Thirty-six friends are renting a party bus to the school prom. Rental of the
party bus will cost $300 up front plus $18 per hour. The friends have the
bus from 5:00 PM to 3:00 AM.
Each friend has agreed to chip in $12. One of the teachers at the high
school, Mr. Jones, has offered to chip in the rest. If he does, how much will
he pay

Based on the fact that town is 2 miles away, the time it took Trinity to travel to town and back was 33 minutes

The time taken can be found as:

= Distance / Speed

Trinity's trip to town took:
= 2  / 4

= 0.5 hours

Trinity's trip back took:

= 2  / 40

= 0.05 hours

The total time it took Trinity to travel to and from town was:

= (0.5 + 0.05) x 60 minutes per hour

= 0.55 hours x 60

= 33 minutes

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For the car travelling with 55 miles per hour-

The distance is a actual length of a path taken by the object.

For, the values given in the question;

1. The unit rate speed for this car is ___ miles per hour

S = D/T

S = 55 miles per hour.

Rate of speed is the same as the speed.

Thus,

The unit rate speed for this car is 55 miles per hour

2. if the car has driven 1/2 (0.5) hours, it traveled ___ miles

S = D/T

D = S×T

S = 55 miles per hour.

T = 0.5

Put the values;

D = 55×0.5

D = 275 miles.

Thus, the car travelled 275 miles.

3. if the car has driven 1 1/2 (1.5) hours, it has traveled ___ miles

S = D/T

D = S×T

S = 55 miles per hour.

Put the values;

D = 55×1.5

D = 825 miles.

Thus, the car travelled 825 miles.

4 If the car has travelled 110 miles, it will take ___ hours

S = D/T

S = 55 miles per hour.

D = 110 miles

T = D/S

Put the values;

T = 110/55

T = 2 hours.

Thus, the time taken by car is 2 hours.

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Answer:

2949.44 Step-by-step explanation: 18,434x4 - four trucks = 73736 73736x.04-2949.44

The best estimation for the area of the triangle is option (C) 21 square units  

The base of the triangles = 6 units

The height of the triangle = 7 units

We know,

The area is  the total space taken by the surface of an object.

Area of the triangle is the half the product of its base length and height.

The area of the triangle = (1/2)×b×h

Where b is the base of the triangle

h is the height of the triangle

Substitute the values in the equation

The area of the triangle = (1/2)× 6× 7

= (1/2)× 42

= 21 square units

Hence, the best estimation for the area of the triangle is option (C) 21 square units  

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The proper format for scientific notation is a x 10^b , 6.75 × 10⁹ is the scientific notation for 6,750,000,000.

The proper format for scientific notation is a x 10^b where a is a number or decimal number.

Given number is 6,750,000,000, we need to write in scientific notation.

To write the number to scientific notation, we need to follow few rules, Move the decimal so there is one non-zero digit to the left of the decimal point.

The number of decimal places you move will be the exponent on the . If the decimal is being moved to the right, the exponent will be negative.

If the decimal is being moved to the left, the exponent will be positive.

6,750,000,000 = 6.75 × 10⁹

Therefore 6.75 × 10⁹ is scientific notation for 6,750,000,000.

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Answer:

6-1

Step-by-step explanation:

Answer:

p+4

Step-by-step explanation:

Answer:

99

Step-by-step explanation:

9 × 11 = 99

Answer:99 you got it right.

Step-by-step explanation:

its easy for a seventh grader.

For this analysis,  4/25  is the f-ratio.

What is f- ratio?

SS between = 30

SS within = 60

Mean square of regression = 30/2 = 15

Mean square of error = 60/15 = 4

So f ratio = 15/4 = 3.75

So it's answer is D.

Solution(15)

Df between = Df total - Df within = 29-27 = 2

So it's answer is b. I.e. 2

Solution(16)

If Df = 18 and there are two independent sample than total sample size = 18+2 = 20

So it's answer is A

Solution(17)

N1=10

N2 = 15

So DF = 10+15-2 = 23

So it's answer is C. I.e. 23

Solution(18)

D = (M1-M2)/spooled = (35-31)/25 = 4/25

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Answer:

Angle BOC = 120°

Angle DOC = 60°

Angle ODC = 90°

Step-by-step explanation:

Triangle ABC is an equilateral triangle, therefore Angle BAC = 60°.

Now that we know Angle BAC, we can find Angle BOC: 2 × 60 = 120°

Angle DOC = ½ Angle BOC ( Radius drawn from centre to midpoint of chord, bisect the angle)

So Angle DOC = ½ (120) = 60°

Angle = 90° because D is the midpoint of chord BD and OD is a radius.

The interval at which the function f ( x ) = - ( x + 8 )² - 1 is decreasing is [-8, ∞).

We are given the function:

f ( x ) = - ( x + 8 )² - 1

We will first simplify the expression:

f ( x ) = - x² - 64 - 16 x - 1

f ( x ) = - x² - 16 x - 65

Now, we will plot the function on a graph.

Now, we can see that, the function is decreasing at [-8, ∞) from the graph of the function.

Therefore, the interval at which the function f ( x ) = - ( x + 8 )² - 1 is decreasing is [-8, ∞).

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Answer:

2x+y=-2

-9x-3y=18

So what you would do is see which one you would like to get rid of (either x, or y in this situation get rid of y)

multiply y by postive 3

3(2x+y=-2)

6x+3y=-6

-9x-3y=18          (both y's cross out since 3y+-3y is equal to zero)

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

-3x=-24 (divide both sides by -3)

---     ---

-3      -3

x= 8 (neg/neg=positive)

Then figure out the x so use either the first or second equation

so in this case I will use the first equation (plug in the x for 8)

2(8)+y=-2

16+y=-2

-16    -16

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

y=-18

Check:

2x+y=-2

2(8)+y(-18)=-2

16+-18=-2

-2=-2 (therfore you know that you are right)

Ansers:

y=-18

x=8

Hope this helps!

The vector function, r(t) that represents the curve of intersection of the two surfaces, the paraboloid and the parabolic cylinder is given by < t, 3t2, 8t2 + 9t4 >. It is attained by applying the concept of vectors to the assigned problem.

What is a vector?

A vector is any quantity that contains both magnitudes as well as direction. Geometrically, one can imagine a vector as a directed line segment, whose length denotes the magnitude of the vector and the direction is shown by the arrow, which is generally taken from its tail to its head. Using an arrow with a line specifies that it is not only scalar but also has some direction.

Calculation of the vector function representing the curve of intersection of the paraboloid and parabolic cylinder

A vector function r(t) is represented as: r(t) = < x, y, z >

Given: y = 3x2                         – 1

z = 8x2 + y2                             – 2

Let,

x = t

Using x = t in equations 1 and 2

y = 3t2

z = 8t2 + y2

Putting the value of y in z, we get,

z = 8t2 + (3t2)2

z = 8t2 + 9t4

Substitute  these values of x, y, and z in vector representation to obtain the result, i.e. < t, 3t2, 8t2 + 9t4 >

Hence, the value of vector function r(t) is: < t, 3t2, 8t2 + 9t4 >

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Answer:

30/32

Step-by-step explanation:

15×2=30

16×2=32

30/32

Answer:

5:2 , 30:12 , 60:24 , etc.

Step-by-step explanation:

To identify ratios equivalent to 15:6, all you need to do is multiply or divide both numbers in the ratio by the same amount to find an equivalent ratio.

So, for example:

1:2 --> 1*2 : 2*2 = 2:4 Both one half, so equal.

Now for 15:6...

Let's divide by the least common denominator ( 3 )

15 / 3 and 6 / 3 = 5 and 2

So 15:6 = 5:2

And we can also multiply the ratio by any constant as well...

For example 15 * 2 and 6 * 2

So 30:12 = 15:6

Hope this helped!

The numerical form of the statement the product of 9 and a number is

9n - 9.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The given statement is 9 is subtracted from the product of 9 and a number.

Let the number be 'n'.

Therefore, The statement 9 is subtracted from the product of 9 and a number can be numerically written as,

9n - 9.

We can also take 9 as a common factor,

9(n - 1).

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The coordinates of the mid point of the given points  (4,-1) and (3,-2) is found as (x,y) = (3.5, -1.5).

In response to the question, we have -

A (4,-1)and B(3,-2) are our two coordinate points.

We must determine the midpoint of the this line AB.

x(m) = [x(1) + x(2)]/2

y(m) = [y(1) + y(2)]/2

A is the first coordinate point (4,-1).

Point B is the second coordinate (3,-2).

Put the given points;

x(m) = [4 + 3)]/2

x(m) = 7/2 = 3.5

Now, for y;

y(m) = [y(1) + y(2)]/2

y(m) = [-1 -2]/2

y(m) = -3/2 = -1.5

Therefore, we get - using the Mid - Point formula (x,y) = (3.5, -1.5).

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In the expression:

[tex] - 2(x - 5) - 3(4x + 4)[/tex]

Apply the rule of BODMAS which states that bracket comes first, and we know that when a number is outside a bracket, it means the number will multiply the number(s) in the bracket. Infact, bracket means multiplication. So, -2 will multiply the values in the bracket beside it, and -3 will multiply the values in the bracket beside it. When that is done, combine everything together (always observe the mathematical signs)

[tex] - 2x + 10 - 12x - 12[/tex]

Now, collect like terms.

[tex] - 2x - 12x + 10 - 12[/tex]

Therefore, final answer is:

[tex] - 14x - 2[/tex]

Answer:

a

Step-by-step explanation:

The commutative property is related to both addition and multiplication. It means that changing the order or position of two numbers while adding or multiplying them does not change the end result.

Since the question specifically asked for multiplication, the answer is a.

6 half-lives are required for the concentration of reactant to decrease to 1.56% of its original value.

Using integrated rate law for first order kinetics as:

[tex][A_t]=[A_0]e^{-kt}[/tex]

Where

[tex][A_t][/tex]is the concentration at time t

[tex][A_0][/tex] is the initial concentration.

Given,

Concentration is decreased to 1.56 % which means that 0.0156 of [tex][A_0][/tex] is decomposed. So,

=> [tex]\frac{[A_t]}{[A_0]}[/tex] = 0.0156

Thus

=> 0.0156 = [tex]e^{-kt}[/tex]

When we simplify it,

Then we get,

kt = 4.1604

k = 4.1604/t

The expression for the half life is:-

Half life = 15.0 hours

[tex]t_{1/2}=\frac{ln2}{k}[/tex]

Where, k is rate constant

So,

[tex]k=\frac{ln2}{t_{1/2}}[/tex]

Apply the value of k then.

[tex]\frac{4.1604}{t}=\frac{ln2}{t_{1/2}}[/tex]

Therefore,

[tex]t=6\times t_{1/2}[/tex]

Therefore, 6 half-lives are required for the concentration of reactant to decrease to 1.56% of its original value.

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For Part F- Option C is correct.

1.5 days for 1 m2 of reef to accumulate 30 mmol of CaCO3

Graph of carbonate concentration versus time calcification rate.

At 270 umol/kg of seawater carbonate ion concentratio the approximate rate of calcification will be 20 mmol CaCO3 per m2 per day.

So it will take 1.5 days for 1 m2 of reef to accumulate 30 mmol of CaCO3

For Part G-

At 250 umol/kg of seawater carbonate ion concentratio the approximate rate of calcification will be 10 mmol CaCO3 per m2 per day.

So it will take 3 days for 1 m2 of reef to accumulate 30 mmol of CaCO3

The rate at which corals that form reefs lay down their calcium carbonate skeleton is known as coral calcification. It serves as a gauge of coral growth, which is crucial for the sustainability of reef ecosystems.

The long-term biodiversity, and possibly the existence, of coral reefs depends on significant reductions in global CO2 emissions as well as good management of water quality to lessen macroalgal competition and aid coral recovery.

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Answer:

To 2 decimal places, we have 91584.38.

Answer:

22) -3jk+12k^2---------24)-3xy^4-7xy^3

Step-by-step explanation:

Answer:

$3.53

Step-by-step explanation:

$30.01- the eggs $5.30= $24.71

24.71÷7= 3.53

Answer:

Step-by-step explanation:

The value of x is 1/ 5

Algebraic expressions are expressions that comprise of variables, factors, coefficients, terms and constants.

They are also made up of mathematical operations such as addition, division, multiplication, subtraction, etc

Given the expression:

3/ 5x + 22 = 28

collect like terms

3/ 5x = 28 - 22

3/ 5x = 6

cross multiply

5x × 6 = 3

30x = 6

Makr 'x' the subject

x = 6/ 30

x = 1/ 5

Thus, the value of x is 1/ 5

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The distance between -2 3/5 and -1​ on a number line is -1 3/5.

A mixed number is a fraction that is made up of a whole number and a proper fraction. A proper fraction is a fraction in which the numerator is less than the denominator. An example of a mixed number is -2 3/5.

In order to determine the distance, -1 would be subtracted from -2 3/5

[tex]-2\frac{3}{5} - (-1)[/tex]

[tex]-2\frac{3}{5} + 1[/tex]

[tex]-\frac{13}{5} + \frac{5}{5}[/tex]

[tex]\frac{5 - 13}{5}[/tex]

-8/5 = -1 3/5

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The shortest distance from the center of a circle to a point on the circle is the radius.

The circular line is drawn equidistant from the center point of a circle, which is a two-dimensional geometry object on a plane.

Any line segment connecting a circle's center to its perimeter is considered a circle's or sphere's radius, and in more recent usage, their length is also considered.

The radius of a circle is the shortest path between any two points on the circle.

Therefore, the shortest distance from the center of a circle to a point on the circle is the radius.

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Pamela will have enough wood for making the third leg as she has a 20 inch piece still left with her.

We are given that:

Pamela wants to make a three legged stool.

She has two pieces of wood: 36 inches and 21 inches.

Length of each leg = 16 inches.

Now, she cut 1 leg from each piece of the wood.

Length of wood pieces left will be given by the expression:

36 inches - 16 inches = 20 inches

and

21 inches - 16 inches = 5 inches.

Yes, Pamela will have enough wood for making the third leg as she has a 20 inch piece still left with her.

Therefore, Pamela will have enough wood for making the third leg as she has a 20 inch piece still left with her.

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The simplified expression for the expression 2y - 7x + 4x² + 3y + 7x is

D. 5y + 4x²

Option D is the correct answer.

We have,

To simplify the expression 2y - 7x + 4x² + 3y + 7x, we combine like terms:

The like terms are:

2y and 3y

-7x and 7x

Group the terms with "y" together: 2y + 3y = 5y

Group the terms with "x" together: -7x + 7x = 0

Combining (1) and (2) for the expression.

Now the expression becomes:

5y + 4x²

Thus,

The simplified expression for the expression 2y - 7x + 4x² + 3y + 7x is

D. 5y + 4x²

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we get - x³ + 3 x² - 6 after subtracting x³ - 2 x² from x² - 6.

We are given two expressions:

x³ - 2 x²

x² - 6

We need to subtract x³ - 2 x² from x² - 6

We get the expression as:

x² - 6 - (x³ - 2 x²)

Opening the brackets, we get that:

= x² - 6 - x³ + 2 x²

Combining the like terms, we get that:

= 3 x² - x³ - 6

Simplifying the expression, we get that:

= - x³ + 3 x² - 6

Therefore, we get - x³ + 3 x² - 6 after subtracting x³ - 2 x² from x² - 6.

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