Compute the requested operating costs as indicated, based on the preceding table and the following information.


Car: six-cylinder compact

Year driven: second

Miles driven: 14,000


The insurance cost for second year is $

.

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

Explanation:

Part A

x = number of years after 1983

Example: x = 2 is the year 1985 since 1985-1983 = 2.

The number of people who drink this beverage declines by 6.5% each year. The multiplier is 1+r = 1+(-0.065) = 0.935

Meaning that if 6.5% of the people leave, then 93.5% remain. The two percentages add to 100%.

This value 0.935 is the base of the exponent portion. We have 0.935^x as the exponent portion.

Out front is the value 5480 which is the starting amount of people.

This leads to the exponential equation y = 5480*0.935^x

It is of the form y = ab^x

a = 5480 = starting population

b = 0.935 = decay factor

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

Part B

The timespan from 1983 to 2023 is 40 years (because 2023-1983 = 40).

Which means we plug x = 40 into the equation we found in part A.

y = 5480*0.935^x

y = 5480*0.935^40

y = 5480*0.06799303620922

y = 372.601838426526

y = 373

Be sure to round to the nearest whole number.

We expect or predict there will be approximately 373 people who remain loyalists to this root beer as of September 2023.

Answer:

Part (a)

[tex]y=5480(0.935)^x[/tex]

where:

Part (b)

373

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

The initial number of people who drink Root Beer (in September 1983):

If the number of people that drink Root Beer instead of Coca-Cola has been declining at the rate of 6.5% per year, then:

Therefore, an exponential equation that represents the number of Root Beer loyalists in Outback for any year is:

[tex]y=5480(0.935)^x[/tex]

where:

The number of years between September 1983 and September 2023 is:

To calculate how many Root Beer loyalists should there be as of September 2023, substitute x = 40 into the equation found in part (a):

[tex]\implies y=5480(0.935)^{40}[/tex]

[tex]\implies y=5480(0.0679930362...)[/tex]

[tex]\implies y=372.601838...[/tex]

[tex]\implies y=373[/tex]

Therefore, there should be approximately 373 Root Beer loyalists as of September 2023.

Therefore , the solution of the given problem of expression comes out to be sixty-seven billion five hundred eighty million.

Each variable must be replaced with a number and arithmetic operations must be performed to check an algebraic equation. Given that 6 + 6 equals 12, the answer variable in the aforementioned case is comparable to 6. We can substitute the variables values with those we know in order to evaluate the expression.

Here,

6.758 1010 in scientific notation

The scientific notation is = 6.758e10.

Engineering notation: 67.58 109 billion; prefix: giga- (G)

6.758 x 1010 standard form

10 Order of Magnitude for scientific notation and conventional forms

=>67580000000  (real number) 

=>67,580,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000  

sixty-seven billion five hundred eighty million

word form.

Therefore , the solution of the given problem of expression comes out to be sixty-seven billion five hundred eighty million.

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Answer:

[tex]8x-10[/tex]

Step-by-step explanation:

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

Distribute:

[tex]=5x+(3)(x)+(3)(-4)+2\\=5x+3x+-12+2[/tex]

Combine Like Terms:

[tex]=5x+3x+-12+2\\=(5x+3x)+(-12+2)\\=8x+-10\\= 8x - 10[/tex]

Answer:

92.5 cubic units

Choice A

Step-by-step explanation:

To approach this problem, separate out the composite solid figure into individual easily manageable components

At the bottom we have a rectangular prism which has a base length of 2a, a height of a and a width of c

Its volume = L X H X W = 2a·a·c= 2a²c

Plugging in values for a and c we get

Volume of rectangular prism

= 2 x (3.7)² x 2

= 54.76 cubic units

On top of this rectangular prism are two right-angled triangular prisms

The volume of a right-angled triangular prism =

Here height = b (confusing :)

base = a

width = c

So volume of each triangular prism
[tex]=\textrm{$\dfrac{1}{2} \times $ base x height x width}\\\\= \dfrac{1}{2} a \times b \times c\\\\ = \dfrac{1}{2} \times 3.7 \times 5.1 \times 2\\\\= 18.87[/tex]

Since there are 2 such prisms the volume of both

= 18.87 x 2 = 37.74 cubic units

Total volume of composite solid = 54.76 + 37.74 = 92.5 cubic units

Answer:

2000 dollar and 6% impound will be your answer

Step-by-step explanation:

The mathematical expression for the given algebraic expression is,

⇒ k / 5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The algebraic expression is,

⇒ One-fifth of a number, k

Now, We can write the mathematical expression for the given algebraic expression is,

⇒ One-fifth of a number, k

⇒ 1/5 of k

⇒ 1/5 × k

⇒ k / 5

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Answer:

Step-by-step explanation:

J:  y = 29 cm + (1 cm/mo)x

Z:  y = 12 cm + (2 cm/mo)x

29 cm + (1 cm/mo)x =  12 cm + (2 cm/mo)x

Solve for x to find how many months it will take for them to have the same length of hair:

29 cm - 12 cm = (2 cm/mo)x - (1 cm/mo)x

17 cm = (1 cm/mo)x

x = (17 cm) / (1 cm/mo) = 17 months

Plug this value for x (17 months) into the equations to find how long their hair will be:

J:  y = 29 cm + (1 cm/mo)(17 mo) = 46 cm

Z:  y = 12 cm + (2 cm/mo)(17 mo) = 46 cm

This shows that it will take 17 months for each girl's hair to be 46 cm long.

Answer:

  a) 144°

  b) 90°

Step-by-step explanation:

You want the measures of the 2nd largest, and the smallest, of the angles in a hexagon whose ratios are 5:5:6:7:8:9.

The interior angles of a hexagon will have a sum of ...

  180°×(n -2) = 180°×(6 -2) = 720°

The sum of the numbers in the given ratio is ...

  5+5+6+7+8+9 = 40

This tells us that multiplying the ratio values by 720/40 = 18 will give the angle values:

  90:90:108:126:144:162

The second largest angle is 144°.

The smallest angle, 90°, is the one that is repeated.

The centroid of the region in the first quadrant bounded by the curves [tex]\(y = x^9\)[/tex] and [tex]\(x = y^9\)[/tex] is [tex]\(\left(\dfrac{10}{11}, \dfrac{10}{11}\right)\)[/tex].

The centroid is given by the following formulas:

[tex]\[\bar{x} = \dfrac{\int_{a}^{b} x \cdot f(x) \, dx}{\int_{a}^{b} f(x) \, dx}\][/tex]

[tex]\[\bar{y} = \dfrac{\int_{c}^{d} y \cdot g(y) \, dy}{\int_{c}^{d} g(y) \, dy}\][/tex]

Where f(x) and g(y) are the functions that define the curves bounding the region.

Since we want to find the centroid of the region in the first quadrant, the intersection points of the two curves in the first quadrant.

The curves intersect at (1, 1).

Now, let's find the centroid of the region in the first quadrant.

First,  find the limits of integration:

1. For x:

The curve  [tex]\(y = x^9\)[/tex] is the upper curve, and it intersects the x-axis at x = 0  and the y-axis at x=1.

So, the limits of integration for x are [tex]\(0 \leq x \leq 1\)[/tex].

2. For y: The curve [tex]\(x = y^9\)[/tex] is the right curve, and it intersects the y-axis at y=0 and the x-axis at y=1.

So, the limits of integration for y are [tex]\(0 \leq y \leq 1\)[/tex].

Now,  set up the integrals:

[tex]\[\bar{x} = \frac{\int_{0}^{1} x \cdot x^9 \, dx}{\int_{0}^{1} x^9 \, dx}\][/tex]

[tex]\[\bar{y} = \dfrac{\int_{0}^{1} y \cdot y^9 \, dy}{\int_{0}^{1} y^9 \, dy}\][/tex]

1. [tex]\(\int_{0}^{1} x \cdot x^9 \, dx\):[/tex]

[tex]\[\int_{0}^{1} x \cdot x^9 \, dx = \int_{0}^{1} x^{10} \, dx[/tex]

                 [tex]= \left[\dfrac{x^{11}}{11}\right]_{0}^{1} = \dfrac{1}{11}\][/tex]

2. [tex]\(\int_{0}^{1} x^9 \, dx\):[/tex]

[tex]\[\int_{0}^{1} x^9 \, dx = \left[\dfrac{x^{10}}{10}\right]_{0}^{1}[/tex]

             [tex]= \dfrac{1}{10}\][/tex]

3.[tex]\(\int_{0}^{1} y \cdot y^9 \, dy\):[/tex]

[tex]\[\int_{0}^{1} y \cdot y^9 \, dy = \int_{0}^{1} y^{10} \,[/tex] dy

                 [tex]= \left[\dfrac{y^{11}}{11}\right]_{0}^{1} = \dfrac{1}{11}\][/tex]

4. [tex]\(\int_{0}^{1} y^9 \, dy\):[/tex]

[tex]\[\int_{0}^{1} y^9 \, dy = \left[\frac{y^{10}}{10}\right]_{0}^{1}[/tex]

            [tex]= \dfrac{1}{10}\][/tex]

Now, the centroid coordinates:

[tex]\[\bar{x} = \dfrac{\frac{1}{11}}{\dfrac{1}{10}} = \dfrac{10}{11}\][/tex]

[tex]\[\bar{y} = \dfrac{\frac{1}{11}}{\dfrac{1}{10}} = \dfrac{10}{11}\][/tex]

So, the centroid of the region is [tex]\(\left(\dfrac{10}{11}, \dfrac{10}{11}\right)\)[/tex].

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Answer:

a. 2/3 < 5/3

b. 2 1/2 > 9/4

c. 2/5 < 3/7

a. 5/3 > 1 1/3

b. 2 1/2 = 10/4

c. 3 5/6 < 21/4

Step-by-step explanation:

2/3 = 0.6667 (Rounded Answer)

5/3 = 1.6667 (Rounded Answer)

2 1/2 = 2.5

9/4 = 2.25

2/5 = 0.4

3/7 = 0.4286 (Rounded Answer)

5/3 = 1.6667 (Rounded Answer)

1 1/3 = 1.3334 (Rounded Answer)

2 1/2 = 2.5

10/4 = 2.5

3 5/6 = 3.8334  (Rounded Answer)

21/4 = 5.25

The area between the x-axis and y = x from x = 3 to x = 6 will be 13.50 square feet.

Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.

The function is given below.

y = x

Integrate the function under the limit from  x = 3 to x = 6 will be given as,

[tex]\begin{aligned} I &= \int^6_3 y dx\\\\ I &= \int^6_3x dx\\\\I &= \left [\dfrac{x^2}{2} \right ]^6_3 \\\\I &= \dfrac{6^2 - 3^2}{2} \end{aligned}[/tex]

Simplify the equation further, then we have

I = (36 - 9) / 2

I = 27 / 2

I = 13.50 square units

The area between the x-axis and y = x from x = 3 to x = 6 will be 13.50 square feet.

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Answer: 32

Step-by-step explanation:

32+33+34 = 99

They are consecutive numbers.

Considering the graph of the curve shown if f(x) = 0 then the value of x is

The x-intercepts of the function's graph, or the zero of a function, is the location on a graph where the function's graph crosses the x-axis.

This is the solution of the graph. it also called the x intercept or the zero

Examining the graph, the points are in exact spot in both the negative and positive part of the x axis

This spot is between 1 and 2 and not up to half way while moving from 1 to 2.

The point can be estimated to be 1.4 hence the values are

(-1.4 0), (1.4, 0)

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The conditional, "If you work 20 hours a week, then you would make $125.00" would be false if this holds true:

c. You work 20 hours a week, and you make $175.00

To arrive at the wrong conclusion, we need to look out for the statement that directly violates the hypothesis that working 20 hours a week will yield $125.

The answer that is in direct conflict with this statement is option C. Here, instead of making $125, the person makes $175 and this is way above the conclusion reached in the original sentence. So, the wrong conditional is C.

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On solving the provided question, we can say that quadratic equation x² - 5x+7=0 => x = 1 , -3

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

x² - 5x+7=0

x(x-1) +3(x-1)

(x-1)(x+3) = 0

x = 1 , -3

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Since the graph of an exponential function passes through (minus 10, minus 1), (2, 8) also intercepts the x-axis at minus 2 units and y-axis at 2 units, a statement which correctly compares the two functions include the following: A. They have the same x-intercept and the same end behavior as x approaches ∞.

In Mathematics, the y-intercept of any graph such as an exponential function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In Mathematics, the x-intercept can be defined as the point at which the graph of an exponential function crosses the x-coordinate and the value of "y" is equal to zero (0).

Based on the information provided about the graph of function f, the x-intercept and y-intercept include the following:

x-intercept = (-2, 0).

y-intercept = (0, 2).

Furthermore, the x-intercept and y-intercept of function g include the following:

x-intercept = (-2, 0).

y-intercept = (0, 8).

Therefore, we can logically conclude that both functions have the same x-intercept of -2.

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Answer:

Rick read for 1 hour.

Step-by-step explanation:

Tina read 3 hours, Larry read twice as long that is 6 hours, Rita read one third of Larry's so 6 times one-third is 2 hours, half that for Rick's hours and you get 1 hour

Answer:

180.4 is 140.9% of 128.

Step-by-step explanation:

180.4 is what percent of 128 Rounded to the nearest tenth?

Answer:

Step-by-step explanation:

I think doubles facts are when you use a different equation to get the same sum, right?

In that case here are some doubles.

1+4=5

2+3=5

3+2=5

4+1=5

5+0=5

Therefore , the solution of the given problem of area is largest map that may be utilized while still fitting on the page is 20/3 inches by 10 inches.

The term "area" refers to how much room a 2D structure or surface occupies. We use these units to measure surface in cm2 or m2. By dividing the length by the breadth of a form, you can determine its area.

Area = length times breadth and Perimeter = 2 (length + width)

Here,

Given: 2 feet by 3 feet is the size of the map.

8 by 10 inches is the size of a sheet of paper; in inches:

12 inches per foot

24 inches are equal to two feet, or two times twelve.

36 inches are equal to three feet, or three times twelve.

Scale factor is 24/36, or two-thirds.

Paper's longer side equals ten inches.

Using the scale, determine how long the shorter side is:

2/3 = x/10

the cross-multiply

3x = 2 × 10

3x = 20

x = (20 ÷ 3)

x=6.23 inches

The largest map that may be utilized while still fitting on the page is 20/3 inches by 10 inches.

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The division equation that could be used to find the amount of jellybeans, b, in ounces, that were in the original bag that Rowan bought is given as follows:

6 = b/9.

The division equation is obtained applying the proportions in the context of this problem.

The number of ounces per bean is given by the division of the total amount of jellybeans and the number of bags.

The parameters for this problem are given as follows:

Hence the division equation is given as follows:

6 = b/9.

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The ratio of green to yellow marbles is 3/2.

What is ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Given:

For every 3 green marbles James has, he has 2 yellow marbles.

We have to find the ratio of green to yellow marbles.

As for every 3 green marbles James has, he has 2 yellow marbles.

So, the the ratio of green to yellow marbles is 3/2.

Hence, the ratio of green to yellow marbles is 3/2.

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In the given word problem amount does Teresa spends is $16.50.

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order  to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Here,

The amount does Jayson Spends = $3.75

According to the question,

Myra spends 3times as much as Jayson . then

Amount does Myra spends = 3× 3.75 = $11.25.

Now Teresa spends $5.25 more than Myra then,

Amount does Teresa spends = 11.25+5.25 = $ 16.50.

Hence In the given word problem amount does Teresa spends is $16.50.

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Answer: 6

Step-by-step explanation:

12 ÷ 6 = 2

30 ÷ 6 = 5

The set W1 could be a basis for R3 if it spans R3 and is linearly independent, but without the specific elements of W1, it's not possible to determine if it meets those criteria.

The specific elements that make up the set W1. However, I can tell you that to be a basis for R3, a set of vectors must meet two criteria:

So, depending on the specific elements of W1, it could be either A, B, or C.

If the set W1 doesn't span R3, it would be A.

If the set W1 is linearly dependent, it would be C.

If both conditions are met the set is a basis, so the answer would be B.

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The number of mandarins in the bag is 3 * 33 + 3 = 102 mandarins.

This is a Diophantine equation problem, which is a type of mathematical problem that looks for integers that satisfy a given equation.

We know that the number of mandarins in the bag is equal to 4n + 3, 5m + 2 and 6p + 3 and 7q + 3 for some integers n, m, p and q.

We also know that the number of mandarins in the bag is equal to 3r, where r is an integer.

From the information provided, we can set up the following equation:

4n + 3 = 5m + 2 = 6p + 3 = 7q + 3 = 3r

Now we can use the information that when he finally put them into 3 piles and he didn't have any left over, meaning that the number of mandarins in the bag is divisible by 3, we can see that the remaining number in each case is 3.

Thus the number of mandarins in the bag is 3 * (some integer) + 3.

We can then use the information that the number of mandarins in the bag was less than 100, meaning the possible value of r is less than 34.

Testing values of r starting from 1, we can see that r = 33 satisfies the equation and the number of mandarins in the bag is 3 * 33 + 3 = 102 mandarins

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The cost for one pound of birdseed should be $0.67. The solution has been obtained using the unitary method.

What is a unitary method?

In the unitary method, the value of a single unit is first calculated, and only then is the value of the necessary number of units calculated. The unitary technique, to put it simply, is used to calculate the value of a single unit from a given multiple.

We know that cost per pound = Total pounds/cost

So, for Mariela

15 pounds = $10.00      

1 pound = $0.67  

For Mark,

12 pounds = $8.00  

1 pound = $0.67

For Daryl,

18 pounds = $12.00    

1 pound = $0.67

Hence, the cost for one pound of birdseed should be $0.67.

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Since, the question is incomplete, the complete question has been attached below

Answer:

56 pages per hour

Step-by-step explanation:

Penny reads 14 pages in 1/4 of an hour.

An hour is 4 times more than 1/4 of an hour (you could think of it as 15 minutes compared to 60 minutes)

Multiply the amount penny reads in 1/4 of an hour (14 pages) by 4 to get the rate she reads in 1 hour.

14 x 4 = 56

Now add the rate of time (per hour) to get that she reads a total of 56 pages per hour.

Hope this helps!

Answer:

y = -2x

Step-by-step explanation:

The equation is y = mx +b

m = the slope

b = y-intercept

The slope = rise/run

Let's pick 2 points (0,0) (2,-4); we see the y decrease by 4 and the x increase by 2, so our slope is

m = -4/2 = -2

Y-intercept is when x = 0, y-intercept is located at (0,0)

So our equation is

y = -2x