A school's administration needs to buy benches and chairs for the gymnasium. They have a total budget of $1,500 and each bench, x, costs $100 while each chair, y, costs $50. Which graph shows an inequality that describes the possible number of benches and chairs the administration can buy?

The number of guests that can be served is 7

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

Meat served: 3 lbs meat with little bone

Pounds of meat available: 27 lbs.

The number of guests needed is calculated using the following equation

Number of guests = Pounds of meat available/Meat served

Substitute the known values in the above equation, so, we have the following representation

Number of guests = 27/3

Evaluate the quotient

Number of guests = 9

Hence, 9 guests can be served with the available meat

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Possible question

Perform the following food service calculation.

Meat served: 3 lbs meat with little bone

Pounds of meat available: 27 lbs.

Number of guests that can be served:

The coordinate of first stop of bus which is halfway through the route. is (9, -9).

What is coordinate?

Using the horizontal and vertical separations from the two reference axes, a coordinate is a pair of numbers that expresses a point's location on a coordinate plane. generally expressed by the x-value and y-value pair (x,y).

We have to find the coordinate of first stop of bus which is halfway through the route.

It means, We have to find the coordinates of the midpoint of line segment which has start point and end point coordinates as A(-10, 10) and B(8, -8).

The formula to get the mid point coordinate of a line segment which start point and end point coordinates as A(x₁, y₁) and B(x₂, y₂) is:

[tex]M(a,b) = (\frac{x_2 -x_1}{2} , \frac{y_2-y_1}{2} )[/tex]

putting the value from question:

[tex]M(a,b) = (\frac{8 -(-10)}{2} , \frac{-8-10}{2} )[/tex]

M(a, b) = (9, -9)

Therefore the coordinate of the midpoint is (9, -9)

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Answer:

87.50%

Step-by-step explanation:

You have to find the difference between the two numbers and divide the result by the first number which is 32. Multiply the answer by 100 to get the answer as a percentage!

Answer:32% of 60 = 87.5

Step-by-step explanation:

Answer:

all the  fractions that are equivalent to 2/5 are 4/10, 6/15, 8/20

Step-by-step explanation:

this is all I can rember

Data Input

Simone paid $13 for an initial year's

The renewal rate is $8 per year

Equation

y = 8x + 13

Table

x (number of years renewed) | (total cost in dollars)

0 -> 13 dollars

1 -> 21 dollars

2 -> 29 dollars

3 -> 37 dollars

4 -> 45 dollars

Answer:720

thats the answer 720

Answer:

Step-by-step explanation:

Since the numbers, we are given are fractions there is this ultimate rule when we divide fractions

the sign changes from division to multiplciation and the second fraction flips

so lets do this

-0.125 = -1/8
-0.5 = -1/2

Now lets put into into an equation

-1/8 * -2 = 1/4

You have that simple interest is computed by the multiplication of p (principal amount), r (interest rate) and t (time).

The previoues sentence can be written algebraically as follow:

I = p x r x t you only have to multiply each factor

where I is the letter for simple interest.

Answer: its 1 over 0 which equals B^-1

Margin of Error:

ANSWER: 1068

Data:

m: cost of the masking tape

As the masking cost the same amount of money: 3m

Then, you add to the cost of the masking the 5.50, you get: 3m+5.50

The symbol to less than is <

You get:

Answer:

Step-by-step explanation:

The probability of an event is represented by the following equation;

Therefore, from a 52-card deck which is better shown with the following image:

There are 4 6's in a 52-card deck and 26 red cards.

*If the events A and B are not mutually exclusive, the probability is:

Then to determine the probability that you dealt a six or a red card:

A line with an undefined slope would be x=___, in which you would put the x value of the coordinate. So, the equation would be x = -6

Answer:

90183

Step-by-step explanation:

Answer: 30 glasses

Step-by-step explanation:

Answer:

30 glasses

Step-by-step explanation:

2:20 = 1:10

1:10 x 3 = 3: 30

How to find Unit Rate:

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ANSWER

EXPLANATION

We are given the number 65,978.

To put it in scientific notation, we will need to put it in a format such that we have a number between 1 and 10 multiplying a power of ten.

So, to do that, we will move the decimal point from the end of the number (65978.) to just after the first number.

Then the number of times we move it will be the power of 10.

Since we will move it to the left, it will be a positive power.

So, we have that the number becomes:

The power is 4 because we moved the decimal four times.

V + F = E + 2

If V=12 and F=8 Find E:

We have to replace the values given of V and F IN THE EXPRESSION:

12 + 8 = E+2

Now, we simply have to solve for E:

12+8 -2 =E

18=E

E=18

If he rides 50 yards then the light will flash 22 times.

Given,

Diameter of wheel =26 inch

Radius of wheel,r=[tex]\frac{26}{2}=13 inch[/tex]

Distance covered by bicycle =50 yards =50*36=1800 inch

First find the perimeter of wheel,

[tex]Perimeter =2\pi r\\\\Perimeter =2*3.14*13\\\\Perimeter =81.64[/tex]

This perimeter represents the distance covered for 1 revolution

Now, to find number of times of revolution,

[tex]\frac{Total\ distance\ covered }{distance\ covered\ for\ 1\ revolution}\\\\=\frac{1800}{81.64}\\\\=22.04[/tex]

So,it will take 22 revolutions to complete the whole distance.

Hence, the light will flash 22 times if he rides 50 yards.

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The answer is 12.6

Step-by-step explanation:

The ratio is calculated with division.

This means we need to do this equation: 88/7.

The answer to 88/7 is 12.57. However, the question states: Round your answer to one decimal place.

This means we round 12.57 up to 12.6.

Answer: its (C) 12.6

Step-by-step explanation:

basically the first person already explained it

the positives are ( lighting detector activates ) column

the true positive its when the detector activates and there is lightning, so 88%

and false positive its when the detector activates but there's no lightning, so 7%

at the end you just divide 88% / 7%

which is 12.57 and you round it

Answer: 10.8 seconds

Step-by-step explanation:

[tex]-16t^2 + 170t+40=10\\\\16t^2 -170t-30=0\\\\t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]

Patriciana has (20/9) nickels and (80/9) dimes of coins .

There are 5 cents in a nickel and 10 cents in a dime.

Let the number of number of nickels be represented by the letter x, so that the number of dimes Patriciana has will be 4x.

So, 5x cents + 10 × 4x cents = 100 cents

5x cents + 40 cents = 100 cents

45x cents = 100 cents

divide through by the coefficient of x

x = 100cents/45cents

x = 20/9 by simplification,

and the number of dimes is calculated by putting 20/9 for x in 4x.

Hence, the number of dimes is 4(20/9) = 80/9 and that of nickels is 20/9.

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The required value of x will be 44°.

An Isosceles Triangle is defined as a triangle with two sides of equal length is an isosceles triangle.

We have been given a triangle in the figure

According to the given figure, we can see that the triangle is an isosceles triangle

As per the property of the isosceles triangle, here two angles are the same.

Now, the sum of angles in a triangle as:

⇒ 68° + 68° + x = 180°

⇒ 136° + x = 180°

⇒ x = 180° -  136°

⇒ x = 44°

Therefore, the required value of x will be 44°.

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Answer:

[tex]\left(x-\dfrac{7}{2}\right)^2+\left(y+\dfrac{7}{2}\right)^2=\dfrac{25}{2}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]

Given endpoints of the diameter of the circle:

To find the center of the circle, substitute the given endpoints into the midpoint formula:

[tex]\begin{aligned} \implies \textsf{Midpoint} & =\left(\dfrac{0+7}{2},\dfrac{-4-3}{2}\right)\\& =\left(\dfrac{7}{2},-\dfrac{7}{2}\right)\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Substitute the found center and one of the given points (0, -4) into the equation and solve for r²:

[tex]\implies \left(0-\dfrac{7}{2}\right)^2+\left(-4-\left(-\dfrac{7}{2}\right)\right)^2=r^2[/tex]

[tex]\implies \left(-\dfrac{7}{2}\right)^2+\left(-\dfrac{1}{2}\right)^2=r^2[/tex]

[tex]\implies \dfrac{49}{4}+\dfrac{1}{4}=r^2[/tex]

[tex]\implies \dfrac{50}{4}=r^2[/tex]

[tex]\implies r^2=\dfrac{25}{2}[/tex]

Therefore, the equation of the circle is:

[tex]\implies \left(x-\dfrac{7}{2}\right)^2+\left(y+\dfrac{7}{2}\right)^2=\dfrac{25}{2}[/tex]

The graph of the circle is attached.

In this problem

we have a vertical parabola open downward

so

the vertex is a maximum

Looking at the graph

The vertex is the point (0,4)

The axis of symmetry is x=0 (y-axis)

The zeros are x=-2 and x=2

The domain is all real numbers -----> interval (-infinity, infinity)

The range is all real numbers less than or equal to 4 ----> interval (-infinity,4]

Answer:

I do believe the answer for you is B. 2 x 10^14.

Step-by-step explanation:

4 x 10^4

Add four zeros to the original number since the exponent to the 10 is positive.

40,000/ 2 x 10^-10

Since the exponent here is a negative number, make 9 zeros behind the decimal point and the 2 at the end.

40,000/.0000000002
Using a calculator, you will get 2e14 which is equivalent to 2 x 10^14. Hope this helped!

Answer:

The answer is B

Step-by-step explanation:

the question is about distance.

what do we use to measure distance ? things like feet, yards, meters, ...

definitely not square feet (areas) or cubic feet (volume).

it is a right-angled triangle. so Pythagoras applies

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle). in our case the 48 ft side.

a and b are the legs. in our case x and x+6.

the saved walking distance is the difference between 48 ft and the sum of the legs (which would be the walking distance, when they cannot get though the lot).

48² = x² + (x + 6)² = x² + x² + 12x + 36

2304 = 2x² + 12x + 36

1152 = x² + 6x + 18

x² + 6x - 1134 = 0

the solution for such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a) =

= (-6 ± sqrt(6² - 4×1×-1134))/(2×1) =

= (-6 ± sqrt(36 + 4536))/2 =

= (-6 ± sqrt(4572))/2 =

= -3 ± sqrt(4572/4) = -3 ± sqrt(1143) =

= -3 ± sqrt(9×127) = -3 ± 3×sqrt(127)

x1 = -3 + 3×sqrt(127) = 30.80828301...

x2 = -3 - 3×sqrt(127) = -36.80828301...

negative numbers for a distance don't make any sense, so

x = 30.80828301... is our solution.

that means the 2 legs are

30.80828301... ft

36.80828301... ft

in total they are

67.61656602... ft

and so they save

67.61656602... - 48 = 19.61656602... ft ≈

≈ 19.617 ft

by walking across the lot.

Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]

Answer:

$30

Step-by-step explanation:

25% of $40 = $10

$10 is the discount price, i.e., $10 is 25% of $40

selling price - discount

= 40 - 10

= $30

Answer:

10.8 sec

Step-by-step explanation:

Setting [tex]h=10[/tex],

[tex]-16t^2+170t+40=10 \\ \\ 16t^2 -170t-30=0 \\ \\ 8t^2 - 85t-15=0 \\ \\ t=\frac{85 \pm \sqrt{(-85)^2-4(8)(-15)}}{2(8)} \\ \\ t \approx 10.8 (t>0)[/tex]

A number is squared. This is added to fifteen and the product of eight and the number, to give zero. ​

the algebraic expression is

Let

x ----> the number

x^2+(15+8x)=0

therefore

x^2+8x+15=0

solve the quadratic equation

Solve by using calculator

x=-5 and x=-3