Six classes of 31,28,27,32,24 and 26 students are to travel on buses that each hold 36 students. How many buses are needed?


Answers

Answer 1

Answer:

5 buses

Step-by-step explanation:

You add all the students up to get 168, because that's the total number of students, and divide it by 36. The buses can only carry 36 people, so you will need 4.666 buses, but you can't have 0.666 of a bus, so you will need 5 buses to fit everyone.


Related Questions

Given: mAngleTRV = 60° mAngleTRS = (4x)° Prove: x = 30 3 lines are shown. A line with points T, R, W intersects with a line with points V, R, S at point R. A line extends from point R to point Z between angle V R W. Angle V R T is 60 degrees and angle T, R, S is (4 x) degrees. What is the missing reason in step 3?

Answers

Answer:

the answer is angle addition postulate

Step-by-step explanation:

Given the proof for x = 30, the missing reason in step 3 is: angle addition postulate

What is Angle Addition Postulate?

Angle addition postulate states that if D is the interior of ∠ABC, therefore, the sum of the smaller angles equals the sum of the larger angle, which is: m∠ABD + m∠DBC = m∠ABC.

The given diagram as shown in the image attached below alongside the proof of x = 30.

T is the interior of straight angle ∠VRS.

m∠VRS = 180° (straight line angle)

Therefore, based on the angle addition postulate, m∠TRS + m∠TRV = 180°.

Thus, given the proof for x = 30, the missing reason in step 3 is: angle addition postulate

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6. Use the data to find the following (Please show work)
2, 3, 5, 7, 8, 10, 11, 11, 13, 15, 17, 18
a. Mean
b. Median
C. Mode
d. Range

Answers

Answer:

1. [tex] \boxed{ \boxed{ \sf{mean = 10}}}[/tex]

2. [tex] \boxed{ \boxed{ \sf{median = 10.5}}}[/tex]

3. [tex] \boxed{ \boxed{ \sf{mode = 11}}}[/tex]

4. [tex] \boxed{ \boxed{ \sf{range = 16}}}[/tex]

Step-by-step explanation:

1. Given data : 2 , 3 , 5 , 7 , 8 , 10 , 11 , 11 , 13 , 15 , 17 , 18

Σx = 2 + 3 + 5 + 7 + 8 + 10 + 11 + 11 + 13 + 15 + 17 + 18 = 120

N ( total number of items ) = 12

Finding the mean

To find the mean, divide the sum of all the items by the number of items.

[tex] \boxed{ \sf{mean = \frac{Σx}{N} }}[/tex]

[tex] \dashrightarrow{ \sf{mean = \frac{120}{12} }}[/tex]

[tex] \dashrightarrow{ \sf{mean = 10}}[/tex]

Mean = 10

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

2. Given data : 2 , 3 , 5 , 7 , 8 , 10 , 11 , 11 , 13 , 15 , 17 , 18

N ( total number of items ) = 12

Finding the position of median

[tex] \boxed{ \sf{median = { \frac{n + 1}{2} }^{th \: item}}} [/tex]

[tex] \dashrightarrow{ \sf{median = {( \frac{12 + 1}{2}) }^{th \: } item}}[/tex]

[tex] \dashrightarrow{ \sf{median = {( \frac{13}{2}) }^{th \: }item }}[/tex]

[tex] \dashrightarrow{ \sf{median = {6.5}^{th \: }}} [/tex] item

[tex] \sf{ {6.5}^{th} }[/tex] item is the average of 6 th and 7 th items.

[tex] \sf{∴ \: median = \frac{ {6}^{th}item + {7}^{th} item}{2}} [/tex]

[tex] \dashrightarrow{ \sf{median = \frac{10 + 11}{2} }}[/tex]

[tex] \dashrightarrow{ \sf{median = \frac{21}{2} }}[/tex]

[tex] \dashrightarrow{ \sf{median = 10.5}}[/tex]

Median = 10.5

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

3. The mode of a set of data is the value with the highest frequency.

Given data : 2, 3, 5, 7, 8, 10, 11, 11, 13, 15, 17, 18

Here, 11 has the highest frequency.

So, Mode = 11

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

4. Highest number = 18

Lowest number = 2

[tex] \boxed{ \sf{range = highest \: number - lowest \: number}}[/tex]

[tex] \dashrightarrow{ \sf{range = 18 - 2}}[/tex]

[tex] \dashrightarrow{ \sf{range = 16}}[/tex]

Hope I helped!

Best regards! :D

A linear correlation scatterplot is also a direct proportionality. True or False

Answers

Answer: False

Step-by-step explanation: A linear correlation scatter plot is one which is aimed at establishing a graphical view of the relationship between two quantitative variables. A linear correlation scatter plot could either be positive which is depicted by a positive gradient which infers direct proportionality, this means an increase in variable A results in increase in variable B while a decrease in variable A results in decrease in variable B. Similarly, it could also exhibit a negative gradient which infers a inverse proportionality meaning a decrease in one variable leads to increase of the other and vice-versa. Hence, a linear scatterplot does not only exhibit direct proportionality.

Solve the linear equation. x - 3 = 7 x = ?

Answers

Answer: x = 10

Step-by-step explanation: You add 3 + 7 which equals 10. 10 minus 3 is 7.

The vertical intercept of the line will always be a snap point.
A. True
B. False

Answers

Answer:

False because the vertical intercept is not always a snap point.

Step-by-step explanation:

In a line graph, the vertical intercept of a line will not always be a point snap. This is because snap points rest on nodes and are used to define boundary or shape of objects in a line graph. So in a case whereby the intercept of the line doesn't rest on a node that defines the boundary or shape of the object, then the vertical intercept may not be a snap point.

False

A vertical intercept is a point where a line crosses the vertical axis, or [tex]\boldsymbol{y-}[/tex]axis.

The vertical intercept of a line in a line graph is not always a snap point. Snap points are used to define the boundary or shape of objects in a line graph, rely on nodes. In the event when the line's intercept does not rest on a node that defines the object's boundary or shape, the vertical intercept may not be a snap point.

False, the vertical intercept of the line may not always be a snap point.

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Use the slope formula to find the slope of the line through the points (1, -2) and (-2,8).
Sorn thatic in

Answers

Answer:

Step-by-step explanation:

(8 + 2)/(-2 - 1)= -10/3


Point T is on line segment SU. Given ST 2x + 1, SU = 4x, and
TU = 5x 4, determine the numerical length of ST.



Answers

Answer:

Step-by-step explanation:

3

*!* find the area and perimeter of the shapes below.

Answers

Answer:

a: 15 in

b:210 cm

c: 21 yds

Step-by-step explanation:

a: to find the area of a triangle multiply the base and the height, then divide the result by two.

b: to find the area of a trapezoid, multiply the median ( the point where the opposite corners cross) and the height.

c: to find the area of a parallelogram, multiply the lenght and the height.

Hope this helps!

The revenue from the sale of specialty golf hats is given by the function R(x) = 31x, where x is the number of hats sold.

a. What is R(200)? Interpret this result

b. What is the revenue from the sale of 3000 hats? Write this in functional notation.

a. R(200) =

Answers

Answer:

[tex]R(200) = 6200[/tex]

[tex]R(3000) = 93000[/tex]

Step-by-step explanation:

Given

[tex]R(x) = 31x[/tex]

Solving (a): R(200)

[tex]R(x) = 31x[/tex]

Substitute 200 for x

[tex]R(200) = 31 * 200[/tex]

[tex]R(200) = 6200[/tex]

This means that the revenue from 200 hats is 6200

Solving (b): Revenue from 3000 hats

[tex]R(x) = 31x[/tex]

Substitute 3000 for x

[tex]R(3000) = 31 * 3000[/tex]

[tex]R(3000) = 93000[/tex]

The above represents the functional notation and the revenue sale is 93000

Mr. Crawford is ordering pizzas and breadsticks for a school pizza party and has a budget of $81, but no more. An order of breadsticks costs $7 and a pepperoni pizza costs $13. Write an inequality that represents the above situation if x represents the number of bread sticks and y represents the number of pizzas.

Answers

Answer:

7x + 13y [tex]\leq[/tex] $81

Step-by-step explanation:

The inequality that represents the situation given will be  7x + 13y ≤ 81.

From the information given, Crawford is ordering pizzas and breadsticks for a school pizza party and has a budget of $81, but no more and an order of breadsticks costs $7 while a pepperoni pizza costs $13.

Therefore, the inequality that represents the situation given will be  7x + 13y ≤ 81.

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f(x) = -x² – 10x + 16
Find f(-7)

Answers

Answer:

-5

Step-by-step explanation:

or, f(x) = -x^2+10x+16

or, f(7) = (-7)^2+10*-7+16 (-7*-7=49)

=49-70+16

=65-70

=-5

Which set of points are NOT collinear?
A
B
D
A and E
E and B
OD and B
OC and A

Answers

the answer is OD and B
The answer is OD B
Answer B

Round each decimal to the place value stated and enter the value in the box a Round 3.892 to the nearest tenth. b. Round 5.424 to the nearest hundredth. c. Round 124.62 to the nearest whole number.​

Answers

Answer:

A) [tex]\huge\boxed{3.9}[/tex]

B) [tex]\huge\boxed{5.42}[/tex]

C) [tex]\huge\boxed{125}[/tex]

Step-by-step explanation:

A) 3.892

To round off to nearest tenth, we'll see the digit in hundredths place. If it is greater than 5 or equal to 5, 1 will be added to the tenths place. If it's not, it will remain the same.

So, it will be like:

=> 3.9

B) 5.424

To round off to nearest hundredth, we'll see the digit in thousandths place. If it is greater than 5 or equal to 5, 1 will be added to the hundredths place. If it's not, it will remain the same.

So, it will be like:

=> 5.42

C) 124.62

To round off to nearest whole number, we'll see the digit in tenths place. If it is greater than 5 or equal to 5, 1 will be added to the ones place. If it's not, it will remain the same.

So, it will be like:

=> 125

what is 8 x 5 = 4 x _______

Answers

Step-by-step explanation:

[tex] \\ 8 \times 5 = 40 \\ 40 = 4 \times 10 \\ \\ 8 \times 5 = 4 \times 10[/tex]

find the interval between: 8:40 pm and 9:30 am​

Answers

Answer:

12 hours 50 minutes

Step-by-step explanation:

8:40 pm to 9:30 am

8:40 pm to 8:40 am = 12 hours

8:40 am to 9:30 am = 50 minutes

The interval between 8:40 pm and 9:30 am is 12 hours and 50 minutes

What is an Interval?

An interval is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers. This range includes all the real numbers between those two numbers.

Given data ,

Let the interval be denoted as [ a , b ] , where a is the start point and b is the final point

Now ,

a = 8:40 pm

b = 9:30 am

The interval can be calculated by ( b - a )

8:40 pm → 8:40 am = 12 hours

8:40 am → 9:30 am = 50 minutes

Therefore , total interval = 12 hours and 50 minutes

Hence , The interval between 8:40 pm and 9:30 am is 12 hours and 50 minutes

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what is 3/2 (7/3n +1)= 3/2

Answers

answer:

n=0

reasoning:

first, distribute by multiplying 3/2 by 7/3n and 1
this makes the equation 7/2n+3/2=3/2
subtract 3/2 from both sides to get 7/2n=0
divide both sides by 7/2 to get n=0

(I believe this is correct, if I messed anything up I apologize, I just worked it out like a normal algebraic equation)

Mrs. Krueger created the expression 4(h + 11) - 15 to estimate the number of hours each her students need to study each way to earn a certain grade average according to the expression how many hours per week does Lindsay needs to study if she wants to have an average of at least 90

Answers

Answer:

15.25 hours atleast.

Step-by-step explanation:

First  rewrite the expression so it helps us find the answer.

4(h+11)-15=90

Distribute -> Substract from both sides -> Divide 61/4

[tex]4(h+11)-15=90\\4h+44-15=90\\4h+29=90\\4h=61\\61/4= 15.25h[/tex]

The question is Find the area.

Answers

Answer:

the area is 9in^3

Step-by-step explanation:

the formula for area of a triangle is 1/2bh, so it's 1/2 x 7.2 x 2.5

Xavier caught a football and ran for eight yards before being pushed 17 yards backward.
Which equation correctly shows his change in yardage?
А
8 + (-17) = -9
-17 + (-8) = -25
B
С
17 + (-8) = 9
D
8 + 17 = 25

Answers

Answer:

Answer A

Step-by-step explanation:Option B is saying that he went back 8 yards and was pushed even farther. Option C is saying he ran foward 17 yards and got pushed back 8. Option D is saying he got pushed foward 17 yards.

Option A is saying that he ran 8 yards and then lost 17 by getting pushed back.

Rank the items from 1 to 4 based on their unit prices.
Use the drop-down menus to label the least expensive
item per pound with "1" and the most expensive item
per pound with "4."
Avocados:
Broccoli:
Carrots:
Onions:

Answers

Answer:Avocados:4

Broccoli:3

Carrots:2

Onions:1

Step-by-step explanation:I did the question it is correct.

Which expressions are equal to z+(z+6)

Answers

Answer:

2(z+3)

Step-by-step explanation:

2z+6

take out the 2: 2(z+3)

Seven times the sum of a number and 2 equals 5

Answers

Answer: The number is -9/7  

Step-by-step explanation:

The statement can be expressed by the equation

7(n + 2) = 5       where n is the number

Now solve for n

7(n+2) = 5   distribute on the left side

7n + 14 = 5

      -14    -14

7n = - 9

n = -9 /7

Write a number that is 90,000 greter than 8,304,088

Answers

Well I would just do 8,304,088 + 90,000. So, that would equal 8,394,088 in all. Hope this helped!
the answers is 8,394,088

proof :

7. Three cubes of edges x cm , 6 cm, and 8 cm are melted and recast into a bigger cube of
edge 12 cm , find the value of x?

Answers

Answer:

10 cm³

Step-by-step explanation:

Volume of a cube = (Side)³

Volume of bigger cube = (12)³

                                           (12)³ = 1728 cm³

Volume of three cubes = (x)³ + (6)³ + (8)³ = 1728

(x)³ = 1728 - (6)³ - (8)³

(x)³ = 1000

x = ∛1000

x = 10 cm³

A small apple weighs 4.5 ounces. if
it is divided into 4 equal Pieces, how
much dose each piece weighs

Answers

Answer:

1.125

Step-by-step explanation:

Each piece weighs 1.125 ounces

What is the fundamental principle of multiplication?

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that small apple weighs 4.5 ounces.

if it is divided into 4 equal Pieces then

Therefore, Weight of apple = 4.5 ounces

Total pieces = 4

Now Weight of 1 piece = 4.5 ÷ 4

= 1.125

Hence the answer is 1.125 ounces

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Please answer this correctly without making mistakes

Answers

She will most likely finish graduation portraits.

I'm not to sure so try not to pick my answer.

what is 84.637 minus 28.56

Answers

Answer:

56.077

Step-by-step explanation:

Answer:

56.077

Step-by-step explanation:

i did it in my caculator lol :)

The costs per load (in cents) of 47 dish-washing detergents tested by a consumer organization are shown here. Find the standard deviation of the sample.

Answers

10.0 is the right answer I believe

|5-x|-|x+8|, if x>5

Answers

Answer:

just do it on ur caslc im pretty sure it would work

Step-by-step explanation:

Find equations of the spheres with center(3, −4, 5) that touch the following planes.a. xy-plane b. yz- plane c. xz-plane

Answers

Answer:

(a) (x - 3)² + (y + 4)² + (z - 5)² = 25

(b) (x - 3)² + (y + 4)² + (z - 5)² = 9

(c) (x - 3)² + (y + 4)² + (z - 5)² = 16

Step-by-step explanation:

The equation of a sphere is given by:

(x - x₀)² + (y - y₀)² + (z - z₀)² = r²            ---------------(i)

Where;

(x₀, y₀, z₀) is the center of the sphere

r is the radius of the sphere

Given:

Sphere centered at (3, -4, 5)

=> (x₀, y₀, z₀) = (3, -4, 5)

(a) To get the equation of the sphere when it touches the xy-plane, we do the following:

i.  Since the sphere touches the xy-plane, it means the z-component of its centre is 0.

Therefore, we have the sphere now centered at (3, -4, 0).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, -4, 0) as follows;

[tex]d = \sqrt{(3-3)^2+ (-4 - (-4))^2 + (0-5)^2}[/tex]

[tex]d = \sqrt{(3-3)^2+ (-4 + 4)^2 + (0-5)^2}[/tex]

[tex]d = \sqrt{(0)^2+ (0)^2 + (-5)^2}[/tex]

[tex]d = \sqrt{(25)}[/tex]

d = 5

This distance is the radius of the sphere at that point. i.e r = 5

Now substitute this value r = 5 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 5²  

(x - 3)² + (y + 4)² + (z - 5)² = 25  

Therefore, the equation of the sphere when it touches the xy plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 25  

(b) To get the equation of the sphere when it touches the yz-plane, we do the following:

i.  Since the sphere touches the yz-plane, it means the x-component of its centre is 0.

Therefore, we have the sphere now centered at (0, -4, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (0, -4, 5) as follows;

[tex]d = \sqrt{(0-3)^2+ (-4 - (-4))^2 + (5-5)^2}[/tex]

[tex]d = \sqrt{(-3)^2+ (-4 + 4)^2 + (5-5)^2}[/tex]

[tex]d = \sqrt{(-3)^2 + (0)^2+ (0)^2}[/tex]

[tex]d = \sqrt{(9)}[/tex]

d = 3

This distance is the radius of the sphere at that point. i.e r = 3

Now substitute this value r = 3 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 3²  

(x - 3)² + (y + 4)² + (z - 5)² = 9  

Therefore, the equation of the sphere when it touches the yz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 9  

(b) To get the equation of the sphere when it touches the xz-plane, we do the following:

i.  Since the sphere touches the xz-plane, it means the y-component of its centre is 0.

Therefore, we have the sphere now centered at (3, 0, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, 0, 5) as follows;

[tex]d = \sqrt{(3-3)^2+ (0 - (-4))^2 + (5-5)^2}[/tex]

[tex]d = \sqrt{(3-3)^2+ (0+4)^2 + (5-5)^2}[/tex]

[tex]d = \sqrt{(0)^2 + (4)^2+ (0)^2}[/tex]

[tex]d = \sqrt{(16)}[/tex]

d = 4

This distance is the radius of the sphere at that point. i.e r = 4

Now substitute this value r = 4 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 4²  

(x - 3)² + (y + 4)² + (z - 5)² = 16  

Therefore, the equation of the sphere when it touches the xz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 16

 

By using the general sphere equation and what we know about planes, we will get:

a) (x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 5^2b) (x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 3^2c) (x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 4^2.

General sphere equation.

The general sphere of radius R centered in the point (a, b, c) is given by:

(x - a)^2 + (y - b)^2 + (z - c)^2 = R^2

If we want a sphere centered in (3, -4, 5) we will have:

(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = R^2

a) We want the sphere to touch the xy-plane, (with z = 0) then the radius must be at least equal to the z-component of the point, so we have R = 5, then the equation is:

(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 5^2

b) This time is the yz-plane, so the radius must be equal to the x-component.

(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 3^2

c) Finally, the xz-plane, this time the radius must be equal to the y-component.

(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 4^2

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