The path of the basketball is modeled by the equation h() = −.25 + 2 + 4 where t is the time in seconds and h(t) is the height of the basketball at time t. What type of vertex (minimum or maximum) would this quadratic function create? Explain, using any method, how you found your answer.

The solution to the equation [tex]4x^2 = 5(4x - 5)[/tex] is x = 5/2."

To solve the equation [tex]4x^2[/tex] = 5(4x - 5), we first simplify the right-hand side by using the distributive property:

Next, we bring all the terms to one side of the equation by subtracting 20x and adding 25 to both sides:

[tex]4x^2 - 20x + 25 = 0[/tex]

This equation is now in the form of a quadratic equation [tex]ax^2[/tex] + bx + c = 0, where a = 4, b = -20, and c = 25. We can solve for x using the quadratic formula:

[tex]x = (-b ± sqrt(b^2 - 4ac)) / 2a[/tex]

Substituting the values of a, b, and c, we get:

x = (-(-20) ±  - 4(4)(25))) / 2(4)

x = (20 ± sqrt(400 - 400)) / 8

x = 5/2

Solve 4 x squared equals 5 left parenthesis 4 x minus 5 right parenthesis.

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Eden consumed a total of 9.75 quarts of sports drinks during both practices.

Eden brings a 0.75-quart bottle of sports drink to each softball practice. At her first practice, she drank 12 bottles of sports drinks. This means she drank a total of:

12 bottles x 0.75 quarts/bottle = 9 quarts

At her second practice, she drank the entire bottle, which is another 0.75 quarts.

Therefore, the total amount of sports drinks Eden consumed during both practices are:

9 quarts + 0.75 quarts = 9.75 quarts

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Answer:

approximately 0.0018 feet, or about 0.0216 inches.

Step-by-step explanation:

The volume of the suitcase is:

V_suitcase = height x length x width

V_suitcase = 5 ft x 4 ft x 4 ft

V_suitcase = 80 cubic feet

The volume of each supply is:

V_supply = base area x height

We know that the base area of each supply is 9 square feet. Let's assume that the height of each supply is h.

So, the total volume of all the supplies that can be put in the suitcase is:

V_total_supplies = V_supply x number of supplies

V_total_supplies = (9 ft^2 x h) x 5120

We want to find the height of each supply, so we can rearrange the equation above to solve for h:

h = V_total_supplies / (9 ft^2 x 5120)

Substituting the values we know:

h = (80 ft^3) / (9 ft^2 x 5120)

Simplifying, we get:

h = 0.0018 ft

So the height of each supply is approximately 0.0018 feet, or about 0.0216 inches.

The third quartile (Q3) of this data set is 29.

A data set is a collection of data that is organized. It is typically structured to allow for easy access and manipulation of the data. It is generally composed of a set of values, observations, or measurements that are related to each other and that can be used to analyze and interpret information. Data sets may include variables, such as names, numbers, addresses, and dates, or they may include images, audio, or video. Data sets can be used for academic research, business analysis, or other purposes.

To calculate Q3, we divide the set into four quarters. The first quarter (Q1) is the set of values from the smallest to the median, which is 18.

The second quarter (Q2) is the set of values from the median to the third quartile, which is 29. The third quarter (Q3) is the set of values from the third quartile to the largest value, which is 36.

The fourth quarter (Q4) is the set of values from the largest value to the smallest value, which is 12. Therefore, the third quartile (Q3) of this data set is 29.

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complete questions as follows-

Answer:

$624

Step-by-step explanation:

The width is the smaller side and there are four sides to a rectangle so 2 sides are 36 cm and 2 sides are 42cm. The perimeter formula follows this P=(L+W)*2 so plugging the variables (42+36)*2= 156. So there are 156 meters of fencing and each meter costs $4.00. Thus, 156*4=$624

The function is   [tex]8100(1.000101369)^{365t}[/tex] and percentage of growth is 84%.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

Here the principal p = $8100

Rate of interest r = 3.7% = 3.7/100 =0.037

Compounded daily then n= 365

Now using compound interest formula then,

=> CI = [tex]P(1+\frac{r}{n})^{nt}[/tex]

=> CI = [tex]8100(1+\frac{0.037}{365})^{365t}[/tex]

=> CI = [tex]8100(1+0.000101369)^{365t}[/tex]

=> CI = [tex]8100(1.000101369)^{365t}[/tex]

Then the function is f(t) = [tex]8100(1.000101369)^{365t}[/tex] .

Now percentage of growth per year is ,

=>  [tex]8100(1.000101369)^{365t}[/tex][tex]\times\frac{1}{100}\%[/tex]

Put t=1 then

=> 8,405.30[tex]\times\frac{1}{100}\%[/tex]

=> 84%

Hence the function is   [tex]8100(1.000101369)^{365t}[/tex] and percentage of growth is 84%.

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Answer:

no solutions

Step-by-step explanation:

y + 7 = y - 3 ( subtract 7 from both sides )

y = y - 10 ( subtract y from both sides )

0 = - 10 ← false statement

this false statement indicates the equation has no solution

Answer:

(a) What percentage of women would not be able to use the original ejection seats designed for men?

To answer this question, we need to find the percentage of women whose weight is outside the range of 140 lb to 201 lb, which is the weight range for which the original ejection seats were designed. We can do this by standardizing the weight distribution of women using the formula:

z = (x - μ) / σ

where z is the standard score, x is the weight of a woman, μ is the mean weight of women, and σ is the standard deviation of the weight of women.

Substituting the given values, we get:

z = (140 - 162) / 46 = -0.478

z = (201 - 162) / 46 = 0.848

Using a standard normal table or a calculator, we can find that the percentage of women whose weight is below 140 lb (corresponding to a z-score of -0.478) is 31.45%. Similarly, the percentage of women whose weight is above 201 lb (corresponding to a z-score of 0.848) is 19.34%. Therefore, the percentage of women who would not be able to use the original ejection seats designed for men is:

31.45% + 19.34% = 50.79%

(b) What weight range would accommodate 99.7% of the female pilots?

To find the weight range that would accommodate 99.7% of the female pilots, we need to find the z-scores that correspond to the 0.15% and 99.85% percentiles of the standard normal distribution. Using a standard normal table or a calculator, we can find that these z-scores are approximately -2.97 and 2.97, respectively.

Substituting these z-scores into the standardization formula, we get:

-2.97 = (x - 162) / 46

x = 63.88 lb

and

2.97 = (x - 162) / 46

x = 260.12 lb

Therefore, the weight range that would accommodate 99.7% of the female pilots is approximately 63.88 lb to 260.12 lb.

(c) What percentage of women would need ejection seats redesigned for them?

To find the percentage of women who would need ejection seats redesigned for them, we need to find the percentage of women whose weight is outside the weight range that would accommodate 99.7% of the female pilots. Using the values from part (b), we can see that the weight range that would accommodate 99.7% of the female pilots is approximately 63.88 lb to 260.12 lb. Therefore, the percentage of women who would need ejection seats redesigned for them is:

100% - 99.7% = 0.3%

This equation is clearly not true, which means there is no real value of x that satisfies it. Therefore, the system of equations represented by line A and line B has no real solutions, the correct option is C.

Line A has a slope of 7, which means any line parallel to it will also have a slope of 7. Therefore, line B can be represented by the equation y = 7x + b, where b is the y-intercept that we need to find.

We know that line B passes through the point (2, 24), so we can substitute these values into the equation to get:

24 = 7(2) + b

Simplifying the right side gives:

24 = 14 + b

Subtracting 14 from both sides gives:

b = 10

Therefore, the equation of line B is y = 7x + 10.

Now we need to find the point of intersection between line A and line B, which is the solution to the system of equations represented by these two lines. To accomplish this, we can put the two equations equal to one another and find x:

7x + 12 = 7x + 10

Subtracting 7x from both sides gives:

12 = 10

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If glass is $0.06 per square inch, the new glass top will cost $80.64.

Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols to solve equations and express relationships between variables. It involves the use of letters and symbols to represent numbers and quantities, and the use of equations and inequalities to solve for unknown values.

Algebra is used to solve a wide range of mathematical problems, including linear equations, quadratic equations, polynomial equations, and systems of equations. It is also used to study functions, which are mathematical relationships between variables that can be represented by graphs or equations.

Algebraic concepts and techniques are used in many fields, including engineering, physics, finance, and computer science. For example, in engineering, algebra is used to model physical systems and to analyze their behavior, while in finance, algebra is used to calculate interest rates, loan payments, and other financial transactions. In computer science, algebra is used to design and analyze algorithms and data structures.

The area of the glass top required for the desk can be found by multiplying the length and width of the desk:

Area = 48 in x 28 in = 1344 square inches

The cost of the glass top can be found by multiplying the area by the cost per square inch:

Cost = 1344 sq in x $0.06/sq in = $80.64

Therefore, the new glass top will cost $80.64.

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A linear function has one independent variable and one dependent variable..

therefore, all are linear except y=x²-6

Answer:

The interval estimate is:

41.5 - 2.45 ≤ true average time ≤ 41.5 + 2.45

or

38.05 ≤ true average time ≤ 44.95

Inequality notation:

[38.05, 44.95]

The interval estimate that will estimate the true average time that people spend brushing their teeth is [39.05, 43.95] seconds.

Given that the mean time spent brushing teeth from the sample is 41.5 seconds, and the margin of error is 2.45 seconds, we can construct a confidence interval estimate using the formula:

(sample mean) ± (margin of error)

Substituting the given values, we get:

41.5 ± 2.45

Simplifying, we get:

[39.05, 43.95]

Therefore, we can be 95% confident that the true average time that all people spend brushing their teeth falls within this interval.

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Answer:

The answer is 8

Step-by-step explanation:

Let total number of rides be represented by x

And total amount spent on the ride and entry fees be y

Entry fees of the park = $10.50

Also, Charge for each ride is given to be $4.50

So, The linear function which describes the situation :

y = 10.50 + 4.50x

Now, Its given that Jay spent a total of $46.50 in the park

So, to find total number of rides taken substitute y = 46.50 in the above linear equation.

⇒ 46.50 = 10.50 + 4.50x

⇒ 4.50x = 36

⇒ x ≈ 8

Thus, Number of rides taken = 8

Answer:

Step-by-step explanation:

use a calculator it's free

Answer:

A. 500 yards

Step-by-step explanation:

By the Pythagorean Theorem:

[tex] \sqrt{ {3}^{2} + {4}^{2} } = \sqrt{9 + 16} = \sqrt{25} = 5[/tex]

The distance from the park to Anita's house is 5 blocks, which is

5 blocks × 100 yards/block = 500 yards.

Answer:

A. 500 yards

Step-by-step explanation:

1 block = 100 yards

one leg: 4*100= 400 yards

second leg: 3*100= 300 yards

hypotenuse:

pythagorean theorem

hypotenuse ^2 = (one leg)^2 + (second leg)^2

hypotenuse ^2= (400)^2 + (300)^2

hypotenuse ^2 = 160,000 + 90,000

hypotenuse = sqrt(250,000)

hypotenuse = 500 yards

Answer:

a) 2 new printers

b) 11 min

Step-by-step explanation:

Given:

5 old printers take 30 min to produce a batch of comic books

4 new printers take 18 min to produce a batch of comic books

.

a) First, we need to find how long does one old and new printer take to produce a batch of comic books:

.

Since 5 old printers take 30 min to do the job, one printer would take 5 times more than this (5 printers work together and they do the job faster than one, that's why we have to multiply):

.

1 old printer does the job in:

5 × 30 = 150 min

1 new printer does the job in:

4 × 18 = 72 min

.

Since one old printer does the job in 150 min, 6 old printers would do this job 6 times faster (that's why we divide):

6 old printers would take:

150 / 6 = 25 min

2 new printers would take:

72 / 2 = 36 min

.

25 < 36

That means, 2 new printers would do this job faster

.

b) In order to find how much less time would this take, we have to subtract:

.

36 - 25 = 11 min

The van would have traveled approximately 8 miles of distance after 12 minutes.

To calculate the distance traveled by the van after 12 minutes, we can use the formula:

y = mx

Where m is the rate of travel, and x is the time in minutes.

To find the value of m, we can use the first two data points:

m = (y2 - y1) ÷ (x2 - x1)

m = (8 - 0) ÷ (10 - 0)

m = 8 ÷ 10

m = 4 ÷ 5

Therefore, the formula becomes:

y = (4 ÷ 5) x

Now, we can substitute x = 12 to find the distance traveled after 12 minutes:

y = (4 ÷ 5) × 12

y = 0.8 × 12

y = 9.6

y ≈ 8 miles

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The complete question is:

A van travels at a constant speed. The table shows the distance y (in miles) that the van travels after x minutes. How far does the van travel after 12 minutes?

Time (minutes), x 0 10 20 30

Distance (miles), y 0 8 16 24

Answer: 63

Step-by-step explanation:

tan(B) = 10/5

B = tan^-1 (10/5)

B = 63.43 ≈ 63

The appropriate test of hypothesis in this case would be a two-tailed test.

A two-tailed test is used when the hypothesis being tested is that there is a difference between the groups being compared, but the direction of the difference is not specified. In this case, the hypothesis being tested is whether sex education classes and free clinics that offer counseling for teenagers reduce the number of pregnancies among teenagers.

The hypothesis does not specify the direction of the difference, only that there is a difference. Therefore, a two-tailed test would be appropriate to determine whether there is a significant difference in the number of pregnancies among teenagers who have access to sex education classes and free clinics compared to those who do not have access.

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The null hypothesis for the alternative hypothesis "the percentage of internet users who use the internet for shopping is greater than 0.40" can be expressed as:
H0: p ≤ 0.40

Here, H0 represents the null hypothesis and p represents the proportion of internet users who use the internet for shopping.

The null hypothesis states that the percentage of internet users who use the internet for shopping is less than or equal to 40%.

In hypothesis testing, we collect data and analyze it to determine whether we can reject the null hypothesis or not.

If the data provides strong evidence against the null hypothesis, we reject it and accept an alternative hypothesis that suggests there is a significant relationship or difference.

However, if the data is not strong enough to reject the null hypothesis, we fail to reject it, but we cannot conclude that the null hypothesis is true.

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The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

-6x + 15 < 10 – 5x and x < 5

What is the inequality equation?

An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

Option 1: x < 5 – This is one of the correct representations. It is obtained by solving the inequality as follows:

-3(2x – 5) < 5(2 – x)

-6x + 15 < 10 – 5x (Distribute on the left and right sides)

-x < -5

x > 5 (Multiply both sides by -1 and reverse the inequality)

Option 2: -6x – 5 < 10 – x – This is not a correct representation. It is obtained by distributing on the left side but incorrectly distributing on the right side.

Option 3: -6x + 15 < 10 – 5x – This is one of the correct representations. It is obtained by distributing on the left and right sides, and then simplifying.

Option 4: x + 6 < 5x – 10 – This is not a correct representation. It is obtained by incorrectly distributing on the right side.

As for the number line representations:

The number line from negative 3 to 3 in increments of 1 with an open circle at 5 and a bold line starting at 5 and pointing to the right represents the solution x < 5, which is correct.

The number line from negative 3 to 3 in increments of 1 with an open circle at negative 5 and a bold line starting at negative 5 and pointing to the left does not represent the correct solution. There is no negative solution to this inequality, so there should not be an open circle or a bold line pointing to the left.

Hence, The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

-6x + 15 < 10 – 5x and x < 5

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The missing property is the distributive property of multiplication.

The distributive property of multiplication is a mathematical property that allows you to simplify expressions that involve multiplying a number or variable by a sum or difference of other numbers or variables.

For the addition of 5 terms with 1z, we have that the term 1 is common to all the factors in the expression, hence the expression can be written as follows:

1z + 1z + 1z + 1z + 1z = 1(z + z + z + z + z) = 5z.

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Mercy will be 27 years old, and her mom will be 37 years old, 7 years from now.

To find Mercy's and her mom's ages, follow these steps:
1. Set up an equation: Let Mercy's age be 2x and her mom's age be 3x.

Their combined age is 50 years, so the equation is 2x + 3x = 50.
2. Solve the equation: Combine the terms on the left side to get 5x = 50.

Then, divide both sides by 5 to find x = 10.
3. Find their present ages: Mercy's age is 2x = 2(10) = 20 years old, and her mom's age is 3x = 3(10) = 30 years old.
4. Find their ages 7 years from now:

In 7 years, Mercy will be 20 + 7 = 27 years old, and her mom will be 30 + 7 = 37 years old.

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Answer:

Step-by-step explanation:

the exact probability of drawing three green marbles from the bag is 0.0735 or approximately 7.35%.

To find the probability of drawing three green marbles from the bag, we need to use the formula for calculating the probability of multiple independent events. The probability of multiple independent events occurring together is the product of the individual probabilities of each event.

Let's first calculate the probability of drawing a green marble on the first draw. We have a total of 6 + 4 + 7 = 17 marbles in the bag, and 7 of them are green. So the probability of drawing a green marble on the first draw is:

P(green on first draw) = 7/17

After we draw a green marble on the first draw, we have 16 marbles left in the bag, including 6 red marbles and 4 blue marbles. Since we don't replace the marble after we draw it, the probability of drawing a green marble on the second draw is:

P(green on second draw) = 6/16

Finally, after we draw a green marble on the second draw, we have 15 marbles left in the bag, including 5 green marbles. So the probability of drawing a green marble on the third draw is:

P(green on third draw) = 5/15

To find the probability of drawing three green marbles in a row, we need to multiply these probabilities:

P(three green marbles) = P(green on first draw) x P(green on second draw) x P(green on third draw)

P(three green marbles) = (7/17) x (6/16) x (5/15)

Simplifying this expression, we get:  

P(three green marbles) = (7 x 6 x 5) / (17 x 16 x 15)

P(three green marbles) = 0.0735

Therefore, the exact probability of drawing three green marbles from the bag is 0.0735 or approximately 7.35%.

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Answer:

Step-by-step explanation:

the volume of the conical section is approximately 604.8 cubic inches. we need to use volume formula of conical section to get the answer

what is conical section ?

A conical section is a geometric shape formed by the intersection of a plane with a cone. A cone is a three-dimensional geometric shape that has a circular base and tapers to a point, while a plane is a two-dimensional flat surface that extends infinitely in all directions.

In the given question,

To find the volume of a conical section, we need to use the formula:

Volume = (1/3) x π x r² x h

where r is the radius of the circular base of the cone, h is the height of the conical section, and π is the constant pi (approximately 3.14159).

In this case, we are given the diameter of the base of the cone, which is 12 inches. We can use the formula to find the radius:

r = d/2 = 12/2 = 6 inches

We are also given the height of the conical section, which is 14 inches. We can now plug these values into the formula:

Volume = (1/3) x π x r² x h

Volume = (1/3) x π x 6² x 14

Volume = (1/3) x π x 36 x 14

Volume = 604.8 cubic inches (rounded to one decimal place)

Therefore, the volume of the conical section is approximately 604.8 cubic inches.

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Answer:

x+48=180-2x (straight lines sum is 180 and corresponding angles)

x+2x=180-48

3x=132

x=44°

Ms. Wilson will receive a amount given by option D. She will receive a refund of $258.

Total taxable income of Ms. Wilson's = $36,201

Status filled by Ms. Wilson is Single.

Amount already paid as federal tax = $5344

From the table,

Taxable amount to be paid by single .

Range of income is 36,200 to 36250 is equal to $5086

Here federal tax paid by Ms. Wilson is higher then tax to be paid.

This implies,

She will receive a refund.

Refund amount = Federal tax amount - Tax to be paid

Substitute the value we have,

⇒Refund amount = $5344 - $5086

⇒Refund amount =$258

Therefore, the Ms. Wilson will receive her refund represented by option D. She will receive a refund of $258.

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