Yes, the distribution of heights for all adults is approximately normal because normal distribution has a bell-shaped curve. The bell curve indicates that the majority of the data points are located around the mean, with fewer data points on either side. Furthermore, normal distribution has certain characteristics that are relevant to this question.
The average height of men is 69.2 inches, while the average height of women is 63.7 inches. Therefore, we can assume that the mean height for both genders would be approximately 66.45 inches, assuming the distribution is equal (i.e., half male, half female).
If we plot the data of both males and females together, the plot will likely resemble a bell curve as per the properties of normal distribution. Since most adults would fall within the average height range, the distribution of heights for all adults is considered approximately normal. Therefore, we can conclude that the distribution of heights for all adults is approximately normal.
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Which of the following is equivalent to the inequality 2x + 13 < 5x - 20?
F. x >-11
G. x<?
H. x>;
J. x < 11
K. x > 11
Answer:
k
Step-by-step explanation:
2x+13<5x−20
Subtract 5x from both sides.
Combine 2x and −5x to get −3x.
Subtract 13 from both sides.
Subtract 13 from −20 to get −33.
Divide both sides by −3. Since −3 is negative, the inequality direction is changed.
x>11
how is probability determined from a continuous distribution? why is this easy for the uniform distribution and not so easy for the normal distribution?
To determine the probability of a continuous distribution we use the integral to determine it and for the normal distribution the integral is not so simple, for that reason it is simpler to use range values from tables.
How is probability determined from a continuous distribution?Probability can be determined from a continuous distribution in the following way:To compute the probability of a given interval for a continuous random variable, the area under the curve over the interval is determined. Integrals are used to calculate this area under the curve, which can be done either numerically or analytically using probability density functions.
For some distributions, such as the uniform distribution, calculating the area under the curve is straightforward. However, for other distributions, such as the normal distribution, it can be more difficult to calculate the integral analytically.
Why is this easy for the uniform distribution and not so easy for the normal distribution?The normal distribution is a continuous probability distribution that is frequently used in statistics. It is defined by its probability density function, which is a bell-shaped curve with a mean and a standard deviation.
Calculating the area under the curve for the normal distribution requires the use of integrals. Integrals are difficult to solve analytically for the normal distribution because the probability density function is not simple. However, it is relatively simple to calculate the probability for a given range of values using standard statistical tables or computer software.
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The perimeter of a rectangular map of the world is 270 cm. It is 90 cm in height. How wide is it?
Answer:
The perimeter of a rectangle is given by:
P = 2(L + W)
where P is the perimeter, L is the length, and W is the width.
In this case, we know that P = 270 cm and L = 90 cm, so we can solve for W as follows:
270 = 2(90 + w)
Divide both sides by 2:
135 = 90 + w
Subtract 90 from both sides:
w = 45
Therefore, the width of the map is 45 cm.
Step-by-step explanation:
a machine that manufactures automobile parts produces defective parts of the time. if parts produced by this machine are randomly selected, what is the probability that at most of the parts are defective? carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (if necessary, consult a list of formulas.)
The probability that at most of the parts are defective is 0.96.
A machine that manufactures automobile parts produces defective parts of the time. If parts produced by this machine are randomly selected, what is the probability that at most of the parts are defective?
The given probability of producing defective parts is P(defective) = 0.15. Now, we need to find the probability that at most of the parts are defective. This can be done by finding the probability of producing 0, 1, or 2 defective parts.
Let X denotes the number of defective parts. So, we have to calculate the probabilities for P(X = 0), P(X = 1), and P(X = 2). To calculate these probabilities, we will use the binomial probability formula:
P(X = x) ={n}C{x} p^x (1 - p)^{n - x}, Here, n = number of parts produced, p = probability of producing defective parts
x = number of defective parts
First, we need to find P(X = 0),
P(X = 0) = (0.85)^5 = 0.4437
P(X = 1) = {5}C{1} (0.15)^1 (0.85)^4 = 0.3672
P(X = 2) = {5}C{2} (0.15)^2 (0.85)^3 = 0.1459
Now, we can find the probability that at most of the parts are defective as follows:
P{at most 2 defective parts}) = P(X = 0) + P(X = 1) + P(X = 2) = 0.957
Therefore, the probability that at most of the parts are defective is 0.96.
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6(x - 2) -3 ≥ -4 ( -3 + 9) +10
Answer:
2x=5 > -14
Step-by-step explanation:
6(x - 2) -3 ≥ -4 ( -3 + 9) +10
6x-12-3 > 12-36+10
6x-15 > -36+22
6x-15 > -14
6x=15 > -14
3 3
2x=5 > -14
NEED HELP DUE TODAY!!!!
2. How do the sizes of the circles compare?
3. Are triangles ABC and DEF similar? Explain your reasoning.
4. How can you use the coordinates of A to find the coordinates of D?
The triangle DEF is twice the size of the triangle ABC and the triangles are similar triangles
How do the sizes of the circles compare?Given the triangles ABC and DEF
From the figure, we have
AB = 1
DE = 2
This means that the triangle DEF is twice the size of the triangle ABC
Are triangles ABC and DEF similar?Yes, the triangles ABC and DEF are similar triangles
This is because the corresponding sides of DEF is twice the corresponding sides of triangle ABC
How can you use the coordinates of A to find the coordinates of D?Multipliying the coordinates of A by 2 gives coordinates of D
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Ixl dilations-find the scale factor and center dilation
The scale factor is 2 and center dilation is reduced.
The scale factor is a ratio that describes how much a figure has been enlarged or reduced. It is calculated by dividing the length of the corresponding sides of the original and dilated figures. If the scale factor is greater than 1, then the figure is enlarged, and if it is less than 1, then the figure is reduced.
To find the scale factor in an IXL dilations problem, you need to compare the corresponding sides of the original and dilated figures.
If the original figure has a side length of 4 units, and the dilated figure has a corresponding side length of 8 units, then the scale factor is 8/4=2. This means that the dilated figure is twice as large as the original figure.
The center of dilation is the point about which the figure is enlarged or reduced. It is the fixed point that remains unchanged during the dilation process.
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Name the shape that will result from connecting the points (-4, 1) , (-4, -4) , (0, 3) , and (0, 6) .
A: Square
B: Rectangle
C: Trapezoid
D: Parallelogram
The shape that results from connecting the points (-4, 1), (-4, -4), (0, 3), and (0, 6) is a trapezoid.
What is a trapezoid?A trapezoid is a geometric form that has four sides, two of which are parallel and two of which are nonparallel (or skew lines). A trapezoid is also known as a trapezium (UK) or a trapeze (US).
The trapezoid's parallel sides are known as the bases, and the two nonparallel sides are known as the legs or lateral sides. The trapezoid is also sometimes referred to as the irregular quadrilateral.
How to identify a trapezoid?A quadrilateral is a shape that has four sides, four vertices, and four angles. The following are the characteristics of a trapezoid:
It has four sidesIt has two parallel sides and two nonparallel sidesIt has two opposite sides that are parallel to one another and two other sides that are not parallelIt has two acute angles and two obtuse anglesIt has diagonals that intersect at a midpointThe formula for the area of a trapezoid is as follows:
Area of a trapezoid = [ (base 1 + base 2) / 2 ] x height
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Which statements are true? Select each correct answer.
A. 40m^6 -4=4(10m^6-1)
B. 32m^4 +12m^3 =4m^3(8m +3)
C. 15m^3-6m=3m(5m^2 -6m)
D. 6m^2+18m=6m^2(1+3m)
Answer:
C. 15m^3-6m=3m(5m^2 -6m) is true.
D. 6m^2+18m=6m^2(1+3m) is true.
A. 40m^6 -4=4(10m^6-1) is not true.
B. 32m^4 +12m^3 =4m^3(8m +3) is not true.
Answer:
C. 15m^3-6m=3m(5m^2 -6m) is true.
D. 6m^2+18m=6m^2(1+3m) is true.
Step-by-step explanation:
1) Adam wants to buy a home priced at $215,000. The bank requires him to make a 5% down payment and
he will finance the rest for 30 years at 4.5% interest. He has to also pay the closing costs below. Find the
a) the down payment b) the amount of the mortgage c) the closing costs d) the amount financed with
closing costs e) the monthly payment f) the total amount repaid g) the amount paid to interest.
Application Fee
Borrower's Credit check
Points
Appraisal Fee
Title Search
Title Insurance
Attorney Fee
Documentation stamp
Processing fee
$ 25
65
1.5% of Mortgage
350
215
450
400
0.30% of Mortgage
1.25% of Mortgage
a market research firm conducts telephone surveys with a historical response rate. what is the probability that in a new sample of telephone numbers, at least individuals will cooperate and respond to the questions? in other words, what is the probability that the sample proportion will be at least ? calculate the probability to decimals. use z-table.
The probability that the sample proportion will be at least k is 0.7580.
Let P be the probability that any one person in the population will cooperate and respond to the questions. We are looking for the probability that at least k people out of n in the sample will cooperate and respond to the questions. Let X be the number of people who cooperate and respond to the questions in the sample. X follows the binomial distribution with parameters n and P.To calculate this, use the following formula:
Z = (X - μ) / σ
Here, X = number of people who cooperate and respond to the questions in the sample
μ = E(X) = np, σ = sqrt(npq)
q = 1 - P
Now, to calculate the probability, first calculate μ = np =
σ = sqrt(npq)
Then, find the z-score using z = (k - μ) / σ.
Now, use the z-table to find the probability corresponding to the z-score obtained in the previous step. The probability obtained from the z-table is the probability that the sample proportion will be at least k.
The probability that the sample proportion will be at least k is 0.7580.
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rita received a $80 gift card for a coffee store. she used it in buying some coffee that cost $7.37 per pound. after buying the coffee, she had $57.89 left on her card. How many pounds of coffee did she buy?
Answer:
3 pounds of coffee.
Step-by-step explanation:
Equation
y = -7.37x + 80
substitute 57.89 for y
57.89 = -7.37 + 80 Subtract 80 from both sides
57.89 - 80 = -7.37 + 80 - 80
-22.11 = -7.37x Divide both sides by -7.37
3 = x
3 pound of coffee
Helping in the name of Jesus.
Answer:
rita received a $80 gift card for a coffee store. she used it in buying some coffee that cost $7.37 per pound. after buying the coffee, she had $57.89 left on her card. How many pounds of coffee did she buy?
Step-by-step explanation:
Let's first find out how much money Rita spent on coffee:
$80 (initial balance) - $57.89 (remaining balance) = $22.11 spent on coffee
Now, let x be the number of pounds of coffee that Rita bought. Since the coffee costs $7.37 per pound, we can set up the equation:
$7.37x = $22.11
Solving for x, we can divide both sides by $7.37:
x = 3
Therefore, Rita bought 3 pounds of coffee.
thanks if you answer
Answer:
[tex]{ \sf{ = 41 \times 100 + 41 \times { \boxed{2}}}} \\ \\ = { \sf{ \boxed{4100} + { \boxed{82}}}} \\ \\ = { \sf{ \boxed{4182}}}[/tex]
Answer:
A- 2
B- 4,100
C- 82
D- 4,182
Write 2/7 + 1/4 as a sum of two equivalent fractions with the same denominator
2/7 + 1/4 = 15/28 ≅ 0.5357143
Add: 2/7 + 1/4 = 2 · 4/7 · 4 + 1 · 7/4 · 7 = 8/28 + 7/28 = 8 + 7/28 = 15/28
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(7, 4) = 28. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 4 = 28. In the following intermediate step, it cannot further simplify the fraction result by canceling.In other words - two sevenths plus one quarter is fifteen twenty-eighths.
Refer to the equation a x 9 = b. If a =3, what is the value of b
The value of' b' is 27 when' a' is three.
The presented equation is a x 9 = b, wherein' a' is a variable and' b' is the product of' a' and nine. we are asked to find the value of' b' when' a' is 3.
Substituting the value of' a' into the equation, we get
3 x 9 = b
27 = b
Thus, the value of' b' is 27 when' a' is three.
On this equation,' a' is a variable, this means that that its cost can trade. still, the value of' b' is dependent on the price of' a'. whilst' a' is 3, the price of' b' is 27. this is an illustration of a easy linear equation, in which the value of one variable is dependent on the figure of any other variable, and can be used to model real-global situations.
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What property of real numbers does each statement demonstrate? (3 + 4) + 1 = 3 + (4 + 1)
Answer: Associative property
Step-by-step explanation:
The definition of the associative property is the answer is the same no matter how the terms are grouped. Hope this helped!
The hypotenuse of a right triangle measures 15 cm and one of its legs measures 14 cm. Find the measure of the other leg. If necessary, round to the nearest tenth
Answer:
The other leg is 5.4 cm
Step-by-step explanation:
Pre-SolvingWe are given that in a triangle, the hypotenuse is 15cm, and one of the legs is 14cm.
We want to find the length of the other leg.
SolvingThe Pythagorean Theorem states that a² + b² = c², where a and b are the legs and c is the hypotenuse.
We can substitute what we know into the theorem.
14² + b² = 15²
196 + b² = 225
Subtract.
b² = 29
Take the square root of b to get:
b = √29 cm
√29 ≈ 5.4 cm
30 points to help me!
Answer:
Step-by-step explanation:
5+3x/4 = 7/12
[(5*4)+3x]/4 = 7/12
(20+3x)/4 = 7/12
20+3x = 7/12*4
20+3x = 7/3
3x = 7/3 - 20
3x = [7-(20*3)]/3
3x = (7-60)/3
3x = -53/3
x = -53/3/3/1 ( reciprocal )
x = -53/3*1/3
x= -53/9
Laura has done a two-factor factorial completely randomized design. From her experiment, Laura has constructed the following incomplete ANOVA display: Source SS DF MS F A 350.00 2 B 300.00 150 AB 200.00 50 Error 150.00 Total 1000.00 18 a. How many levels of factor B did she use in the experiment? b. How many degrees of freedom are associated with interaction? c. The error mean square is d. The mean square for factor A is e. How many replicates of the experiment were conducted? f. What are your conclusions about interaction and the two main effects? g. An estimate of the standard deviation of the response variable is h. If this experiment had been run in blocks (CRBD) there would have been degrees of freedom for blocks.
a. Two levels of factor B were used in the experiment.
b. The degrees of freedom associated with interaction are 50.
c. The error mean square is 6.00. d. The mean square for factor A is 175.00.e. The experiment was conducted with three replicates.f. The interaction is significant. Factor A is significant. Factor B is not significant.g. An estimate of the standard deviation of the response variable is 2.449. h. If the experiment had been run in blocks (CRBD) there would have been 12 degrees of freedom for blocks.Solution:Factorial design: A factorial design is an experimental design that consists of two or more factors, each with two or more levels, and each subject is assigned to one and only one level of each factor. The objective of a factorial experiment is to analyze the effect of each factor on the response variable and to examine if there is any interaction between factors.a. Two levels of factor B were used in the experiment.b. Interaction degrees of freedom = AB = 50.c.
Mean square for error: MSE = 150/10 = 15.d. Mean square for factor A: MS(A) =[tex]SSA/dfA = 350/2 = 175.e.\\[/tex] Three replicates were conducted (from the error df = 10).f. Interaction is significant. Factor A is significant. Factor B is not significant.g. Estimate of the standard deviation of the response variable: sqrt(15/2) = 2.449.h. If the experiment had been conducted in a CRBD, there would have been 12 degrees of freedom for the block.
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14x+312=2(12x+34)
What is the value of x?
A. 2 over 3
B. 5 over 4
C. 3 over 2
D. 8 over 3
Answer:
None of the given options matches the value we got for x, but the closest option is A. 2 over 3. However, we need to note that x is not a whole number, it's a decimal.
Step-by-step explanation:
Let's solve the given equation
14x+312=2(12x+34)
Distribute the 2 on the right-hand side
14x+312=24x+68
Subtract 14x from both sides
312=10x+68
Subtract 68 from both sides
244=10x
Divide both sides by 10
x=24.4
Answer:
2 over 3
Step-by-step explanation:
none of the options match the value of x
What is the surface area?
5 yd
6 yd
5 yd
5 yd
4 yd
square yards
The surface area of the rectangular prism is 170 square yards.
What is the surface area formula?Surface area is the total area of a three-dimensional shape's surface. Add the areas of all six faces to find the surface area of a cuboid with six rectangular faces. Alternatively, label the cuboid's length (l), width (w), and height (h) and use the formula: surface area (SA)=2lw+2lh+2hw.
To calculate the surface area of the rectangular prism, add the areas of each of its faces.
The front and back faces are 5 yards by 6 yards in size, so each has an area of:
5 yards x 6 yards equals 30 square yards
The top and bottom faces are 5 yards by 5 yards, so each has an area of:
5 yards x 5 yards equals 25 square yards
The two side faces have dimensions of 6 yards by 5 yards, for a total area of:
30 square yards = 6 yards x 5 yards
As a result, the surface area of the rectangular prism is as follows:
Front face area plus back face area plus top face area plus bottom face area plus left side face area plus right side face area
= 30+30+25+25+30+30
= 170 square yards
As a result, the rectangular prism has a surface area of 170 square yards.
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Purchasing the correctly sized BMX bike is based on the height of the rider. In order to fit a customer, the salesperson can use the equation b=0. 29h+1. 35
where b
is the size of the BMX bike frame in inches and h
is the height of the rider in inches
The slope in the equation b = 0.29h + 1.35 is the measure of the rate at which the bike frame size changes with the height of the rider.
The slope in the equation b = 0.29h + 1.35 refers to the coefficient of the variable h, which represents the height of the rider. The slope is the measure of the rate at which the bike frame size changes with the height of the rider.
In this equation, the slope is 0.29, which means that for every inch increase in the rider's height, the bike frame size increases by 0.29 inches. The slope is a crucial component of the equation as it determines the proportionality of the two variables.
Moreover, the slope is essential in analyzing the relationship between the rider's height and the bike frame size.
It plays a vital role in determining the appropriate size of the BMX bike frame and analyzing the relationship between the two variables.
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Complete Question:
Purchasing the correctly sized BMX bike is based on the height of the rider. In order to fit a customer, the salesman can use the equation b 0.29h +1.35 where b is the size of the BMX bike frame in inches and h is the height of the rider in inches.
Which sentence explains the slope in the equation?
About 24% of flights departing from New York's John F. Kennedy International Airport were delayed in 2009. Assuming that the chance of a flight being delayed has stayed constant at 24%, we are interested in finding the probability of 10 out of the next 100 departing flights being delayed. Noting that if one flight is delayed, the next flight is more likely to be delayed, which of the following statements is correct? . (A) We can use the geometric distribution with n = 100, k = 10, and p = 0.24 to calculate this probability. (B) We can use the binomial distribution with n = 10, k = 100, and p = 0.24 to calculate this probability. (C) We cannot calculate this probability using the binomial distribution since whether or not one flight is delayed is not independent of another. (D) We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability
The statement that is correct is (D) We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability.
The binomial distribution can be used to calculate the probability of a certain number of successes in a given number of trials, where each trial has a fixed probability of success.
The probability of a flight being delayed is 0.24, and the probability of a flight not being delayed is 0.76. Therefore, the probability of exactly 10 flights out of 100 being delayed can be calculated using the binomial distribution with n = 100, k = 10, and p = 0.24.
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Y is directly proportional to x if x=20,when y=160,then what is the value of x when y=3. 2
Answer: 0.4
Step-by-step explanation:
I genuinly cant be asked to explain.
a box contains 75 red marbles, 37 white marbles, and 19 blue marbles if a marble is randomly selected from the box, what's the probability that it is not blue
The probability that it the marble taken out of the box is not blue is [tex]\frac{112}{131}[/tex].
What is the probability?Probability is a branch of math that studies the chance or likelihood of an event occurring.
There are [tex]75[/tex] red marbles, [tx]37[/tex] white marbles, and [tex]19[/tex] blue marbles.
If a marble is randomly selected from the box, we have to find the probability that it is not blue.
Then the total number of marbles = [tex]75 + 37 + 19 = 131.[/tex]
The probability that a marble is not blue:-
[tex]P[/tex](Not blue) = [tex]P[/tex](Red or White)
[tex]P[/tex](Red or White) = [tex]\frac{(75 + 37)}{131}[/tex]
[tex]P[/tex](Red or White) = [tex]\frac{112}{ 131}[/tex]
[tex]P[/tex](Not blue) = [tex]1 - P[/tex](Blue)
[tex]P[/tex](Not blue) = [tex]1 - \frac{19}{131}[/tex]
[tex]P[/tex](Not blue) = [tex]\frac{112}{ 131}[/tex]
Therefore, the probability that a marble selected from the box is not blue is [tex]\frac{112}{131}[/tex].
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Given that the number 33,554,432 is equal to 2^25 , explain how you know that 33,554,432 is not a square number
First of all, perfect squares do not end in 2.
The exponent has to be an even number when 2 is the base. For example 2^8 = 64. 8 is an even number. So 64 is a square number.
find the length of the cord pt.3
According to the circle theorem, we can find the length of the cord, x = 4 units.
Define circle theorem?Geometrical assertions known as "circle theorems" set forward significant conclusions pertaining to circles. These theorems provide significant information regarding several aspects of a circle.
A circle's chord is a line segment that hits the circle twice on its edge, separating it into two equal pieces. The circle is divided into two equal pieces by the longest chord of the circle, which runs through its centre.
Here in the given circle,
As per the intersecting chords theorem,
AB × CB= BE × BD
⇒ 6 × 6 = 9× x
⇒ x = 36/9=4
Therefore, the length of the chord, x = 4 units.
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The net of a triangular prism is shown. a) Work out the length x. b) Work out the area of the shaded face. 3 cm 7 cm 5 cm 8 9 cm Not drawn accurately
The length of the side on the prism is 5cm. The area of the shaded region is 72 cm².
What is area?Area is the total amount of area occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the region that its boundary encloses. The quantity of unit squares that span a closed figure's surface is its area. Square units like cm² and m² are used to quantify area. A shape's area is a two-dimensional measurement.
The region inside the perimeter or boundary of a closed shape is referred to as the "area". Such a shape has at least three sides that can be joined together to create a boundary. The "area" formula is used in mathematics to describe this type of space symbolically.
In this figure,
The 5cm flap will be adjacent to the side x. Therefore,
Length of the side x= 5cm
Area of the shaded region= l×b
because the shaded region is a rectangle.
area= 9*x
=9*5= 45 cm²
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The distance between new orleans and houston is 353 miles. At 12:20pm, a bus leaves houston for new orleans at a speed of 60mph. 45 minutes late, a motorcycle leaves new orleans for houston at a speed of 72mph. At what time will the bus and the motorcycle pass each other if neither stops or changes speed?
As per the given distance, the bus and the motorcycle will pass each other at 4:50 pm.
Now, let's find the distance the bus travels during that time. We know the speed of the bus is 60 mph, so we can use the formula distance = speed x time. Thus, the distance the bus travels is:
distance = speed x time
distance = 60 x t
Next, let's find the distance the motorcycle travels during the same time. The speed of the motorcycle is 72 mph, so we can use the same formula to find the distance the motorcycle travels:
distance = speed x time
distance = 72 x (t - 3/4)
Here, we subtract 3/4 from the time because the motorcycle leaves 45 minutes later than the bus. Remember, we need to convert 45 minutes to hours by dividing it by 60. Therefore, 45 minutes is equal to 3/4 of an hour.
Now that we have both distances, we can set them equal to each other since the bus and the motorcycle will meet at the same point in time:
60t = 72(t - 3/4)
Let's simplify and solve for "t":
60t = 72t - 54
12t = 54
t = 4.5
Therefore, it will take 4.5 hours for the bus and the motorcycle to meet each other. But, we need to find out what time that will be. We know the bus left at 12:20 pm, so we add 4.5 hours to that time:
12:20 pm + 4.5 hours = 4:50 pm
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Jason and Scott plan on biking to the center of town to get ice cream at the convenience store. Since Scott
had to put air in his tires, Jason was able to get 1 mile ahead of Scott before Scott left the house. Both
bikers rode at a speed of 15 miles per hour.
Write an equation in y = mx + b form that represents Jason's trip. Jason =
a.
Write an equation in y = mx + b form that represents Scott's trip.
Will Jason and Scott meet before they both reach the store? Explain.
If you were to graph both lines on the same coordinate plane, predict what your graph would look
like.
Answer:
a. Jason's equation in y = mx + b form is y = 15x + 1.
b. Scott's equation in y = mx + b form is y = 15x.
Since both are moving at the same speed, they will meet at the point where their distances from the starting point are the same. Let d be the distance from Scott's starting point to the store. Then, the distance from Jason's starting point to the store is d + 1. Using the formula distance = rate × time, we can set up an equation:
15t = d
15t - 1 = d + 1
Solving for t in both equations, we get t = d/15 and t = (d+2)/15, respectively. Equating these expressions for t, we get d/15 = (d+2)/15, which simplifies to d = -2. This means that they will not meet before reaching the store, as Jason is already 1 mile ahead of Scott and will stay ahead throughout the trip.
If we were to graph both lines on the same coordinate plane, we would have two parallel lines with a slope of 15, where Jason's line would intersect the y-axis at 1.
