The function f(x) is 4x5 – 3x has exactly 5 roots according to the Fundamental Theorem of Algebra.
How to find number of roots ?According to the Fundamental Theorem of Algebra, a polynomial function of degree n has exactly n roots (also known as zeros).In other words, if f(x) is a polynomial function of degree n, then there exist n values of x, called roots or zeros, that satisfy the equation f(x) = 0.The Fundamental Theorem of Algebra is important because it guarantees the existence of solutions to polynomial equations, which are equations that have the form f(x) = 0, where f(x) is a polynomial function.In this case, the polynomial function is f(x) = 4x^5 - 3x, which is of degree 5. Therefore, the function has exactly 5 roots according to the Fundamental Theorem of Algebra.The correct answer is therefore d) 5 roots.
Complete question :
According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?
f(x) = 4x5 – 3x
1 root
2 roots
4 roots
5 roots
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a bank gives interest at a rate of 3.5% each year. If you start an account at the bank with 3500 SWEDISH krona, how much money will you have in the account after a year
Answer:
$3624.48
Step-by-step explanation:
This is a bank interest formula that is -> P(1 +/- r/n)^rt
3500(1 + 0.035/12)^12*1
The answer is 3624.48
The figure shows the location of three points around a lake. The length of the lake, BC, is also shown.
(The figure is not drawn to scale.)
A picture of a right triangle ABC with right angle at B is shown. The length of the side AC is labeled as 6 miles. The length BC of the triangle is labeled as 4 miles. This length BC is also the length of an irregular gray shaded shape.
Which of the following choices is closest to the distance (in miles) between points A and B? (5 points)
Question 7 options:
1)
3.16 miles
2)
3.46 miles
3)
4.47 miles
4)
4.90 miles
Answer:
3) 4.47 miles
Step-by-step explanation:
AC is the the hypotenuse
so, 6*6 = 36, and 4*4 = 16
36-16=20
square root of 20 is 4.472135...
so, 4.47
a candidate for political office wants to determine if there is a difference in his popularity between men and women. to test the claim of this difference, he conducts a survey of voters. the sample contains 250 men and 250 women, of which 44% of the men and 52% of the women favor his candidacy. do these values indicate a difference in popularity? use a 0.01 significance level.
Yes, these values indicate a difference in popularity. Using a 0.01 significance level, the p-value for this test is 0.0018, which is less than the significance level.
This means that there is statistical evidence to support the claim that there is a difference in the candidate's popularity between men and women.
1. The candidate has a population of voters that he wishes to test to see if there is a difference in his popularity between men and women.
2. He conducts a survey of 250 men and 250 women, 44% of the men favoring his candidacy and 52% of the women favoring his candidacy.
3. To determine if there is a significant difference between the two samples, we first calculate the difference in proportions between the two groups:
52% - 44% = 8%.
4. We then use a 0.01 significance level to conduct a two-tailed z-test for proportions to determine if there is a statistically significant difference between the two groups.
5. The p-value for this test is 0.0018, which is less than the significance level of 0.01.
6. This means that there is statistical evidence to support the claim that there is a difference in the candidate's popularity between men and women.
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multiplication of matrices
with full workings and explanations
The product of matrices A and B is matrix C
a) [tex]C = (3 )[/tex]
b) [tex]C = \begin{pmatrix}-30\end{pmatrix}[/tex]
c) [tex]C = \begin{pmatrix}14&20\end{pmatrix}[/tex]
d) [tex]C =\begin{pmatrix}20&5\end{pmatrix}[/tex]
What is multiplication of matrices?
The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix
Given data ,
a)
Let the 2 matrices be A and B
The value of matrix A is
[tex]A = \begin{pmatrix}4&5\end{pmatrix}[/tex]
The value of matrix B is
[tex]B = \begin{pmatrix}2\\ \:-1\end{pmatrix}[/tex]
The product of matrix A and B is C
The value of matrix C is
[tex]C = \begin{pmatrix}4&5\end{pmatrix}\begin{pmatrix}2\\ -1\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}4\cdot \:2+5\left(-1\right)\end{pmatrix}[/tex]
[tex]C = (3 )[/tex]
Therefore , the value of matrix C is [tex]C = (3 )[/tex]
b)
Let the 2 matrices be A and B
The value of matrix A is
[tex]A = \begin{pmatrix}2&6\end{pmatrix}[/tex]
The value of matrix B is
[tex]B = \begin{pmatrix}-3\\ \:-4\end{pmatrix}[/tex]
The product of matrix A and B is C
The value of matrix C is
[tex]C = \begin{pmatrix}2&6\end{pmatrix}\begin{pmatrix}-3\\ -4\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}2\left(-3\right)+6\left(-4\right)\end{pmatrix}[/tex]
[tex]C = \begin{pmatrix}-30\end{pmatrix}[/tex]
Therefore , the value of matrix C is [tex]C = \begin{pmatrix}-30\end{pmatrix}[/tex]
c)
Let the 2 matrices be A and B
The value of matrix A is
[tex]A = \begin{pmatrix}1&2\end{pmatrix}[/tex]
The value of matrix B is
[tex]B = \begin{pmatrix}4&6\\ 5&7\end{pmatrix}[/tex]
The product of matrix A and B is C
The value of matrix C is
[tex]C =\begin{pmatrix}1&2\end{pmatrix}\begin{pmatrix}4&6\\ 5&7\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}1\cdot \:4+2\cdot \:5&1\cdot \:6+2\cdot \:7\end{pmatrix}[/tex]
[tex]C = \begin{pmatrix}14&20\end{pmatrix}[/tex]
Therefore , the value of matrix C is [tex]C = \begin{pmatrix}14&20\end{pmatrix}[/tex]
d)
Let the 2 matrices be A and B
The value of matrix A is
[tex]A = \begin{pmatrix}0&5\end{pmatrix}[/tex]
The value of matrix B is
[tex]B = \begin{pmatrix}3&6\\ 4&1\end{pmatrix}[/tex]
The product of matrix A and B is C
The value of matrix C is
[tex]C =\begin{pmatrix}0&5\end{pmatrix}\begin{pmatrix}3&6\\ 4&1\end{pmatrix}[/tex]
On simplifying the matrix C , we get
[tex]C = \begin{pmatrix}0\cdot \:3+5\cdot \:4&0\cdot \:6+5\cdot \:1\end{pmatrix}[/tex]
[tex]C =\begin{pmatrix}20&5\end{pmatrix}[/tex]
Therefore , the value of matrix C is [tex]C =\begin{pmatrix}20&5\end{pmatrix}[/tex]
Hence ,
The product of matrices A and B is matrix C
a) [tex]C = (3 )[/tex]
b) [tex]C = \begin{pmatrix}-30\end{pmatrix}[/tex]
c) [tex]C = \begin{pmatrix}14&20\end{pmatrix}[/tex]
d) [tex]C =\begin{pmatrix}20&5\end{pmatrix}[/tex]
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How do I find the inverse of j(x)=√x - 10 + 4
The inverse of y = √x - 10 + 4 is y = x^2 + 26 + 8x
What in mathematics is inverse?
A function that "undoes" another function is known as an inverse in mathematics. To put it another way, if f(x) produces y, then y will produce x when y is fed into f's inverse function. Invertible refers to a function that has an inverse, which is represented by the symbol f1.
Given that:
J(x) = √x - 10 + 4
y = √x - 10 + 4
now replace x with y
x = √y - 10 + 4
now solve for y , x = √y - 10 + 4
x + 4= √y - 10
Squaring both the side
x^2 + 16 + 8x = y - 10
y = x^2 + 26 + 8x
Hence the inverse of y = √x - 10 + 4 is y = x^2 + 26 + 8x
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Identify this system of equations:
y=4x-4
y=-4x+4
A. Consistent and Independent
B. Consistent and Dependent
C. Inconsistent
And also, this question isn't required, but if the 2 slope-intercept forms are opposite, do they equal each other. (Like the question above, 4x-4+ and -4x+4)
The system is consistent and independent.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We have the system of equations:
y = 4x - 4
y = -4x + 4.
Let's take the quotient between both the equations as;
(y/y) = (4x - 4)/(-4x + 4)
1 = (4x - 4)/(-4x + 4)
Solve for x;
1*(-4x + 4) = 4x - 4
-4*x + 4 = 4x - 4
-4x - 4x = -4 - 4
-8*x = -8
x = -8/-8 = 1.
To find the value of y, we can input this value of x in one of the equations:
y = 4 x1 - 4 = 0.
Then we have only one solution, (1, 0).
Therefore, the system is consistent and independent.
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How would I solve this equation?
[tex]\sqrt{x}({x}+{1})=0[/tex]
Tyler eat 6 crackers for a snack each weekday. On Friday, he drops 3 and only eats 3. What is the total number of crackers Tyler eats during the week?
Answer: 39 crackers
Step-by-step explanation:
There are seven days a week
Only Friday, he eats half, so 6 left
6 times 6 = 36
36+ 3= 39
Which ordered pair is a solution to the linear inequality below?
x+4y less than 4
A. -3,5
B. 0,4
C. 2,3
D. -8,-2
The solution to the given inequality that is x+4y<4 is (-8,-2) as it only gives the correct result for the equation.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left part, 5x 4, is bigger than the right part, 2x + 3. An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Here,
x+4y<4
(-8,-2)
-8+4*-2=-16<4
The provided inequality, x+4y4, has a solution of (-8,-2) because it alone provides the solution to the equation.
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Larry and Peggy are making decisions about their bank accounts. Larry wants to deposit $350 as a principal amount, with an interest of 4% compounded quarterly. Peggy wants to deposit $350 as the principal amount, with an interest of 6% compounded monthly. Explain which method results in more money after 2 years. Show all work.
Peggy's method will make more money.
What is compound interest?Compound interest is the sum of interest on principal and interest on interest of previous period.
Given, that principal is same in both cases,
Also, Peggy will get total interest = 2×6 = 12%.
Whereas, Larry will get 1 % per quarter compounded quarterly.
Therefore, Larry will get (101/100)⁸%.
Hence, 12 > (101/100)^8 and Simple interest method will make more money.
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1. Jayda drank % of a gallon of water on Monday.
On Tuesday, she drank 1 ½ times as much water
as she did on Monday.
How many gallons of water did Jayda drink in
all?
If Jayda's goal is to drink a gallon by Wednesday,
how many more gallons does she need to drink?
identify the type of data that would be used to describe percent of body fat what is an example of the data
As per the requirement of body fat measurement, we measure the body fat in continuous data type.
What is continuous data type?Measureable data is referred to as continuous data. The values in this data are not constant and can take on an endless number of different forms. You can also divide these measures up into smaller, independent components.
What is the advantage of continuous data over discrete data?Since it may employ decimal points and have infinite values, it is more precise and comprehensive than discrete data.
The type of data that would be used to describe percent of body fat is continuous data. An example of the continuous data type is Height of a person.
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Find the total snowfall for this year if it snowed 1/10 inch in November, 2 1/5 inches in December and 1 3/4 inches in January.
Answer: Just add them up. 5 1/20
Step-by-step explanation:
1+1+2=4. For the fractions, find the LCM. The LCM is 20 so you make all the fractions denominator 20. 2/20, 4/20, 15/20. Now you get 5 1/20 in the end
Select the equation of a line with a slope of 5 that passes through the point (2, –3).
Multiple choice question.
cross out
A)
y=5x – 13
cross out
B)
y=5x – 3
cross out
C)
y=5x+7
cross out
D)
y=5x+2
Answer: A) y = 5x – 13
Step-by-step explanation:
The equation is y=mx + b
We know the slope is 5 and the y-intercept is at ( 0, -13)
So our equation is y = 5x - 13
So, the answer is A
What happens if the insured tenant and the insurance company fail to agree on the amount of loss?.
Appraisal , If the insured and this insurer are unable to reach an understanding regarding the actual cash value or the extent of the loss, then, upon the written demand of either party, each shall choose a qualified and impartial appraiser and notify the other of the appraiser selected within 20 days of the demand.
What does the word "appraisal" mean?
A valuation by an authorized person of a piece of property, such as real estate, a company, a collectible, or an antique, is known as an appraisal.
An accreditation from a regulatory body overseeing the appraiser's area of practice is required for an authorized appraiser.
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The perimeter of your rectangular pool is 130ft. Three time the length is equal to 10 times the width. Find the length and width of the pool. Find the area if the pool.
Answer:
Length = 50 ft
Width = 15 ft
Area = 750 ft²
Step-by-step explanation:
Define the variables:
Let W be the width of the rectangle.Let L be the length of the rectangle.Create two equations with the given information.
Given:
Three times the length is equal to 10 times the width.⇒ 3L = 10W
Given:
The perimeter of the rectangle is 130 ft.⇒ 2W + 2L = 130
Rearrange the second equation to make W the subject:
⇒ 2(W + L) = 130
⇒ W + L = 65
⇒ W = 65 - L
Substitute this into the first equation and solve for L:
⇒ 3L = 10(65 - L)
⇒ 3L = 650 - 10L
⇒ 13L = 650
⇒ L = 50
Substitute the found value of L into the second equation and solve for W:
⇒ 2W + 2(50) = 130
⇒ 2W + 100 = 130
⇒ 2W = 30
⇒ W = 15
Therefore:
Length of the rectangular pool = 50 ftWidth of the rectangular pool = 15 ftSubstitute the found values of W and L into the formula for area of a rectangle to find the area of the pool:
⇒ Area = W × L
⇒ Area = 15 × 50
⇒ Area = 750 ft²
Diego opened a savings account with $20 to start before he started earning $10 for every hour of babysitting. Is there a proportional relationship between time and amount saved for Diego?
Answer: No, it is not proportional.
Explanation:
We can see that Diego opened an account with $20, meaning that there is going to be a y-intercept of 20 in a graph. Therefore, with a y-intercept of 20 and not zero, we can say that there is not a proportional relationship between and time and amount saved for Diego.
My friend Umpt has no more than 30 mimstoons...........
An inequality that combines two simple inequalities is known as a compound inequality.
What is a compound inequality?It is an inequality when two simple inequalities are combined to form it.The graph that represents the inequality's solution set can be seen in the image below.Combining one or more inequalities results in a compound inequality.The values of x in compound inequality are 1/14 and 2/3. We must determine the compound's value.A compound inequality in mathematics is a clause that joins two claims with the conjunction "and" or "or."Both of the statements in a compound sentence are true simultaneously if the conjunction "and" is used to connect the statements.If "or" is used to connect the statements, the compound phrase is true if at least one of the statements is true.
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[tex]2(3x-4)+10=5(x+4)[/tex]
x = 18
2(3x - 4) + 10 = 5(x + 4) 6x - 8 + 10 = 5x + 206x + 2 = 5x + 20x + 2 = 20A full box of cereal contains 12 1/2 cups. Each morning for breakfast Jules eats a serving of cereal that is 1 1/2 cups size. How many servings are in a full box of cereal?
Number of servings that are in a full box of cereal is 8.33 servings
Total quantity of cereal contains in the box = [tex]12\frac{1}{2}[/tex] cups
Convert the mixed fraction to simple fraction
[tex]12\frac{1}{2}[/tex] cups = 25/2 cups
Total quantity of cereal eats in each serving = [tex]1\frac{1}{2}[/tex] cups
Convert the mixed fraction to simple fraction
[tex]1\frac{1}{2}[/tex] cups = 3/2 cups
Number of servings in a full box of cereal = Total quantity of cereal contains in the box ÷ Total quantity of cereal eats in each serving
Here we have to use the division
Substitute the values in the equation
Number of servings in a full box of cereal = 25/2 ÷ 3/2
= 25/2 × 2/3
= 25/3
= 8.33
Therefore, a full box contains 8.33 servings
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What is the value of f(x) = 1/2x + 5 when x = 4?
Answer:
f(x)=7
Step-by-step explanation:
f(x)= 1/2x+5 ; x=4
f(4)= 1/2(4)+5
f(4)= 2+5
f(x)=7
Hope this helps, because I just did this lesson and I was confused at first, but with practice you will get it!
The ratio r:h is 5:8 and the ratio h:u is 4:7. Work out the ratio r:h:u in its simplest form
The simplest form of the ratio r:h:u is 5 : 8 : 14.
What is the ratio?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
We have,
r : h = 5 : 8 .........(i)
h : u = 4:7 ........(ii)
Multiplying the (i) and (ii) by numbers that will make 'h' have the same value in the ratios
Multiplying (i) by 1
(r : h)*1 = (5 : 8)*1
= r : h = 5 : 8
Multiplying (ii) by 2
(h : u)*2 = (4:7) *2
= 8 : 14
the ratio r : h : u in the simplest form = 5 : 8 : 14.
Hence, the simplest form of the ratio r:h:u is 5 : 8 : 14.
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C
10x + 12 = 2(5x+6)
WITH SOLUTION
Answer:
0
Step-by-step explanation:
10x + 12 = 2(5x+6)
or, 10x + 12 = 10x + 12
or, 10x - 10x = 12 - 12
or, 0 = 0
.
. . so, 0 is the answer.
Step-by-step explanation:
1st : distribute10x + 12 = 2(5x + 6)
10x + 12 = 10x + 12
2nd : subtract 12 from both sides10x + 12 = 10x + 12
10x + 12 - 12 = 10x + 12 - 12
3rd : simplify subtract the numbers 10x = 10x4: subtract 10x from both sides10x = 10x
10x - 10x = 10x - 10x
5: simplify combine like terms 0 = 0____________________________________________
hope it helps uh..!! ♥️need help please help me
Using the slope-intercept form, the slope, y-intercept and equation of the graph are -1/7, 5 and y = -1/7x + 5 respectively
Equation of Straight LineThe general equation of straight line is given in slope-intercept form as
y = mx + c.
In the graph given, the function is a straight line with slope and y-intercept.
Taking two points from the graph.
A= (5, 0)B = (-2, 1)The slope of the equation can be calculated using the points
slope (m) = y₂ - y₁ / x₂ - x₁
m = 1 - 0 / -2 - 5
m = 1 / -7
The slope is -1/7
From the graph, we can see the point in which the line passes through the y - axis and it is known as the y - intercept.
The y - intercept on this graph is 5
The slope- intercept form can be written as
y = -1/7x + 5
a) When x = -1, y = ?
y = -1/7x + 5
y = -1/7(-1) + 5
y = 1/7 + 5
y = 36/7
b) When y = 7, x = ?
y = -1/7x + 5
7 = -1/7x + 5
x = -14
c) The y - intercept of the graph is 5
d) The x-intercept of the graph is at -2.2
e) The slope of the line is -1/7
f) The equation of the line is given as y = -1/7x + 5
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The table shows the dates, times, and high and low tide heights.
Cresap Bay Tide Table
Date
Time
Low/high tide
Thursday, Feb. 7
1:26 a. M.
2. 6 ft (low)
7:26 a. M.
6. 4 ft (high)
2:29 p. M.
–0. 8 ft (low)
9:21 p. M.
4. 8 ft (high)
Friday, Feb. 8
2:24 a. M.
1. 5 ft (low)
8:22 a. M.
6. 5 ft (high)
3:16 p. M.
–1. 6 ft (low)
10:02 p. M.
5. 1 ft (high)
Which list shows the low tides from lowest to highest?
a–1. 6, –0. 8, 1. 5, 2. 6
b–0. 8, –1. 6, 1. 5, 2. 6
c–0. 8, 1. 5, –1. 6, 2. 6
d2. 6, 1. 5, –0. 8, –1. 6
The list that shows the low tides from lowest to highest is -1.6 < -0.8 < 1.58 < 2.6 and this can be determined by using the given data.
The correct option is A).
Given,
In the question:
The table shows the dates, times, and high and low tide heights.
Now, According to the question:
The following steps can be used in order to determine the list that shows the low tides from lowest to highest:
Step 1 - According to the given table, the low tide on Thursday, Feb 7 at 1;26 am is 2.6 ft.
Step 2 - According to the given table, the low tide on Thursday, Feb 7 at 2:29 pm is -0.8 ft.
Step 3 - According to the given table, the low tide on Friday, Feb 8 at 2:24 am is 1.5 ft.
Step 4 - According to the given table, the low tide on Friday, Feb 8 at 3:16 pm is -1.6 ft.
Step 5 - Arrange the data of low tides given in the above steps in increasing order:
-1.6 < -0.8 < 1.58 < 2.6
The correct option is A).
Hence, The list that shows the low tides from lowest to highest is -1.6 < -0.8 < 1.58 < 2.6 and this can be determined by using the given data.
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Regina made 1,240 pot holders. She wants to sell them in packages of 10. How many
packages will she have? Explain your thinking.
Answer:
124
Step-by-step explanation:
1,240/10 is 124. You divide by 10.
The number of packages of 10 for the 1240 pot holders is 124.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of pot holders = 1240
Number of pot holders in one pack = 10
The number of packages.
= 1240 ÷ 10
= 1240/10
= 124
Thus,
The number of packages of 10 is 124.
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Which equation is true?
Answer:
B
Step-by-step explanation:
Answer choice B would equal -3/4
The table below shows the temperature, in degrees Fahrenheit, in Boston, Massachusetts, over a 10-hour interval
Time
A
B
C
D
1 am to 5 a.m.
5 a.m. to 7 a.m.
7 am to 10 a.m.
1am.
10 am to 11 a.m.
29° F
5am
Temperature (Fahrenheit)
Over which interval does the temperature have the greatest average rate of change?
20° F
7 am
18 F
10 a.m.
25° F
11am.
28 F
Answer:i don’t know
Step-by-step explanation:
What are the values of x and y?
Using linear pairs, [tex]y=102[/tex].
Using the angle sum in [tex]\triangle TRS[/tex], [tex]x=70[/tex].
A cyclist rode 3.75 miles in 0.3 hours
A. how fast was she going in miles per hour?
B. At that rate, how long will it take her to go 4.5 miles?
The cyclist takes 0.36 hours to travel 4.5 miles.
What is distance?The actual length covered by the body is defined as distance travelled, whereas displacement is the straight path between the initial and final points.The imperial and customary systems use the unit miles per hour (symbol: mph) to measure speed. It represents the number of statute miles traveled in one hour.Here given that,
The distance travelled by the cyclist 3.75 miles.
Time = 0.3 hour
Distance / Time = Speed
By substituting,
3.75 / 0.3
= 12.5 miles per hour is the speed.
2) Distance = 4.5 miles, speed = 12.5 miles per hour.
Distance / Speed = Time
Time = 4.5 / 12.5
=0.36 hours
Therefore it takes 0.36 hours to travel 4.5 miles.
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