The lunchroom workers at Guffy Middle School can move a total of 600 students through 5 lunch lines in exactly 1 hour. How many students move through each lunch line per minute?

Answer:

y = - 3

Step-by-step explanation:

A line parallel to the x- axis is a horizontal line with equation

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (2, - 3 ) with y- coordinate - 3 , then

y = - 3 ← equation of line

Answer:

Step-by-step explanation:

If this was an entire circle, the area could be found by using

Area = pi * r^2 where r = 9

To take the central angle into account, use this formula

Area = 120/360  * pi * r^2

Area = 1/3 * pi * 9^2

Area = 27 pi

area  = 84.78 cm^2  which isn't there.

Answer:

Step-by-step explanation:

Answer:

$280

Step-by-step explanation:

7•40=$280

Answer:

(0,2)

Step-by-step explanation:

Cords are ( 0, 4 ) and ( 4, -4)

x1 + x2 / 2 , y1 +y2/2

0 + 4 / 2 , 4 - 4 / 2

4/2,0/2

(2,0)

The explicit formula is \(an = 275 (0.91)^n-1\)

After the eight hour we would have 142.11 mg

The explicit formula for decay is a mathematical formula that, given a substance's initial quantity and decay rate, predicts how much of a material will be left behind after a specified period of time.

The formula shows that the amount of the substance remaining after a certain amount of time is exponentially decreasing.

We have that that after the 8th hour;

a8 = 275(0.91)^8-1

a8 = 142.11 mg

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Answer:

-5 and -The zeros of a parabola are the points on the parabola that intersect the line y = 0 (the horizontal x-axis). Since these points occur where y = 0,

The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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Answer: 1256.63706

Step-by-step explanation: A=(π20)2

The approximate area of the circle segment bounded by arc DE and chord DE is approximately 17.72 square units.

To approximate the area of the circle segment bounded by arc DE and chord DE, you can use the following formula:

Area = (1/2) * r^2 * (θ - sinθ)

Where:

r is the radius of the circle (r = 20 in your case).

θ is the central angle in radians (47° converted to radians is approximately 0.8203 radians).

Let's calculate it:

θ = 47° * (π / 180) ≈ 0.8203 radians

Now, plug these values into the formula:

Area = (1/2) * (20^2) * (0.8203 - sin(0.8203))

Area ≈ (1/2) * 400 * (0.8203 - 0.7317)

Area ≈ (1/2) * 400 * 0.0886

Area ≈ 17.72 square units

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Answer:

-5

Step-by-step explanation:

All of the numbers to the left of the origin on the x-axis are negative.

Hope this helps!

Answer:

5^ -8  or  1/ 5^8

Step-by-step explanation:

(5^-2)^4

We know that a^b^c = a^(b*c)

(5^-2)^4 = 5^(-2*4) = 5^(-8)

We know that a^ - b = 1/ a^b

5^ -8 = 1/ 5^8

The number of strides the runner will make during 1 hour run will be =

10,800.

To calculate the distance or number of strides made by the runner in an

hour, the graph given above is considered as follows;

The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.

From the graph

20 minutes= 3600 strides

60 minutes = X strides

make X the subject of formula;

x= 3600×60/20

= 216000/20

= 10,800

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Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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The only true statement about the domain of the given function is:

B. f(x) is negative for all x < -5

The domain of a function is defined as the set of values that we can possibly plug into our function. This set is the x values in a function such as f(x).

Now, we are given the function as:

f(x) = \(\frac{2}{x^{2} } + 3x - 10\)

When x < -5, we have:

f(-4) = \(\frac{2}{(-4)^{2} } + 3(-4) - 10\)

f(-4) = -21.875

This suggests that for all values below x = -5 will result in negative values

When x > 2

f(3) = \(\frac{2}{3^{2} } + 3(3) - 10\)

f(3) = -0.78

Thus, it will get positive for higher values but it can also be negative as seen here.

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Step-by-step explanation:

1)

7x+20°+3x=180°{straight angle}

10x=180-20

x=160/10

x=16°

again,

y=7x+20{vertically opposed angle r equal}

Answer:

1. x = 20

y = 120

2. x = 263

Step-by-step explanation:

•••

As AOB is a line,

( 7x - 20 ) + 3x = 180

7x - 20 + 3x = 180

10x - 20 = 180

10x = 180 + 20 = 200

10x = 200

x = 200/10 = 20

Then, as COD is a line,

y + 3x = 180

y + 3(20) = 180

y + 60 = 180

y = 180 - 60 = 120

•••

2. Draw a parallel line AB and CD.

Then,

Angle BAE + Angle y = 180 [Co-interior angles]

56 + y = 180

y = 180 - 56 = 124

Angle DCE + Angle z = 180

41 + z = 180

z = 180 - 41

z = 139

Now, z + y = 139 + 124 = 263

\(\)

Answer:

Step-by-step explanation:

Past: The birds flew away quickly

Present: The geese honk at the passerby

Future: The ducklings will hatch soon

Answer:

[Past] The birds flew away quickly.

[Present] The geese honk at passersby.

[Future] The ducklings will hatch soon.

_______________________________

I can't see the options on the second image.

Designing an easy do-it-yourself compost bin:

Drawing and Description:

The compost bin can be a simple structure made of wood or wire mesh. It consists of four sides, a bottom, and a removable lid. The sides and bottom are connected securely to form a rectangular shape, while the lid allows for easy access to the contents inside.

The bin can be placed directly on the ground or on a solid surface, depending on personal preference.

Materials Used:

Wood or wire mesh (depending on preference)

Nails or screws to assemble the structure

Size of the Bin:

The size of the bin can vary based on the available space and the amount of compostable materials you generate. A suitable size for a home compost bin could be approximately 3 feet wide, 3 feet deep, and 3 feet tall.

Substances Used to Fill It:

To fill the compost bin, you would need a mix of "green" and "brown" materials. "Green" materials include fruit and vegetable scraps, coffee grounds, tea leaves, grass clippings, and plant trimmings. "Brown" materials consist of dry leaves, shredded newspaper, cardboard, and small twigs.

Household Items That Can Go in It:

You can add a variety of household items to the compost bin, such as fruit and vegetable peels, eggshells, coffee grounds, tea bags, yard waste (leaves, grass clippings, plant trimmings), shredded paper, cardboard, and natural fibers (like cotton or wool scraps).

Time for Compost to Be Ready:

The time it takes for the compost to be ready varies depending on factors like temperature, moisture, and the type of materials used. Generally, it takes about 2 to 6 months for compost to fully decompose and become ready to use.

Using the Compost:

Once the compost has broken down into a dark, crumbly, and earthy material, it is ready to use. You can spread it in your garden beds or pots as a nutrient-rich soil amendment. It improves soil structure, retains moisture, and provides essential nutrients for plants' growth.

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Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

Answer:

4

Step-by-step explanation:

Answer:

the answer is 4 geng geng geng geng

psdt: thanks for the points

Step-by-step explanation:

have a good night ^-^

Answer:

w = -44

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

-w - 2 = 42

Step 2: Solve for w

Step 3: Check

Plug in w into the original equation to verify it's a solution.

Here we see that 42 does indeed equal 42.

∴ w = -44 is the solution to the equation.

Answer:

3 * 6 = 18

Step-by-step explanation:

53 * 26 =

= (50 + 3) * (20 + 6)

= 50 * 20 + 50 * 6 + 3 * 20 + 3 * 6

= 1000 + 300 + 60 + 18

Answer: 3 * 6 = 18

Answer:

x=3

(26x+50degreese) = 134 degreese

Step-by-step explanation:

Answer:

R = 16:25

Step-by-step explanation:

Given that,

Johan mixes 2 2/3 pints of blue paint and 4 1/6 pints of yellow paint.

We need to find the ratio of blue paint to yellow paint. It can be calculated as follows :

\(R=\dfrac{\text{blue paint}}{\text{yellow paint}}\\\\=\dfrac{2\dfrac{2}{3}}{4\dfrac{1}{6}}\\\\=\dfrac{\dfrac{8}{3}}{\dfrac{25}{6}}\\\\=\dfrac{8}{3}\times \dfrac{6}{25}\\\\=\dfrac{16}{25}\)

So, the required ratio is 16:25.

The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

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

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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Answer:

How many boxes are there?

Answer:

23

Step-by-step explanation:

x=2 y=-7

-3y + x

=-3(-7)+2

=21+2

=23

Answer:

the 1 cause it's a 100

Step-by-step explanation:

100 + 80 + 9