A middle school principal is signing the diplomas of the school's graduating eighth graders. She previously signed 37 diplomas. Now, she is signing more diplomas at a rate of 0.5 per second.
Write an equation that shows how the total number of diplomas signed, y, depends on the number of seconds the principal spends signing them, x.

y=

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer: y-intercept = y= -1/2x, point-slope = (y-4)=-1/2(x+8)

Step-by-step explanation:

The value of tan 2π/3 without calculator is -√3.

The value of tan 2π/3 without calculator is calculated by applying trig identities as follows;

the value of π = 180 degrees

So we can replace the value of π in the function with 180 degrees as follows;

tan ( 2π / 3) = tan (2 x 180 / 3)

tan (2 x 180 / 3) = tan (2 x 60)

tan (2 x 60) = tan (120)

tan (120) if found in the second quadrant, and the value will be negative since only sine is positive in the second quadrant.

tan (120) = - tan (180 - 120)

= - tan (60)

= -√3

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Answer:

45

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

Finding the common denominator is really just finding the gcf of 7 and 10. The gcf of 7 and 10 is 70. So the common denominator is 70.

The smallest positive integer n such that t \($\sqrt[4]{56 \cdot n}$\)  is an integer is 686.

We have to find the smallest positive integer n such that \($\sqrt[4]{56 \cdot n}$\) is an integer

To find the smallest positive integer n such that  \($\sqrt[4]{56 \cdot n}$\)   is an integer, we need to determine the factors of 56 and find the smallest value of n that, when multiplied by 56, results in a perfect fourth power.

The prime factorization of 56 is:

56 = 2³ × 7

The prime factors of 56 need to be raised to multiples of 4.

Therefore, we need to determine the smallest value of n that includes additional factors of 2 and 7.

To make the expression a perfect fourth power, we need to raise 2 and 7 to the power of 4, which is 2⁴ × 7⁴

The smallest value of n that satisfies this condition is:

n = 2 × 7³ = 2× 343 = 686

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Answer:

I hope that helps!

x = -4

Understanding statistical questions and data distributions is an important concept in data analysis and statistics. A statistical question is one that can be answered by collecting and analyzing data.

These questions typically ask about a population or group of individuals and are often related to trends or patterns.

Data distributions refer to the way data is spread out or distributed within a dataset. This can include measures like the mean, median, and standard deviation. Understanding data distributions is important for making accurate interpretations and predictions based on the data.

To practice understanding statistical questions and data distributions, it's important to work with real-world datasets and ask questions that can be answered using statistical analysis.

This can involve looking at trends and patterns in the data and interpreting the results in a meaningful way. By building these skills, you can become better equipped to analyze and interpret data in a variety of settings.

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Answer:

Step-by-step explanation:

let numerator=x

denominator=x+3

again

\(\frac{x+2}{x+3+2} =\frac{2}{3} \\3(x+2)=2(x+5)\\3x+6=2x+10\\3x-2x=10-6\\x=?\)

x=4

number is

\(\frac{4}{4+3} \\=\frac{4}{7}\)

nCx⋅px⋅(1−p)n−x

llllllllllllllllllllllllllllllllllllll

Answer:

Interval notation (-5,3]

The surface area of the sphere, to the nearest whole number, is 1318 cm².

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

The surface area of a sphere is expressed as:

SA = 4πr²

Where r is the radius of the sphere and π is the mathematical constant pi.

Given that the volume V is 4500 cm³.

First, we solve for the radius:

Volume =  (4/3)πr³

4500 = (4/3)πr³

4500 × 3 = 4πr³

13500 = 4πr³

r³ = 13500/4π

r = ∛( 13500/4π )

Now that we have the radius, we can calculate the surface area of the sphere using the formula:

SA = 4πr²

Substituting the radius we found:

SA = 4 × π × ∛( 13500/4π )²

SA = 1318 cm²

Therefore, the surface area is approximately 1318 cm².

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The geometric sequence will be greater than the arithmetic sequence at the 8th term

Geometric sequence

Here, we have

First term, a = 3

Common ratio, r = 3 i.e. 9/3 = 3

So, the n-th term of the geometric sequence is

G(n) = 3 * 3^n-1

Arithmetic sequence

Here, we have

First term, a = 300

Common difference, d = 500 i.e. 800 - 300 = 500

So, the n-th term of the arithmetic sequence is

A(n) = 300 + 500(n - 1)

When G(n) is greater than A(n), we have:

3 * 3^n-1 > 300 + 500(n - 1)

This gives

3^n > 300 + 500(n - 1)

Using a graphing calculator, we have:

n > 7.4

The next integer value of n is

n = 8

Hence, the geometric sequence will be greater than the arithmetic sequence at the 8th term

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Answer: (-4s-1)*(-8) + (-4)*(-8s+7)

You have the right idea, but you swapped the items in the wrong order. Meaning that you applied the derivative to the wrong pieces as shown in the order above. It seems you have to follow this specific order for the computer to accept the answer.

Probability helps us to know the chances of an event occurring. The number of times Tamika should expect the spinner to land on green or yellow is 60.

Probability helps us to know the chances of an event occurring.

\(\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\)

Total number of sections on the spinner = 5

Number of sections with green or yellow sections = 2

Number of trials = 150

Now, the number of times Tamika should expect the spinner to land on green or yellow is,

Expected Number of lands on green or yellow = 150 × (2/5) = 60

Hence, the number of times Tamika should expect the spinner to land on green or yellow is 60.

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Answer:

r ≈ 1.91mm

Step-by-step explanation:

A coin is tossed and a six-sided die numbered 1 through 6 is rolled. Find the probability of tossing a head and then rolling a

number greater than 5.

The probability of tossing a head and then rolling a number greater than 5 is

(Round to three decimal places as needed.)

step 1

we have that

the probability of tossing a head is equal to

P=1/2

step 2

The probability of rolling a number greater than 5

we have

total cases=6

possible values greater than 5=1

so

P=1/6

step 3

The probability of tossing a head and then rolling a number greater than 5 is

P=(1/2)*(1/6)

P=1/12

Answer:

Step-by-step explanation:

x can be anything so let’s use 0, 1, 2, and 3 for x values

to find the y values, we just plug in the x values into the equation

when x = 0

y = 5/4(0) -2

y = 0 -2

y = -2

(0, -2) (x = 0, y = -2)

when x = 1

y = 5/4(1) -2

y = 5/4 -2

y = 5/4 -8/4

y = -3/4

(1, -3/4) (x = 1, y = -3/4)

when x = 2

y = 5/4(2) -2

y = 10/4 -2

y = 5/2 -4/2

y = 1/2

(2, 1/2) (x = 2, y = 1/2)

when x = 3

y = 5/4(3) -2

y = 15/4 -2

y = 15/4 -8/4

y = 7/4

(3, 7/4) (x = 3, y = 7/4)

Answer:

Table shown below

Step-by-step explanation:

Table of Values

We are given the function:

\(\displaystyle y=\frac{5}{4}x-2\)

And it's required to fill the table of values for x and y with the condition that there are only integers.

Given the expression has a denominator of 4, to ensure there are no decimals in the results, we select values of x that are multiple of 4.

Select the values: {-4,0,4,8}

Now calculate the corresponding values of y.

x=-4

\(\displaystyle y=\frac{5}{4}(-4)-2=-5-2=-7\)

y=-7

x=0

\(\displaystyle y=\frac{5}{4}(0)-2=0-2=-2\)

y=-2

x=4

\(\displaystyle y=\frac{5}{4}(4)-2=5-2=3\)

y=3

x=8

\(\displaystyle y=\frac{5}{4}(8)-2=10-2=6\)

y=8

The filled table is shown in the attached image

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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Answer:

B. 24%

Step-by-step explanation:

Filling the character requirement lol

Answer:

b

Step-by-step explanation:

it gies in and out the equation

The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Answer:

the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.

Answer:

32.0

Step-by-step explanation:

i really can't explain it but comment if need more help

and can u take better picture

Step-by-step explanation:

8 ÷ (w+10)

when you are quotient think divide.

Answer:

\(-\frac{9}{1}\)

Step-by-step explanation:

Its just the same way as making positive 9
a fraction, but just add the negative sign.

Hope this helps :))

Answer:

x=35

y=72.5

Step-by-step explanation:

Answer:

x=35 , y=72.5

Step-by-step explanation:

I'm not amazing at explaining but x is obviously 35 as its across from it and looks like it's the same angle, we'll be able to test this when we figure out y. Both of the y values are the same number so you just need to figure out

2y + 35 = 180

Minus 35 from both sides

2y = 145

Then we can divide 2 from both sides

y = 72.5

Then we test for x

2y + x = 180

Plug in y

145 + x = 180

Minus 145 from both sides

x= 35

There's your answer! I hope I cleared up any confusion

Step-by-step explanation:

y-2=2(x-0)^2

Vertex: (0,2)

Axis of Symmetry is x=0

Opens upward

Hope that helps :)

Answer:

No solution

Step-by-step explanation: