There is a statistically significant difference in life expectancy between people who ate fruits and vegetables and people who did not eat fruits and vegetables by hypothesis
State the null hypothesis and the alternative hypothesis.
The null hypothesis (H₀) is that there is no difference in life expectancy between people who ate fruits and vegetables and people who did not eat fruits and vegetables.
The alternative hypothesis (Ha) is that there is a difference in life expectancy between the two groups.
H₀: μ₁ = μ₂
Ha: μ₁ ≠ μ₂
Determine the appropriate test statistic and significance level.
Since we are comparing the means of two independent samples, we can use a two-sample t-test.
We will use a significance level of α = 0.05.
We can use a calculator or statistical software to calculate the test statistic.
t = -2.379
df = 8.98
p-value = 0.042
where t is the test statistic
The p-value is 0.042, which is less than the significance level of 0.05.
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Find the volume of the shape below. Round to the nearest tenth. Use
the pi button on the calculator.
12 ft
Volume=
4 ft
ft3
The volume of the cone with a diameter of 4ft and height 12ft is approximatelly 50.3 ft³
What is the volume of the cone?A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.
The volume of a cone is expressed as;
V = (1/3)πr²h
The figure in the image is a cone.
Diameter of the base of the cone d = 4ft
Radius r = diameter/2 = 4/2 = 2ft
Height h = 12ft
Plug the given values into the above formula and solbr for the volume.
V = (1/3)πr²h
V = (1/3) × π × r² × h
V = (1/3) × π × (2 ft )² × 12ft
V = 50.3 ft³
Therefore, the volume is 50.3 ft³.
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Help me please find EC
The length of segment EC is 24 in the given triangle
A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.
3x=2(x+4)
Apply distributive property on RHS
3x=2x+8
Subtract 2x from both sides
x=8
The segment EC =3x
=3(8)
=24
Hence, the length of EC is 24 in the given triangle
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show that the solution to the differential equation dp/dt=-0.1P is P=495e^1.1t
We have shown that the solution to the differential equation dp/dt = -0.1P is P = 495e^(1.1t).
We have,
To show that the solution to the differential equation dp/dt = -0.1P is
P = 495e^(1.1t),
we can use separation of variables and integration.
Starting with the differential equation:
dp/dt = -0.1P
We can separate the variables by dividing both sides by P and multiplying both sides by dt:
dp/P = -0.1 dt
Integrate both sides:
∫ dp/P = -0.1 ∫ dt
Integrating the left-hand sid.
ln|P| = -0.1t + C
where C is the constant of integration.
To solve for C, we can use an initial condition.
Suppose that when t = 0, P = P0.
Then we have:
ln|P0| = -0.1(0) + C
ln|P0| = C
Substituting this value of C back into the equation for P.
ln|P| = -0.1t + ln|P0|
ln|P/P0| = -0.1t
Taking the exponential of both sides.
P/P0 = e^(-0.1t)
Multiplying both sides by P0.
P = P0 e^(-0.1t)
We can substitute P0 = 495 (since P(0) = 495 is given in the solution) and e^(-0.1t) = e^(1.1t)/e^t.
P = 495 e^(1.1t)/e^t
Simplifying the expression by combining the exponentials.
P = 495 e^(0.1t)
which is the same as the given solution.
Therefore,
We have shown that the solution to the differential equation dp/dt = -0.1P is P = 495e^(1.1t).
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John has 6 different flags that he wants to hang on the wall. How many different ways can the flags be arranged in a row?
There are 6 different ways can the flags be arranged in a row.
We have,
Total number of flags = 6
So, to find the number of ways to arranged n object = n!
Then, the number of ways to arrange the flag
= 6!
= 6 x 5 x 4 x 3 x 2 x 1
=120 x 6
= 720 ways
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Khalil's dining room is 3 meters wide and 7 meters long. Khalil wants to install a new wood floor. It will cost $7.84 per square meter. How much will Khalil's new floor cost?
The total cost to install new wood floor in a room is $164.64.
Given that, Khalil's dining room is 3 meters wide and 7 meters long.
We know that, area of a rectangle is Area = Length×Width
Area of a room = 7×3
= 21 square meters
Total cost = Total area × Cost of per square meter
= 21×7.84
= $164.64
Therefore, the total cost to install new wood floor in a room is $164.64.
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how to solve for the below problems
The Taylor polynomial of degree 3 for sin(x) for x near 0 is,
sin (x) = x - 1/6 x³
The ratio is sin (x) / x = 1 - 1/6 x².
Limit is 1.
Given function is sin(x).
We have to find the Taylor Polynomial for sin (x).
We know that,
f(x) = sin(x), so f(0) = sin (0) = 0
f'(x) = cos (x), so f'(0) = cos (0) = 1
f''(x) = -sin (x), so f''(0) = sin (0) = 0
f³(x) = -cos (x), so f³(0) = -cos(0) = -1
Taylor polynomial is,
sin (x) = {[f(0) (x - k)⁰] / 0!} + {[f'(0) (x - k)¹] / 1!} + {[f''(0) (x - k)²] / 2!} + {[f³(0) (x - k)³] / 3!}
Here c = 0.
sin (x) = 0 + x + 0 + (-x³/6)
sin (x) = x - 1/6 x³
The ratio,
sin (x) / x = (x - 1/6 x³) / x = 1 - 1/6 x²
When x tends to 0 in the expression, 1 - 1/6 x², the value tends to 1 - 0 = 1.
Hence the required Taylor polynomial is sin (x) = x - 1/6 x³.
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Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0). Determine the coordinates of the vertices for the image if the preimage is translated 3 units up.
A′(−3, 0), B′(0, 4), C′(−3, −3)
A′(−3, 6), B′(0, 10), C′(−3, 3)
A′(−6, 3), B′(−3, 7), C′(0, 0)
A′(0, 3), B′(3, 5), C′(0, 0)
The coordinates of the vertices for the image is A′(−3, 6), B′(0, 10), C′(−3, 3).
The vertices of the preimage triangle ABC are given as A(-3,3), B(0,7), and C(-3,0). To translate the preimage 3 units up, we need to add 3 to the y-coordinate of each vertex. Therefore, the vertices of the image triangle A'B'C' will be A'(-3,6), B'(0,10), and C'(-3,3). Thus, option B, A′(−3, 6), B′(0, 10), C′(−3, 3), is the correct answer.
To check the answer, we can plot the points on a coordinate plane and observe that the image triangle is obtained by moving the preimage triangle 3 units up. Translation is a type of transformation in which the position of a figure is changed without changing its shape or orientation.
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Jasica Parker would like to have $83,000 to buy a new car in 7 years. To accumulate $83,000 in 7 years, how much should she invest monthly in a sinking fund with 3% interest compounded monthly?
Jasica should invest $878.84 per month in a sinking fund with 3% interest compounded monthly to accumulate $83,000 in 7 years.
How much should Jasica invest monthly in a sinking fund with 3% interest?To determine how much Jasica should make in a sinking fund, we can use the formula for the future value of an annuity due:
FV = PMT x [tex](((1 + r/n)^nt[/tex] - 1) / (r/n))
Where:
FV = future value
PMT = monthly payment
r = interest rate (as a decimal)
n = number of compounding periods per year
t = number of years
In this issue, we are solving for PMT.
Given:
FV = $83,000,
r = 0.03 (3% expressed as a decimal),
n = 12 (monthly compounding),
t = 7 years.
Plugging in the values, we have:
$83,000 = PMT x [tex](((1 + 0.03/12)^(12*7)[/tex] - 1) / (0.03/12))
Simplifying:
$83,000 = PMT x (94.4523)
PMT = $83,000 / 94.4523
PMT = $878.84 (rounded to the nearest cent)
Therefore, Jasica should invest $878.84 per month in a sinking fund with 3% interest compounded monthly.
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Triangle ABC ~ triangle DEF.
triangle ABC with side AB labeled 11, side CA labeled 7.6 and side BC labeled 7.9 and a second triangle DEF with side DE labeled 2.2
Brainliest for right answer!!!!
Will give Brainliest and points!!!!
Determine the measurement of FD.
FD = 1.52
FD = 1.58
FD = 1.1
FD = 5.5
Answer:
The answer is **FD = 1.52**.
Since triangle ABC ~ triangle DEF, we know that the ratio of their corresponding sides is equal. So, we have:
```
AB/DE = AC/DF = BC/EF
```
We are given that AB = 11, DE = 2.2, and AC = 7.6. Substituting these values into the first equation, we get:
```
11/2.2 = 7.6/DF
```
Cross multiplying, we get:
```
11 * DF = 2.2 * 7.6
```
```
DF = (2.2 * 7.6) / 11
```
```
DF = 1.52
```
Step-by-step explanation:
HELP I NEED TO TURN THIS IN IN 10 MINUTES!!
The doubling period of a bacterial population is 15 minutes. At time t=110 minutes, the bacterial population was 70000
What was the initial population at time t=0?
Find the side of the bacterial population after 5 hours
Answer:
Step-by-step explanation:
1. the initial population at t=0 is 1
2. 16
Engineers and architects often use transformed shapes to design objects or structures. Analyze a building or structure around you and describe the transformations that you see using geometric vocabulary. How does the transformed shape contribute to the design of the object?
and give me an answer that I can actually use please
Answer:
Many buildings and structures around us involve transformed shapes in their design. For example, a skyscraper may have a rectangular base that is transformed into a triangular shape as it reaches higher levels. This transformation is achieved by using a technique called tapering, where the building's width gradually decreases as it goes up, resulting in a triangular shape at the top.
Another common transformation is the use of rotation, which is seen in the design of many cylindrical structures like water towers or chimneys. The cylinder is rotated around its axis to create a three-dimensional shape.
These transformed shapes contribute to the design of the object in many ways. For instance, the triangular shape of a skyscraper's top helps to reduce wind resistance and improve stability. Tapering also allows more sunlight to reach street level and reduces the impact of shadows on the surrounding area. In the case of cylindrical structures, rotation can provide structural stability while minimizing the amount of material used in the construction.
Overall, the use of transformed shapes in building and structure design helps to achieve specific aesthetic and functional goals, from stability to energy efficiency.
Step-by-step explanation:
Answer:
The Empire State Building is a skyscraper in Midtown Manhattan, New York City, on Fifth Avenue between West 33rd and 34th Streets. It has a roof height of 1,250 feet (381 m), and with its antenna spire included, it stands a total of 1,454 feet (443.2 m) high. Its name is derived from the nickname for New York, the Empire State.
The Empire State Building is an example of a transformed shape. The original shape is a square, but the architects transformed it into a triangle by adding a spire to the top. The spire adds height and visual interest to the building. It also helps to make the building more stable.
The use of transformed shapes in the design of the Empire State Building contributes to its overall aesthetic appeal. The building is both visually striking and structurally sound. It is a testament to the skill and ingenuity of the architects who designed it.
Here are some other examples of transformed shapes in buildings and structures:
* The Parthenon in Athens, Greece, is a rectangular building with a triangular pediment at each end. The pediments are decorated with sculptures that depict scenes from Greek mythology.
* The Eiffel Tower in Paris, France, is a wrought iron lattice tower that was built for the 1889 World's Fair. The tower is a transformed shape of a regular hexagon.
* The Gateway Arch in St. Louis, Missouri, is a stainless steel arch that spans the Mississippi River. The arch is a transformed shape of a catenary curve.
These are just a few examples of the many ways that transformed shapes are used in the design of buildings and structures. Transformed shapes can be used to add visual interest, create a sense of movement, or simply to make a building more structurally sound.
Step-by-step explanation:
It costs a car company $25,000,000 to develop and market the model of a new car. The company sells each car for $30,000 . Which of the following represents the number of cars, c , that the car company must sell to make over $5,000,000 in profit?
Answer: so if it cosst 25,000,000 dollars to market a car and they sell it for 30,000 dollars they would need to sell 167 cars to get 5.1 million dollars or 166 for 5.0 million
I need help ASAP!!
The length of a rectangle is 4 meters longer than its width.
The area of the rectangle is
117m^2.
What is the width of the rectangle?
HINT: you can use DESMOS for this kind of problem.
Answer:
w(w + 4) = 117
w^2 + 4w = 117
w^2 + 4w - 117 = 0
(w - 9)(w + 13) = 0
w = 9 meters
The width of the rectangle is 9 meters, and the length of the rectangle is 13 meters.
If the went in the oven at 3:40pm and it needs to bake for 35 minutes. What time will it be fully baked
well, first of all, you don't want to go into the oven, is too hot and you'll get burned, so you may not want to do that.
now, if we start to bake something at 3:40pm and it requires 35 minutes, it'll be done by 3:40 + 35, or 3pm and 40 + 35 minutes, or 3pm plus 75 minutes or 3pm plus 60 + 15 minutes, but since 60 minutes is 1hr, that'd be 3pm plus 1hr plus 15 minutes, 4:15pm.
A wheel has 5 equally sized slices numbered from 1 to 5.
Some are grey and some are white.
The slice numbered 1 is grey.
The slices numbered 2, 3, 4, and 5 are white.
The wheel is spun and stops on a slice at random.
Let X' be the event that the wheel stops on a white slice, and let P(X) be the
probability of X
Let not X' be the event that the wheel stops on a slice that is not white, and let
P (not X) be the probability of not X.
Event
X
not X
(a) For each event in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter
the probability of the event.
(b) Subtract.
Outcomes
12345
0
0
O
1- P(not X) -
0
O
O
Probability
00000 P(not X) -
P(X) -
010
8
X
(c) Select the answer that makes the sentence true.
1-P (not X) is the same as (Choose one)
8
X
5 1
X
4
3
2
The random probability of event X, wheel stopping on a white slice is 0.9 while the probability of not X, wheel stopping on Grey slice is 0.1
What is the explanation for this?Total numbers on wheel = total possible outcomes
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Grey colored portion = {3}
White colored portion = {1, 2, 4, 5, 6, 7, 8, 9, 10}
X = Event that wheel stops on a white slice
P(X) = number of white slices ÷ total number of slices
P(X) = 9 / 10 = 0.9
P(not X) = 1 - P(X)
P(not X) = 1 - 0.9 = 0.1
Therefore, the probability that wheel stops on a white slice is 0.9 while, the probability that wheel does not stop on a white slice is 0.1
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Please help me out‼️‼️‼️‼️〽️
We can see that the dot plot is seen below.
What is a dot plot?We can see here that An example of a graphical representation of data is a dot plot. It is a number line with dots above each value to indicate the frequency or count of that value.
Depending on the type of data being shown, the dots are often arranged either horizontally or vertically.
Dot plots are known to be useful for showing the distribution of data, particularly for small data sets.
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CRITICAL THINKING The total area of the polygon is 176 square feet. What is the value of $x$ ?
A drawing of a polygon. It consists of a rectangle with two triangles on either side. Length of the rectangle is 16 feet. The width of the rectangle is 8 feet and is same as the height of the triangles. Lengths of the base of each triangle is labeled as x.
$x=$
ft
The value of x is, x = 6 ft
Now, We can formulate;
Area of the polygon = area of the square + 2(area of the triangle)
Here, We have;
Area of the polygon = 176 ft²
So, Area of the square = length × width
= 16 × 8
= 128
And, Area of the two triangles = 2( 1/2 x base x height)
= 2(1/2 × x × 8)
= 8x
Now, Plug in the above values into the equation for area of the polygon.
Thus: We get;
176 = 128 + 8x
Subtract 128 from each side
176 - 128 = 8x
48 = 8x
Divide both sides by 8
6 = x
x = 6 ft
Thus, The value of x is, x = 6 ft
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whats the interests going to be for a mortgage thats 245,000 with a down payment of 44,000 & making a payment of
1205.11 monthly
Answer:
The mathematical equation for calculating the monthly interest is
I = P * (r / n)
where:
I is the monthly interest
P is the loan amount minus the down payment (i.e., $245,000 - $44,000 = $201,000 in this case)
r is the annual interest rate (i.e., 3.5%)
n is the number of payments per year (i.e., 12 for monthly payments)
then I = $201,000 * (0.035 / 12) = $711.06
Can someone please tell me what's the answer to convert 35 deca to km and m. my school is about to start
Answer:
1km:100decameter(dam)
Step-by-step explanation:
so 35dam:0.35km
and 35dam:0.00035m
the rectangular wall measures 14 ft by 12 feet. Each square foot of wallpaper costs 2.90. Find the cost of covering the wall with paper?
Answer:
487.20
Step-by-step explanation:
1. find the area of a rectangle ( length x width)
14ft x 12ft = 168ft²
2. Multiply the number of feet needed to becovered by the price of one foot of paper
168ft x 2.90 = 487.20
Geomerty Math PLSSS ANSWER
Answer: first do multiplcation for each part then add everythink to find total volume
Step-by-step explanation:
The sum of two numbers is 5 the product of the same two numbers is 20
The two numbers are 4 and 1.
What are the two numbers?To solve the problem, we will use algebraic equations.
We will call 2 numbers x and y. So, we know that:
------ x + y = 5 (equation 1)
------ xy = 20 (equation 2)
We will solve for y in terms of x:
y = 5 - x
We will substitute for y into equation 2 and simplify:
x(5 - x) = 20
5x - x^2 = 20
x^2 - 5x + 20 = 0
As a quadratic equation which will be solved using the quadratic formula, the solutions are x = 4 and x = 1. We can check that these solutions satisfy both equation 1 and equation 2.
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Which distribution is positively skewed?
The distribution that is positively skewed is Option C.
What is a positive skew ?A positive skew is a statistical pattern, in which the majority of the data points are concentrated at one end within the range and wherein the tail is longer on the right side of the graph.
This phenomenon is also identified as a "right-skewed distribution," oppositely to its counterpart: the negative skew or "left-skewed distribution."
In conclusion, the distribution that is positively skewed is the third distribution or Option C.
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Slope! answer the questions below please i need help! and i need a good grade!!!
The equation of a line for the given graph is y=2x+5.
From the given graph, the coordinate points are (0, 5) and (1, 7)
Part A:
Slope = (7-5)/(1-0)
= 2
Part B:
The slope mean for the relationship between the number of races and the number of track meets 2 races per track
Part C:
Substitute m=2 and (x, y)=(0, 5) in y=mx+c, we get
5=2(0)+c
c=5
Part D:
Substitute m=2 and c=5 in y=mx+c, we get
y=2x+5
Therefore, the equation of a line for the given graph is y=2x+5.
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An example of an early application of statistics was in the year 1817. A study of chest
circumference among a group of Scottish men exhibited an approximately normal
distribution. Their chest circumference ranged from 33 to 48 in., with a mean chest
measurement of 40 in. and a standard deviation of 2 in. Use the Empirical rule to help
you understand the distribution of chest circumferences in the study.
What range of chest measurements contains 68% which falls closest to the mean?
What would you expect the chest measurements to be for the 2.5% of the men with
the smallest chest measurements in the population?
a) The range of chest measurements contains 68% which falls closest to the mean is between 38 inches and 42 inches
b) The chest measurements for the 2.5% of the men with the smallest chest measurements in the population to be approximately 36 inches
Given data ,
The Empirical rule, also known as the 68-95-99.7 rule, is a statistical guideline that describes the approximate distribution of data in a normal distribution.
Approximately 68% of the data falls within one standard deviation (σ) of the mean (μ)
Approximately 95% of the data falls within two standard deviations of the mean (μ ± 2σ)
Approximately 99.7% of the data falls within three standard deviations of the mean (μ ± 3σ)
It would be within one standard deviation of the mean for the range of chest measures that accounts for 68% of the data and is closest to the mean. Since the standard deviation is 2 inches and the mean chest measurement is 40 inches, we can get the range as follows:
Mean - 1 standard deviation = 40 - 2 = 38 inches
Mean + 1 standard deviation = 40 + 2 = 42 inches
b)
We may look at the bottom end of the distribution to obtain the chest dimensions for the 2.5% of males with the smallest chest measurements in the population. The empirical rule states that 2.5% or less of the data goes outside of two standard deviations of the mean. So, using the following formula, we can get the chest size of the 2.5% of men:
Mean - 2 standard deviations = 40 - 2(2) = 36 inches
Hence , the standard deviations are solved
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Are all intersecting lines perpendicular? Draw a picture to help explain your answer
Not all intersecting lines are perpendicular.
What are perpendicular lines?Perpendicular lines require a 90-degree angle of intersection, creating the formation of right angles.
Nonetheless, unlike perpendicular lines that necessitate exactly 90 degrees of intersections, other types of driven lines can be at varying angles beside these.
As such, it is critical to highlight that in general intersecting lines come with different angles of intersection, and only those featuring exact 90-degree angle of intersection become normal cases of intersecting lines, becoming one among many subtypes existing today.
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Write an equation for the parabola that has the
given vertex and passes through the given point.
Vertex
(0,0)
Point
(3,18)
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=3\\ y=18 \end{cases} \\\\\\ 18=a(3-0)^2+0\implies 18=9a\implies \cfrac{18}{9}=a\implies 2=a \\\\\\ y=2(~~x-0~~)^2 + 0\implies \boxed{y=2x^2}[/tex]
The equation P = 24+2.94w represents Barrington's
water bill, where:
P is the price per month, and w is the amount of water they
use in one month, in thousands of gallons.
Answer the below questions. Round any decimals to two
places.
dollars when they use 0
dollars for every one-thousand
1. Barrington pays … type your answer…
gallons of water.
2. They pay type your answer....
gallons of water used.
3. Barrington paid type your answer...
thousand gallons last month.
dollars when they used 11-
Barrington pays 24 for 0 gallons of water and Barrington pays 55.9 for 11 gallons of water
Calculating the amount paid for gallons usedGiven that we have
P = 24 + 2.9w
When they used 0 gallons, we have
P = 24 + 2.9(0)
P = 24
When they used 11 gallons, we have
P = 24 + 2.9(11)
P = 55.9
Hence, the amount paid for 11 gallons is 55.9
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5. You and some friends are going on a recreation hike and need to hire a guide. Your
friends want you to pick the best guide to hire for the hike.
Larry charges an initial fee of $50 plus $15 per mile on the hike.
Connie charges a flat rate of $200 for an entire hike.
● Teo charges $20 per mile on the hike.
a. Write an equation to represent the total cost C, for m miles on the hike for eac
guide.
Larry -
Connie -
Teo -
The equations to represent the total cost C, for m miles on the hike for each guide are C(m) = 50 + 15m, C(m) = 200 and C(m) = 20m
Writing an equation to represent the total cost C, for m milesFrom the question, we have the following parameters that can be used in our computation:
Larry
Initial fee = 50
Rate = 15 per mile
Connie
Initial fee = 200
Teo
Rate = 20 per mile
Represent the number of miles with m
So, we have
Larry
Initial fee = 50
Rate = 15 per mile
C(m) = 50 + 15m
Connie
Initial fee = 200
C(m) = 200
Teo
Rate = 20 per mile
C(m) = 20m
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The product of two numbers is 126 . The smaller number is 5 less than the larger number. Which of the following equations can be used to solve for the larger number?
Answer:
Step-by-step explanation:
45