of the
sat
5) The senior classes at High School A and High School B planned separate trips to New York City.
The senior class at High School A rented and filled 5 vans and 4 buses with 205 students. High
School B rented and filled 5 vans and 13 buses with 475 students. Each van and each bus carried
the same number of students. How many students can a van carry? How many students can a
bus carry?

The diameter across this loop was 236.6 feet

Perimeter is a mathematical term, which means total outer boundary of a figure, we define it only for two dimensional figures.

Perimeter = Sum of length of the all the sides

However, if we assume that Evan ran around the loop's outer edge and not inside the loop,

we can use the formula for the circumference of a circle,

which is C = πd,

where C is the circumference, d is the diameter, and π is approximately 3.14.

We can rearrange the formula to solve for the diameter,

which is d = C/π.

Plugging in the given value for the circumference, we get:

d = 744/π ≈ 236.6 feet

Therefore, if Evan ran around the outer edge of the loop, the diameter of the circle is approximately 236.6 feet.

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1000 meters is equal to 3280.84 feet. To convert from meters to feet, you must multiply the number of meters by 3.28084. This is due to the fact that a meter is slightly longer than a foot.

One meter is equivalent to 3.28084 feet. Therefore, to compute 1,000 meters in feet, you must multiply 1,000 meters by 3.28084. Doing this calculation yields a result of 3,280.84 feet. The meter is the primary unit of measurement for length in the International System of Units, or SI. The SI base unit for length is the meter, which is defined as the length of the path travelled by light in a vacuum in 1/299,792,458 seconds. In other words, the meter is the distance light travels in a vacuum in 1/299,792,458 of a second. The meter is also referred to as the "meter of the air," since it is the length of the path travelled by light in the air in the same time.The foot is a unit of length in the British Imperial and US customary systems of measurement, and is equivalent to 1/3 of a yard. One foot is equal to 0.3048 meters.

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Answer:

8.417

Step-by-step explanation:

The amount of 101 inches is equal to 8.4167 feet.

To convert inches to feet, we divide the number of inches by 12, since there are 12 inches in 1 foot.

As 1 foot= 12 inches

Therefore, to convert 101 inches to feet, we divide 101 by 12:

= 101 inches / 12 inches/foot

= 8.4167 feet

So, 101 inches is equal to 8.4167 feet.

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Answer:

- 1/2< x ≤ 3

Step-by-step explanation:

The filled circle (at point 3) indicates that 3 is included in the inequality and the clear circle at -1/2 indicates that -1/2 is not included

The value of p is 5/8

A complex fraction is a rational expression that has a fraction in its numerator, denominator or both. In other words, there is at least one small fraction within the overall fraction.

Examples of complex fraction include ½/¾, ⅚/½

⅚/p = ⅔/½

= 5/6 ÷ p = ⅔ ÷ 1/2

= 5/6 × 1/p = 2/3 × 2/1

= 5/6p = 4/3

15 = 24p

divide both sides by 24

p = 15/24

p = 5/8

therefore the value of p is 5/8

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Answer:

Step-by-step explanation:

(5/3)[tex]d^{3}[/tex]*(-1/3)[tex]x^{3}[/tex]=(-5/9)[tex]d^{3} x^{3}[/tex]

Due to inflation, a fixed quantity of money can buy 5% less every year. If camille has enough in her wallet to buy 86 movie tickets right now, the same amount of money could buy 69 movie tickets in 4 years.

Inflation is the sustained increase in the general price level of goods and services in an economy over a period of time. When inflation occurs, each unit of currency buys fewer goods and services; consequently, inflation reduces the purchasing power of money. Here, inflation reduces the purchasing power of money by 5% every year.

Let's assume that Camille has enough in her wallet to buy 86 movie tickets right now. After 1 year, the same amount of money would be able to buy 86 * (100 - 5) / 100 = 81.7 movie tickets, since the purchasing power of the same amount of money would have decreased by 5%.

After 2 years, the same amount of money would be able to buy 81.7 * (100 - 5) / 100 = 77.6 movie tickets, since the purchasing power of the same amount of money would have decreased by another 5%.

After 3 years, the same amount of money would be able to buy 77.6 * (100 - 5) / 100 = 73.7 movie tickets, since the purchasing power of the same amount of money would have decreased by another 5%.

After 4 years, the same amount of money would be able to buy 73.7 * (100 - 5) / 100 = 69.9 movie tickets, since the purchasing power of the same amount of money would have decreased by another 5%.

However, since movie tickets cannot be bought in fractional amounts, we would round down to the nearest whole number, so the same amount of money could buy 69 movie tickets in 4 years.

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Answer:

x = 17/32

Step-by-step explanation:

Firstly, you want to simplify by combining like terms:

4x(3+5)—10 = 4 · 3 + 5 – 10

32x—10 = 7

Add ten to both sides:

32x - 10 = 7

+10             +10

32x = 17

Divide both sides by 32:

32x = 17

/32      /32

32 divided by 32x makes x

so we get x = 17/32

(we dont divide 17/32 since we would get an irrational number (0.53125))

The three solutions to the equation are (0, 1), (1, 12) and (2, 25)

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

y = 12x + 1

Next, we set x to 0, 1 and 2

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

y = 12 * 0 + 1

y = 1

y = 12 * 1 + 1

y = 13

y = 12 * 2 + 1

y = 25

As an ordered pair, we have

(0, 1), (1, 12) and (2, 25)

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The measurement of AB is given as follows:

AB = 16.23.

The three trigonometric ratios are defined as follows:

For the angle of 52º, we have that:

Hence the measurement of AB is obtained as follows:

cos(52º) = 10/AB

AB = 10/cos(52º)

AB = 10/0.616

AB = 16.23.

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Answer:

22yrs

Step-by-step explanation:

So, the money will grow to $600 in about$$ 22 years.

For a cardboard:

The area of the cardboard is:

Length = 1 m 5 cm = 105 cm

Breadth = 80 cm

Area = Length x Breadth = 105 cm x 80 cm = 8400 cm²

The area of the cardboard in square meters is:

1 m = 100 cm

Length = 1 m 5 cm = 105 cm = 1.05 m

Breadth = 80 cm = 0.8 m

Area = Length x Breadth = 1.05 m x 0.8 m = 0.84 m²

The area covered by the ribbons is the area of the cardboard that is not painted. From the previous calculations, we know that the area of the cardboard is 8400 cm² and the area that was painted is 4700 cm². Therefore, the area covered by the ribbons is:

Area covered by ribbons = Total area of the cardboard - Area that was painted

Area covered by ribbons = 8400 cm² - 4700 cm²

Area covered by ribbons = 3700 cm²

The area of the cardboard is (105 cm) x (80 cm) = 8400 cm².

The area covered by the ribbons is 3700 cm².

So, the area of the cardboard that was painted is 8400 cm² - 3700 cm² = 4700 cm².

The area of the cardboard is 8400 cm² or 0.84 m². The area covered by the ribbons is 3700 cm². So, the area that needs to be painted is the difference between the area of the cardboard and the area covered by the ribbons, which is:

8400 cm² - 3700 cm² = 4700 cm²

To convert to square meters, we divide by 10000:

4700 cm² ÷ 10000 = 0.47 m²

Therefore, the cost of painting the remaining area is:

0.47 m² × ₹25/m² = ₹11.75

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The value of the angles x is 121 degrees

It is important to note that the sum of interior angles of a polygon takes the expression

(n -2) 180

Then, we have;

(6-2) 180

720

Then, add all the angles and equate to 720. we get;

105 + 88 + 142 + 140 + 124 + x = 720

Add the values

599 + x = 720

Collect the like terms

x = 720 - 599

x = 121 degrees

Hence, the value is 121 degrees

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The value of the hypotenuse x is 19.1

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

Rise = 17

Angle = 63 degrees

The hypotenuse, x is then calculated using the following laws of sines

sin(63) = 17/x

Make x the subject

So, we have the following representation

x = 17/sin(63)

Evaluate the expression

This gives

x = 19.1

Hence, the value of x is 19.1

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The marginal benefit of selling one more bouquet within the range between 400 and 600 is $12.

To find the marginal benefit in this range, we need to calculate the additional benefit of selling one more bouquet within this range.

First, let's find the benefit per bouquet in the range between selling 400 and 600 bouquets:

Total benefit in the range = $7,200 - $4,800 = $2,400

Number of bouquets in the range = 600 - 400 = 200

Benefit per bouquet in the range = Total benefit / Number of bouquets = $2,400 / 200 = $12

So for each bouquet sold within the range between 400 and 600, the benefit is $12.

Therefore, the marginal benefit of selling one more bouquet within the range between 400 and 600 is $12.

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Answer:

36

Step-by-step explanation:

Answer:

The second option!

Step-by-step explanation:

Sorry if i was wrong... :(

The function which would match the graph shown as in the task content is; y = -1/2 (x - 6) (x + 5).

It follows from the task content that; the zeroes of the parabola are; -5 and 6;

Therefore, we have that;

y = a (x - 6) (x + 5).

To determine the value of a; use the y-intercept such that we have; (0, 15).

15 = a (0 - 6) (0 + 5)

15 = -30a

a = -1/2.

Ultimately, the required function to match the graph is; y = -1/2 (x - 6) (x + 5).

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Answer:

Part A:

The equation for the amount of money Nora would spend after the discount is applied on a shirt that costs d dollars is:

c = d - 0.05d

c = 0.95d

Part B:

Let x be the total value of the clothes Nora can buy before the discount is taken.

After the discount is applied, she can spend a total of $57, so we have:

0.95x = 57

x = 60

Therefore, Nora can buy a total of $60 worth of clothes before the discount is taken.

Counting to 20 in Spanish is a relatively straightforward process. The first step is to learn the numbers from 1 to 10, which are:

1 - uno

2 - dos

3 - tres

4 - cuatro

5 - cinco

6 - seis

7 - siete

8 - ocho

9 - nueve

10 - diez

Once you have these numbers memorized, it's easy to continue counting up to 20. Simply add the numbers from 11 to 19 to the base number, diez.

11 - once (diez + uno)

12 - doce (diez + dos)

13 - trece (diez + tres)

14 - catorce (diez + cuatro)

15 - quince (diez + cinco)

16 - dieciséis (diez + seis)

17 - diecisiete (diez + siete)

18 - dieciocho (diez + ocho)  

19 - diecinueve (diez + nueve)

20 - veinte

As you can see, the only exception is the number 15, which has its own unique word, "quince." Other than that, all of the numbers from 11 to 19 follow the same pattern of adding "diez" to the appropriate digit. And once you reach 20, you're done! It's important to note that Spanish has gendered nouns, so when counting objects, you will need to use the appropriate article and adjective to match the gender of the noun. For example, if you are counting "dogs," you would say "uno perro," but if you were counting "cats," you would say "una gata."

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Answer:

1  uno

2  dos

3  tres

4  cuatro

5 cinco

6 seis

7 siete

8 ocho

9 nueve

10 diez

11 once

12 doce

13 trece

14 catorce

15 quince

16 dieciséis

17 diecisiete

18 dieciocho

19 diecinueve

20 veinte

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

2x3=6

6x4=24

Answer:

48 miles per hour

Step-by-step explanation:

To convert Aneesha's speed from miles per hour to feet per second, we can use the formula:

speed in feet per second = speed in miles per hour * feet per mile / seconds per hour

So, Aneesha's speed in feet per second is:

50 miles per hour * 5,280 feet per mile / 3600 seconds per hour = 792 feet per second

Morris is traveling 3 feet per second less than Aneesha, so his speed in feet per second is:

792 feet per second - 3 feet per second = 789 feet per second

To convert Morris's speed back to miles per hour, we can use the formula:

speed in miles per hour = speed in feet per second * seconds per hour / feet per mile

So, Morris's speed in miles per hour is:

789 feet per second * 3600 seconds per hour / 5,280 feet per mile = approximately 48 miles per hour.

The table is

Balloon        Helium in the tank

1                                14.4

2                                13.9

3                                13.4

4                                12.9

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

Given function is h = 14.9 - 0.5b  .....(i)

Where b is the number of ballon.

Putting b = 1 in equation (i)

h(1) = 14.9 - 0.5×1

h(1) = 14.4

Putting b =2 in equation (i)

h(2) = 14.9 - 0.5×2

h(2) = 13.9

Putting b = 3 in equation (i)

h(3) = 14.9 - 0.5×3

h(3) = 13.4

Putting b = 4 in equation (i)

h(4) = 14.9 - 0.5×4

h(4) = 12.9

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The required, Mmusi borrowed R3000 from Aggie as per the given conditions.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on loan.

Amount = Principal [1 + rate×time]

Let's call the amount Mmusi borrowed from Aggie "P".

After two years, he has to pay back
= P + P * 18% * 2
= P + 0.18 * P * 2
= P + 0.36P
= 1.36P

So if he has to pay back R4080, we can set up an equation to solve for P:

1.36P = 4080

To find P, we can divide both sides by 1.36:

P = 4080 / 1.36 = 3000

So Mmusi borrowed R3000 from Aggie.

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Let x be the number of toppings and y be the cost of the sundae. We know that a sundae costs $2 without any toppings, and each topping costs $0.50. Therefore, the equation that describes the relationship between x and y is:

y = 2 + 0.5x

This equation can be represented on a graph, with x on the horizontal axis and y on the vertical axis. As x increases, y increases by $0.50 for each additional topping. The graph will be a line with a slope of 0.5 and y-intercept of 2, meaning that the line passes through the point (0,2) and rises by $0.50 for each unit increase in x.

In linear regression, one variable, called a dependent variable, is related to one or more independent variables by a linear equation.

A function has the following format: y = f(x).

In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.

That is, the input of the function is the independent variable and the output is the dependent variable.

In the case of multiple inputs, all the inputs are independent variables.

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Answer: Seed needed for the new lawn = 125 pounds

Step-by-step explanation:

Knowing the amount of seed needed for their old lawn will help Mr. and Mrs. Quigley calculate the amount of seed needed for their new lawn based on the size of the area.

First, let's calculate the area of the old lawn:

Area = length × width

Area = 10 ft × 20 ft

Area = 200 square feet

Next, we can determine the seed requirement per square foot for the old lawn:

Seed requirement per square foot = total seed needed ÷ area of the lawn

Seed requirement per square foot = 5 pounds ÷ 200 square feet

Seed requirement per square foot = 0.025 pounds per square foot

Now, let's calculate the area of the new lawn:

Area = length × width

Area = 100 ft × 50 ft

Area = 5000 square feet

To find the amount of seed needed for the new lawn, we can multiply the seed requirement per square foot by the area of the new lawn:

Seed needed for the new lawn = Seed requirement per square foot × area of the new lawn

Seed needed for the new lawn = 0.025 pounds per square foot × 5000 square feet

Therefore, Mr. and Mrs. Quigley will need 125 pounds of grass seed for their new lawn based on the calculations using the information from their old lawn.  

Answer:

Step-by-step explanation:

2y>-5

y>-2.5

You need to find a number that, when multiplied by a given number modulo a certain value, produces a remainder of 1. This can be done using the extended Euclidean algorithm, and the resulting inverse is the residue of the coefficient modulo the modulus.

Finding the inverse of a modulo involves finding a number that, when multiplied by a given number modulo a certain value, produces a remainder of 1. This process is important in modular arithmetic, where calculations are performed with remainders of a fixed integer modulus.

To find the inverse of a modulo, you can use the extended Euclidean algorithm, which is a method for finding the greatest common divisor of two integers.

The steps for finding the inverse of a modulo are as follows:

1. Identify the number you want to find the inverse of (let's call it "a") and the modulus (let's call it "m").

2. Use the extended Euclidean algorithm to find the greatest common divisor of "a" and "m", and the coefficients x and y such that ax + my = gcd(a,m).

3. If gcd(a,m) = 1, then "a" has an inverse modulo "m" and the inverse is given by x mod m.

4. If gcd(a,m) is not equal to 1, then "a" does not have an inverse modulo "m".

In step 3, x mod m represents the residue of x modulo m, which is the unique non-negative integer less than m that is congruent to x modulo m. In other words, it is the remainder when x is divided by m.

For example, to find the inverse of 5 modulo 7, we can use the extended Euclidean algorithm to find that 2(5) + (-1)(7) = 1. Therefore, the inverse of 5 modulo 7 is 2.

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