gotten out of fear for danger.

Typical examples of unsought products include the following:

Other options such as furniture, laundry detergent, toothpaste and refrigerator are products that are constantly being used by the consumers.

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Answer:

G-10

Step-by-step explanation:

because i dont have time to expalin

The function rule for g(x) is g(x) = -4x

The function is given as

f(x) = 4x

The transformation is given as reflection across the x-axis

The rule of this transformation is

(x, y) = (x, -y)

So, we have

g(x) = -f(x)

This gives

g(x) = -4x

Hence, the function rule for g(x) is g(x) = -4x

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Answer:

P = 3.86n

Step-by-step explanation:

the price will be how many sets you buy multiplied by the price.

a. Less than 25 years: M: 4, F:  5    

25 to 35 years: M: 17, F: 6    

More than 35 years: M: 8, F: 10

b. The probability that the selected employee is male or their age is more than 35 years is 0.44.

a. The given data represents the Health Expenditures of employees by Age and Gender. We can summarize the data in a table by organizing the information based on the age groups and genders.

The summarized table is as follows:

| Age (years)           | Male | Female |

|-----------------------|------|--------|

| Less than 25 years    | 4    | 5      |

| 25 to 35 years        | 17   | 6      |

| More than 35 years    | 8    | 10     |

b. To find the probability that the selected employee is male or his age is more than 35 years, we need to calculate the probabilities of two events and then subtract the probability of their intersection.

1. Event A: The selected employee is male.

  We calculate the probability of Event A by dividing the number of males in the sample by the total number of individuals in the sample:

  P(A) = (Number of males in the sample) / (Total number of individuals in the sample)

       = (4 + 8) / 50

       = 12 / 50

       = 0.24

2. Event B: The selected employee's age is more than 35 years.

  We calculate the probability of Event B by dividing the number of individuals with age more than 35 in the sample by the total number of individuals in the sample:

  P(B) = (Number of individuals with age > 35 in the sample) / (Total number of individuals in the sample)

       = (8 + 10) / 50

       = 18 / 50

       = 0.36

3. Intersection of Event A and Event B: The selected employee is male and has an

age more than 35 years.

  We calculate the probability of the intersection by dividing the number of males with age more than 35 in the sample by the total number of individuals in the sample:

  P(A and B) = (Number of males with age > 35 in the sample) / (Total number of individuals in the sample)

             = 8 / 50

             = 0.16

Finally, we use the formula for the probability of the union of two events to calculate the probability that the selected employee is male or his age is more than 35 years:

P(A or B) = P(A) + P(B) - P(A and B)

         = 0.24 + 0.36 - 0.16

         = 0.44

Therefore, the probability that the selected employee is male or his age is more than 35 years is 0.44.

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Type I error is We conclude that the mean is not 34 years when it really is 34 years. The correct option to this question is C.

Rejecting the null hypothesis when it is in fact true is a Type I mistake. It entails drawing conclusions about outcomes that are statistically significant when, in fact, they were just the consequence of chance or unrelated causes.

The significance level you select (alpha or ) determines the likelihood that you will make this mistake. You determined that figure at the start of your research to determine the statistical likelihood of getting your results (p-value).

The typical significance level is 0.05 or 5%. If the null hypothesis is accurate, your results only have a 5% chance or less of occurring.

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Expression B: 3x + 10y

Expression A: 7x - 4y

The difference in calculation of expression A vs expression B is due to the signs in between the parenthesis in both expression respectively. The sign of the 2nd parenthesis in expression B will change because of the the negative sign before it. While that of the 2nd expression in A will remain the same because of the positive sign.

Expression B: (5x + 3y) - (2x - 7y)

To solve this, we need to expand the parenthesis:

5x + 3y -(2x) -(-7y)

Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.

5x + 3y -2x + 7y

collect like terms:

5x-2x + 3y + 7y

= 3x + 10y

Expression A: (5x + 3y) + (2x - 7y)

To solve this, we need to expand the parenthesis:

5x + 3y +(2x) + (-7y)

Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.

5x + 3y + 2x - 7y

collect like terms:

5x +2x +3y -7y

= 7x - 4y

True

The statement "A system composed of two linear equations must have at least one solution if the straight lines represented by these equations are nonparallel," is true.

What is a system of linear equations?

In algebra, a system of linear equations is a collection of two or more linear equations with the same variables.

If these linear equations represent two or more lines that aren't parallel, the equations are said to form a system of equations with at least one solution.

The intersection of the lines is the location where an equation system has a solution.

Two lines are parallel if they have the same slope and never intersect.

If two lines have different slopes, they are nonparallel and intersect at a point.

How can one tell if a statement is true or false?

If a claim can be verified by evidence, logic, or reason, it can be considered true.

On the other hand, a statement is false if it is inaccurate or misleading, or if it contradicts existing facts, logic, or reason.

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The area of streetlamp illuminates approximately 660.19 square meters of the street.

What is the area?

An area is a measure of the size or extent of a two-dimensional surface or region. It is the amount of space inside a flat, two-dimensional shape or figure. The area is typically measured in square units

The area of a circle is given by the formula A = πr², where r is the radius. In this case, the diameter (which is the same as the distance across the circle through the center) is 29 meters, so the radius is half of that, or 14.5 meters.

Using the formula for the area of a circle, we have:

A = πr²

A = 3.14 x 14.5²

A ≈ 660.19 square meters

Therefore, the streetlamp illuminates approximately 660.19 square meters of the street.

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The candle starts at a height of 25 centimeters and burns at a rate of 0.625 centimeters per hour.

The given table shows the height of a candle as it burns continuously over time. The first column represents time in hours, ranging from 0 to 1, while the second column represents the corresponding height in centimeters.

From the data, we can observe that the candle starts at a height of 25 centimeters when the time is 0 hours. As time progresses, the height of the candle decreases gradually. Specifically, for every hour that passes, the candle burns 0.625 centimeters.

Therefore, the main answer is that the candle starts at a height of 25 centimeters and burns at a rate of 0.625 centimeters per hour.

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