4. Write an equation for the quadratic below in VERTEX form and STANDARD form.
a) VERTEX form
y=-1 (1₁)
b) STANDARD form (Hint: expand the
vertex form above)
f(x) =
(-1,0)
(0, 3)
(1,4)
0
(3,0)



Help me please!!!!!!

the statement that is true is that Desmond's aquarium has a higher concentration of chemical solution than Megan's aquarium, even though they added the same amount of water and chemical solution.

How to solve the question?

To compare the chemical concentration of the two aquariums, we need to convert the amount of chemical added to a common unit of measurement. Let's convert Megan's chemical solution to mL per 2 gallons, which is equivalent to 7.57 L per 3785.41 mL of water. This means that Megan added 7.57 mL of the chemical solution for every 2 gallons of water in her aquarium.

Desmond added 8 mL of the chemical solution for every 2 gallons of water in his aquarium. So, both Megan and Desmond added the same amount of chemical to their aquariums.

However, the concentration of the chemical in the water would be different since Megan added the chemical at a higher rate than Desmond. Megan added 7.57 mL of chemical per 2 gallons of water, while Desmond added 8 mL of chemical per 2 gallons of water. This means that the concentration of the chemical in Megan's aquarium would be lower than that in Desmond's aquarium.

Therefore, the statement that is true is that Desmond's aquarium has a higher concentration of chemical solution than Megan's aquarium, even though they added the same amount of water and chemical solution.

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YOUR COMPLETE QUESTION IS ;-Morgan and Desmond each added the same amount of water to their aquariums. Megan mixed 5 mL of a chemical solution with every gallon of water for her aquarium. Desmond mixed 8 mL of the chemical solution with every 2 gallons of water for his aquarium.Which of these statements is true?

The diameter of the circle is 3 miles.

Given that, a circle with circumference of 9.42 miles, we need to find diameter of the circle,

Circumference = π × diameter

9.42 = 3.14 × diameter

Diameter = 9.42 / 3.14

Diameter = 3

Hence, the diameter of the circle is 3 miles.

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The expression is written as 2x - 9 = 17 and x = 13

Algebraic expressions are simply defined as expressions that are known to consist of terms, variables, constants, coefficients and factors.

These expressions are also seen as expressions containing mathematical or arithmetic operations.

These operations are listed as;

From the information given, we have that;

the difference between twice a number and nine is 17.

Let the number be x, we get;

2x - 9 = 17

collect the like terms

2x = 17 + 9

add the values

2x = 26

Divide the values

x = 13

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The complete question:

Write an equation for the following verbal expression: the difference between twice a number and nine is 17. Find the number

Answer: B

Step-by-step explanation:

If you do the vertical line test, which means if you drew a vertical line(straight up and down line) anywhere on the graph and there should never be more than 1 point.  A, C, D all have multiple points that touch more than once.

answer B

a) The way to get the number after 15 is by finding the fourth term

b) The general term of the given sequence in the form of Tₙ = 2 + 6n

c) The term in the sequence equal to 45 is; The 8th term

The formula for the nth term of an arithmetic sequence is:

aₙ = a + (n - 1)d

where:

a is first term

d is common ratio

The sequence is given as:

3, 9, 15,....,57

Thus:

a = 3

d = 9 - 3 = 6

aₙ = 3 + (n - 1)6

aₙ = 3 + 6n - 1

aₙ = 2 + 6n

The term after 15 is the fourth term. Thus:

a₄ = 3 + (4 - 1)6

a₄ = 21

The term that is equal to 45 is:

3 + (n - 1)6 = 45

(n - 1)6 = 42

n - 1 = 7

n = 8

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Answer:

Angles of:

1 = 87 degree, 2= 62 degree

Step-by-step explanation:

Here, we have a Vertically opposite angle so equate both the equations and get the value of x. then substitute the value of x in both equations.

hope it helps!

On adding the provided equations, 4x +7y= 17 and 9x + 13y = 46 the resultant equation we will be getting is 13x + 20y = 63.

In order to perform addition of two equations together, we are needed to add the left-hand side of each equation and the right-hand side of each equation separately. This gives us:

(4x + 7y) + (9x + 13y) = 17 + 46

Combining like terms on both the sides, we will be getting ,

13x + 20y = 63

Therefore, from the above calculations this inference can be drawn that the overall equation is calculated to be  13x + 20y = 63.

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The complete question is :

4x +7y= 17

9x + 13y = 46

when these equations are added together, what will the overall equation be? assume that no equations need to be reversed.

Answer:

The marginal cost is the additional cost added by increasing the quantity. This is also known as the additional cost “at the margin.” The marginal revenue is the additional revenue added by increasing the quantity. This is also known as the additional revenue “at the margin.”

Step-by-step explanation:

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The height of the cone that has a volume of 100 cubic inches is calculated to the nearest tenth as: h ≈ 6.0 in.

To find the height of the cone, recall he formula for finding the volume of a cone which is expressed as:

Volume (V) = 1/3πr²h

Given the following:

Volume = 100 in.³

Radius (r) = 8/2 = 4 in.

Plug in the values:

100 = 1/3 * 3.14 * 4² * h

100 = 16.7 * h

Divide both sides by 16.7

100/16.7 = h [Division property of equality][

h ≈ 6.0 in.

The height is approximately 6.0 inches.

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Answer:

Step-by-step explanation:

sorrry

The height of the ball after 4 seconds if it was kicked from the top of a 25 foot tall hill at 72 feet per second is 57 feet.

We are given that the height of the ball after t seconds is given by the polynomial −16[tex]t^{2}[/tex] + vt + h. We need to find the height of the ball after 4 seconds if it was kicked from the top of a 25 foot tall hill at 72 feet per second.

Substituting v = 72 and h = 25 in the given polynomial, we get:

-16[tex]t^{2}[/tex] + 72t + 25

To find the height of the ball after 4 seconds, we substitute t = 4 in the above polynomial:

-16[tex](4)^{2}[/tex] + 72(4) + 25 = -256 + 288 + 25 = 57

Therefore, the height of the ball after 4 seconds is 57 feet.

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The probability that their first child will not roll its tongue and will have the normal number of fingers is 25%.

To determine the probability that their first child will not roll its tongue and will have the normal number of fingers, we need to know the probability of each event separately and then multiply them together.

Assuming that rolling the tongue is a dominant trait and the father is homozygous recessive for the finger trait, the probabilities are:

The probability that the first child will not roll its tongue is 25% (or 0.25), as both parents are heterozygous and carry the dominant allele.

The probability that the first child will have the normal number of fingers is 100% (or 1), as the father is homozygous recessive for the trait and will only pass on the normal allele.

Multiplying the two probabilities together, we get

0.25 x 1 = 0.25 or 25%

Therefore, there is probability of 25% that their first child will have the normal number of fingers and will not roll its tongue.

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Correct statement is,

No, because (2, 2) is a solution to neither equation.

We have to given that;

Equations are,

y - x = - 4  .. (i)

- 3x - 2y = - 10   .. (ii)

Now, Plug x = - 2 and y = 2 into above equations as;

y - x = - 4

2 - (- 2) = - 4

2 + 2 = - 4

4 ≠ - 4

- 3x - 2y = - 10

- 3 × - 2 - 2 × 2 = - 10

6 - 4 = - 10

2 ≠ - 10

Thus, Correct statement is,

No, because (2, 2) is a solution to neither equation.

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The mass of African elephant is 30 times of Silverback gorilla, so, the value of m is found to be 30 which is an integer.

The mass of an African elephant is about 6 x 10⁶ grams. The mass of a silverback gorilla is about 2 x 10⁵ grams. Solution using unitary method,

Mass of elephant = 6 x 10⁶ grams

Mass of gorilla = 2 x 10⁵ grams

Let us say that m gorillas are weighting equal to one elephant. We need to find the value of m, such that,

6 x 10⁶ = m x 2 x 10⁵

Dividing both sides by 2 x 10⁵, we get:

m = 6 x 10⁶ / 2 x 10⁵

m  = 30

Therefore, the value of m is 30.

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Complete question - The mass of an African elephant is  6 x 10⁶ grams. The mass of a silverback gorilla is 2 x 10⁵ grams.

A. Using these estimated values, the mass of the African elephant is about 3 x 10 times the mass of the silverback gorilla, where m is an integer.

What is the value of m?

Answer:

a. 1.26

b. 0.1038

Step-by-step explanation:

The p-value is 1.0000 (rounded to four decimal places). This means that we fail to reject the null hypothesis, which in this case would be that the population mean is equal to the sample mean of 26.2.

To find the test statistic, we need to use the formula:

test statistic = (sample mean - population mean) / (standard deviation / square root of sample size)

Since the population standard deviation is given as 6, we can plug in the values:

test statistic = (26.2 - population mean) / (6 / √40)

To find the population mean, we can use the fact that the sample mean is an unbiased estimator of the population mean, so:

population mean = sample mean = 26.2

Plugging in the values, we get:

test statistic = (26.2 - 26.2) / (6 / √40) = 0

The test statistic is 0.

To find the p-value, we need to use a t-distribution table or calculator. Since we have a sample size of 40, we can use the t-distribution with 39 degrees of freedom.

Using a calculator or table, we can find that the area to the right of 0 (since the test statistic is 0) is 0.5. Since this is a two-tailed test, we need to double this value to get the p-value:

p-value = 2 * 0.5 = 1.0000
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Answer: A

Step-by-step explanation:

hope this helps

The interval that has the greatest average rate of change is given as follows:

B. Between 5 and 7 tires

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.

For each interval, the change in the input is of 2 tires.

The outputs are given as follows:

The rate is only positive between 5 and 7 tires, hence it has the greatest average rate of change.

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Answer:

5/6

Step-by-step explanation:

divide each by 6 and you get 5/6

have a good day :)

If 28 people were surveyed, 7 more people voted for spinach than for broccoli.

The amounts are obtained applying the proportions in the context of the problem.

The fractions for each vegetable are given as follows:

Then the amounts, out of 28 people, are given as follows:

Then the difference between spinach and broccoli is given as follows:

14 - 7 = 7.

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The answer of the given question based on line plot graph is , the data points are , 1,6,9,12,18.

A box-and-whisker plot, also known as a box plot, is a graphical representation of a data set that shows the distribution of the data and provides information about its central tendency and variability.

To construct a box-and-whisker plot from the given line plot, we need to find the following five data points:

The minimum value, which is the smallest number of miles Habib hiked in the past 18 days.

The first quartile (Q1), which is  median of  lower half of  data set.

The median, which is  middle value of data set.

The third quartile (Q3), which is the median of the upper half of the data set.

The maximum value, which is the largest number of miles Habib hiked in the past 18 days.

Based on the line plot, we can estimate the five data points as follows:

The minimum value appears to be 1 miles.

The first quartile appears to be around 6 miles, which is the median of the data points from day 1 to day 9.

The median appears to be around 9 miles, which is the middle value of the entire data set.

The third quartile appears to be around 12 miles, which is the median of the data points from day 10 to day 18.

The maximum value appears to be 18 miles.

These five data points can be used to construct a box-and-whisker plot that summarizes the distribution of the data.

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The unknown are heights are shown in the complete table:

Person/Item            Shadow length(ft)            Height (ft)

Terrace                             7.5                                  5

Bird feeder                         9                                   6

Swing set                           12                                  8

Maple tree                        91.5                                61

From the question, we are to determine the value of the unknown heights in the given table.

The given table is:

Person/Item            Shadow length(ft)            Height (ft)

Terrace                             7.5                               5

Bird feeder                         9

Swing set                           12

Maple tree                        91.5

From the first item in the table, the ratio of Height to Shadow length is

5/ 7.5 = 2/3

We can multiply the shadow lengths with this ratio to get the corresponding heights

9 × 2/3 = 6

12 × 2/3 = 8

9 × 2/3 = 61

Thus,

The complete table is:

Person/Item            Shadow length(ft)            Height (ft)

Terrace                             7.5                                  5

Bird feeder                         9                                   6

Swing set                           12                                  8

Maple tree                        91.5                                61

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A function requires that each input or independent variable has exactly one output or dependent variable, which is not the case if Brent weighs himself every week and his weight changes every time. The correct option is No/false.

Independent variable and dependent variable are two sets of values that explain a connection in mathematics. Each input value in a function corresponds to exactly one output value.

Therefore, the input is the week and the output is Brent's weight, but there are multiple outputs for the same input week which violates the definition of a function.

Therefore, The answer is No/false

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Answer:

Sarah can have the plumber work on her faucet for six (6) hours maximum

Step-by-step explanation:

It's important to remember that using the binomial approximation assumes a large population size, which may not be the case here.

To answer your questions, we will use R commands to calculate the probabilities.

(a) To find the probability that exactly 6 of the students will be full-time, we can use the "dhyper" function in R. The parameters are x = 6, m = 30 (number of full-time students), n = 20 (number of part-time students), and k = 10 (sample size).

R command:
```R
dhyper(x = 6, m = 30, n = 20, k = 10)
```

(b) To find the probability that at most 8 of the students will be full-time, we can use the "phyper" function in R, which calculates the cumulative probability. We need to calculate P(X ≤ 8).

R command:
```R
phyper(q = 8, m = 30, n = 20, k = 10)
```

(c) To use the binomial approximation, we can use the "dbinom" function in R with p = 0.6 (probability of full-time student) and n = 10 (sample size). We want to calculate P(X = 6).

R command:
```R
dbinom(x = 6, size = 10, prob = 0.6)
```

Compare this result with the answer in part (a). If the difference is relatively small, it's appropriate to use the binomial approximation in this scenario.

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Answer:

10 × 3.5 = 35

22 × 3.5 = 77

The dimensions of the new rectangle are 35 and 77.

Answer:

A. 400 ounces is 25lbs so yeah

Step-by-step explanation:

The differences between the exponential functions y = 3(2)^x and y = -3(0.5)^x is given as follows:

An exponential function is defined as follows:

y = ab^x.

In which:

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Chen's condition does not take into consideration the impact of gravity on the ball's height, so the calculation of the ball's height at any point in time is incorrect. 

Based on the information given, Chen used the following formula to determine the height of the ball.

[tex]h(t) = -16t^2 + vt + h0[/tex]

where h(t)= height of the ball at time t, v = initial velocity (16 feet/second), and h0 = initial height (6 feet).

However, Chen's equation is flawed. The sign of acceleration due to gravity being a constant factor of [tex]-32 ft/s^2[/tex] is wrong. The correct formula is:

[tex]h(t) = -16t^2 + vt + h0 - (1/2)gt^2[/tex]

where g is the acceleration due to gravity [tex](-32 ft/s^2).[/tex]

hence, Chen's condition does not take into consideration the impact of gravity on the ball's height, so the calculation of the ball's height at any point in time is incorrect. 

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Answer:

SAS (Side-Angle-Side)

The boys sold 200 tickets and the girls sold 230 tickets.

Let's represent the number of tickets boys sold as x.

Then, the number of tickets girls sold would be 15% more than the number of tickets boys sold, which is 1.15x.

As per the percent rule:

Together, the total number of tickets sold is given as 430:

x + 1.15x = 430

Combining like terms, we get:

2.15x = 430

Solving for x, we get:

x = 200

So the boys sold 200 tickets, and the girls sold 1.15x = 1.15(200) = 230 tickets.

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