The watering can contained 5 1/2 quarts of water. After all the plants were watered, only 4 cups remained. How many cups of water were used to water the garden?

Answer:

99

Step-by-step explanation:

Answer:

(a)x=100

(b)Maximum Height, h=53 Units

(c)x=200 Units

Step-by-step explanation:

Given the equation which describes the path of the baseball

[tex]h = -0.005x^2 + x + 3[/tex]

(a)Equation of the axis of symmetry

For a quadratic function of the form [tex]y=ax^2+bx+c[/tex], its equation of the axis of symmetry is determined by the equation:

[tex]x=-\dfrac{b}{2a}[/tex]

In the function given: a=–0.005, b=1

Therefore:

[tex]x=-\dfrac{1}{2*-0.005}=\dfrac{1}{0.01}\\\\x=100[/tex]

Equation of the axis of symmetry, x=100

(b)Maximum height reached by the baseball

The maximum height reached by the baseball occurs at the line of symmetry.

Therefore, when x=100

Maximum Height, [tex]h = -0.005(100)^2 + 100 + 3[/tex]

=53 Units

(c)When the height =3 feet, we want to determine the value of x.

[tex]h = -0.005x^2 + x + 3\\3 = -0.005x^2 + x + 3\\-0.005x^2 + x=0\\x(-0.005x + 1)=0\\-0.005x + 1=0\\-0.005x =-1\\$Divide both sides by -0.005\\x=200 Units[/tex]

Final answer:

The equation of the axis of symmetry is x = -100, the maximum height reached by the baseball is 103 feet, and to find the specific distance traveled when caught at 3 feet would require solving the quadratic equation given.

Explanation:

The equation h = –[tex]0.005x^2[/tex]+ x + 3 describes the path of a baseball hit into the outfield, where h is the height and x is the horizontal distance the ball travels.

a. What is the equation of the axis of symmetry?

The equation of the axis of symmetry for a quadratic equation in the form of [tex]ax^2 + bx + c[/tex] is given by x = –b/2a. Hence, for our equation, the axis of symmetry is x = –(1)/(2×–0.005) = –100.

b. What is the maximum height reached by the baseball?

The maximum height can be found by substituting the x-value of the axis of symmetry into the original equation. So, h = –[tex]0.005(100)^2[/tex] + 100 + 3 = 103 feet.

c. An outfielder catches the ball three feet above the ground. How far has the ball traveled horizontally when the outfielder catches it?

To find the horizontal distance when h is 3, we set the equation equal to 3: –[tex]0.005x^2 + x + 3 = 3.[/tex] Simplifying gives x values where the ball is at 3 feet off the ground. After simplification, one possible solution would be the distance before the ball reaches its peak. However, solving this particular quadratic may require a calculator for precise roots, implying the distances at which the ball is 3 feet high.

the answer would be 11 out of 30 because there is 11 boys in total and the total of boys and girls is 30 so the answer is 11 out of 30

The probability that a randomly selected person who can bike to school is a boy is 7/16 or 0.4375, which means there is a 43.75% chance that the person is a boy.

To determine the probability that a randomly selected person who can ride a bike to school is a boy, we will use the provided data.

Looking at the data table, we can see there are 7 boys who can bike to school, and the total number of students who can bike to school is 16 (this is the sum of boys and girls who can bike). In probability terms, the boys who can bike are the 'favorable outcomes' and the total students who can bike are the 'possible outcomes'.

Probability is calculated by dividing the number of favorable outcomes by the number of possible outcomes. Thus, the probability a randomly selected person can ride a bike to school is a boy is 7/16, or approximately 0.4375.

This means, if we were to randomly select a person who can bike to school, there is a 43.75% chance that the person is a boy. I hope this explanation helps explain how to determine probability using a data set.

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Answer:

-6x-5

Step-by-step explanation:

Answer:

6x^2-10

Step-by-step explanation:

(5x^2+2)-(-4x^2+7)+(-3x^2-5)=

5x^2+2+4x^2-7-3x^2-5=

5x^2+4x^2-3x^2+2-7-5=

9x^2-3x^2-5-5=

6x^2-10

Answer:

2 1/2 bars each.

Step-by-step explanation:

That would be 15/6.

Answer:

0.98

Step-by-step explanation:

Work Shown:

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

P(A or B) = 0.13 + 0.85 - 0

P(A or B) = 0.98

Note that P(A and B) is 0. This is because we are told A and B are mutually exclusive events. This means both events cannot happen simultaneously. An example would be flipping a coin to have it land on heads and tails at the same time.

Answer:

18/25

25/25 - 7/25 = 18/25

It is simplified

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Using 6 decimals for pi = 3.141592

[tex]Formula: C= \pi d\\[/tex]

[tex]C=(3.141592)(24in)\\C=75.398223in[/tex]

So first, we have to find 4% of 13.29.

13.29*0.04=0.5316, or rounding is 0.53.

Now add 0.53 and 13.29=13.82

I hope this helps.

Answer:

  20°

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary.

  ∠C = 180° -∠E = 180° -160°

  m∠BCD = 20°

Answer:

Answer is A

Step-by-step explanation:

A rebate is a reduction in the price of a vehicle generally offered by the manufacturer.

Option A is the correct answer.

A rebate is a type of incentive offered by a seller or manufacturer to encourage customers to purchase their products.

It is a partial refund of the purchase price that is offered to the customer after the sale has been made.

We have,

A rebate is a type of incentive that is offered by the manufacturer to the customer.

It is a refund of a portion of the purchase price of a product, in this case, a vehicle.

The rebate amount can vary based on the make and model of the vehicle, the time of year, and other factors.

Rebates are usually offered in the form of a check or a discount on the purchase price of the vehicle.

Cashback and special APR financing are also incentives that are commonly offered by car manufacturers, but they do not directly reduce the purchase price of the vehicle.

Cashback is usually a cash incentive that is given to the customer after the purchase of the vehicle, while special APR financing is a promotional interest rate offered on the car loan.

Dealer promotions are also common, but they are not typically offered by the manufacturer, and they may or may not involve a price reduction.

Thus,

A rebate is a reduction in the price of a vehicle generally offered by the manufacturer.

Learn more about rebates here:

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Answer:

a, c, b, a

Step-by-step explanation:

Answer:

60

Step-by-step explanation:30+30

Answer:

I think this is 120.

Answer:a wide cylinder

Step-by-step explanation:

Answer:

0.8 miles

Step-by-step explanation:

multiply 0.4 by 2

Answer: 0.8

Step-by-step explanation:

times it by 2

Answer:

24/121, the 2nd choice on edg

Step-by-step explanation:

4/11 times 6/11 so that becomes 24/121

Answer:

24/121

Step-by-step explanation:

Answer:

its the second, third, and fifth one

Step-by-step explanation:

Answer:

6 rolls of paper is needed to cover the living room

The cost of the 6 rolls is $95.40

Step-by-step explanation:

There are four walls here, two 12 ft by 9ft walls, and two 18 ft by 9ft walls

Area of a rectangle = length * height

Area of walls 1&3 = 18 * 9 = 162 [tex]ft^{2}[/tex]

Area of walls 2&4 = 12 * 9 = 108 [tex]ft^{2}[/tex]

Total area of walls = 162 + 108 = 270 [tex]ft^{2}[/tex]

One roll for every 50 [tex]ft^{2}[/tex]

270 ÷ 50 = 5.4 rolls

Since you cant buy 0.4 rolls of wallpaper, you need to buy one whole roll instead

6 rolls of paper is needed to cover the living room

One roll costs $15.90

6 rolls * 15.90 = $95.40

Answer:Jenny can make

18

identical necklaces, each containing 5 green and 6 blue beads.

Explanation:

Assume, each necklace contains

G

green and

B

blue beads and we have

N

such necklaces. All these variables are natural numbers.

Then we can establish the following equations in natural numbers:

N

⋅

G

=

90

N

⋅

B

=

108

Our task is to find a maximum

N

for which these two equations have a solution in natural numbers.

Obviously,

N

is a maximum common denominator of

90

and

108

.

To find the maximum common denominator of

90

and

108

, let's represent these two numbers as a product of prime numbers:

90

=

2

⋅

3

⋅

3

⋅

5

108

=

2

⋅

2

⋅

3

⋅

3

⋅

3

As we see, the maximum common denominator (a product of all prime numbers that are identical for both

90

and

108

) is

P

=

2

⋅

3

⋅

3

=

18

Therefore, assigning

N

=

18

,

G

=

5

and

B

=

6

, we obtain the solution:

Maximum number of identical necklaces is

N

=

18

with each necklace containing

G

=

5

green beads and

B

=

6

blue beads.

Answer

Step-by-step explanation:

Answer: 5

Step by Step Explanation:

Answer:

73.72

Step-by-step explanation:

Using law of Sines in area:

A(triangle) = S1 * S2 * sin(theta) /2

A(triangle) = 12 * 15 * sin(55) / 2 = about 73.72 when rounded

ANSWER: 73.72

We have been given that you invest $100,000 in an account earning 8% interest compounded annually. We are asked to find the time it will take the amount to reach $300,000.

We will use compound interest formula to solve our given problem.

[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,

A = Final amount after t years,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

t = Time in years.  

[tex]8\%=\frac{8}{100}=0.08[/tex]

[tex]300,000=100,000(1+\frac{0.08}{1})^{1\cdot t}[/tex]

[tex]300,000=100,000(1.08)^{t}[/tex]

[tex]\frac{300,000}{100,000}=\frac{100,000(1.08)^{t}}{100,000}[/tex]

[tex]3=(1.08)^{t}[/tex]

[tex](1.08)^{t}=3[/tex]

Let us take natural log on both sides of equation.

[tex]\text{ln}((1.08)^{t})=\text{ln}(3)[/tex]

Using natural log property [tex]\text{ln}(a^b)=b\cdot \text{ln}(a)[/tex], we will get:

[tex]t\cdot \text{ln}(1.08)=\text{ln}(3)[/tex]

[tex]\frac{t\cdot \text{ln}(1.08)}{\text{ln}(1.08)}=\frac{\text{ln}(3)}{\text{ln}(1.08)}[/tex]

[tex]t=\frac{1.0986122886681097}{0.0769610411361283}[/tex]

[tex]t=14.274914586[/tex]

Upon rounding to nearest tenth of year, we will get:

[tex]t\approx 14.3[/tex]

Therefore, it will take approximately 14.3 years until the account holds $300,000.

The statements A and D are true.

Based on the diagram, here are the true statements:

A. measure of angle EDF=53 degrees:

This is true because angle EDF and angle CDE are supplementary angles, meaning they add up to 180 degrees.

Since we're given that measure of angle CDE=127 degrees, we can find measure of angle EDF by subtracting 127 from 180:

measure of angle EDF = 180 degrees - 127 degrees = 53 degrees.

D. measure of angle GAE=53 degrees:

This is true because angle EDF and angle GAE are corresponding angles.

Corresponding angles are pairs of angles that are on opposite sides of a transversal and that share a common endpoint with the transversal.

They are equal in measure.

Since we've already determined that measure of angle EDF=53 degrees, we can conclude that measure of angle GAE=53 degrees as well.

Therefore, the statements A and D are true.

Answer:

100

Step-by-step explanation:

just took the test

The caller must consider 10 possibilities for each of the two unknown digits in the 4-digit extension. Since the first and last digits are confirmed as 5, there are 10 x 10 = 100 possible extensions they might have to try.

To calculate the number of possible extensions the caller might have to try, we can look at the structure of the 4-digit extension. Given that the first and last digits are known to be 5, the caller is unsure about the second and third digits.

Each of the unknown digits can be any number from 0 to 9. Since there are 10 possibilities for each of these two positions (the second and third digits), to find the total number of combinations, we multiply the possibilities for each digit.

The calculation is as follows:
Number of possibilities for the second digit = 10 (0-9)
Number of possibilities for the third digit = 10 (0-9)

Therefore, the total number of possible extensions is:
10 (possibilities for the second digit)  imes 10 (possibilities for the third digit) = 100 possible extensions.

Answer:

x = 2

y = -8

Step-by-step explanation:

Since it already gives you x, all you need to do is plug it into the equation:

5x + 4y = -22

5(2) + 4y = -22

10 + 4y = -22

Then, subtract 10 from both sides:

10 + 4y = -22

- 10         - 10

__________

4y = -32

Finally, divide both sides by 4:

4y = -32

y = -8

So now you have, x = 2 and y = -8

Answer:

X=2

5x +4y= -22

5(2)+4y = -22

10+4y= -22

4y= -22-10

4y= -32

Y= -8

The answers are :

X = 2

Y = -8

Step-by-step explanation:

Answer:

a cross section is the intersection of a solid and a plane.

Step-by-step explanation:

Explanation:

The equation y = ax^2+bx+c has the value of 'a' determine how wide or narrow the graph is. The closer 'a' is to zero, then the wider it gets; while the further 'a' is from 0, the narrower it gets.

What we need to do is look for equations in which the 'a' value is furthest from 0. In this case, it's with y = -10x^2 since a = -10 is furthest from zero compared to a = -0.9 and a = 9. Set up a number line to help see this. You can also use absolute values to get the job as well.

Therefore, y = -10x^2 has the most narrowest graph.

Answer: c. 18.3

Step-by-step explanation: 100 times .6 equals 60 so if you divide 11 by .6 you get 18.3

Answer:

here you go

Step-by-step explanation:

add them all together = 60

+ 40 = 100

4 boxed

40 divided by 4 = 10

add 10 onto each number

red = 21%

silver = 34%

grey = 26%

black = 19%

all of them added together = 100%

Answer: 6

Step-by-step explanation:

The answer is 6 because subtract 6-9x=6x-10x-24

Answer:

4 cups, 3 ounces