Suppose a truck rental costs $20 plus $0.30 for each mile
driven. If your total cost of a rental was $39. 80, how many miles
did you drive?

The midpoint of the line joining the endpoints (-1, 5) and (-8, -4) will be (-4.5, 0.5).

Given that:

Endpoints, (-1, 5) and (-8, -4)

The coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The midpoint is calculated as,
(x, y) = [(-1 - 8) / 2, (5 - 4) / 2]

(x, y) = (-9 / 2, 1 / 2)

(x, y) = (-4.5, 0.5)

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The initial investment will be doubled after approximately 14.6 years.

The formula for continuous compounding is given by the formula A = Pe^(rt). We we want to find the time it takes for the initial investment to double, so we can set A = 2P and solve for t:

2P = Pe^(rt)

e^(rt) = 2

Taking the natural logarithm of both sides, we get:

rt = ln(2)

t = ln(2)/r

Substituting the values:

t = ln(2)/0.0475

t = 14.5925722223

t ≈ 14.6 years.

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In linear equation, The graph in option 3 models the length of the new rectangle.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

According to the problem,

width of the rectangle is  x units

Area of the rectangle is 10 square units

Length of the rectangle is given by f(x) = 10/x

Now if width becomes (x+1) units

∴ Length will be represented as 10/(x+1)

Now from the given options we need to find the exact graph of              f(x) = 10/(x +1)

Here if x = 4 , y =2

So the point (4 , 2) is satisfied which is only happening in the graph of option 3

Option 3 represents the correct graph.

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The volume of the tank that will be filled with water through which the given relation is satisfied is [tex]22.5ft^{3}[/tex]

What about volume of cuboid?

The volume of a cuboid is the amount of space occupied by the three-dimensional solid figure known as a cuboid. A cuboid is a box-shaped object with six rectangular faces, where each face has a pair of parallel sides, and opposite faces are equal in size and shape.

The formula for calculating the volume of a cuboid is:

Volume = length x width x height

where length, width, and height are the three dimensions of the cuboid.

The unit of measurement for the volume of a cuboid will depend on the unit of measurement used for each dimension. For example, if the length, width, and height are measured in centimeters, then the volume of the cuboid will be expressed in cubic centimeters (cm³). Similarly, if the dimensions are measured in meters, the volume will be expressed in cubic meters (m³).

According to the given information:

As, we know that volume of cuboid is = length x breath x height

Here, length = 5 feet, breath = 3 feet and height = 1.5 feet

Volume of the aquarium = 5 x 3 x 1.5 =  [tex]22.5ft^{3}[/tex]

So, the given result is  [tex]22.5ft^{3}[/tex]

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Answer:

To find the monthly payments, we can use the PMT function in Excel or a financial calculator. The formula is:

PMT(rate, nper, pv)

where rate is the interest rate per period, nper is the total number of periods, and pv is the present value (i.e. loan amount).

For this problem, the interest rate is 8%/12 = 0.0066667 per month, the number of periods is 4 years * 12 months/year = 48 months, and the present value is $10,000. Therefore, the formula becomes:

PMT(0.0066667, 48, 10000)

Evaluating this formula gives a monthly payment of $242.42.

To find the total interest for the loan, we can multiply the monthly payment by the number of periods (i.e. 48) and subtract the loan amount. This gives:

total interest = monthly payment * number of periods - loan amount

total interest = $242.42 * 48 - $10,000

total interest = $2,678.16

Therefore, the monthly payments are $242.42 and the total interest for the loan is $2,678.16.

Step-by-step explanation:

The population predicted after two hours is approximately 666.5 bacteria as they have exponential growth.

The continuous exponential growth model is given by the formula:

P(t) = P0 * [tex]e^{(rt)[/tex]

where P0 is the initial population, r is the relative growth rate (expressed as a decimal), t is the time in hours, and P(t) is the predicted population after t hours.

In this case, P0 = 535, r = 0.12 (12% per hour), and t = 2. Plugging in these values, we get:

P(2) = 535 * [tex]e^{(0.12*2)[/tex] ≈ 666.5

Therefore, the population predicted after two hours is approximately 666.5 bacteria (rounded to the nearest tenth).

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350 is the answer

Step-by-step explanation:

I hope it helps

This stock trade generated a profit of $600 and a 7.69% return on investment.

The total amount received from selling the shares, after commission.

The total cost of purchasing the shares = $7800

Total amount received from selling the shares = $8400

The commission paid for purchasing the shares and for selling the shares will cancel out since they will both be subtracted, so we do not need to consider them.

Profit on this stock transaction = Total amount received - Total cost of purchasing

= $8400 - $7800

= $600

To calculate the percentage return on investment, we need to divide the profit by the total cost of purchasing the shares, and then multiply by 100 to express it as a percentage.

Percentage return on investment = (Profit / Total cost of purchasing) x 100%

= ($600 / $7800) x 100%

= 7.69%

Therefore, the profit on this stock transaction was $600 and the percentage return on investment was 7.69%.

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Answer:

  A

Step-by-step explanation:

You want to know which inequality must be true regarding the side lengths of a triangle.

The triangle inequality requires the sum of any two side lengths be greater than the length of the third side:

  a + b > c . . . . . choice A

__

Additional comment

This means it must also be true that ...

  a + c > b

  b + c > a

Of course, this means the sum of the two shortest sides must be more than the longest side. It also means any side length must lie between the sum and difference of the other two side lengths:

  |a - b| < c < a + b

The version of this inequality most often seen uses the > or < symbol. Some authors use the ≥ or ≤ symbol instead. This allows triangles that look like a line segment and have zero area.

Tom can choose from 7,000 possible schedules if every possible course is available at the time he's registering.

Tom can choose 22,400 possible schedules when the number of acceptable courses is doubled. The number of possible schedules is increased by a factor of approximately 3.2

(a) If every possible course is available at the time Tom is registering, he can choose from:

5 choices for English x 5 choices for History x 5 choices for Math/Stats x 8 choices for Computer Science x 7 choices for general Science

= 5 x 5 x 5 x 8 x 7

= 7000 possible schedules.

(b) If the number of acceptable courses in each of the five areas is doubled, Tom can choose from:

10 choices for English x 10 choices for History x 10 choices for Math/Stats x 16 choices for Computer Science x 14 choices for general Science

= 10 x 10 x 10 x 16 x 14

= 22400 possible schedules.

The number of possible schedules is increased by a factor of:

22400 / 7000 = 3.2 (approximately)

So the number of possible schedules is increased by a factor of approximately 3.2 when the number of acceptable courses is doubled in each of the five areas.

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See text below

While making up his schedule for spring semester, Tom complains that he doesn't have very many choices of schedule because of the general education requirements he has to meet. His advisor tells Tom that he has to take one course from each of English (5 choices), History (5 choices), Math/Stats (5 choices), Computer Science (8 choices), and general Science (7 choices). Does Tom have a legitimate gripe?

(a) If every possible course is available at the time he's registering, how many possible schedules can he choose from (disregarding when the classes meet)?

Tom can choose   -------- from possible schedules.

(b) In an unprecedented effort to make the general education requirements more accessible, the dean of Tom's college decides to double the number of acceptable courses in each of those five areas. What effect does this have on the number of possible schedules?

Tom can choose ----------- from possible schedules when the number of acceptable courses are doubled. The number of possible schedules is increased by a factor of-------

Answer:

picture

Step-by-step explanation:

The distance between each big tick mark is 1, (for example take 2 and 1, 2 minus 1 equals to 1), however, in between each of these big tick marks are four small tick marks. The distance between each small tick mark is the distance between each big tick mark divided by the amount of small tick marks plus 1 (1 divided by 4, which is 1/4).

So in this number line you count by 1/4.

Fro the one to one functions g and h defined, the value of :

g⁻¹(6) = 2

h⁻¹(x) = 7x + 8

(h⁻¹ o h)(1) = 1

Given one to one functions h and g.

We have that,

g(2) = 6

So, g⁻¹(6) = 2

We have,

y = (x - 8) / 7

Switch x and y.

x = (y - 8) / 7

7x = y - 8

y = 7x + 8

So, h⁻¹(x) = 7x + 8

(h⁻¹ o h) (x) = h⁻¹ (h(x))

                  = h⁻¹ ((x - 8) / 7)

                  = 7 ((x - 8) / 7)) + 8

                  = x - 8 + 8

                  = x

(h⁻¹ o h) (1) = 1

Hence the functions are found.

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Answer:

[tex]\dfrac{137}{3}\approx 45.7\; \sf m[/tex]

Step-by-step explanation:

To find the velocity function, integrate the acceleration function (and add a constant of integration).

[tex]\begin{aligned}\displaystyle v(t)=\int a(t) &= \int (2t + 2)\; \text{d}t\\\\&=\int 2t \; \text{d}t+\int 2\; \text{d}t\\\\&=\dfrac{1}{2} \cdot 2t^{(1+1)}+2t+\text{C}\\\\&=t^2+2t+\text{C}\end{aligned}[/tex]

To find the constant of integration, C, substitute v(0) = -15 into the velocity function and solve for C:

[tex]\begin{aligned}v(0)=(0)^2+2(0)+\text{C}&=-15\\0+0+\text{C}&=-15\\\text{C}&=-15\end{aligned}[/tex]

Therefore, the velocity function (in m/s) is:

[tex]v(t)=t^2+2t-15[/tex]

As we want to find the distance travelled during the given time interval 0 ≤ t ≤ 5, we first need to determine if the particle momentarily stops at any point in the given interval (and therefore changes direction). The particle will stop when its velocity is zero, so when v(t) = 0:

[tex]\begin{aligned}v(t)&=0\\\implies t^2+2t-15&=0\\t^2+5t-3t-15&=0\\t(t+5)-3(t+5)&=0\\(t-3)(t+5)&=0\\\\\implies t&=3, -5\end{aligned}[/tex]

As time is positive only, the velocity is zero at t = 3 seconds.

Therefore, at t = 3, the particle changes direction and begins to move in the opposite direction. Therefore, the displacement between 0 ≤ t ≤ 5 consists of two parts: 0 ≤ t ≤ 3 and 3 ≤ t ≤ 5.

To find the distance travelled, first find the displacement function by integrating the velocity function:

[tex]\begin{aligned}\displaystyle s(t)=\int v(t) &= \int (t^2+2t-15)\; \text{d}t\\\\&= \int t^2\; \text{d}t+\int 2t\; \text{d}t-\int 15\; \text{d}t\\\\&=\dfrac{1}{3}t^3+t^2-15t\left(+\text{C}\right) \end{aligned}[/tex]

Distance is the absolute value of displacement.

As we want to find the distance travelled for the intervals 0 ≤ t ≤ 3 and 3 ≤ t ≤ 5, we need to add the absolute values of displacement for these intervals. So, the absolute values of the definite integrals for these intervals:

[tex]\begin{aligned}\textsf{Distance}&=\left|\int^3_0 v(t)\right|+\left|\int^5_3 v(t)\right|\\\\&=\left|\left[\dfrac{1}{3}t^3+t^2-15t\right]^3_0\right|+\left|\left[\dfrac{1}{3}t^3+t^2-15t\right]^5_3\right|\\\\&=\left|\left(\dfrac{1}{3}(3)^3+(3)^2-15(3)\right)-\left(\dfrac{1}{3}(0)^3+(0)^2-15(0)\right)\right|+\\&\left|\left(\dfrac{1}{3}(5)^3+(5)^2-15(5)\right)-\left(\dfrac{1}{3}(3)^3+(3)^2-15(3)\right)\right|\\\\&=\left|(-27-0)\right|+\left|\left(-\dfrac{25}{3}-(-27)\right)\right|\end{aligned}[/tex]

             [tex]\begin{aligned}&=27+\dfrac{56}{3}\\\\&=\dfrac{137}{3}\end{aligned}[/tex]

Therefore, the total distance travelled during the given time interval is 137/3 ≈ 45.7 meters.

The statement that shows the quantity of gallons of gas that he can buy would be =g≤11.82. That is option A.

The total number of money he has to spend on his vehicle = $230

The amount of money he wishes to save = $160

The remaining amount he can spend = 230+160 = $70

The amount he wishes to spend on oil change = $24.95

The remaining amount = 70-24.95

= $40.05

The cost per gallon of gas = $3.81 per gallon.

The quantity of gallons of gas he can purchase = 40.05/3.81 = 10.51 gallons.

Therefore the quantity of gallons of gas he can purchase would be g≤11.82

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The percent of the parcels weighed between 16 ounces and 40 ounces is 81.9%.

To solve this problem, first, find the z-scores for the weights of 16 ounces and 40 ounces using the given mean and standard deviation:

z1 = (16 - 32) / 8 = -2

z2 = (40 - 32) / 8 = 1

Next, we need to find the area under the standard normal distribution curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this area. Using a calculator, we get:

P(-2 < Z < 1) = 0.8186

So, approximately 81.9% of the parcels weighed between 16 ounces and 40 ounces.

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Answer:

a. 45°

b. Arc KPR and Arc RLP

c. Arc PR and Arc RL

d. Arc LQ, Arc QR, and Arc RP

Step-by-step explanation:

a. 90/2=45°

b. Observation

c. They both have measures of 90 degrees

d. Arc Addition Postulate

Answer:

see below

Step-by-step explanation:

angle lcr appears to be a right angle

therefore if a line bisects LCR it would split the angle into 2 congruent halves:

so

90/2=45

m<LCR=45

b) arc KP and arc PR

c)

arc KL and arc LQ

d) arc PR, arc RQ and arc QL

Answer:

Step-by-step explanation:

Z:

the angle b/n z and  65 is 90 b/c its a square and they are found on a straight line (180)

- 65 + 90 + z = 180

-155 + z = 180

-z= 180 - 155= 25

x:

-x + 90 = 180

- x= 180 - 90 = 90

y:

in this case now we have an inner triangle which has only one missing angle so as we know for any triangle ABC; <A + <B + <C = 180 so

- y + x + 65=180

-y+ 90 + 65= 180

-y=180 - 155

- y = 25

Answer:

If only 60% of the seeds planted by the class grow into plants, we can find the number of plants by multiplying the total number of seeds planted by the percentage of seeds that grow, expressed as a decimal.

To do this, we can start with the total number of seeds planted, which is 20, and multiply by 0.6:

20 x 0.6 = 12

Therefore, the class has 12 plants.

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The critical value t* for a two-tailed 95% confidence interval with 19 degrees of freedom is approximately 2.093.

The critical value t* depends on the degrees of freedom (df) and the desired level of confidence. For a 95% confidence interval and a sample size of n=20, the degrees of freedom would be df = n-1 = 19.

Using a t-distribution table with 19 degrees of freedom (since n-1=20-1=19), we can find the value of t* that corresponds to a 95% confidence level. For a two-tailed test (which is typically used for a confidence interval), the area in each tail is 0.025 (since 1 - 0.95 = 0.05, and we need to split this evenly between the two tails).

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Answer:

The probability that atleast one ticket labeled 2-6 is drawn is 0.94

Numbered ticket = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Number of draws = 4

Required picks = {2, 3, 4, 5, 6}

Recall :

Probability = required outcome / Total possible outcomes

Probability of choosing a required ticket :

5/10 = 1/2

Therefore, the probability that none of the required tickets is chosen :

(1/2 × 1/2 × 1/2 × 1/2) = 1/16

The probability that atleasr one ticket labeled 2-6 is drawn is :

1 - P(none is chosen) = 1 - 1/16 = 15/16 = 0.9375

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Answer:

The perimeter of a square is four times the length of one side, so we can write:

4s = 24x + 36

Dividing both sides by 4, we get:

s = 6x + 9

Therefore, the length of one side of the fence is 6x + 9 units.

Step-by-step explanation:

Answer:

We need to find the percentage of tomato plant that has a height less than or equal to 3.88 feet.

We know that the tomato plant heights are normally distributed with a mean of 3.56 ft and a standard deviation of 0.25 ft.

Thus, the percentage P(x≤3.88) of the heights being less than 3.88 can be calculated using the z-score z, given

Answer

About 89.97% of tomato plants.

Answer:

89.97%

Step-by-step explanation:

Answer: it is more probable that Peter will finish ahead of Francis and Christopher than that both Anthony and Peter will receive ribbons.

Share Prompt

Step-by-step explanation:

Answer:

110.5

Step-by-step explanation:

The first step is to find the measure of angle RVT

Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)

RVT = 1/2 ( 97+42)

RVT =1/2 ( 139)

RVT = 69.5

Now RVT and RVU equals a straight line so they add to 180

RVT + RVU = 180

69.5 + RVU = 180

RVU = 110.5

The limits which describe the end behavior of the function are given as follows:

The end behavior of a function refers to how the function behaves as the input variable (typically denoted as x) approaches positive or negative infinity. In other words, the end behavior describes the long-term behavior of the function as x becomes very large (either positively or negatively).

We can see that the left of the graph approaches y = 1, hence the limit is given as follows:

[tex]\lim_{x \rightarrow -\infty} f(x) = 1[/tex]

The right of the graph approaches y = 0, hence the limit is given as follows:

[tex]\lim_{x \rightarrow \infty} f(x) = 0[/tex]

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A graph of the transformed function [tex]y=\frac{1}{(x+2)^2} +5[/tex] is shown in the image attached below.

In Mathematics and Geometry, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image;

g(x) = f(x + N)

On the other hand, the translation a geometric figure upward simply means adding a digit to the value on the positive y-coordinate (y-axis) of the pre-image;

g(x) = f(x) + N

Since the parent function is [tex]y = \frac{1}{x^{2} }[/tex], it ultimately implies that the transformed function would be created by translating the parent function to the left by 1 units and 5 units upward as shown below.

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The scale she use for the axes on her scatter plot are:

For the y-axis she should use a scale from 0 to 180 in 10-dollar intervals.

For the x-axis she should use a scale from 0 to 8 in one-hour intervals.

A scatter plot is a type of graph that displays values for two variables as a set of points on a two-dimensional coordinate system.

These are the appropriate scales for the axes on Caroline's scatter plot as they will allow for a clear visualization of the relationship between the number of hours spent in the mall and the amount of money spent.

The y-axis should show the amount of money spent, and a scale from 0 to 180 in 10-dollar intervals will provide enough range to accommodate the highest value in the data set (175 dollars) and allow for clear and easy-to-read axis labels.

Similarly, the x-axis should show the time spent in the mall, and a scale from 0 to 8 in one-hour intervals will also provide enough range to accommodate the highest value in the data set (7 hours) and allow for clear and easy-to-read axis labels.

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Note that the best name for the line segment indicated is  [tex]\overleftrightarrow {AB}[/tex]

A line segment is a section of a straight line that is bounded by two different end points and contains every point on the line between them. The Euclidean distance between the ends of a line segment determines its length.

Other types of lines are:

Lines that are parallel. Two lines in the same plane, either intersecting or not.

Lines that cross. Intersecting lines are two or more lines that cross in a plane.

Lines that are concurrent. Concurrent lines are defined as numerous lines that cross through each other at the same place.

Points that are curved.

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Full Question:

See attached image.