The water from an outdoor fountain follows a path that is shaped like a parabola. The arch created by the water is 32 inches wide and 27 inches high.


Use the description of the fountain to label the three points on the graph, modeling the path of the water

Answer:5

Step-by-step explanation:

5098

Answer:

\(x^{2} -16\)

a = 1

b=0

c= -16

i assume the next question is to factor that...

(x-4)(x+4)

Step-by-step explanation:

Answer:

Approximately 68% of the students have grade point averages that are between 2.13 and 2.99.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this question, we have that:

Mean = 2.56

Standard deviation = 0.43

What percentage of the students have grade point averages that are between 2.13 and 2.99?

2.56 - 0.43 = 2.13

2.56 + 0.43 = 2.99

Within one standard deviation of the mean, so, by the Empirical Rule:

Approximately 68% of the students have grade point averages that are between 2.13 and 2.99.

The  equation of the parabola with the following properties y = (-1/4)(x+3)^2 -1

To find the equation of a parabola, we can use the formula f(x) = ax^2 + bx + c, where a, b and c are congruent vertices.

Alternatively, we can use PF = PM to find the equation of the parabola.

vertex is half way between the focus and directrix

It's a downward opening parabola, general form

y= a(x-h)^2 + k

where (h,k) = vertex= (-3,-1)

plug in another point on the parabola to solve for a which gives

am answer with either x coefficient = -1'/4 or =4 Check the math.

one or the other is right another point is the y intercept = 9a-1

Another point is directly to the right of the focus  (-1, -2)  It's 2 down from the directrix and 2 to the right of the focus, equidistant.   plug that point into y= a(x+3)^2 -1 and solve for "a"  

-2 = a((-1+3)^2 -1

-2 = 4a -1

4a = -

a = -1/4

The parabola is y = (-1/4)(x+3)^2 -1

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The assumption in answering the question is that no student scored 0

From the question, we have the following parameters that can be used in our computation:

The bar chart

On the bar chart, we hae

Students that score more than 8 = 5

Students in the class = 33

The (b) is calculated by considering all students that score more than 0 from the histogram

This means that the assumption is that no student scored 0

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Answer:

Find the values of the trigonometric functions of from the information given.

cot() = − 5/9 , cos() > 0Find the values of the trigonometric functions of from the information given.

cot() = − 5/9 , cos() > 0

Step-by-step explanation:

Find the values of the trigonometric functions of from the information given.

cot() = − 5/9 , cos() > 0

The following food-cost problems:

FC ÷ FC % = SP: 2.75 ÷ 25% = 11.

FC ÷ SP = FC %: 3.80 ÷ $15.00 = 25.33%.

SP x FC % = FC: 24.00 x 21% = 5.04.

To complete the food-cost problems, we will apply the given formulas and solve for the missing values.

FC ÷ FC % = SP

Given: FC = 2.75, FC % = 25%

Substituting the values into the formula, we have:

2.75 ÷ 25% = SP

To divide by a percentage, we convert the percentage to a decimal by dividing it by 100:

2.75 ÷ 0.25 = SP

Simplifying the division, we get:

11 = SP

Therefore, the selling price (SP) is 11.

FC ÷ SP = FC %.

Given: FC = 3.80, SP = $15.00

Substituting the values into the formula, we have:

3.80 ÷ $15.00 = FC %

To divide by a dollar amount, we can simply perform the division:

0.2533... = FC %

Therefore, the food cost percentage (FC %) is approximately 25.33%.

SP x FC % = FC

Given: SP = 24.00, FC % = 21%

Substituting the values into the formula, we have:

24.00 x 21% = FC

To multiply by a percentage, we convert the percentage to a decimal by dividing it by 100:

24.00 x 0.21 = FC

Simplifying the multiplication, we get:

5.04 = FC

Therefore, the food cost (FC) is 5.04.

In summary:

2.75 ÷ 25% = 11

3.80 ÷ $15.00 = 25.33%

24.00 x 21% = 5.04

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The sample space is (R, G, P, Y).(OB)

What is sample space?

A sample space is a collection  of possible outcomes of a random experiment. The sample space is represented by the symbol, “S”.  A sample space may contain a  finite number of outcomes which depends on the experiment.

You spin a spinner with 4 sections: 1 red (R), 1 green (G), 1 purple (P), and 1

yellow (Y).

So here is 4 sections

Red(R), Green (G), Purple (P), Yellow(Y)

So there are 4 sections in sample space

The sample space for one spin of the spinner is  (R, G, P, Y).

Hence, the sample space is (R, G, P, Y).

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hello

to answer precisely, i have to see the graphs in the question but overall, the answer should look like something like the graph in the attached file

Answer:  -7/5

Step-by-step explanation:

2x+3y-12=0

Step-by-step explanation:

Thats. That. boi. byś.

Answer:

4

Step-by-step explanation:

2(0) + 3y = 12

3y = 12

  4

Hopefully this helps you!!!

The value of x for the chord is:

x = 12

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc.

Recall that: If two chords intersect inside the circle, then they cut each other in such a way that the product of the lengths of the parts is the same for the two chords.

Using the above principle, we can say:

3 * x = 4 * 9

3x = 36

x = 36/3

x = 12

Thus, the value of x for the chord is 12.

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Answer:

6/8

9/12

12/16

Step-by-step explanation:

Answer:

None

Step-by-step explanation:

No solutions exist for the system of equations because the system is illogical: 3x+y=3x+y, but 18≠16.

The inequality that describes the problem is C. 8x ≤ 16

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Since Kamari's Sweet Treats, cookies are packaged in boxes of 8 and the most a box can cost is $16. This will be:

8x ≤ 16

The correct option is C.

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Answer:

ZDM is not a name for the angle, 6 square units is the area, A the cylindar, 26 degrees

Step-by-step explanation:

Area of triangle is 1/2 base x height

116-90 = 26 degrees to angle ABC

Answer:

graph A

Step-by-step explanation:

When looking at a graph, there are two different axes. The vertical values--marked by the center up/down line--are "y-values"; and this is called the "y-axis"

The horizontal values--marked by the left/right line--are "x-values"; and this is called the "x-axis"

For the x-axis, values to the left side of the origin (the place where the y-axis and x-axis intercept) are smaller than 0--they are all negative values.

Values to the right side of the origin are positive--greater than 0.

For the y-axis, positive numbers are on the top half [once again, the midpoint / 0 is where the two lines are both = to 0; the origin] and negative numbers are on the bottom half.

Ordered pairs (points) are written as (x,y)

(x-value, y-value)

We are looking for a graph that decreases (along the y-axis), hits a point below the origin, and goes flat/stays constant.

When a graph is decreasing (note: we read graphs from left to right), the line of the graph is slanted downwards (it looks like a line going down).

So, if we look at the graphs, we can see Graph A descending, crossing the y-axis {crossing the middle line /vertical line / y-axis} at a value of -7, and then staying constant (it is no longer increasing or decreasing because the y-values stay the same)

hope this helps!!

The set of side measurements that could be used to form a triangle are 8, 14, 20.

The concept that will be used is the concept of triangle inequality theorem.

To know if the given 3 side lengths are a triangle, then the use of the  triangle inequality theorem comes into play.

This rule tells us that when we sum 2 sides of a triangle  the value must be greater than the third side.

Then this rule can be applied as

The first option; 8, 14, 20

a+b>c  = 8+14>20

a+c>b  =  8+20>14

b+c>a   = 20+14>8

Therefore, first option is correct.

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Answer:

here, x=3y-z then,

(substitute value of y and z)

x=3×4-1

=12-1

x=11ans

The Emily soccer team has the higher ratio of wins to losses.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of win to loss of Emily soccer team = 9 : 12

Ratio of win to loss of Grant soccer team = 10 : 15

9 : 12 = 9 / 12 = (9 × 5) / (12 × 5) = 45 / 60

10 : 15 = 10 / 15 = (10 × 4) / (15 × 4) = 40 / 60

If 60 games are losses, then 45 games are wins for Emily soccer team.

If 60 games are losses, then 40 games are wins for Grant soccer team.

Higher ratio is for Emily soccer team.

Hence higher ratio of wins to losses is for Emily soccer team.  

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The Slope of the line that passes through the points (3,8) and (8,13) is

1.  

Equation =  slope(m)  = (y₂ - y₁) / (x₂ - x₁)

                                     = (13-8) / (8-3)

                                     = 5 / 5 = 1

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The amount more in income tax that Cho pays than Helen each month would be £56.

First, find Helen's yearly salary :

= 1, 720 x  12

= £ 20, 640

Both Cho's and Helen's annual salaries fall within the Basic rate tax bracket.

Cho 's monthly tax would be:

= (( 24, 000 - 12, 570 ) x 20 % ) / 12

= £ 190. 50

Helen's monthly tax :

= (( 20, 640 - 12, 570 ) x 20 % ) / 12

= £ 134.50

The difference is therefore :

= 190. 50 - 134.50

= £56

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The expected value of buying one scratch-off ticket will be $42,400.

Given that:

25,000 scratch-off lottery tickets are sold by the state. Each entry fee is $2. One hundred tickets will reward the player $10, twenty-five tickets will win the player $100, and one ticket will win the player $5000 out of the total of 25,000 tickets.

The expected value of buying one scratch-off ticket is calculated as,

Expected value = $2 x 25,000 - ($10 x 100 + $100 x 25 + $5,000 x 1)

Expected value = $50,000 - ($1,000 + $2,500 + 5,000)

Expected value = $50,000 - $7,600

Expected value = $42,400

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\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The approximate volume of the resulting composite figure is 1075.29 cubic inches.

V_prism = l x w x h

V_prism = 20 x 9 x 6

V_prism = 1080 cubic inches

Next, we need to find the volume of the half-sphere. The formula for the volume of a sphere is:

V_sphere = (4/3) x π x r^3

Since we have a half-sphere, we need to divide the result by 2:

V_half-sphere = (1/2) x (4/3) x π x (3/2)^3

V_half-sphere = (1/2) x (4/3) x 3.14 x (2.25)

V_half-sphere = 4.71 cubic inches

Now that we have the volume of the half-sphere, we can subtract it from the volume of the prism to get the volume of the resulting composite figure:

V_composite = V_prism - V_half-sphere

V_composite = 1080 - 4.71

V_composite = 1075.29 cubic inches (approx)

Therefore, the approximate volume of the resulting composite figure is 1075.29 cubic inches.

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Answer: (total amount paid - $40) / 0.05

Step-by-step explanation:

Given the following :

Monthly fee = $40

Additional fee = $0.05 per minute on phone

Given the the amount paid for the month is available, number of minutes he was on phone can be determined thus :

Total amount to be paid = monthly fee + additional fee

Additional fee = $0.05 × n

Where n = number of minutes on phone

Hence,

Total amount paid = $40 + $0.05n

If the amount paid is known, the number of minutes on phone can be calculated thus;

(Total amount paid - monthly fee) = $0.05n

n = (Total amount paid - monthly fee) / fee per minute on phone

(total amount paid - $40) / 0.05

The half-life when the decay rate is 0.091 is approximately 7.62 units of time.

A physical model is a representation of a system or phenomena that may be used to forecast or analyse its behaviour. Physical models can be made using materials that have qualities close to those of the real system or from scaled-down replicas of the genuine system. A mathematical model, on the other hand, is a collection of equations or connections that use mathematical relationships and symbols to describe how a system or phenomena behaves.

Given that the decay rate is 0.091.

The half life is given as:

t1/2 = ln(2) / λ

Substituting the value of decay we have:

t1/2 = ln(2) / 0.091

t1/2 ≈ 7.62

Hence, the half-life when the decay rate is 0.091 is approximately 7.62 units of time.

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