From a 128-foot tree, an object is thrown straight up into the air then follows a trajectory. The height S(t) of the ball above the building after t seconds is given by the function S(t) = 96t - 16t^(2). How long will it take the object to reach maximum height?

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Work Shown:

x = number of dimes

y = number of quarters

x+y = 157 coins total

-------------------------------

$26.50 = 2650 cents

1 dime = 10 cents

x dimes = 10x cents

1 quarter = 25 cents

y quarters = 25y cents

total value = 10x+25y = 2650 cents

-------------------------------

We have this system of equations

x+y = 157

10x+25y = 2650

Let's solve for y in the first equation

x+y = 157

y = 157-x

Then plug this into the second equation and solve for x.

10x+25y = 2650

10x+25(157-x) = 2650

10x+25(157)+25(-x) = 2650

10x+3925-25x = 2650

-15x+3925 = 2650

-15x = 2650-3925

-15x = -1275

x = -1275/(-15)

x = 85 is the number of dimes

Then use this to find the value of y

y = 157-x

y = 157-85

y = 72 is the number of quarters

-------------------------------

Check:

85 dimes + 72 quarters = 157 coins total

85 dimes = 85*10 = 850 cents

72 quarters = 72*25 = 1800 cents

850 cents + 1800 cents = 2650 cents = $26.50

This confirms the answers.

Answer:

so 85 dimes and 72 quarter coins are in the box

Step-by-step explanation:

Given; Total number of coin =1557 Total amount money =26.50 To find Number of dimes and quarters in the box. In order to find the solution, make equation of number of coin and amount money. solve for unknown.Let, Number of dimes = x Number of quarters = y As, it is given that total number of coin is 157. x + y = 157 ......(a) Also, the total money is $ 26.50. .. 0.10x+0.25y = 26.50 ..(b)To, solve equation (a) & (b), put value of y from (a) to (b); From (b); From (a); y= 157 0.10x+0.25(157 - x) = 26.50 0.10x+39.25 - 0.25x = 26.50 0.15x+39.25 = 26.50 39.25 26.50 = 0.15x 12.75 = 0.15x 12.75 0.15 = x 85 = x Now, put value of x in equation (a); x + y 85+ y = y= 72

Given

A roofer tosses a hammer off the roof of a house that is 12 feet above the surface of the ground. the graph shows the height above the surface of the ground, y, in feet the hammer is x seconds after being thrown from the roof

Solution

The final answer

Option C

All the students are paid equal amount of $270. Therefore, no oneis paid more.

For student A, the amount paid for 20 hours will be:

= (67.50 / 5) × 20

= 13.50 × 20

= $270

For student B, the amount paid for 20 hours will be:

= (189/14) × 20.

= $270

For Student C, the amount paid for 20 hours will be:

p = 13.5h

where h = number of hours

p = 13.5 × 20 = $270

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Answer:

D yeyeyeye! <3

Answer:

8 years8 years

Explanation:

Let Eli's age be represented as x

Sydney's age = 11

half on Eli's age = x/2

7 more than half on Eli's age = x/2 + 7

If 7 more than half on Eli's age is Sydney's age, then;

x/2 + 7 = 11

Subtract 7 from both sides

x/2 + 7 - 7 = 11-7

x/2 = 4

Multiply both sides by 2;

x/2 * 2 = 4 * 2

x = 4 * 2

x = 8

Hence Eli is 8 years old

2 feet : 12/5 minutes

1/8 foot: 1 2/3 minutes

3 feet : 4 2/3 minutes

1 5/8 feet :2 minutes

A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, whereas the ratio of lemons to oranges is 6:8. Ratios contrast two figures by typically dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.

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Let's call x to the first number ans y to the second number.

The first of two numbers is twice the second:

x = 2y

Seven more than the second number is equal to 6 less than the first number:

7 + y = x - 6

Isolating x:

7 + y + 6 = x

13 + y = x

Combining last equation with first equation:

2y = 13 + y

2y - y = 13

y = 13

Then:

x = 2*13

x = 26

The equation of the dimensions of the rectangular plot is W² + 30W - 20,000 = 0

Let

Since the rectangular plot of ground is 30 meters longer than it is wide, we have that

L = W + 30

Since the area of the rectangular plot is A = LW where

Since A = 20,000 m², we have that

LW = 20,000

(W + 30)W = 20,000

W² + 30W = 20,000

W² + 30W - 20,000 = 0

Using the quadratic formula, we have that

[tex]W = \frac{-30 +/- \sqrt{30^{2} - 4 X (-20000)} }{2 X 1} \\W = \frac{-30 +/- \sqrt{900 + 80000} }{2} \\W = \frac{-30 +/- \sqrt{80900} }{2} \\W = \frac{-30 +/- 284.43}{2} \\W = \frac{-30 +/- 284.43}{2}\\W = \frac{-30 - 284.43}{2} or \frac{-30 + 284.43}{2}\\W = \frac{-314.43}{2} or \frac{254.43}{2}\\W = -157.22 or 127.23\\[/tex]

Since W cannot be negative, we have W = 127.23

Since L = W + 30

L = 127.23 + 30

L = 157.23

So, the dimensions are

So, the equation of the dimensions of the rectangular plot is W² + 30W - 20,000 = 0

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Answer:

C. 152

Step-by-step explanation:

8 × 10 + 6 × 12 = 80 + 72 = 152

The figures are congruent and the corresponding sides are AC = KM, AB = KL and BC = LM

Congruent figures in geometry are identical in shape and size.

In other words, congruent figures are geometric figures that have the same shape and size.

If the figures are polygons, then they are congruent if all the corresponding sides and corresponding angles are congruent.

Therefore, the polygons above are triangles, they are congruent if the corresponding sides and angles are equal.

Therefore, the figures(triangles) are congruent by the following rules:

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The length of the scraps of wood when placed side by side is 53 inches.

A line plot is a graph that is made up of a number line and check marks above the numbers on the number line. The check marks above the number line represents the frequency of the data. For example, there are two checkmarks above 7. This means that there are two scraps of woods that measure 7 inches.

In order to determine the approximate length of the scraps of wood if they are placed side by side, add the length of each scrap of wood together.

Addition is a mathematical operation that is used to determine the sum of two or more numbers. The sign that is used to denote addition is +.

[tex]5\frac{1}{2} + 6 + (6\frac{1}{2}. 3) + (7. 2) + 8[/tex] =

[tex]5\frac{1}{2} + 6 + 19\frac{1}{2} + 14 + 8[/tex] = 53 inches

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The number of tiny toys that Toby's Tiny Toys need to sell to reach its break-even point is 13,475.

The break-even point is the production and sales units that will ensure that Toby's Tiny Toys does not incur a loss or generate a profit.

At the break-even point, the total revenues are equal to the total costs (fixed and variable).

Selling price per unit = $16.50

Variable expenses per unit = $12.50

Contribution margin per unit = $4 ($16.50 - $12.50)

Fixed expenses = $53,900

Break-even point in units = Fixed costs/Contribution margin per unit

= 13,475 ($53,900/$4)

Thus, we can conclude that Toby’s Tiny Toys needs to sell 13,475 to break even.

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The number of Toby's tiny toys is 13,475 which needs to sell to reach its break-even point.

The overall revenues and entire costs are equal at the break-even point (fixed and variable).

The production and sales units that will verify that Toby's Tiny Toys does not suffer a loss or make a profit are the break-even point.

$16.50 is the selling price per unit.

Variable costs amount to $12.50 per unit.

The contribution margin = $16.50 - $12.50 = $4 per unit equals

Fixed costs is $53,900.

Break-even point = Fixed costs / Contribution margin

Break-even point = $53,900/$4

Apply division operation to get

Break-even point = 13,475

Thus, the number of Toby's tiny toys is 13,475 which needs to sell to reach its break-even point.

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Answer:

Step-by-step explanation:

5) Domain: -3<=x<=2

Range: 4<=y<=-3

6)  Domain: {-3,-2,-1,0,1,2}

Range: {4,3,2,1,0,-1,-2,-3}

Do you need number 7 too?

:]

Answer: to solve this equation, multiply both sides of the equation by 2.

Step-by-step explanation: by multiplying both sides of the equation by 2, you are effectively eliminating the fraction on the left, making the answer x = 16.

Answer:

first plot the positive 2 on the y axis

plot (0,2)

Then from (0,2) go up 2 and right 2.

Answer in attached image

The given statement " If x > 12, then x +9>20. The value of x is 14. Therefore, x +9>20" is Hypotesis of a true conditional statement is true, so the conclusion is also true. This is Law of Detachment.

The Hypothesis is the first or “If” portion of the conditional statement or p. The Conclusion is the second or “then” part of the conditional statement or q.

If the hypothesis is true and the conclusion is true, the conditional statement if p, then q is true. If the hypothesis is true but the conclusion is false, the statement is false.

The following assertion "X + 9 > 20 if x > 12. X has a value of 14. Thus, x + 9 > 20 "The conclusion follows logically from the hypothesized truth of the conditional statement. This is the Detachment Law.

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The expected number of juniors in the committee is 1.3

The question is incomplete, the complete question is given below:

A committee of 3 members is selected from a club made up of 13 juniors members and 17 senior members. What is the expected number of juniors in the​ committee?

The expected number of juniors in the committee is computed here as:

Juniors in the committee=13

Seniors in the committee=17

Total number of members=(13+17)=30

Fraction of juniors in total members=13/30

So expected number of juniors in the committee:

=Fraction of juniors in total members*Total number of members to be selected

=(13/30)*3

=1.3

Therefore 1.30 is the expected number of juniors in the committee

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Answer:

4.24ms-²

Step-by-step explanation:

S: x. write suvat and sub in values

u:4.2

v:14.8

a:?

t:2.5

use correct equation

v=u+at

sub values in

14.8=4.2+2.5a

rearrange to get a

10.6/2.5= a

a=4.24

An equation which represents the proportional relationship between the x and y-values is: C. y = 2x​.

A direct variation represents two variables that are directly proportional to each other, which simply means as one variable increases, the other variable also increases and vice-versa.

Mathematically, a proportional relationship can be represented by the following equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) based on the data points given:

k = y/x

k = 20/10

k = 2

Therefore, the required equation is as follows:

y = 2x

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Complete Question:

As the x-value increases by 20, the y-value increases by 10. Which of the following equations represents the relationship between the x and y-values?

A. y = 2 + x

B. y = 2 - x

C. y = 2x​

Answer:

15 purple beads

Step-by-step explanation:

Calculate total beads

[tex]\frac{9}{\frac{3}{8} } =\frac{72}{3} =24[/tex]

Calculate how many beads are purple

[tex]24-9=15[/tex]

Hope this helps

There are total 15 purple beads.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

given:

Fraction of blue beads = 3/8

Total blue beads = 9

let the total number of beads be x.

So, 3/8x = 9

x= 9. 8/3

x= 72/3

x= 24

So, number of purple beads = 24 -9= 15 beads

Hence, there total 15 purple beads.

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Answer: 2

Step-by-step explanation:

      We will use the slope formula to find the slope of the line going through these two points.

[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

[tex]\displaystyle \frac{0-2}{-5--4} =\frac{-2}{-5+4} =\frac{-2}{-1} =2[/tex]

      The slope of this line is 2.

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The probability that Cynthia's morning porridge will be just right is 15%.

Probability is defined as the likeliness of an event to happen. It can be determined by dividing the total number of the desired outcome by the total number of samples.

The sum of the probabilities in a probability distribution is always 1.

If there are three outcomes: too cold, just right, and too hot, then the sum of their probabilities is equal to 1 or 100%.

P(too cold) + P(just right) + P(too hot) = 100%

35% + P(just right) + 50% = 100%

P(just right) = 100 - (35 + 50)

P(just right) = 100 - 85

P(just right) = 15%

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By using differentials the error in the volume estimation is 7.29 cubic centimeters.

The volume of a cube (V), in cubic centimeters, is equal to the cube of the side length (L), in centimeters, whose formulas are:

V = L³

Now we proceed to estimate the volume differential by using first derivatives:

dV = 3 · L² · dL

Where dL is the length differential, in centimeters.

If we know that L = 9 cm and dL = 0.03 cm, then the error in the computed volume of the cube is:

dV = 3 · (9 cm)² · (0.03 cm)

dV = 7.29 cm³

The error in the volume estimation is 7.29 cubic centimeters.

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a) The total mass of sugar used is 1.7 kg.

b)The mass of sugar he has left is 0.3 kg.

A fraction is a numerical value that represents a piece of a total in mathematics. The total can be any number, a specific value, or a single item. Fractions are denoted by the symbol p/q.

Given:

Total mass of sugar Mr tan has = 2 kg

Fraction of sugar used to make dessert = 1/4 kg

Fraction of sugar used to bake some cakes = 3/5 kg

The total mass of sugar used is determined as,

= Mass of sugar used to make dessert + Mass of sugar used to bake some cakes

Mass of sugar used to make dessert = (1/4 of 2) kg = 1/2 kg

Mass of sugar used to bake some cakes = (3/5 of 2) kg = 6/5 kg

Total mass of sugar used = (1/2 + 6/5) kg = 17/10 = 1.7 kg

Mass of sugar left with him =  Total mass of sugar - Total mass of sugar used

= 2 kg - 1.7 kg  = 0.3 kg

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The complete question is: "Mr tan had 2 kg of sugar. He used 1/4 kg of sugar to make dessert and 3/5 kg of sugar to bake some cakes.

(a) What was the total mass of sugar used?

(b) How much sugar did he have left?"

Answer:

x = 12

Step-by-step explanation:

To justify q || r :

11x - 28 + 7x - 8 = 180 because they would be supplementary angles and their sum would be equal to 180°

add like terms

18x - 36 = 180 add 36 to both sides

18x = 216 divide both sides by 18

x = 12

Answer:16

Step-by-step explanation:

x-[tex]\sqrt{x}[/tex]=12

x=16

Answer:

  2.7 - h < 2.3

Step-by-step explanation:

You want an inequality to represent the relationship described by "Stella wants to know the number of hours (h) by which she must reduce her 2.7 hour half-marathon time to run in under 2.3 hours."

If h is the number of hours by which the time is reduced, Stella wants ...

  2.7 -h < 2.3 . . . . . . . . . representative inequality

__

Additional comment

The solution would be h > 0.4. Stella must reduce her time by more than 0.4 hours.

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The formula to find the surface area of a cylinder is:

In this case, we have:

B. 140π units²