A car servicing station is running a special offer. The breakdown of the cost for different services is given below.

Membership Fee: $50 (one-time cost)
Air Freshener Cost: $4 per car per month
Washing Cost: $10 per car per month
Tire Replacement Cost: $400 per car
Tire Pressure Check Cost: $15 per month

The total cost for 12 months of this service for n cars is given by the expression below.
568n + 230

Answer:

40 un.

Step-by-step explanation:

The diagonals of the rhombus bisect each other at right angle. This gives us that

By the Pythagorean theorem,

[tex]VE^2=VS^2+ES^2,\\ \\VE^2=6^2+8^2,\\ \\ VE^2=36+64,\\ \\VE^2=100,\\ \\VE=10\ un.[/tex]

The sides of the rhombus are all of the same length, then the perimeter of the rhombus is

[tex]P_{VENU}=4\cdot 10=40\ un.[/tex]

The answer is D. C ÷ d = π, where C is circumference and d is diameter.

Answer:

Step-by-step explanation:

[tex]\text{The formula of a circumference of a circle:}\ C=d\pi\\\\d-diameter\\\\d\pi=C\qquad\text{divide both sides by}\ d\\\\\pi=\dfrac{C}{d}[/tex]

Answer:

NO

Step-by-step explanation:

2/10 have a common term of 2.  reduce both the numerator and denominator by dividing both by 2.

2/2 = 1  

10/2 = 5

the reduced fraction woudl be 1/5

Answer:

No 2/10 is not the same as 4/5

Step-by-step explanation:

The reason why is because If you doubled 2/10 then it would be 4/20 not 4/5 and if you divided by 4/5 by 2 then it would be a complex fraction of 2/1/2 that is why the statement 4/5 is equal to 2/10 is false.

Answer: C

He forgot the negative sign on 1/2x

Answer:

Yes

6(x+0.4) is equivalent to 3(2x+0.8)

Step-by-step explanation:

Given in the questions two expressions

6(x + 0.4)

3(2x + 0.8)

We will apply distributive law

It is a law relating the operations of multiplication and addition, stated symbolically

6(x + 0.4)

= 6(x) + 6(0.4)

= 6x + 2.4

3(2x + 0.8)

= 3(2x) + 3(0.8)

= 6x + 2.4

Since both equations when expanded have same answers, hence they are equivalent

Answer:

75

Step-by-step explanation:

To find the volume of a squared pyramid use the formula:

Volume of a squared pyramid = × base area × height

Base area = Side× side

( A square has the same length and breadth)

= 5 × 5 = 25 in

Volume of a squared pyramid =  [tex]\frac{1}{3}[/tex] × 25 × 9

= 75 [tex]in^{3}[/tex]  

The population of a town decreasing at a rate of 1.5% per year from an initial number of 4500 will drop below 4000 in approximately 9 years, around the year 2019.

The topic of this question concerns a decrease in population over time, which is generally described using exponential decay in mathematics. When we talk about a decrease of 1.5% per year, we're looking at an exponential decay factor of 1 - 0.015 = 0.985. We follow this process to determine the duration for the population to reduce below 4000:

Basically, it means:

4500 * (0.985^n) < 4000

. By solving this inequality, we find that

n ≈ 8.29

. Therefore, we can estimate the town's population will drop below 4000 in the 9th year (since we can't have a fraction of a year), which would be

2019

if we start counting from 2010.

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The population of the town would drop below 4000 in 2024.

To determine the year when the population of the town drops below 4000, we can use the formula for exponential decay:

Population = Initial population × (1 - Decay rate)^Time

where:

Population is the population at a given time

Initial population is the initial population (in 2010, which is 4500)

Decay rate is the decrease rate per year (1.5% or 0.015)

Time is the number of years since 2010

We want to find the Time when the Population is less than 4000. So, we can set up an inequality:

4000 > 4500 × (1 - 0.015)^Time

Dividing both sides by 4500, we get:

0.889 > (1 - 0.015)^Time

Taking the natural logarithm of both sides, we get:

ln(0.889) > Time × ln(1 - 0.015)

Dividing both sides by ln(1 - 0.015), we get:

Time ≈ 13.92

Since we're looking for the year when the population drops below 4000, we round up to the nearest whole year. Therefore, the population of the town would drop below 4000 in 2024.

Answer:

Choice B best fits the data shown

Step-by-step explanation:

We employ the scatter-plot feature in Ms. Excel and then add an exponential trend line selecting the display equation on chart option. The attachment below is an image from the excel workbook where the task was performed.

From the attachment the regression equation was obtained as;

[tex]y=3.799e^{0.7x}[/tex]

But;

[tex]e^{0.7}=2.01[/tex]

Thus, the regression equation can be expressed as;

[tex]y=3.80*2.01^{x}[/tex]

Answer:

Section A: Sally drives from her house to her friend's house.

Section B: Sally stops to visit her friend.

Section C: Sally drives from her friend's house to the post office to drop off a card.

Section D: Sally drives back to her house.

Step-by-step explanation:

As you can see in the graph, the point (0,0) is the location of Sally's house. In that point the distance is 0 and the time is 0.

In Section A she drives 3 miles in 6 minutes from her house to her friend's house.

In Section B, the distance does not change, this means that Sally stopped at her friend's house for 4 minutes.

In Section C she drives (for 4 minutes) 1 mile from her friend's house to some place (In this case the post office).

In Section D she comes back to 0 distance, then, she drives back to home.

Answer:

C

Step-by-step explanation:

given

x² = 64 ( take the square root of both sides )

x = ± [tex]\sqrt{64}[/tex] = ± 8

Tamara omitted the negative square root → C

Tamara made the mistake of only finding the positive square root, not the negative square root.

The mistake that Tamara made in finding the solution to the equation x^2=64 is that she only found the positive square root, not the negative square root.

When solving a quadratic equation like this, you need to consider both the positive and negative square roots, because both values satisfy the equation. So the correct solution to x^2=64 is x=8 and x=-8.

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Exponential decay because it is decreasing

Answer:

70 in³ (answer d)

Step-by-step explanation:

The volume of a pyramid with base area A and height h is

V = (1/3)(A)(h).

Here, V = (1/3)(21 in²)(10 in) = 70 in³

Answer:

Step-by-step explanation:

The product of three and a number x: 3 · x = 3x

The sum of four and the product of three and a number x:

4 + 3x

Answer:

In parallelogram ABCD

FD is perpendicular to BC

BE is perpendicular to CD

Consider triangle BEC and triangle DFC

FC = EC (Given)

Angle BEC = Angle DFC (=90°)

Angle BCE = Angle DCF (common)

Therefore triangle BEC is congruent to triangle DFC (AAS congruency)

DF = BE (CPCT)

Since the altitudes are equal their bases will also be equal

Therefore BC = DC

Therefore BC = DC = AD = AB

Therefore ABCD is a rhombus

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Since [tex]\(ABCD\)[/tex] is a parallelogram with all four sides congruent, [tex]\(ABCD\)[/tex] is a rhombus. Hence, [tex]\(ABCD\)[/tex] is proven to be a rhombus.

To prove that parallelogram [tex]\(ABCD\)[/tex] is a rhombus, we need to show that all sides are congruent.

Given:

1. [tex]\(ABCD\)[/tex] is a parallelogram.

2. [tex]\(BE \perp CED\).[/tex]

3. [tex]\(DF \perp BFC\).[/tex]

4. [tex]\(CE \cong CF\).[/tex]

Proof:

1. Parallelogram Properties:

  - In a parallelogram, opposite sides are congruent and parallel.

  - Therefore, [tex]\(AB \parallel CD\)[/tex] and [tex]\(AD \parallel BC\)[/tex].

  - Also, [tex]\(AB \cong CD\)[/tex] and [tex]\(AD \cong BC\)[/tex].

2. Congruent Segments:

  - [tex]\(CE \cong CF\) (given).[/tex]

  - Since [tex]\(BE \perp CED\)[/tex] and [tex]\(DF \perp BFC\)[/tex], [tex]\(BE\)[/tex] and [tex]\(DF\)[/tex] are heights from [tex]\(B\)[/tex] and [tex]\(D\)[/tex] respectively to line [tex]\(CED\)[/tex].

3. Triangle Congruence:

  - Consider [tex]\(\triangle CEF\)[/tex]. Since [tex]\(CE \cong CF\)[/tex] and [tex]\(BE \perp CED\)[/tex], [tex]\(DF \perp BFC\)[/tex], [tex]\(\triangle CEF\)[/tex] is isosceles with base [tex]\(EF\)[/tex].

4. Diagonals in Parallelogram:

  - Diagonals of a parallelogram bisect each other.

  - Since [tex]\(\triangle CEF\)[/tex] is isosceles and [tex]\(CE = CF\)[/tex], the diagonals [tex]\(BE\)[/tex] and [tex]\(DF\)[/tex] bisect each other at [tex]\(E\)[/tex] and [tex]\(F\)[/tex].

5. Symmetry and Congruence:

  - Since diagonals bisect each other and the height from [tex]\(B\)[/tex] and [tex]\(D\)[/tex] are equal, segments from [tex]\(B\)[/tex] and [tex]\(D\)[/tex] to the diagonals are congruent.

6. Sides of Parallelogram:

  - From symmetry and congruence, all sides of the parallelogram are equal.

  - Therefore, [tex]\(AB \cong BC \cong CD \cong DA\)[/tex].

Conclusion:

Since [tex]\(ABCD\)[/tex] is a parallelogram with all four sides congruent, [tex]\(ABCD\)[/tex] is a rhombus.

Hence, [tex]\(ABCD\)[/tex] is proven to be a rhombus.

Answer:

21

Step-by-step explanation:

Answer:

[tex]\dfrac{7.7.7.7.7}{7.7}[/tex]

Step-by-step explanation:

Finding the expression of the value [tex]\dfrac{7^{5} }{7^{2}}[/tex] is just like taking the spread out value of the two variables raised to their exponents.

[tex]\dfrac{7^{5}}{7^{}}=\dfrac{7.7.7.7.7}{7.7}[/tex]

So if we multiply all the values together we get:

=[tex]\dfrac{16807}{49}[/tex]

=343

This method is just one of the methods that can be used to finding the quotient of a variable raised to an exponent.

1) 2 and 3

2) skewed right

3) skewed left

Answer:

3/2

Step-by-step explanation:

mm,m

Based on the calculations below, the slope of this graph is equal to: C. 2/3.

In Mathematics and Euclidean Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]

By substituting the given data points (0, -2), and (3, 0) into the formula for the slope of a line, we have the following;

Slope of graph = (0 - (-2))/(3 - 0)

Slope of graph = (0 + 2)/(3 - 0)

Slope of graph = 2/3

Based on the graph, the slope is the change in y-axis with respect to the x-axis, and it is equal to 2/3.

The correct answer is C. The graph of the function [tex]y = (1/3)^x[/tex] decreases from left to right, exhibiting exponential decay as x increases.

To complete the table for the function [tex]y = (1/3)^x[/tex], we need to substitute the given values of x into the equation and calculate the corresponding values of y.

Let's start by substituting -3 into the equation:

y = (1/3)^(-3)

y = 1/(1/3)^3

y = 1/1/27

y = 27

Next, let's substitute -1 into the equation:

y = (1/3)^(-1)

y = 1/(1/3)^1

y = 1/(1/3)

y = 3

Then, let's substitute 0 into the equation:

y = (1/3)^0

y = 1

After that, let's substitute 1 into the equation:

y = (1/3)^1

y = 1/3

Lastly, let's substitute 2 into the equation:

y = (1/3)^2

y = 1/9

Therefore, the completed table is as follows:

x | -3 | -1 | 0 | 1 | 2 | 3

y | 27 | 3 | 1 | 1/3 | 1/9 | 1/27

To graph the function y = (1/3)^x, we plot the points from the completed table on a graph. The graph of this function is an exponential decay curve that starts at (0, 1) and decreases as x increases. The curve is steeper for larger x values and approaches the x-axis as x approaches infinity.

In terms of the given options, the correct answer would be C. The graph of the function decreases from left to right.

[tex]The \: money \: of \: each \: after \: Fred \: paid \: his \: debt: \frac{84 - 12}{2} = \$36 \\ John \: gave \: Fred:36 + 12 = \$48[/tex]

Answer:

36

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the number of games played be x.  68% of x comes out to 17 games.

Then 0.68x = 17.  Mult. both sides by 100:  68x = 1700.

Divide 68 into 1700 to obtain x, the number of games played:  x = 25

The team plays in 25 games.

Answer:6.928

Step-by-step explanation: formula A=√ 3*(side^2/4)

The area would be 7 cm

See the image

Answer would be D which is L

Answer:

L

Step-by-step explanation:

Most people prefer to use a unit of measurement that gives a number they can easily visualize, usually between 0.1 and 1000.

You wouldn't use centimetres, because that is a unit of length, and grams are a unit of mass.

The amount of milk in a half-gallon carton is about 2 L or 2000 mL, so you would measure the milk in litres (L).

Answer:

2

Step-by-step explanation:

In order to solve a system using the additional method, we would need to multiply the first equation by '2' in order for the x’s to add out.

We have the following equations:

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

[tex] -2x + 2y = 6 [/tex] --- (2)

We will multiply equation (1) by 2 and equation (2) by 3 to cancel the x's.

[tex] 2 ( 3x - y = 3 ) = [/tex] [tex] 6x - 2 y = 6 [/tex]

[tex] 3 ( -2x + 2 y = 6 ) = -6x + 6y = 36 [/tex]

Answer:

1.5(x)

Step-by-step explanation:

find out how many hours are in 90 minutes

1.5

x miles

Answer:

Yes

-2(3x-7) is equivalent to 5+6x-19-12x

Step-by-step explanation:

Given in the question two expression

-2(3x-7)

5+6x-19-12x

We will apply distributive law to solve first expression

a(b + c) = ab + ac

-2(3x-7)

-2(3x) + -2(7)

-6x -14

For the second expression rearrange the terms

5+6x-19-12x

-12x+6x -19+5

-6x -14

Since both equations when expanded have same answers, hence they are equivalent

Answer:

2

Step-by-step explanation:

Each time you flip a coin, there is a 50% change of it landing on tails.  So half the time you should get a tails.  

Half of 4 is 2, so you will likely get 2 tails.

Final answer:

When you flip a coin 4 times, the best prediction for the number of tails is 2, based on the equal 50-50 chance for heads or tails on each toss. However, you may actually get any number of tails from 0 to 4 due to randomness.

Explanation:

If you flip a coin 4 times, the best prediction for the number of times it will land on tails can be determined by understanding probability. Each coin flip represents an independent event with a 50-50 chance of landing on either heads or tails. Therefore, over a small number of flips, such as 4, it is expected that you will get tails approximately half the time. However, it is possible to see any combination of heads and tails.

When considering all the possible outcomes of flipping a coin 4 times:

4 heads, 0 tails (HHHH)

3 heads, 1 tail (HHHT, HHTH, HTHH, THHH)

2 heads, 2 tails (HHTT, HTHT, HTTH, THHT, THTH, TTHH)

1 head, 3 tails (HTTT, THTT, TTHT, TTTH)

0 heads, 4 tails (TTTT)

Given that each of these outcomes is equally likely, the prediction would be 2 tails because it is the average outcome. However, it is important to recognize that while 2 tails is the most likely single outcome, any number of tails between 0 and 4 is possible due to the randomness of each flip.

Answer:

Step-by-step explanation:

Area = L * W

2/5 * 1/3 =

2 * 1 = 2

5 * 3 = 15

= 2/15 inches squared

What we do is find area

Area of rectangle=(l*w)

length=2/5

width=1/3

Area=2/5*1/3

Answer=2/15

Answer=2/15