round each number to the nearest 10, 100 and 1000: b:500

Answer:

32 students

Step-by-step explanation:

24 divided by .75 is 32

Based on the information given, there'll be 32 students.

Let the total number of students be represented by x.

From the information, it was stated that 75% of the students are boys and that there are 24 boys. Therefore, the total number of students will be:

75% × x = 24

0.75x = 24

x = 24/0.75

x = 32

There are 32 students.

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Answer:

87/10

is already in the simplest form. It can be written as 8.7 in decimal form (rounded to 6 decimal places).

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 87 and 10 is 1

Divide both the numerator and denominator by the GCD

87 ÷ 1

10 ÷ 1

Reduced fraction:  

87 /10

Therefore, 87/10 simplified to lowest terms is 87/10.

Hope this helps!

Answer:

120

Step-by-step explanation:

The value of x is 7 using the concept supplementary.

What is supplementary angle?

Angles that add up to 180 degrees are referred to as supplementary angles.

The image of a transversal angles is added.

Angle 7 = angle 5 since they are vertically opposite angle.

The sum of interior angle on the same side of the transversal is 180 degree.

angle 5 + angle 4 = 180°

Replace angle 5 by angle 7:

angle 7 + angle 4 = 180°

Substitute the value of angle 7  and angle 4:

(7x + 5)° + 126° = 180°

7x+ 131 = 180

Subtract 131 from both sides:

7x  = 49

Divide both sides by 7:

x  = 7

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\(U(\stackrel{x_1}{4}~,~\stackrel{y_1}{-2})\qquad N(\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{4}}} \implies \cfrac{2 +2}{-3} \implies \cfrac{ 4 }{ -3 } \implies - \cfrac{4 }{ 3 }\)

Answer:

1384.7

Step-by-step explanation:

42/2     21^2x3.14=1384.74

Hope this Helps :)

The answer is -9x + 6 2/3.

Answer:

\(\frac{1}{27}\)

Step-by-step explanation:

Remember that negative exponents just mean reciprocal.

So:

\(3^{-3} = \frac{1}{3^{3}} = \frac{1}{27}\)

Answer:

D. 1/27

Step-by-step explanation:

1. \(3^-^3\) is equivalent to \(\frac{1}{3*3*3}\)

Therefore, the answer is D. 1/27.

Step-by-step explanation:

x+85+x+44+63=180(sum of angles of a triangle)

or,2x+192=180

or,2x=180-192

or,x=-12

Angle A=x+44

=-12+44

=32°

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6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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you just have to multiply the coast of the chicken with the number of chicken you want.

so, $4.99 × 5 = $24.95

Therefor, the answer is $24.95.

Answer:

25

Step-by-step explanation:

The correct solution of the expression 3/4 ( 6x - 4) = 1/2 (x + 4) with the property that justify each step is shown below.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 3/4 ( 6x - 4) = 1/2 (x + 4)

Now, Solve the expression as;

⇒ 3/4 ( 6x - 4) = 1/2 (x + 4)

⇒ 9/2x - 3 = 1/2x + 2                        By Distributive property

⇒ 9/2x - 3 - 1/2x = 1/2x + 2 - 1/2x     Subtraction property of equality

⇒ (9/2 - 1/2)x - 3 = 2                        Combine like terms

⇒ 4x - 3 = 2                                     Subtraction property

⇒ 4x - 3 + 3 = 2 + 3                         Addition property of equality

⇒ 4x = 5

⇒ 1/4 × 4x = 1/4 × 5                          Multiplication property of equality

⇒ x = 5/4

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Answer:

$4.75

Step-by-step explanation:

As the price per pound is a one-to-one ratio, one could just simply multiply by using: 0.7 lbs * ($6.79 / 1 lb) = $4.75/1 = $4.75

Answer:

$4.75

Step-by-step explanation:

Answer:

The surface area of the triangular prism is \(A=122\:in^2\).

Step-by-step explanation:

The surface area of any prism is the total area of all its sides and faces. A triangular prism has three rectangular sides and two triangular faces.

An equilateral triangle is a triangle with all three sides of equal length.

To find the surface area, the area of each face is calculated and then add these areas together.

The formula \(A=\frac{1}{2} bh\) is used to find the area of the triangular faces, where A = area, b = base, and h = height.

The formula \(A=lw\) is used to find the area of the three rectangular side faces, where A = area, l = length, and w = width.

The surface area of the triangular faces is:

\(A=\frac{1}{2} (4)(3.5)+\frac{1}{2} (4)(3.5)\\A=2\cdot \:4\cdot \:3.5\cdot \frac{1}{2}\\A=1\cdot \:4\cdot \:3.5\\A=14\:in^2\)

The surface area of the three rectangular side faces is:

\(A=4\cdot9+4\cdot9+4\cdot9=108\:in^2\)

The surface area of the triangular prism is \(A=14+108=122\:in^2\).

Answer: the value of the expression is 28

Step-by-step explanation:

we simply substitute the letters in for the numbers.

5(3)(3) - 7(3) + (4)

we just multiply all of those together.

45 - 21 + 4

answer: 28

Answer:

the value of the expression is 28

Step-by-step explanation:

since we have already been given the values of a, b and c ,we must substitute them in the expression like this:

5(3)(3)-7(3)+4

28

Answer:

geometry

The ratio of the angle measures of a pentagon is 4:5:3:8:7. What is the measure of the smallest

The sum of the interior angles of a pentagon is 180(5-2) = 540º

so

4x + 5x + 3x + 8x + 7x = 540

solve for x and sub into 3x

Answer:

2.4 or 12/5

Step-by-step explanation:

The slope formula is (y2-y1) divided by (x2-x1).

First, you label each number by their x and y.

-4 will be axis x 1

2 will be axis y 1

-9 will be axis x 2

-10 will be axis y 2.

Then substitute the variable into the formula.

(-10 subtract 2) divided by (-9-(-4)).

Next, solve. Once you solve you will get -12/-5 = 2.4

Finally, simplify the answer. if it is already simplify, that will be the answer.

Since there are four choices for each question, the total number of ways to fill out the answer sheet is 4⁵, or 4x4x4x4x4, which is equal to 1024.

It involves finding the most efficient and effective solution to a problem by exploring multiple options and assessing the pros and cons of each.

This can be found by calculating the number of possible ways to fill out the answer sheet.

Since there are four choices for each question, the total number of ways to fill out the answer sheet is 4⁵, or 4x4x4x4x4, which is equal to 1024..

To explain why this is happening, it is helpful to look at an example. Let's say the five questions are A, B, C, D, and E.

If a person wants to fill out the answer sheet so that four answers are correct and one is incorrect, they can either choose the correct answer for four of the questions, and then choose an incorrect answer for the fifth question, or they can choose the incorrect answer for four of the questions, and then choose the correct answer for the fifth question.

In terms of calculating the number of ways to fill out the answer sheet, this means that for each of the five questions, there are four possible ways to answer (four choices for each question). This means that there are 4

The answer to this question is 1024. This can be found by calculating the number of possible ways to fill out the answer sheet. Since there are four choices for each question, the total number of ways to fill out the answer sheet is 4⁵, or 4x4x4x4x4, which is equal to 1024.

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Answer:

the large boxes=70

the small boxes= 60

Step-by-step explanation:

large boxes) 60 x 70 = 4,200

small boxes) 25 x 60 = 1,500

                                      5,700

Answer:

13,125 ducks

Step-by-step explanation:

The ratio of ducks:geese on the first day was:

175:63

On the last day (end of migration), he counted 4,725 geese.

To find the number of ducks using the same ratio, we are first going to divide 4,725 by 63 to find what number all the ducks and geese multiplied by:

4,725/63 = 75

The geese multiplied by 75. This means the ducks also multiplied by 75:

175*75 = 13,125

Barnaby counted 13,125 ducks.

Hope it helps (●'◡'●)

Answer:

The value is  \(P(X \le 22) = 0.2\)

Step-by-step explanation:

From the question we are told that

   The lower limit of the interval is  \(a = 20\)

    The upper limit of the interval is  \(b = 30\)

Generally the cumulative distribution function for uniform distribution is mathematically represented as  

   \(F(x) = \left \{ {{0 \ \ \ \ \ \ \ \ \ \ \ for x < a } \atop {\frac{x - a}{b-a} \ \ \ \ \ \ for  a \le x \le b }} \atop { 1 \ \ \ \ \ \ \ \ \ \ \  for  x >  b}\right.\)

Generally  the probability that an oil change job is completed in less than or equal to 22 minutes is mathematically represented as

              \(P(X \le 22) = \frac{22 - 20}{30 - 20 }\)

=>          \(P(X \le 22) = 0.2\)

Answer:

Blank 1: 50

Blank 2: 95

Blank 3: is not

Blank 4: is not

Step-by-step explanation:

A right angle is 90 degrees, and a rectangle is a plane figure that has four straight sides and four right angles.

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

\(let ~b=8~m,h=6in\)

\(SA=4(bh/2)+b^2\)

\(=2(8)(6)+(8)^2\)

\(=96+64\)

\(=160in^2\)

The correct answers are A) 7cm, C) 9cm and D) 12cm

The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.

If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.

Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:

⇒  \(\frac{2cm}{7 feet} = \frac{x cm }{yfeet}\)

where y is the length of the line in real life. Solving for y, we get:

⇒  \(y = \frac{7 feet} {2cm} *x\)  

⇒  \(y = 3.5 x feet\)

If we put x = 2cm (given) then, y = 7 feet

For y = 21 feet, the value of x = 6cm.

Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.

So, the lines on the drawing that are greater than 21 feet in real life are:

A) 7cm, C) 9cm, D) 12cm

Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm

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Answer:

Step-by-step explanation:

What are the dimensions of the garden with the largest area she can enclose?

The dimensions of the garden with the largest area she can enclose are length for cedar side = 7 foot and width for other side =  10 foot

Let L = length of the fence and W = width of the fence.

Also, let L be the length of cedar fencing.

Since we require one side of cedar fencing and the other 3 sides of cheaper metal fencing, and the cedar fencing costs $13/foot and the cheaper material costs $7/foot, the total cost of fencing is C = 13L + 7L + 2W × 7

= 13L + 7L + 14W

= 20L + 14W.

Since the total amount my friend wants to spend on fencing is $280, C = 280.

So, 20L + 14W = 280

10L + 7W = 140 (1)

Also, the area of the rectangular area is A = LW

From (1), L = (140 - 7W)/10

Substituting L into A, we have

A = LW

A = (140 - 7W)W/10

A = 14W - 0.7W²

To find the value of W that makes A maximum, we differentiate A with respect to W.

So, dA/dW = d(14W - 0.7W²)/dt

dA/dW = 14 - 1.4W

Equating it to zero, we have

14 - 1.4W = 0

14 = 1.4W

W = 14/1.4

W = 10 feet

To determine if this value maximizes A, we differentiate dA/dW with respect to W.

So, d²A/dW² = d(14 - 1.4W)/dW = -1.4

Since d²A/dW² = -1.4 < 0, W = 10 feet is a maximum point.

Since L = (140 - 7W)/10,

substituting W = 10 into the equation, we have

L = (140 - 7W)/10

L = (140 - 7 × 10)/10

L = (140 - 70)/10

L = 70/10

L = 7 feet

So, the dimensions of the garden with the largest area she can enclose are length for cedar side = 7 foot and width for other side =  10 foot

What is the largest area that can be enclosed?

The largest area that can be enclosed is area = 70 foot-squared

Since the area A = LW

Substituting the values of L and W into the e quation, we have

A = LW

A = 7 × 10

A = 70 ft²

So, the largest area that can be enclosed is area = 70 foot-squared

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Answer:

The slope is 0, then the line is horizontal.

y = 6

Step-by-step explanation:

Answer:

A=b×h

A=3x5

A=15

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