A ball is thrown from an initial height of 2 meters with an initial upward velocity of 15 m/s. The ball's height h (in meters) after t
seconds is given by the following.
h=2+15t-5t^2

Find all values of t for which the ball's height is 7 meters
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)

The correct way to name the figure shown is PQ. This figure consists of two perpendicular lines, P and Q, which intersect at a point. The lines are labeled P and Q, so the correct name for the figure is PQ.

Perpendicular lines are those two lines that intersect each other at a 90 degree angle. These lines are also known as orthogonal lines. When two lines intersect at a 90 degree angle, they are said to be perpendicular.

The figure is a basic geometric shape and is used to illustrate the concept of perpendicular lines. In the figure shown, the angle formed by the intersection of the two lines is a right angle, so the lines are perpendicular.

The figure can also be used to illustrate the concept of a transversal. A transversal is a line that intersects two other lines at different points. In the figure, the line PQ is a transversal intersecting the two lines P and Q.

In conclusion, the correct way to name the figure shown is PQ. This figure is used to illustrate the concepts of perpendicular lines, line segments, and transversals.

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Answer:

1: 10

Step-by-step explanation:

2/2 =2

20/2 = 10

Pat ran more miles by the end of the week with a total of 8.25 miles. Pat ran 0.5 miles more than Toby.

Algebra is a branch of mathematics that deals with mathematical expressions and equations, using letters and symbols to represent numbers and quantities. It involves the manipulation and solving of equations and inequalities involving variables.

In algebra, variables are represented by letters, usually x, y, or z, and they can represent any number or quantity. Algebraic expressions are formed by combining variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division.

To determine who ran more miles by the end of the week, we need to calculate the total number of miles each person ran. We can do this by adding up the miles from each day:

Pat: 2.75 + 3 + 2.5 = 8.25 miles

Toby: 2 + 2.25 + 3.5 = 7.75 miles

Therefore, Pat ran more miles by the end of the week with a total of 8.25 miles. Pat ran 0.5 miles more than Toby.

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The complete question is:

The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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The probability of getting exactly one face card is 0.72.

According to the questions two cards are drawn from a deck.

Since, we know that

Total number of cards in a deck = 52

Total number of face cards =  3 × 4 = 12

So, the number of ways of selecting 2 cards from a deck = \(^{52} C_{2}\)

And, the total number of ways of  getting exactly one face cards

= \(^{12} C_{1} \times ^{40} C_{1}\)  + \(^{40} C_{1} \times ^{12} C_{1}\)

= 2\(^{40} C_{1} \times ^{12} C_{1}\)

Therefore, the probability of getting exactly one face card

= \(\frac{2(^{40} C_{1} \times ^{12} C_{1})}{^{52C_{2} } }\)

\(= \frac{2(\frac{40 \times 39!}{1!\times 39!} \frac{12\times 11!}{11!}) }{\frac{52\times 51\times 50!}{2!\times50!} }\)

\(= \frac{2(40\times 12)}{26\times 51}\)

\(=\frac{2\times 480}{1326}\)

= 0.72

Hence, the probability of getting exactly one face card is 0.72.

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Answer:

The answer is 912

Step-by-step explanation:

Answer:

See below for proof.

\(S_{500}=125250\)

Step-by-step explanation:

Given arithmetic series:

Therefore:

\(S_n=1+2+3+...+(n-2)+(n-1)+n\)

\(S_n=1+(1+1)+(1+2)+...+(1+n-3)+(1+n-2)+(1+n-1)\)

\(S_n=1+(1+1)+(1+2(1))+...+(1+(n-3)(1))+(1+(n-2)(1))+(1+(n-1)(1))\)

Let:

Therefore:

\(S_n=a+(a+d)+(a+2d)+...+(a+(n-3)d)+(a+(n-2)d)+(a+(n-1)d)\)

Reverse the order:

\(S_n=(a+(n-1)d)+(a+(n-2)d)+(a+(n-3)d)+...+(a+2d)+(a+d)+a\)

Add the two expressions for Sₙ:

\(2S_n=(2a+(n-1)d)+(2a+(n-1)d)+(2a+(n-1)d)+...+(2a+(n-1)d)\)

Therefore, the term (2a + (n – 1)d) has been repeated n times:

\(2S_n=n(2a+(n-1)d)\)

Divide both sides by 2:

\(S_n=\dfrac{1}{2}n(2a+(n-1)d)\)

\(S_n=\dfrac{1}{2}n(a+a+(n-1)d)\)

Replace  a with  a₁  (first term) and a + (n – 1)d  with  aₙ (last term):

\(S_n=\dfrac{1}{2}n(a_1+a_n)\)

To find the sum of the series 1 + 2 + 3 + ... + 500, substitute the following values into the formula:

Therefore:

\(\implies S_{500}=\dfrac{1}{2}(500)(1+500)\)

\(\implies S_{500}=250(501)\)

\(\implies S_{500}=125250\)

Answer:

Step-by-step explanation:

Given the function

f(x) = 2x³ -3x²+ 7

putting x=-1 to find f(-1)

f(-1) =  2(-1)³ -3(-1)²+ 7

      = -2 + 3 + 7

      = 8

putting x=1 to find f(1)

f(1) =  2(1)³ -3(1)²+ 7

      = 2 - 3 + 7

      = 6

putting x=2 to find f(2)

f(2) =  2(2)³ -3(2)²+ 7

      = 16 - 12 + 7

      = 11

Therefore,

Answer:

see below

Step-by-step explanation:

Use pythagorean theorem:

\(a^{2} +b^{2} =c^{2} \\\)

For example, if we are given the lengths:

Short side: 3

Hypotenuse: 5

and we have to find the other side length:

\(a^{2} +b^{2} =c^{2} \\3^{2} +b^{2} =5^{2} \\9+b^{2} =25\\b^{2} =16\\b=4\)

So, the missing side length would be 4.

Hope this helps!  :)

To use long division in polynomials, we follow steps similar to normal long division, but we look for the terms from higher degree to lower.

We are dividing:

By:

We want to multiply the divisor by some expression that will make the higher term equal to the higher term of the dividend. The higher term of the dividend is 4x³, to get to that, we can multiply the divisor by 2x²:

Now we have the same term, so we just substract what we have got from the dividend:

Notice that we don't have a third degree term anymore.

So, until now we have done:

- Multiplied the divisor by 2x²

- Got a remainder of -5x² + 3

Now, we just repeat with the remainder.

We want to multiply 2x - 1 so that the higher term is -5x², so we can multiply by -5x/2:

And we do the substraction:

So, now we have got:

- Multiplied the divisor by 2x² and then by -5x/2

- Got a remainder of -5x/2 + 3

Now, we repeat once more:

To get -5x/2, we multiply the divisor by -5/4:

And we substract from the remainder:

So, we have done:

- Multiplied the divisor by 2x² then -5x/2 then -5/4

- Got a remainder of 7/4

This means that th result of the division is:

And the remainder is:

But, the answer wants us to write what the dividend is equal to.

Let's write first in the division form:

Notice that we result is the quotient plus the remainder divided by the divisor.

If we multiply both sides by the divisor, we will get:

That is the answer.

Using the Binomial probability distribution,

The probability that exactly two customers in the sample will default on their payments is 0.31..

We have given that,

4% of total customers a mortgage company default on their payments .

The probability of success i.e number of customers default on their payments (p) = 4%

= 0.04

The probability of failure (q) = 1-p = 1-0.04 = 0.06

Total number of customers in sample (n) = 20

we have to find out the probability that exactly two customers in the sample will default on their payments.

Using the Binomial probability distribution,

P(X=x)= ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾

the required probability is P(X= 2 )

Now, P(X= 2) = ²⁰C₂(0.04)²(0.06)¹⁸

=> P(X=2) = 190 × 0.0016 × 1.0155 = 0.31

Hence, the required probability is 0.31

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We need to read the graph and see which statement describes the function.

We will see that the correct option is A: "The function is negative when x < 0"

First let's see the important things of the graph:

Then we know that this is an inverse function like:

y = f(x) = 1/x

Now let's see which statement correctly describes the function:

A) The function is negative when x < 0.

This is true, you can see that when x < 0, the function is below the horizontal axis, thus for x < 0 the function is negative.

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To find the mean number of calories in the sample of hamburgers, we sum up all the calorie values and divide by the total number of hamburgers.

340 + 350 + 300 + 250 + 270 + 340 = 1850

To calculate the mean, we divide the sum by the number of hamburgers:

1850 / 6 = 308.33

Therefore, the mean number of calories in the sample of hamburgers is 308.3 (rounded to one decimal place).

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Answer:

a = \(\frac{b-4}{-2y}\)

Step-by-step explanation:

ay + 4 = 3ay - b  Subtract 4 from both sides

ay = 3ay -b - 4  Subtract 3ay from both sides

ay - 3ay = b - 4  Factor out the a

a (y -3y)  = b =4  Combine like terms

a(-2y) = b - 4  Divide both sides by -2y

a = \(\frac{b-4}{-2y}\)

Answer:

x = 5

Step-by-step explanation:

5(2x-5) +10x = 75

10x -25 +10x = 75

20x - 25 = 75

20x = 100

x = 5

Answer:

m = 8

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

When any 2 lines are parallel, they will have the same slope but different y-intercepts.

∴ Our parallel line's slope will be 8.

Answer:

8x+120 is the answer

Step-by-step explanation:

8(x+15)

=8x + 8×15

=8x+120

If one of the zeros in the quadratic polynomial is 4, then the value of k is 3.

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x. A polynomial is a mathematical expression that only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are also known as indeterminates in mathematics.

Here,

4 is a root/zero of polynomial

P(x)  =   (k-2) x²  - 2 x  - (k+5)

P(4) = 0

(k - 2) 4²  - 2 * 4 - (k+5)  = 0

15 k - 45 = 0  

k = 3

The value of k if 4 is one of the zeros of the quadratic polynomial is 3.

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Complete question:

If one of the zeros of a quadratic polynomial(k-2)x^2-2x-(k+5) is 4 , find value of k.

Answer:

13, 14, 15, 16

Step-by-step explanation:

Call the first number  n.  Then the next three consecutive numbers (assuming integers) are  n + 1, n + 2, n + 3.

The mean is the total of the numbers divided by how many there are.

\(\frac{n+(n+1)+(n+2)+(n+3)}{4}=14.5\)

Simplify and multiply by 4.

\(4n+6=58\\4n=52\\n=13\)

The first number is 13.

The median is 14.5, halfway between the "middle" numbers 14 and 15.  This is just a check; no additional equation is necessary.

Step-by-step explanation:

\((A-B) = ( - 2, \: - 2, \: - 2, \: - 2)\)

The mean GPA is greater than 2.75.

A= 4.0, A- = 3.7, B+ = 3.three, and many others. Total the first-class factors, and overall the credit hours. Divide the overall satisfactory points by means of the overall credit score hours.

Grade point average (GPA) is the measure used to summarize your instructional fulfillment at Griffith. After the e-book of final grades every trimester, your software and career.

GPA is calculated and could be utilized by the college to tell choices, which include the subsequent: educational progression.

Divide the total range of grade factors earned with the aid of the total number of letter-graded units undertaken.

Mean GPA = total / 50    

                  = 2.75.

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Answer: if you want me to solve x here if you want me to solve y here, look at the picture

Step-by-step explanation: hope this help

Answer:

82-5(15)=18-75=7

Step-by-step explanation:

Answer:

9.018

Step-by-step explanation:

Answer: 9.018

Step-by-step explanation:

do 4.5 times 2 which is 9, then 0.4x0.4+0.2 which gives u 9.018.

Hope this help :)

Answer:

I think C. Not exactly sure though

The expression could NOT be changed to have a denominator of 24 in order to solve is 12/20 - 2/8.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

1. 12/ 18- 1/4

= 6 x 2 / 6 x  3- 1/4

= 2/3 - 1/4

= 32/24 - 6/24

2. 12/20  - 2/8

= 3/5 - 1/4

= 12/20 - 5/20

3. 8/16 - 1/6

= 1/2 - 1/6

= 12/24 - 4/24

4. 6/16 - 2/6

= 3/8 - 1/3

= 9/24 - 8/34

Thus, the fraction cannot a denominator of 24 in order to solve is 12/20- 2/8.

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You can use the procedures listed below to determine a circle's radius:

Determine the information given: You must first determine what other measurements are given before calculating the radius. Usually, the circle's diameter or circumference is specified.

Utilize the formula: Once the given information has been located, you can use the formula that connects the radius to that measurement. The radius of a circle is calculated using the following formulas: r = d/2 (where d is the diameter) or r = C/2 (where C is the circumference).

Replace values: Enter the specified diameter or circumference into the relevant formula, then solve for the radius.

Simplify: If necessary, make the expression simpler to arrive at the final result.

For example, if the diameter of a circle is 10 cm, you can find the radius by dividing the diameter by 2:

r = d/2 = 10/2 = 5 cm

So the radius of the circle is 5 cm.

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B. Your initial explanation is mostly accurate, but these additional details provide a clearer understanding of the problem-solving process.

A. The process you described is commonly known as problem-solving or decision-making. Here's a breakdown of the steps involved: Identify the problem, Generate alternative solutions, Evaluate alternatives, Select the best solution, Implement the solution.

Identify the problem: The first step is to clearly identify and define the problem at hand. This involves understanding the nature of the problem, its causes, and its consequences or effects. Without a clear understanding of the problem, it would be difficult to find an appropriate solution.

Generate alternative solutions: Once the problem is identified, the next step is to brainstorm and generate multiple possible solutions or approaches to address the problem. This step encourages creativity and exploration of different options.

Evaluate alternatives: After generating alternative solutions, each option should be evaluated carefully. Factors such as feasibility, cost, time, resources required, and potential risks or benefits should be considered. This evaluation helps in narrowing down the options to those that are most viable.

Select the best solution: Based on the evaluation, one or more solutions may stand out as being the most effective or suitable for solving the problem. The best solution is selected based on its ability to address the problem efficiently and meet the desired objectives.

Implement the solution: Once the best solution is chosen, it is put into action. Implementation may involve planning, executing tasks, allocating resources, and managing the necessary steps to bring the solution to fruition.

It's important to note that the order of the steps may vary depending on the context and the complexity of the problem. While it's generally logical to evaluate and select the best solution before implementing it, sometimes it may be necessary to iterate through the steps, re-evaluate options, or make adjustments during the implementation phase.

Regarding the other options you mentioned:

A. This option suggests starting with identifying the best solution without understanding the nature of the problem or considering other possible solutions. As you correctly pointed out, this approach is flawed because it skips important steps in the problem-solving process.

C. This option implies evaluating and selecting the best solution before understanding the problem or considering other alternatives. Again, this is incorrect because a thorough understanding of the problem and exploration of multiple solutions should precede the evaluation and selection stage.

D. This option suggests implementing the solution before evaluating and selecting the best one. However, it's generally more effective to assess the potential effectiveness of different solutions before committing to their implementation.

In summary, your initial explanation is mostly accurate, but these additional details provide a clearer understanding of the problem-solving process.

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