a bicyclist is competing in a 75 mile bike race. at a speed if 20 miles per hour,how many minutes would it take the biker to complete the race?
Answers
Answer:
The answer if you divide with a calculator would be 3.75, but if you put that in time form, the time would be 4 hours and 15 minutes
Step-by-step explanation:
Related Questions
The switchboard in a Denver law office gets an average of 8.2 incoming phonecalls during the noon hour on Thursdays. Find the probability that more than 4 calls will be received during the noon hour, on some particular Thursday. Assume calls are independent of each other.
Answers
Answer:
The probability that more than 4 calls will be received during the noon hour, on some particular Thursday is 0.9113.
Step-by-step explanation:
The random variable X can be defined as the number of incoming phone calls during the noon hour on Thursdays.
The random variable X describes a finite number of occurrences of an event in a fixed time interval.
The random variable X follows a Poisson distribution with parameter λ = 8.2.
The probability mass function of X is:
\(P(X=x)=\frac{e^{-8.2}(8.2)^{x}}{x!};x=0,1,2,3...\)
Compute the probability of more than 4 calls as follows:
\(P(X>4)=1-P(X\leq 4)\)
\(=1-\sum\limits^{4}_{x=0}{\frac{e^{-8.2}(8.2)^{x}}{x!}}\\\\=1-[0.00027+0.00225+0.00923+0.02524+0.05174]\\\\=1-0.08873\\\\=0.91127\\\\\approx 0.9113\)
Thus, the probability that more than 4 calls will be received during the noon hour, on some particular Thursday is 0.9113.
For the following, find the arc length:
(Use pi=3.14 and round your final answer to the hundredths.)
X=
Answers
\(\textit{arc's length}\\\\ x = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=10\\ \theta =\frac{\pi }{3} \end{cases}\implies x=10\cdot \cfrac{\pi }{3}\implies x\approx 10.47\)
The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. Step 1 of 2: Suppose a sample of 1453 suspected criminals is drawn. Of these people, 377 were captured. Using the data, estimate the proportion of people who were caught after being on the 10 Most Wanted list. Enter your answer as a fraction or a decimal number rounded to three decimal places.
Answers
Answer:
The proportion of people who were caught after being on the 10 Most Wanted list is 0.259.
Step-by-step explanation:
Proportion of people who were caught after being on the 10 Most Wanted list.
Number of people caught divided by the size of the sample.
In this question:
377 people caught.
1453 suspected criminals.
Then
\(p = \frac{377}{1453} = 0.259\)
The proportion of people who were caught after being on the 10 Most Wanted list is 0.259.
1. A new compact has a sticker price of $14500. Options add another $982. Destination charges are $592. Dealer preparation is 5% of the total price. Sales tax is 7%. Tag fee is $145. Title fee is $45. What is the total price of the vehicle?
2. The selling price of a used car is $8850. Trade in allowance is $1500. Tax is 8%. Tag fee is $130. Title fee is $35. Finance charges are 9.5% annual simple interest. What is the total price of the financed amount? What are the total finance charges? What are the monthly payments if the vehicle is financed for 3 years? What is the total deferred price of the car?
3. The total deferred price of a car is $28000. After a down payment of $2100, the monthly payments are $380. How long is the financing agreement?
4. Stanley bought a new car with a sticker price of $19200. The dealer agreed to a 6% discount. The sales tax was 8% of the selling price. The tag fee was $65, and the title fee was $45. What is the total price of the car? The interest rate is 9% for financing the car for 5 years. What is the total deferred price after all the payments were made?
5. Mark bought a truck with a sticker price of $23000 plus additional options totaling $3500. He received a 4% discount and a $1500 trade-in allowance. The tax was 7%, tag fee was $125, and title fee was $75. He bought an extended warranty for $700, which was financed into the total cost of the truck. The interest rate was 6.5% for 5 years. How much are the monthly payments?
Answers
The total price of the vehicle would be $18,192.88.
The total deferred price of the car would be $11,191.60.
The length of the financing agreement is 68 months .
The total deferred price after the payments was $19,601.84.
The monthly payments would be $516.92.
How to find the price of the vehicle ?Subtotal = Base price + Options + Destination charges
Subtotal = $14,500 + $982 + $592 = $16,074
Dealer preparation = 5% of subtotal
Dealer preparation = 0.05 x $16,074 = $803.70
Sales tax = 7% of subtotal
Sales tax = 0.07 x $16,074 = $1,125.18
Total price = Subtotal + Dealer preparation + Sales tax + Tag fee + Title fee
Total price = $16,074 + $803.70 + $1,125.18 + $145 + $45 = $18,192.88
How to find the total deferred price ?Tax = 8% of selling price = 0.08 x $8,850 = $708
Tag fee = $130
Title fee = $35
Total amount financed = Amount financed + Tax + Tag fee + Title fee = $7,350 + $708 + $130 + $35 = $8,223
Annual interest rate = 9.5%
Number of years financed = 3
Total finance charges = $8,223 x 0.095 x 3 = $2,341.595
Total financed amount = $8,223 + $2,341.595 = $10,564.595
Monthly payments = Total financed amount / (Number of years financed x 12 months) = $10,564.595 / (3 x 12) = $293.4615
Total deferred price = Selling price + Total finance charges = $8,850 + $2,341.595 = $11,191.595
How to find the length of the financing agreement ?Total deferred price = $28,000
Down payment = $2,100
Total amount financed = Total deferred price - Down payment = $28,000 - $2,100 = $25,900
Monthly payments = $380
Number of months = Total amount financed / Monthly payments = $25,900 / $380 = 68.16
The financing agreement is approximately 68 months long.
How to find the deferred price after the payments ?Sticker price = $19,200
Discount = 6% of sticker price = 0.06 x $19,200 = $1,152
Selling price = Sticker price - Discount = $19,200 - $1,152 = $18,048
Sales tax = 8% of selling price = 0.08 x $18,048 = $1,443.84
Total price = Selling price + Sales tax + Tag fee + Title fee = $18,048 + $1,443.84 + $65 + $45 = $19,601.84
How to find the monthly payments ?Using the formula for monthly payments on a loan:
P = (PV x r x (1 + r)^ n) / ((1 + r) ^ n - 1)
= ($26,515.80 x 0.005265 x (1 + 0.005265) ^ 60 ) / ((1 + 0.005265) ^ 60 - 1) = $516.92
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Can somebody give me an answer? ill give brainiest.
Answers
Answer:
The mystery divisor is 18
Step-by-step explanation:
In the beginning, I found it by simply dividing the dividend by the quotient which gave me the divisor of 18. You can start the division equation again and add in the divisor 18 and it'll give you the exact answer.
Another way you'll know it's correct, is by dividing the dividend by that divisor and it'll give you the quotient 225 just like in the image.
Use the given data to construct a box plot and identify the 5-number summary. Eleven different second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings (mmHg) are listed below.
{ 130, 135, 140, 120, 130, 130, 144, 143, 140, 130, 150 }
Answers
Answer:
\( Min =120, Max= 150\)
The first quartile can be calculated with this data:
130, 135, 140, 120, 130, 130
And the middle value is:
\( Q_1 = \frac{140+120}{2}=130\)
The median is the value in the 6th position from the dataset ordered and we got:
\( Median= 135\)
The third quartile can be calculated with this data:
135 140 140 143 144 150
And the middle value is:
\( Q_3 = \frac{140+143}{2}=141.5\)
The five number summary for this case:
Min. 1st Qu. Median Mean 3rd Qu. Max.
120.0 130.0 135.0 135.6 141.5 150.0
The boxplot is on the figure attached
Step-by-step explanation:
We have the following data given:
130, 135, 140, 120, 130, 130, 144, 143, 140, 130, 150
If we sort the values on increasing order we got:
120 130 130 130 130 135 140 140 143 144 150
The minimum and maximum are:
\( Min =120, Max= 150\)
The first quartile can be calculated with this data:
130, 135, 140, 120, 130, 130
And the middle value is:
\( Q_1 = \frac{140+120}{2}=130\)
The median is the value in the 6th position from the dataset ordered and we got:
\( Median= 135\)
The third quartile can be calculated with this data:
135 140 140 143 144 150
And the middle value is:
\( Q_3 = \frac{140+143}{2}=141.5\)
The five number summary for this case:
Min. 1st Qu. Median Mean 3rd Qu. Max.
120.0 130.0 135.0 135.6 141.5 150.0
The boxplot is on the figure attached
Eva is 5 years younger than 3 times Bill's age. If Eva is 2 years old, how old is Bill?
Answers
Answer:
17 years old.
Step-by-step explanation:
5 years than 3 times can be represented as 5*3.
5*3=15.
If Eva is 2, and Bill is 15 years older, 2+15=17.
Therefore, Bill is 17 years of age.
What is the extraneous root of this problem?
Answers
Answer:
a: -6
Step-by-step explanation:
\(\sqrt{5(-6)+6} =\sqrt{-24} = -6\\\)
This equation is not correct, therefore A is not a root and is extraneous
the sum of 23 and twice a number
Answers
Answer:
23 + 2n
Step-by-step explanation:
Hello!
"Twice a number" can be represented as 2 times n, or 2n
"The sum of 23 and twice a number" can be shown as 23 + 2n, given that twice a number is 2n.
Other common phrases in algebra:
"The difference of a and b" = (a) - (b)"The product of a and b" = (a) * (b)"The quotient of a and b" = (a) ÷ (b)Solve for p
P-16 = 27
OA) p = -11
OB) p = 11
OC) p = 43
OD p = 9
Answers
Answer:
\(p - 16 = 27 \\ p = 27 + 16 \\ { \boxed{p = 43}}\)
Answer:
P =43
Step-by-step explanation:
P-16 = 27
Add 16 to each side
P-16+16 = 27+16
P =43
<1 and <5 are ___ angles.
right
vertical
alternate interior
corresponding
angles.
Answers
Answer:
corresponding
Step-by-step explanation:
<1 and <5 are corresponding angles because they are on the same side of the transversal and on the same side of l and m
What values of b satisfy 3(2b + 3)² = 36?
Answers
Answer:
The values of b that satisfy the equation are:
b = (2√3 - 3) / 2
b = (-2√3 - 3) / 2
In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.
Step-by-step explanation:
To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:
1. Divide both sides of the equation by 3:
(2b + 3)² = 12
2. Take the square root of both sides:
√[(2b + 3)²] = √12
Simplifying further:
2b + 3 = ±√12
3. Subtract 3 from both sides:
2b = ±√12 - 3
4. Divide both sides by 2:
b = (±√12 - 3) / 2
Simplifying further:
b = (±√4 * √3 - 3) / 2
b = (±2√3 - 3) / 2
Therefore, the values of b that satisfy the equation are:
b = (2√3 - 3) / 2
b = (-2√3 - 3) / 2
In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.
In ms. Morales's class the ratio of boys to girls is 3:7. The class sizes at Ms.morales's school range from 22 to 34 students per class. What is the total number of students in Ms. Morales class
Answers
The total number of students in Ms. Morales's class is either 20 or 30, depending on the value of x.
Let the ratio of boys to girls in Ms. Morales's class be 3x:7x, where 3x represents the number of boys and 7x represents the number of girls.
The total number of students in the class is equal to the sum of the number of boys and the number of girls, which is 3x + 7x = 10x.
We don't know the value of x, but we do know that the class size is between 22 and 34 students.
Therefore, we can set up an inequality based on the total number of students:
22 ≤ 10x ≤ 34
Dividing all parts of the inequality by 10, we get:
2.2 ≤ x ≤ 3.4
Since x represents a whole number of students, the possible values for x are 3 (if there are 30 students in the class) or 2 (if there are 20 students in the class).
If x = 3, then the total number of students is:
10x = 10(3) = 30
If x = 2, then the total number of students is:
10x = 10(2) = 20
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which expression is equivalent to n+n-0.18n
a. 1.18n
b. 1.82n
c. n- 0.18
d. 2n - 0.82
Answers
Answer:
Simplifying the expression `n + n - 0.18n`, we get:
n + n - 0.18n = 2n - 0.18n
Therefore, the expression `n + n - 0.18n` is equivalent to `2n - 0.18n`.
Looking at the answer choices:
a. 1.18n
b. 1.82n
c. n- 0.18
d. 2n - 0.82
We can see that choice d is equivalent to the simplified expression `2n - 0.18n`.
Therefore, the answer is d. 2n - 0.82.
Step-by-step explanation:
A multiple choice test contains 10 questions with 5 answer choices. What is the probability of correctly answering 5
questions if you guess randomly on each question?
Answers
The answer is 1/2 because there are total 10 questions. So, the probability of getting 5 correct answers is 5/10 that is 1/2.
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Interval estimation of a population mean, population standard deviation unknown The Business Environment and Enterprise Performance Survey (BEEPS), developed by the European Bank for Reconstruction and Development and the World Bank, is a survey of more than 4,000 firms in 22 transition countries. Conducted in 2000, BEEPS gathered information on the impediments to business growth in transition countries. As part of BEEPS, firms that export goods answered the question, "How many days does the preshipment inspection take from the time you submit your goods until the time they are released?" For the sample of 46 exporting firms in Turkey, the sample mean x was 2.8 days, and the sample standard deviation s was 3.4 days. The standard deviation of the population distribution is unknown, but you are willing to assume that the population distribution is not highly skewed and contains no outliers. To develop a 90% confidence interval estimate of the mean number of days it takes for exported goods to be released in Turkey, use the Use the Distributions tool to compute a 90% confidence interval estimate for the mean number of days it takes for exported goods to be released in Turkey. t Distribution Degrees of Freedom = 35 -1 0 2 You are 90% confident that the mean wait time for exported goods to be released in Turkey is between and days. The confidence interval estimate you calculated is appropriate because: The wait time for exported goods to be released in Turkey is normally distributed. You are assuming the population distribution is not highly skewed nor contains outliers and the sample size is at least 30. Using the t distribution means the sampling distribution of the mean does not need to be normal.
Answers
The 90% confidence interval estimate for the mean number of days it takes for exported goods to be released in Turkey is between 1.9 and 3.7 days. This confidence interval is appropriate because the wait time for exported goods to be released in Turkey is normally distributed, and we are assuming the population distribution is not highly skewed or contains outliers.
We also used the t distribution, which means the sampling distribution of the mean does not need to be normal. This allows us to use the t distribution to account for any potential non-normality in the population, since the sample size is at least 30.The confidence interval you calculated is appropriate because it takes into account the fact that the population standard deviation is unknown. Finally, assuming the population distribution is not highly skewed or containing outliers is a reasonable assumption since you are confident in the data quality. All of these factors combine to make the confidence interval estimate you calculated appropriate.
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I’m timed please help
The David family traveled to silver lake in five hours. Their return trip took 7/8 of the time it took to travel to the lake. How long did the return trip take
O 4 1/8
O 4 3/8
O 5 5/7
O 5 7/8
Answers
can you get this answer
Answers
Answer:
1/128
Step-by-step explanation:
use formula: an = a1 × r ^ n-1
a1 = 4
r = 0.5
n = 10
a10 = 1/128
The function f(x) varies inversely with x and f(x)=0.5 when x = 0.15.
What is f(x) when x = 2.5?
Answers
Answer:
0.03
Step-by-step explanation:
Standard equation of inverse variation:
y = k/x
In function notation it is
f(x) = k/x
We are given f(0.15) = 0.5
0.5 = k/0.15
k = 0.5 * 0.15
k = 0.075
The function is
f(x) = 0.075/x
For x = 2.5,
f(2.5) = 0.075/2.5
f(2.5) = 0.03
Answer: 0.03
Using a standard deck of cards, a gamer drew one card and recorded its value. They continued this for a total of 100 draws. The table shows the frequency of each card drawn.
Card A 2 3 4 5 6 7 8 9 10 J Q K
Frequency 4 7 5 6 7 6 8 10 7 10 8 12 10
Based on the table, what is the experimental probability that the card selected was a 3, 5, or 7?
one fifth
one third
3 over 10
6 over 13
Answers
This can be simplified to 19/100, which is equivalent to 6/31 or approximately 0.19 or 19%. The answer is: 6 over 31.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain. Probability can be expressed as a fraction, decimal, or percentage.
The question asks for the experimental probability of drawing a 3, 5, or 7 from a deck of cards, given the frequency table provided.
The frequency table tells us how many times each card was drawn out of a total of 100 draws.
To calculate the frequency of drawing a 3, 5, or 7, we add the frequencies of these cards: 4 (for 3) + 6 (for 5) + 6 (for 7) = 16. Note that we do not include the frequencies of any other cards.
To calculate the probability of drawing a 3, 5, or 7, we divide the frequency of these cards (16) by the total number of draws (100): 16/100 = 0.16. This means that in our experiment, we drew a 3, 5, or 7 approximately 16% of the time.
The total number of draws is 100, and the frequency of cards 3, 5, and 7 is 7+6+6=19.
Therefore, the experimental probability of drawing a 3, 5, or 7 is:
19/100 = 0.19
This can be simplified to 19/100, which is equivalent to 6/31 or approximately 0.19 or 19%.
Therefore, the answer is: 6 over 31.
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HELP PLS !% POINTS!!
Answers
Answer:
149 sq. ft
Step-by-step explanation:
For the triangle:
Base = 16-9 = 7 ft
Area of Triangle = 1/2 of b.h
= 1/2 of 7 * 6
= 21 sq. ft
Area of Rectangle = l.b
= 5 * 16
= 128 sq. ft
Total Area = 149 sq. ft
Find the opposite of each integer. 0=
Answers
Answer:
The opposite of 0 is 0
Hope that helped
Need help with my work:(
Answers
Answer:
D
Step-by-step explanation:
Because each of them divided by 7 = the number of classrooms
use an appropriate taylor series to find the first four nonzero terms of an infinite series that is equal to ln(5/3).
Answers
The appropriate Taylor series for an infinite series with the first four nonzero terms equal to ln(5/3) is 0/1!, 0/2!, 0/3!, and 0/4! .......
What is taylor series?An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics. Near this point, the function and the sum of its Taylor series are equivalent for the majority of common functions. The polynomial or function of an infinite sum of terms is the Taylor series. The exponent or degree of each succeeding term will be greater than the exponent or degree of the one before it.
The formula is:
∑n=0 to ∞(fⁿ(a)(x-a)ⁿ)/n!
Here,
∑n=0 to ∞(fⁿ(a)(x-a)ⁿ)/n!
at n=1,
=0/1!
at n=2,
=0/2!
at n=3,
=0/3!
at n=4,
=0/4!
Appropriate taylor series for first four nonzero terms of an infinite series that is equal to ln(5/3) is 0/1!, 0/2!, 0/3!, 0/4!.......
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Encontrar 2 números cuya suma sea 49 y su diferencia sea 23
Answers
Answer:
Step-by-step explanation:
D
Does anyone know this?
Answers
Answer: 8.6?
Step-by-step explanation:
Choose the best graph that represents the linear equation:
-x = 2y + 1
Answers
The line slants downward from left to right, indicating that as x increases, y decreases.
The given linear equation is -x = 2y + 1. To represent this equation graphically, we need to rearrange it into the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.Rearranging the given equation, we get:2y = -x - 1
Dividing both sides by 2:y = (-1/2)x - 1/2
The slope of the line is -1/2, which means that for every unit increase in x, y decreases by 1/2 unit. The y-intercept is -1/2, indicating that the line intersects the y-axis at (0, -1/2).
Based on this information, the best graph that represents the linear equation y = (-1/2)x - 1/2 is a straight line with a negative slope of -1/2, starting at the point (0, -1/2) and extending infinitely in both directions.
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The area model shows 2 1 4
What is 2 x 2 1/4?
2 1/2
2 3/4
4 1/4
4 1/2
Answers
Answer:
4 1/2
Step-by-step explanation:Because 2x2 =4 and 2x1/4 = 1/2 so it is 4 1/2
As the CAPS document outlines, the Content Specification and Content Clarification for Patterns, Functions, and Algebra shows sequenced mathematics content topics and a content area spread. In the Intermediate Phase, select one topic and report on the topic sequence and content area spread. Your report should demonstrate mathematics concepts and procedures’ hierarchical and logical progression.
Answers
Answer:
Step-by-step explanation:
In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."
The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:
Introduction to Variables and Expressions:
Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.
Solving One-Step Equations:
Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.
Solving Two-Step Equations:
Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.
Writing and Graphing Linear Equations:
Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.
Systems of Linear Equations:
Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.
Word Problems and Applications:
Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.
The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.
By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.
11) In a triangle, the ratio of the measures of three angles is 2:5:8. Find the measures of
each angle in the triangle. Show proportions.
Answers
Answer:
Sum of interior angles of a triangle always = 180 degrees
add the individual ratios to get a sum composite ratio:
2+5+8 = 15
180 / 15 = 12
Multiply individual ratios:
{2:5:8} * 12 = 24:60:96
Check:
24 + 60 + 96 = 180
Step-by-step explanation:
I hope it's help