If a certain train fare costs $5.00 for the first
10 miles of service, $0.25 per mile for the next
40 miles, and $0.10 per mile for each additional
mile, what would the train fare be to travel a
total distance of 100 miles?

Answer:

Arithmetic => each new term differs from the previous term by a fixed amount

an = a1 + d (n − 1)

Geometric => each element after the first is obtained by multiplying the previous number by a constant factor

an = a1 (r)^(n − 1)

4,8,16,32 the difference is not fixed so it is a geometric so it is ratio

the ratio is 2 and n is 5 so 4*(2)^4 =4*16=64

To generate the terms of a series given in sigma notation, replace the index of summation with consecutive integers from the first value to the last value of the index.

if you also want the sum of them

arithmetic -> (n/2)(a1+an)

geometric -> (a1*(1-r^n))/(1-r) or

      when the sequence is infinite you can use a1/(1-r)

Step-by-step explanation:

Arithmetic => 1,3,5,7,9,11,13,15....

Geometric => 1,2,4,8,16,32,64....

Step-by-step explanation:

Factor out two from the expression. The answer should be 2(2*(-2, 3)-(6, -7))

The least miles per gallon this trip is 25 miles per gallon

The given parameters are:

Distance = 450 miles

Tank size = 18 gallons

The least miles per gallon this trip is calculated as:

Miles per gallon = Distance/Tank size

This gives

Miles per gallon = 450/18

Evaluate the quotient

Miles per gallon =25

Represent as an inequality

x >= 25

Hence, the least miles per gallon this trip is 25 miles per gallon

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She will have $2118 in her account after five years

The given parameters about the compound interest are

Principal Amount, P = $1,900

Interest Rate, R = 2.2%

Time, t = 5

Compound interests are different from simple interest, and they are calculated using the following compound interest formula

CI = P(1 + R)^t - P

To calculate the amount, we have:

A = P + CI

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

Substitute the known values in the above equation

A = 1900 * (1 + 2.2%)^5

Express 2.2% as decimal

A = 1900 * (1 + 0.022)^5

Evaluate the sum

A = 1900 * (1.022)^5

Evaluate the exponent

A = 1900 * 1.11495

Evaluate the product

A = 2118

Hence, she will have $2118 in her account after five years

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Answer:

25, 26, and 27 are the three consecutive integers.

Step-by-step explanation:

Let the numbers be represented as x, x + 1 and x + 2.

We can write the equation:

[tex]x+(x+1)+ (x+2)=78[/tex]

Opening the brackets and simplifying:

[tex]x+x+1+x+2=78[/tex]

[tex]3x+3=78[/tex]

Subtract 3 from both sides.

[tex]3x=75[/tex]

Divide both sides by 3.

[tex]x=25[/tex]

Since the three consecutive integers are x, x + 1 and x + 2, replace x with 25.

∴ 25, 26 and 27 are the three consecutive integers.

Answer:

25 , 26 and 27

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

You save ⅓ of entry fee, so you save 1.20 and you pay 2.40. We only really care about the 1.20 reduction. 5 / 1.2 = 4.16 so he must go 5 times to get the 5 back

Answer:

[tex]x > 60[/tex]

Step-by-step explanation:

[tex]x-30 > 30[/tex]
[tex]x > 60[/tex] (add 30 onto both sides of the inequality)

Step-by-step explanation:

First thing first, let find the x value of where P and Q both meet y=5, we know that y=5, and y=2x^2+7x-4, so using transitive law,

[tex]5 = 2 {x}^{2} + 7x - 4[/tex]

[tex]2 {x}^{2} + 7x - 9[/tex]

[tex]2 {x}^{2} - 2x + 9x - 9[/tex]

[tex]2x(x - 1) + 9(x - 1)[/tex]

[tex](2x + 9)(x - 1) = 0[/tex]

[tex]x = 1[/tex]

[tex]2x + 9 = 0[/tex]

[tex]x = - \frac{9}{2} [/tex]

Now, to find the gradient of the curve let take the derivative of both sides

[tex]5 = 2 {x}^{2} + 7x - 4[/tex]

[tex]0 = 4x + 7[/tex]

[tex]4x + 7[/tex]

Plug in -9/2, let call that point P

[tex]4( \frac{ - 9}{2} ) + 7 = - 11[/tex]

Plug in 1, let call that point Q

[tex]4(1) + 7 = 11[/tex]

So the gradient of the curve at point P (-9/2,5) is -11

The gradient of the curve at point Q (1,5) is 11.

[tex]\boldsymbol{\sf{5+4\cdot(8-6)^{2} \ \ \longmapsto \ \ [Subtract \ 6 \ from \ 8.] }}[/tex]

      [tex]\boldsymbol{\sf{5+4\cdot2^{2} }}[/tex]

Calculates 2 to the power of 2 and gets 4.

      [tex]\boldsymbol{\sf{5+4\cdot4 \ \ \longmapsto \ \ [Multiply] }}[/tex]

      [tex]\boldsymbol{\sf{5+16 \ \ \longmapsto \ \ [Add]}}[/tex]

      [tex]\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ 21}}}}[/tex]

Answer:

5+16x

Step-by-step explanation:

5+4x(8−6)

2

Subtract 6 from 8 to get 2.

5+4x×2

2

Calculate 2 to the power of 2 and get 4.

5+4x×4

Multiply 4 and 4 to get 16.

5+16x

This shows that 76 cookies will be made with the total pounds of cookies

Fractions are written as a ratio of two integers. Given the following parameters

Total pounds of cookies made = 4 3/4 pounds

Total pounds of cookies made = 19/4 pounds

If he uses 1/16 pound of dough for each cookie, the total amount of cookies made is given;

Number of cookies = 19/4 ÷ 1/16

Number of cookies = 19/4 * 16/1

Number of cookies = 19 * 4

Number of cookies = 76

This shows that 76 cookies will be made with the total pounds of cookies

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Answer:

the correct answer is 25

The estimated thickness of 2 sheets of paper, given the parameters, is 0.0216 cm.

The thickness of a sheet of paper can be measured using a screw gauge or vernier caliper.

If the thickness of a ream of paper, which contains 500 sheets, is given, a sheet will be x/500 thick.

The thickness of 2 sheets of paper will be the thickness of a sheet multiplied by 2.

Number of reams of paper in a box = 5 reams

1 ream = 500 sheets

500 sheets = 5.4 cm thick

The thickness of 2 sheets of paper = 0.0216 cm {5.4cm x 2/500)}

Thus, the estimated thickness of 2 sheets of paper, given the parameters, is 0.0216 cm.

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Assume that one ream of paper is 5.4 cm thick.

Answer:

v = -3w

Step-by-step explanation:

water level/volume = -3 x weeks

v = -3w

Answer:

x = 3

Step-by-step explanation:

see image. Instead of distributive property, let's multiply by 2 to get rid of the fraction and also the parenthesis on the left. See image.

Then subtract 5 and finally, divide by 3 to solve. See image.

Based on the information provided, the individuals in this study are: D. the students.

A study can be defined as a strategic process or technique through which a scientist (researcher) observes and measures the effect of a risk factors, diagnostic test, or treatments on a particular population of interest.

In Mathematics, a variable can be defined as the measurable conditions, events, characteristics, individuals, or behaviors that a scientist (researcher) can control or observe when performing a study.

Based on the information provided, the individuals in this study are the students and these include the following subclasses:

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The students are the individuals in this study and is therefore denoted as option D.

This refers to a group of people which are chosen or taken from a large population for measurement or surveys.

In this scenario, the study was conducted in a school with different types of students according to their grades such as freshman, sophomore etc. This therefore makes the individuals in the study to be students and is the most appropriate choice.

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Answer:

m∠RQS = 109°

Step-by-step explanation:

Angles on a straight line sum to 180°.

Therefore:

⇒ m∠RQS + m∠SQT = 180°

⇒ (15x + 4) + (10x + 1) = 180

⇒ 15x + 4 + 10x + 1 = 180

⇒ 15x + 10x + 4 + 1 = 180

⇒ 25x + 5 = 180

⇒ 25x + 5 - 5 = 180 - 5

⇒ 25x = 175

⇒ 25x ÷ 25 = 175 ÷ 25

⇒ x = 7

Now that we have found the value of x, substitute this into the expression for m∠RQS:

⇒ m∠RQS = 15(7) + 4

                  = 105 + 4

                  = 109°

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The average number of pages she reads per hour is 19 pages per hour

The given parameters are:

Number of pages = 76 pages

Number of hours = 4 hours

The average number of pages she reads per hour is calculated using the following formula

Average = Number of pages/Number of hours

Substitute the known values in the above equation

Average = 76 pages/4 hours

Evaluate the quotient

Average = 19 pages per hours

Hence, the average number of pages she reads per hour is 19 pages per hours

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Answer: 3(t-y)

Step-by-step explanation:

The term difference refers to subtraction, so that means t-y in parenthesis since you would have to solve that first.

Then after you'd solve that, then you would multiply it by 3

Hope I helped :)

The rate of the slower jet is 672 miles per hour.

The rate of the slower jet is 752 miles per hour.

Two jets leave an air base at the same time and travel in opposite directions.

One jet travels 80 mi/h faster than the other.

let

x = rate of the slower jet

faster jet = 80 + x

Therefore,

rate = distance / time

The two jets are 11392 miles apart.

(80 + x)8 + 8x = 11392

640 + 8x + 8x = 11392

640 + 16x = 11392

16x = 11392 - 640

16x = 10752

divide both sides by 16

x = 10752 / 16

x = 672 miles per hour

rate of the faster jet = 80 + 672 = 752 miles per hour

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Answer:

6

Step-by-step explanation:

Solve for y:

[tex]y/8=9/12[/tex]

Multiply both sides by 8:

[tex]y=72/12[/tex]

Solve fraction

[tex]y=6[/tex]

Answer: one

Step-by-step explanation:

parallel faces are the ones that are opposite to each other.

Answer:

one

Step-by-step explanation:

there is only one pair of parallel faces.

Answer:

[tex]x=1+\sqrt[n]{y}[/tex]

Step-by-step explanation:

Since: [tex](x-1)*(x-1)*(x-1)=y[/tex]

that would imply: [tex](x-1)=\sqrt[3]{y}[/tex]

This is a bit more clear, if you write the equation as:

[tex](x-1)^3=y[/tex]

and then take the cube root of both sides

[tex]\sqrt[3]{(x-1)^3}=\sqrt[3]{y}[/tex]

Which simplifies to

[tex]x-1=\sqrt[3]{y}[/tex]

Now add 1 to both sides, and you get the equation:

[tex]x=1+\sqrt[n]{y}[/tex]

The statements that applies are;

The property of power function is known to be peculiar to the field of math. A power function is known to be one that is made up of a variable base that tends to be raised to a fixed power.

Note that the function is one that is made up of a constant base that is often raised to a variable power.

Following the property of power function, we can be able to obtain the information above.

Therefore, The statements that applies are;

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Answer:

So g(6) comes out to be 2.

Step-by-step explanation:

So f(6)=5 means when f acts on 6, the result is 5....so the inverse would take 5 back to 6...or g(5)=6

So f(2)=6 means that f reassigns 2 to 6....so the inverse would take 6 back to 2....or g(6)=2

hope this helps :)

Answer: 3

Step-by-step explanation:

If f(x) = y, then invf(y) = x
So, f(5) = invg(5) = 3

2/3 is 400% of 1/6

0.2 is 12.5% of 1 3/5

From the question, we are to determine what percent of 1/6 is 2/3

Let the value be x

Thus,

We can write that

2/3 is x% of 1/6

This means

2/3 = x/100 × 1/6

Now, solve for x

2/3 = x/100 × 1/6

2/3 = x/600

x = (2×600)/3

x = 400

Hence, 2/3 is 400% of 1/6

We are to determine what percent of 1 3/5 is 0.2

Let the value be y

That is,

0.2 is y% of 1 3/5

This can be written as

0.2 = y% × 1.6

0.2 = y/100 × 1.6

Now, solve for y

0.2 = y/100 × 1.6

0.2 = 1.6y/100

1.6y = 0.2 × 100

1.6y = 20

y = 20/1.6
y = 12.5

Hence, 0.2 is 12.5% of 1 3/5

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Answer: 65.86 inches

Step-by-step explanation:

Length of the hypotenuse (length of diagonal) :  a^2 + b^2 = c^2

The length (a)= 57

The height (b) =33

57^2= 3,249

33^3= 1,089

3,249 + 1,089 = c^2

4,338 = c^2

We next square root both sides to find c by itself (length of the diagonal)

[tex]\sqrt{4,338} = c[/tex]

c= 65.8634952...

You can then round to however many decimals are required.

To the hundreds place: 65.86 inches

Answer:

49°

Step-by-step explanation:

The circumference of a circle measures 360 degrees, so arc XW is 98°.

So, angle XWY is 49°.