group of 280 elementary school students and 40 adults are going on a field trip. They are planning to use two different types of buses to get to the destination. The first type of bus holds 50 people and the second type of bus holds 56 people.



Andre says that 3 of the first type of bus and 3 of the second type of bus will hold all of the students and adults going on the field trip.

Is Andre correct?

For the given proportional relationship, it is found that the unit rate is of 1.5 inches per second, and the meaning of the points is given as follows:

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality, also called the unit rate.

For this problem, the unit rate is given as follows:

k = 4.5/3 = 1.5/1 = 1.5 inch per second.

The meaning of the points are given by:

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Answer:

22.4

Step-by-step explanation:

28% of 80 = [tex]\frac{28}{100}[/tex] of 80

=[tex]\frac{28}{100}[/tex] of 80 = [tex]\frac{28}{100}[/tex]*80

cut the zeros

=[tex]\frac{28}{10}[/tex]*8

=[tex]\frac{28}{5}[/tex]*4

=[tex]\frac{112}{5}[/tex]

=22.4

The possible perimeters are 140 feet, 148 feet and 160 feet.

In order to determine the width that would be used to determine the possible perimeters, the formula for the area would have to be rewritten.

A rectangle is a 2-dimensional quadrilateral with four right angles and two diagonals that bisect each other at right angles.

Area of a rectangle = length x width

Width = area / length

1200 / 40 = 30 feet

1200 / 50 = 24 feet

1200 / 60 = 20 feet

Perimeter of a rectangle = 2 x (length + width)

Perimeter when width is 30 feet : 2(40 + 30) = 140 feet

Perimeter when width is 24 feet : 2(24 + 50) = 148 feet

Perimeter when width is 20 feet : 2 (20 + 60) = 160 feet

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Z-score of 10 is -1.25; Z-score of 20 is 1.25; Z-score of 12 is -0.75; Z-score of 17 is 0.50; and Z-score of 16 is 0.25.

To calculate this, we use the following notations and formulas:

Mean = (sum of the values) / n

Variance = ((Σ(x - mean)^2) / (n - 1)

SD = Standard deviation = Variance^0.5

Z-score = (x - Mean) / SD

Where;

n = number of obsrvations = 5

x = each observation

We now proceed as follows:

Mean = (10 + 20 + 12 + 17 + 16) / 5 = 15

Variance = ((10-15)^2 + (20-15)^2 + (12-15)^2 + (17-15)^2 + (16-15)^2) / (5-1) = 64 / 4 = 16

SD = Variance^0.50 = 16^0.5 = 4

Z-score of 10 = (10 – 15) / 4 = –1.25

Z-score of 20 = (20 - 15) / 4 = 1.25

Z-score of 12 = (12 - 15) / 4 = –0.75

Z-score of 17 = (17 - 15) / 4 = 0.50

Z-score of 16 = (16 - 15) / 4 = 0.25

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(a) The change in the tram's elevation (speed) each second is 3 meters/Sec

(b) The total change in temperature of the substance was 160 Celsius.

(a) The tram moves downward 21 meters in 7 second. So, the speed of the tram is 21/7 = 3 meters/Sec, which is the tram’s elevation each second.

We know that, speed = (total distance travel)/(Total travelling time)

(b) The substance was heated by 4 Celsius each hour for 40hours.

Therefore, the total change in temperature is = (4x40) = 160 celcius.

The degree Celsius is the unit of temperature on the Celsius scale, originally known as centigrade scale

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Answer:

(a) The change in the tram's elevation (speed) each second is 3 meters/Sec

(b) The total change in temperature of the substance was 160 Celsius.

Step-by-step explanation:

The height from which any two objects is thrown affects their time of motion, the greater the height, the more time the objects spend in air and vice versa.

The time of motion of an object is the time taken for an object to travel from point of projection to the projection plane or it can be said as the time a projected object spent in air.

The time taken for an object dropped from a certain height is calculated as follows;

h = vt + ¹/₂gt²

where;

when the object is dropped from rest, v = 0

h =  ¹/₂gt²

t = √(2h/g)

Thus, the height from which any two objects is thrown affects their time of motion, the greater the height, the more time the objects spend in air and vice versa.

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Answer:

8a-2ab

Step-by-step explanation:

5a-2b+2b+3a-2ab

Simplify 'a'

5a+3a=8a

Simplify 'b'

2b+2b=4b

8a-2ab

If we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour,then we would need 38 number of cups.

Given that we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour.

We are required to find the number of cups that are needed.

Fraction is the combination of two numbers,one above the division sign and other one below the division sign. The number which is above the division sign is known as numerator and the number which is below the division sign is known as denominator.

Measuring cup=1/3

Number of cups needed in recipe=12+2/3=38/3

Number of cups needed=38/3/1/3

=38 cups

Hence if we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour,then we would need 38 number of cups.

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The equation which represents the height of the books is  [tex]s(b)=\frac{5}{4} b[/tex]

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. An equation between two sums of monomials of degree 0 or 1 is known as a linear equation.

The books are stacked one above the other and each book is [tex]1\frac{1}{4}[/tex] inches thick.

So to calculate the total height of the stack we have to multiply the number of books in the stack with the thickness of each book.

The total thickness is represented in the from of a function as

s(b) and the thickness of each book is [tex]1\frac{1}{4}=\frac{5}{4}[/tex] inches

total height=[tex]\frac{5}{4}\times b[/tex]

Therefore the required equation is  [tex]s(b)=\frac{5}{4} b[/tex].

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Answer:

75 =x

Step-by-step explanation:

We can use angle addition to find the measure of angle x

30 + 45 = x

75 =x

Answer:

x = 75°

Step-by-step explanation:

x = 30° + 45°

x = 75°

Answer:

Step-by-step explanation:

Find the area of the figure. (Sides meet at right angles.)

1 rettangle on a square

Area Rectangle

(2+2+5)*5=

9*5=

45in²

Area of the Square

5*5=

25in²

sum

45+25=

70in²

Answer: 46.5 by 19.5

Step-by-step explanation:

P=perimeter of panel. L=length. W=width

L=3W-12

P=2L+2W

132=2(3W-12)+2W

132=6W-24+2W

132=6W+2W-24

132=8W-24

156=8W

W=19.5

P=2L+2W

132=2L+2(19.5)

132=2L+39

2L=93

L=46.5

46.5 by 19.5

Answer:

Derek needs to pay 3 more pounds

Answer:

A. $0.22 per tortilla

B. $0.19 per tortilla

Step-by-step explanation:

A. All you gotta do is divide the money by the amount of product.

4.40 ÷ 20  = 0.22

B. All you gotta do is divide the money by the product.

8.55 ÷ 45 = 0.19

Therefore, the best pack to spend your money on would be the larger pack  B.

There will be an outcome of 16380 times.

What is an outcome?

The football team will play 14 games

and each game can result in one of 2

Hence, the total possible number of outcomes for the season is [tex]2^{14}[/tex].

Now, let us explain

Let the result can be represented by an 'ordered set" i.e. 14- box.

|1|2|3|4|5|6|7|8|9|10|11|12|13|14|

Hence, the first box can be filled in 2 ways.

Similarly, all boxes.

Hence, the total number of cases will be,

2*2*2*2.... 14 times

=  [tex]2^{14}\\[/tex]

=16380 times.

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The intersection is the set of all elements in both sets, so the answer is {-2, 4, 8}.

The union is the set of all elements in at least one of the sets, so the answer is {-2, 0, 3, 4, 5, 6, 8}.

The slope of f is m= -0.05577.

Given : The winning times for the​ 200-meter dash can be approximated by  f(x) = - 0.05577x+146.2 , where x is the year.

To find : The slope of f

Solution : Using slope intercept form a linear function is represented as

y = mx+b

where, m is the slope and b is the y-intercept.

We can write the function as  f(x) = - 0.05577x+146.2

Comparing with slope intercept form,

m= -0.05577 and y-intercept = 146.2

Therefore, The slope of f is m= -0.05577

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Answer:8/15 part of rain gauge is filled after 1 hour.

Step-by-step explanation:

Answer:

k < - 10 or k > 10

Step-by-step explanation:

inequalities of the type | x | > a have solutions of the form

x < - a or x > a , then

3k < - 30 or 3k > 30 ( divide each interval by 3 )

k < - 10 or k > 10

The domain of the function given on the graph is basically all numbers which are real and greater than or equal to -3.

Given a graph of a function.

We are required to choose the correct domain of the function from the options.

Function is basically a relationship between two or more variables that are expressed in equal to form. The values that we enter in the function are known as part of domain of that function and the values that we get from the function are known as part of range of that function.

Because the lowest point on x axis on which the curve starts is -3 and it continuously increases, so the domain of the function given on the graph is basically all real numbers which are greater than or equal to -3.

Hence the domain of the function given on the graph is all real numbers which are greater than or equal to -3.

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Question is incomplete as it should include the attached figure.

Answer:

√38

Step-by-step explanation:

√38

step 1: Check which squared numbers can be multiplied by another number to get 38.

Start with these numbers: 4, 9, 16, and 25

Step 2: Testing out the numbers

√25 × __ = 25 can't be divided by 38

√16 × ___ = 16 can't be divided by 38

√9 × ____ = 9 can't be divided by 38

√4 × ____= 4 can't be divided by 38

Step 3: Answer

After trying the square root numbers that could possibly work with √38 none work; which means √38 can't be simplified. So the answer is √38

I hope this helps!

After solving for x in the constructed equation, 97100 bushels were harvested last year.

What is an equation?

Constructing equation to determine no. of bushels.

Bales from the previous year = x + 0.45 x

= 140795 1.45 x

= 140795 X

= 97100 bales

After solving for x in the constructed equation, 97100 bushels were harvested last year.

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Answer:97100

Step-by-step explanation:

The function which results from the reflection of the given function; f(x) = 3^x is; f(x) = 3^(-x).

It follows from the task content that the function given is; f(x) = 3^x.

The function in discuss is reflected across the y-axis, hence, it follows from transformation rules that the resulting function involves multiplying x by -1 as follows;

f(x) = 3^(-1×x)

f(x) = 3^(-x).

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======================================================

Work Shown:

First replace every copy of n with 2

[tex]a_n = 3*(a_{n-1}) - 6\\\\a_2 = 3*(a_{2-1}) - 6\\\\a_2 = 3*(a_{1}) - 6\\\\a_2 = 3*(7) - 6\\\\a_2 = 21 - 6\\\\a_2 = 15\\\\[/tex]

Notice how the second term [tex]a_2[/tex] relies on the first term [tex]a_1[/tex]

Then repeat for n = 3

[tex]a_n = 3*(a_{n-1}) - 6\\\\a_3 = 3*(a_{3-1}) - 6\\\\a_3 = 3*(a_{2}) - 6\\\\a_3 = 3*(15) - 6\\\\a_3 = 45 - 6\\\\a_3 = 39\\\\[/tex]

Same goes with n = 4

[tex]a_n = 3*(a_{n-1}) - 6\\\\a_4 = 3*(a_{4-1}) - 6\\\\a_4 = 3*(a_{3}) - 6\\\\a_4 = 3*(39) - 6\\\\a_4 = 117 - 6\\\\a_4 = 111\\\\[/tex]

Finally plug in n = 5

[tex]a_n = 3*(a_{n-1}) - 6\\\\a_5 = 3*(a_{5-1}) - 6\\\\a_5 = 3*(a_{4}) - 6\\\\a_5 = 3*(111) - 6\\\\a_5 = 333 - 6\\\\a_5 = 327\\\\[/tex]

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

We have this summary:

[tex]a_1 = 7\\\\a_2 = 15\\\\a_3 = 39\\\\a_4 = 111\\\\a_5 = 327\\\\[/tex]

The first five terms are:  7, 15, 39, 111, 327

Answer:

1022 minutes

Step-by-step explanation:

Let x be the number of minutes the executive used the phone

There is a base charge of $35 and only minutes greater than 900 min are charged at the rate of $0.40 per minute

So total bill A = 35 + 0.4(x-900)

We know the bill was $83.80

So we can rewrite the equation as

35 + 0.4(x-900) = 83.30

and solve for x

To make it easier for computational purposes

1)  Multiply both sides by 10

[tex]35\cdot \:10+0.4\left(x-900\right)\cdot \:10=83.8\cdot \:10[/tex]

2) Perform individual multiplication

[tex]350+4\left(x-900\right)=838[/tex]

3)  Subtract 350 from both sides

[tex]350+4\left(x-900\right)-350=838-350[/tex]

4)  Simplify

[tex]4\left(x-900\right)=488[/tex]

5) Divide both sides by 4

[tex]\frac{4\left(x-900\right)}{4}=\frac{488}{4}[/tex]

6) Simplify

[tex]x-900=122[/tex]

7) Add 900 to both sides to isolate x

[tex]x-900+900=122+900[/tex]

8) Simplify to obtain x

[tex]x=1022[/tex]

Answer: The executive used the phone for 1022 minutes that month

The experimental research conducted by the scientist takes into account the following factors:

a)The change in temperature is the independent variable.

b) The effect of temperature on the chimp's act of aggression is the dependent variable.

c)The dependent variable is continuous.

d)The scale of measurement used to measure the dependent variable is interval.

e) The research method being used here is experimental.

In the above experiment the researcher wants to see the change in the aggression of the chimp when there is a change in temperature in the zoo.

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