A recipe calls for 4 apples to serve 6 people. If Jack is planning to serve a crowd of 33 people, how many apples should he use?

Considering that the pumpkin is on the ground at x = 0 and x = 50, it is found that:

5. The roots of the quadratic function are: r1 = 0, r2 = 50.

6. The function is written as follows: y = a(x - 0)(x - 50).

7. The leading coefficient is a = -0.0992.

8. The function is: y = -0.0992(x - 0)(x - 50).

9. Applying the distributive property, the function is: y = -0.0992(x² - 50x).

10. The graph is given at the end of the answer.

A quadratic function of roots x' and x'' is defined as follows:

y = a(x - x')(x - x'').

In the context of this problem, the roots are the values of x when the pumpkin is on the ground, hence:

x' = 0, x'' = 50.

Hence, considering the roots, the function is written as:

y = a(x - 0)(x - 50).

The maximum height obtained by the pumpkin is of 62 feet, after a horizontal distance of 25 feet(mean of the roots), hence the vertex is given by these following coordinates:

(25, 62)

The coordinates are used to find the value of a, which is the leading coefficient of the function, as follows:

62 = a(25² - 50 x 25)

62 = -625a

a = -62/625

a = -0.0992.

Then the equation is written as:

y = -0.0992(x - 0)(x - 50).

The distributive property means that the outer term multiplies each the inside terms, and then the common terms are added, hence the function is:

y = -0.0992(x² - 50x).

Which is sketched at the end of the answer.

The pumpkin is on the ground when x = 0 and x = 50.

The maximum height obtained by the pumpkin is of 62 feet, after a horizontal distance of 25 feet.

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This is an instance of conditional probability and the formula to use is;

Where:

P(A|B) = the probability of event A occurring given that event B occurred

P(A ∩ B) = the probability that both events A and B occur

P(B) = the probability of event B

Therefore, the probability that A occurs given that B occurs is 5/6

Answer:

No

Step-by-step explanation:

Answer:

Step-by-step explanation:

Question a: Solve for c

0.9c = 17.01 - 18.9r

c = 17.01-18.9r/0.9

c = 18.9 - 2.1r

Question b: Solve for r

18.9r = 17.01-0.9c

r =  9 - [tex]\frac{0.9}{18.9}[/tex]c

r = -10/21c + 9

(0.9/18.9 = 10/21)

Question c:

It will be best to use the equation that solves for c because this helps us determine how much chicken is bought.

c = 18.9 - 2.1r

Substitute r with 3.25

c = 18.9 - 2.1(3.25)

c= 18.9 - 6.825

c = 12.075

We identify the proportional relationship because it does not have a constant term, the correct option is:

y = (1/4)x

A proportional relationship between two variables x and y is written as:

y = k*x

Where k is called the constant of proportionality.

Here the options are:

The only option that has not a constant term is the second one:

y = (1/4)*x

And that is the proportional relationship.

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Answer:

y=(1/4)x

Step-by-step explanation:

I took the test :)

Answer:

Nah

Step-by-step explanation:

The nth term for the given series is given by 4n-3.

What is meant by series?

The number series is 1, 5, 9, 13, 17,...

Common deviation (d)=5-1=4

A=1 is the first phrase.

A+(n1)d=1+(n1) is the formula for the nth term.

4=4n−3

∴tn =4n−3

The nth term for the given series is given by 4n-3.

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Answer:

yes

Step-by-step explanation:

ac goes straight forever and df does straight forever and they are parallel

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{6}{5} x + 1[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 5y - 6x = 5[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 5y = 6x + 5[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{6}{5} x + \frac{5}{5} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{6}{5} x + 1[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

−3.11×10^2

Step-by-step explanation:

Step-by-step explanation:

The length of the band is the number of units it covers

The actual length of the band is: \mathbf{40 + 10\pi}40+10π

The diameter of 1 pencil is given as:

\mathbf{d = 10}d=10

The circumference of 1 pencil is:

\mathbf{C = \pi d}C=πd

So, we have:

\mathbf{C = 10\pi }C=10π

Multiply by 4, to calculate the circumference of all pencils

\mathbf{4C =4 \times 10\pi }4C=4×10π

\mathbf{4C =40\pi }4C=40π

The rubber band covers a quarter of the 4 pencils.

So, we divide by 4

\mathbf{C = 10\pi }C=10π

The length of the band on one pencil is:

\mathbf{L = 10}L=10

Multiply by 4, for the 4 pencils

\mathbf{L = 40}L=40

So, the actual length of the band is:

\mathbf{Length = 40 + 10\pi}Length=40+10π

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A triangle is translated 6 units left and then dilated by a factor of 0.5. the statement about the triangle's image and pre-image that is correct is: The image and pre-image are not congruent figures because one of the  transformations is a rigid transformation, and the other is not.

Transformation is a term that refers to movement of an image from one position to the other.

When the intervals or distances between the points of the image being moved is not altered then the transformation is rigid transformation. However when the interval is altered it is a rigid transformation.

Translation is a rigid transformation while dilation is a non rigid transformation.

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Answer:

The answer is C

Step-by-step explanation:

The equivalent expression is 54 divided by 18, and the quotient is 3.

Answer:

860 degrees

Step-by-step explanation:

-210+210=0

0+650=650

650+210=860

The area of the hot tub to be installed for local spa is 6358.5 in².

For the given question;

The diameter of the hot tub to be installed for local spa is 90 inches.

Then, radius is 90/2 = 45 inches.

The area of the circle is;

Area = πr²

Where,  π = 3.14

Put the values;

Area = 3.14×45²

Area = 6358.5

Thus, the area of the hot tub to be installed for local spa is 6358.5 in².

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Answer: 9. y=[tex](x+4)^2-3[/tex]

10. y=[tex]-(x-5)^2+5[/tex]

11. y=[tex](x-2)^2+1[/tex]

12. y=[tex]x^2-3[/tex]  or y=[tex](x-0)^2-3[/tex]

Step-by-step explanation:

======================================================

Explanation:

x = number of hours

y = total cost

The equation is y = 25x+250 since 250 is the initial cost, aka y intercept, and 25 is the slope telling us how much the cost goes up per hour (aka rate of change).

I recommend making a table of values to help see how/why that equation works out.

Plug in y = 1275 and isolate x.

y = 25x+250

1275 = 25x+250

1275-250 = 25x

1025 = 25x

25x = 1025

x = 1025/25

x = 41 hours

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

Check:

If the customer rents the car for 41 hours, then they pay 25*41 = 1025 dollars on top of the initial fee of $250.

The total cost is therefore 1025+250 = 1275 dollars to confirm the answer.

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

Extra info:

41 hours = 24 hours + 17 hours = 1 day + 17 hours

41 hours = 41/24 = 1.70833 days approximately

Given:

You plan to retire in 35 years and would like to have 1,000,000$ in investments.

So, the time = 35 years

And A = 1,000,000

compounded daily, n = 365

Rate of the interest = r = 7% = 0.07

We will find the initial investment = P

We will use the following formula:

Substitute with the values of A, r, n, and t

Solve the equation to find P

So, the answer will be $86,313.86

The angle x= 33 degree.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean. The sign "" is used to denote angles. The Greek letter,,, etc. can be used to represent the angle measurement between the two rays. If different types of angles, such as a positive angle and a negative angle.

Positive Angle: If angle goes in counterclockwise, then it is called a positive angle.

Negative Angle: If angle goes clockwise direction, then it is called a negative angle.

360= 87*3+3x

360-261=3x

33=x

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It will take 30 weeks to have to have the same amount of money as my sister if I have $60 and my sister has $120. I am saving $7 per week and my sister is saving $5 per week.

A mathematical sentence that uses the equal sign, =, to show that two expressions are equal is known as an equation. Look for key words or phrases such as "is," "the same as," or "equals" to determine where to place the equal sign when writing a word sentence as an equation. Make an equation out of the word sentence.

A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.

The given condition,

You have $60 and your sister has $120. You are saving $7 per week and your sister is saving $5 per week.

Let x be the time period in weeks. So we need same amount of money.

60+7x=120+5x

This is the equation needed.

2x=60

x=30 weeks

If I have $60 and my sister has $120, it will take 30 weeks for me to have the same amount of money as my sister. I save $7 per week, and my sister saves $5 per week.

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Percent of the games do not cost $1 or $2 is 35%.

A fraction of a number out of 100% is referred to as a percentage, sometimes known as a percent. Percentage refers to a portion of a total amount and signifies "per 100." For instance, 45% signifies 45% of the total or 45 out of 100.

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

Given,

games = 58

5/8 is 62.5%

2.5% + 62.5% = 65%

100%-65% = 35%

A third of the games (35%) are free.

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Complete question -

At a carnival, 58 of the games cost $1. Another 2.5% of the games cost $2. What percent of the games do not cost $1 or $2?

The point which describe the rate of change for the line modeled by y = 4/3x+2 would be; C. Vertical change of 4 units for each horizontal change of 3 units

Suppose that the considered linear equation is of the form y=mx+c

Then, when we change x by 1 unit, then:

[tex]y + \delta y = m(x + 1) + c\\mx + c + \delta y = mx + c + m\\\delta y = m[/tex]

where  [tex]\delta y[/tex]  shows the change in y as x changes by 1 unit.

It is found that this change is the value of 'm' called slope of the line this equation represents (each linear equation represents a line).

We have been given that the line modeled by y = 4/3x+2

The slope is given as m = 4/3

The point which describe the rate of change for the line modeled by y = 4/3x+2 would be;

C. Vertical change of 4 units for each horizontal change of 3 units

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Hey there!

[tex]3-3k+7k=5b[/tex]

Assuming you're trying to solve for b or k, I'll solve both.

Solve for b:

[tex]3-3k+7k=5b[/tex]

We will need to flip the equation:

[tex]5b=4k+3[/tex]

Now, let's divide both sides by 5:

[tex]\frac{5b}{5} =\frac{4k+3}{5}[/tex]

[tex]b=\frac{4}{5} k+\frac{3}{5}[/tex]

Solve for k:

[tex]3-3k+7k=5b[/tex]

Let's add -3 to both sides:

[tex]4k+3+-3=5b+-3\\4k=5b-3[/tex]

Now, let's divide both sides by 4:

[tex]\frac{4k}{4} =\frac{5b-3}{4}[/tex]

[tex]k=\frac{5}{4} b+\frac{-3}{4}[/tex]

Now, we've solved for b and k.

Hope this helps!

The percentage of students that use the internet for more than 402 minutes =  16%

Percentage

Percentage, often referred to as percent, is a fraction of 100. Percentage means "per 100," and denotes part a total amount. For example, 45% represents 45 out of 100.

calculate the percentage-

The empirical rule states that

68% of the population lies within 1 standard deviation of the mean

95% of the population lies within 2 standard deviations of the mean

99.7% of the population lies within 3 standard deviations of the mean

Standard Deviation

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

The percentage will be illustrated in this:

P(X > 402) = P(X > 30 + 1 × 102)

= (1-0.68) / 2

= 0.32/2

= 16%

The percentage of students that use the internet for more than 402 minutes =  16%.

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If we reflect a triangle in a line, translate a triangle, rotate a triangle, and reflect it in a point result in an image that will be congruent to the original( pre-image) triangle.

This is a problem from triangular geometry. We can solve this problem by following a few steps.

Here a triangle ABC is given and the triangle is at first reflected and then translated, thereafter it rotates and is later reflected.

After all, these processes the value of ∠A, ∠B, and ∠ C remains the same as usual concerning ∠A''', ∠B''', ∠ and C'', as they just changes coordinates not geometric structures.

After all these processes the length of the triangle AB, AC, BD, and A'''B''', B'''C''', C'''A''' remains the same as usual.

∵ We can conclude that ΔABC ≅ ΔA'''B'''C'''

( As AB = A'''B''', BC = B'''C''', ∠ABC = ∠ A'''B'''C''' )

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an ice cream cone has a diameter of 8 cm and a slant height of 8.4 cm. find the lateral surface area of the cone then The lateral surface area of the cone is 105.2 cm².

What is lateral surface area?

The lateral surface area is the area of all the sides of a 3-dimensional object excluding its base and top.

Lateral surface area = πr√(h² + r²)

Where:

π = pi = 3.14

r = radius = 8/2 = 4cm

h = √8.4² - 4² = 7.38

3.14 x 4 x √(7.38² + 4²)

= 105.4 cm

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The range of values, in interval notation is [-6,14] .

What is interval notation in math?

the values with a distance of 10 units from 4.

Maximum value to the right, 10 units from 4 is 4+10 = 14

Maximum value to the left, 10 units from 4 is 4 - 10 = -6

So, all the range of values, in interval notation is [-6,14]

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Step-by-step explanation:

-1 × -3/10

=> 3/10

Multiplicative Inverse/Reciprocal of 3/10 = 10/3

Justin has sold 5 popsicles so from the original 9 if we take away 5, he has 4 popsicles left to eat.