Solve the problem as directed. The rate traveled from Amarillo to Austin by a bus averages 65 miles per hour. The bus arrived in Austin after eight hours of travel. An automobile averages 80 miles per hour. Using the inverse variation relationship, show what the time would be for the automobile to complete the trip. a0 hours

Answers

Answer 1

65*8 = 520 miles traveled

520/80 = 6.5 hours for the car

Answer 2

Answer:

The automobile would take 6.5 hours to complete the trip.

Step-by-step explanation:

This is a case of a inverse variation relationship because when you increase the speed of traveling the time of arriving will reduce, now we have to define the equation and the variables:

Inverse variation equation: [tex]x1y1=x2y2[/tex]

[tex]x1[/tex]: speed of the bus, 65 miles per hour

[tex]y1[/tex]: time to Austin by bus, 8 hours

[tex]x2[/tex]: speed of the automobile, 80 miles per hour

[tex]y2[/tex]: time to Austin by automobile, unknown

Now we can replace the values in the equation and clear [tex]y2[/tex], this is:

[tex]65*8=80*y2\\y2=\frac{65*8}{80} =\frac{520}{80} =6.5\\[/tex]

The automobile would take 6.5 hours to complete the trip.


Related Questions

thirty-eight and ninety-seven hundredths kilograms in standard form

Answers

Standard form - Regular typing and writing with numbers

so it's 38.97 kg

Answer:

The answer is 38.97 kilograms.

Step-by-step explanation:

Thirty-eight and ninety-seven hundredths kilograms in standard form is 38.97 kilograms.

Thirty eight is simply 38.

And ninety-seven hundredths means that 97 is written after decimal. This is because when there exists an 'and' in a mathematical number, this means there is a decimal.

So, the answer is 38.97 kilograms.

record the product. use expanded form to help. 5×162=

Answers

5x2x9x9

10x81

810 is your answer

(b) how many measurements must be averaged to get a margin of error of ±0.0001 with 98% confidence? (round your answer up to the nearest whole number.)

Answers

Given that the scale readings of the laboratory scale is normally distributed with an unknown mean and a standard deviation of 0.0002 grams.

Part A:

If the weight is weighted 5 times and the mean weight is 10.0023 grams, the 98% confidence interval for μ, the true mean of the scale readings is given by:

[tex]98\% \ C. \ I.=\bar{x}\pm z_{\alpha/2}\left(\frac{\sigma}{\sqrt{n}}\right) \\ \\ =10.0023\pm2.33\left(\frac{0.0002}{\sqrt{5}}\right) \\ \\ =10.0023\pm2.33(0.000089) \\ \\ =10.0023\pm0.00021 \\ \\ =(10.0023-0.00021, \ 10.0023+0.00021) \\ \\ =(10.0021, \ 10.0025)[/tex]

Thus, we are 98% confidence that the true mean of the scale readings is between 10.0021 and 10.0025.



Part B:

To get a margin of error of +/- 0.0001 with a 98% confidence, then

[tex]\pm z_{\alpha/2}\left(\frac{\sigma}{\sqrt{n}}\right)=\pm0.0001 \\ \\ \Rightarrow2.33\left(\frac{0.0002}{\sqrt{n}}\right)=0.0001 \\ \\ \Rightarrow\left(\frac{0.0002}{\sqrt{n}}\right)= \frac{0.0001}{2.33} =0.0000429 \\ \\ \Rightarrow\sqrt{n}= \frac{0.0002}{0.0000429} =4.66 \\ \\ \Rightarrow n=4.66^2=21.7156\approx22[/tex]

Therefore, the number of measurements that must be averaged to get a margin of error of ±0.0001 with 98% confidence is 22.
Final answer:

To find the number of measurements that must be averaged to get a margin of error of ±0.0001 with 98% confidence, you can use the formula for the margin of error.

Explanation:

To find the number of measurements that must be averaged to get a margin of error of ±0.0001 with 98% confidence, we can use the formula for the margin of error:

Margin of Error = Z * (Standard Deviation / √(Sample Size))

Given that we want a margin of error of ±0.0001 and a confidence level of 98%, we can find the corresponding Z-value using a standard normal distribution table.

Once we have the Z-value, we can rearrange the formula to solve for the sample size, which represents the number of measurements that must be averaged.

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Divide (8.6 x 108) by (3.2 x 103). Express your answer in scientific notation.

Answers

In doing this division, we will first divide the 8.6 by the 3.2 to get 2.6875.  Thankfully, that number is already in scientific notation so we don't have to worry about changing it.  Now for the rest of the problem.  When the bases are the same, and they are both 10's, you subtract the exponents.  [tex]10^{8-3}[/tex]   gives us 10^5.  The answer then in scientific notation is [tex]2.6875*10^5[/tex].

Mary is making some shirts for her school's drama department. The fabric store has 3 1/6 yards of the fabric she wants in stock. But this quantity of fabric can make only 1 1/3 shirts. What length of fabric does Mary need to buy if she wants to sew 2 shirts?

A)1 1/6
B)2 3/8
c)3 5/6
D)4 3/4

Answers

Solve this problem using an equation of ratios.

3 1/6 yards of the fabric she wants in stock. But this quantity of fabric can make only 1 1/3 shirts

Write the ratio

3 1/6 yards to 1 1/3 shirts:

19
---
 6 
---------------
4
---
 3

We need to reduce this.  The first (upper) ratio is 19/6; the second (lower() ratio is 4/3.  We can mult. numerator and denom. of 4/3 both by 2 to obtain the equivalent ratio 8/6.

Then we have the ratio

19/6
--------  which can be reduced to 19/8.  That's  (19/8) yard/shirt.  We can use
8/6       this as a conversion factor.

To make 2 shirts, Mary will need  (19/8 yards per shirt)(2 shirts) of material, or 38/8 yards, or 19/4 yards (answer).

Trevor had 4 small boxes of raisins to share equally among himself and 2 friends.



How many boxes of raisins would each person receive?



A.




B.




C.




D.


Answers

Divide:   4 boxes / 3 persons = (4/3) box per person.

263,148 what is the value of the digit 6 in this number?

Answers

the ten thousands place

sixty thousand

hope this helps :)
sixth thousand hope it helps

Write three decimals that have a sum of 27.905. Parts of the needed decimals are listed below! thanks!

14. + 8. + 4. = 27.905

Answers

we have to add three decimals that have a sum of 27.905
parts that are given is 14. + 8. + 4.
if we add these we get the sum of 26, so we need 1.905 more, if we add 0.95 + 0.5 + 0.5 we get 1.905
So, if the numbers are 14.905, 8.50 + 4.50 and we add these numbers we get the answer 27.905
14.905 + 8.50 + 4.50 = 27.905
Thus, the three decimals that have sum of 27.905 are 14.905, 8.50 and 4.50.

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. n = 4, x = 3, p =

Answers

Final answer:

To find the probability of x successes in a binomial distribution, use the binomial probability formula. Substituting the given values into the formula will yield the probability.

Explanation:

To find the probability of x successes in a binomial distribution with n trials and probability of success p, we use the binomial probability formula. The formula is:

P(x) = (nCx) * p^x * (1-p)^(n-x)

Using the given values n = 4, x = 3, and p = ..., we can substitute these values into the formula to calculate the probability.

For example, if p = 0.5, the probability is:

P(3) = (4C3) * 0.5^3 * (1-0.5)^(4-3) = 4 * 0.125 * 0.5 = 0.25

Average speed of Car 1 = 45 mph.
Average speed of Car 2 = 65 mph.
Time elapsed between start of Car 1 and start of Car 2 = 18 minutes.
how long until the cars lapse

Answers

I'm assuming the two cars start from the same point! 

Let's measure time t from the time when Car 2 starts. 

Then the distances travelled by the cars up to the time of overtaking, t, must be the same. 

And we need to measure all time in hours, so 18 mins. is 0.3 hours. 

So, 45 x (0.3 + t) = 65 x t, so 20t = 13.5, so t = 13.5/20 = 27/40 = 40.5/60, i.e. 40 min 30 sec

It will take 40.5 minutes for Car 2 to catch up to Car 1 after its 18-minute head start.

To find out how long it will take for Car 2 to catch up to Car 1, we first need to determine the distance Car 1 travels during the 18-minute head start.

Convert 18 minutes to hours.

18 minutes ÷ 60 minutes/hour = 0.3 hours

Calculate the distance Car 1 travels during the 18-minute head start.

Distance = Speed × Time

Distance = 45 mph × 0.3 hours

Distance = 13.5 miles

Now that we know Car 1 has traveled 13.5 miles when Car 2 starts, we need to find out how long it takes for Car 2 to catch up, which is essentially the time needed to cover this distance at the speed difference between the two cars.

Calculate the relative speed of Car 2 compared to Car 1.

Relative Speed = Speed of Car 2 - Speed of Car 1

Relative Speed = 65 mph - 45 mph

Relative Speed = 20 mph

Calculate the time it takes for Car 2 to catch up.

Time = Distance ÷ Relative Speed

Time = 13.5 miles ÷ 20 mph

Time = 0.675 hours

Convert the time from hours to minutes for better understanding.

0.675 hours × 60 minutes/hour = 40.5 minutes

So, it will take 40.5 minutes for Car 2 to catch up to Car 1 after its 18-minute head start.

HELP ME

On a Saturday, Tyler earned $97.20 waiting tables at a restaurant. He earned $9.25 an hour, and an additional $60.20 in tips. How many hours did he work that day? (Write and solve an equation to solve this problem.)

sorry my writing is messy

Answers

$97.20 divided by $9.25 is 10 hours

If one side of a square notebook measures 20 cm, what is the area of the front cover of the notebook?

Answers

Salutations!

We know tat square has equal sides, so we will just multiply 20 twice as in [tex]S*S[/tex] or [tex]S^2[/tex]. Both of them are equal.

Area of the front cover of the notebook = [tex]s^2[/tex]

                                                              = [tex]20*20[/tex]

                                                               = [tex]400cm^2[/tex]

Hope I helped (:

have a great day!

Carol ate 2/5 of the cake, Dima ate 3/8 of the REMAINING cake, mom ate the rest.
If it was a POUND cake, how many OZ did MOM eat? PLEASE HELP ASAP, GIVING BRAINLIEST.

Answers

she would've eaten half of the cake, or 8 oz.

Her mum ate 31/40 of the cake

Given the weight of the cake to 1 pound

If Carol ate 2/5 of the cake, the remaining fraction of the cake will be 1 - 2/5 = 3/5

If Dima ate 3/8 of the REMAINING cake, then the fraction of cake Dima ate will be:

Dima = 3/8 * 3/5

Dima = 9/40

Fraction of the cake that her mum ate = 1 - 9/40 = 31/40

Hence her mum ate 31/40 of the cake

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How do you represent any number in an equation?

Answers

any unknown number in an equation you represent with a variable
You can represent it as a variable.

which equation is not true for the solution x = -8

Answers

-3 1/4 ≠ 1/3x-2 3/4 

Explanation: I tried all the other answers and the results match the expression, however, when I plug in -8 into this equation, the results are not equivalent.

What is 1/7^9 × 1/7^-6

Answers

[tex]\bf \cfrac{1}{7^9}\cdot \cfrac{1}{7^{-6}}\implies \cfrac{1\cdot 1}{7^9\cdot 7^{-6}}\implies \cfrac{1}{7^{9-6}}\implies \cfrac{1}{7^3}\implies \cfrac{1}{343}[/tex]

show the zero property of multiplication using the number 25

Answers

Anything divided by 0 is 0 for example 25x0=0 12020202020x0=0

For the expression below, write an equivalent expression that involves x only. assume x is positive.

Answers

Could you please elaborate on this question, which expression below. I will gladly help answer your inquires.

Which of the following sets of points is a direct variation?

(0, 0); (2, 4); (5, 15)
(0, 0); (-1, -2); (1, 2)
(3, 6); (-2, 4); (-1, 2)
(0, 5); (1, 6); (2, 7)

Answers

I got the second one. Good Luck. Hope it helped.

Answer:

(0, 0); (-1, -2); (1, 2) and (0, 5); (1, 6); (2, 7).

Step-by-step explanation:

The set will have a direct variation if each pair is added or subtracted by a common number in each component. You also can see it graphically, if the points form a straight growing line then the set is a direct variation. Then,

In the first set we have

(0,0), (0+2,0+4), (0+2+3, 0+4+11). The behavior is not uniform, then it is not a direct variation.

Second set: (-1, -2); (0,0); (1, 2)

(-1,-2)(-1+1,-2+2), (-1+1+1, -2+2+2). The behavior is uniform and it is increasing, then it is a direct variaton.

Third set:

(-2, 4), (-2+1,4-2), (-2+1+4, 4-2+4). The behavior is not uniform, then it is not a direct variation.

Fourth set:

(0,5), (0+1, 5+1), (0+1+1, 5+1+1). The behavior is uniform and it is increasing, then it is a direct variaton.

One card is drawn at random from the deck of cards shown. Which of the following probabilities is equal to one?

P(even or odd)P(even and odd)P(not yellow)

Answers

P(even or add).
I hope i helped!
If so, Please mark as brainliest!

Answer:

P(Even or ODD) ( .Y .)

Step-by-step explanation:

Theoretically, what would happen if a nation had an unlimited supply of a certain resource?

Answers

There are several ways this could go, this is my theory. This would be very dangerous because if one Nation had an unlimited supply of a certain resource, other Nations would possibly go to war. Also, the Nation would have trouble controlling its citizens, immigration, and power. 

jillian bought 1/2 pound of turkey and 1 1/3 pound of cheddar cheese at the deli. both items are on sale for $6 per pound. how much does each turkey cost>

Answers

To calculate the cost of the turkey, multiply the weight of the turkey (1/2 pound) by the cost per pound ($6). The total cost for the turkey is $3.

Jillian bought 1/2 pound of turkey and 1 1/3 pounds of cheddar cheese at the deli, with both items on sale for $6 per pound. To find out how much the turkey costs, you need to multiply the weight of the turkey by the cost per pound. Here's how you do it:

Determine the weight of the turkey: 1/2 pound.Multiply the weight of the turkey by the cost per pound: (1/2 pound) x ($6/pound).Calculate the cost: 1/2 x 6 = $3.

Therefore, the cost of the turkey is $3.

A movie rental gives a free popcorn to every 15th customer and a free movie rental to every 4th customer. Which customer was the first to win both prizes?

Answers

The 60th customer will win both prizes. 
In both cases, start with 0.  

Every 15th customer includes #15, #30, #45, #60, etc.

Every 4th customer includes #4, #8, #12, #16, #20, #24, #28, #32, #36, #40, #44, #48, #52, #56, #60

#60 is the first customer to win both prizes.

What is the value of log5 125

Answers

 Answer:

[tex]log_5125=3[/tex]

Step-by-step explanation:

Given : [tex]log_5125[/tex]

We have to find the value of [tex]log_5125[/tex]

Consider the given expression [tex]log_5125[/tex]

Rewrite 125 in power- base form, [tex]125=5^3[/tex]

[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)[/tex]

[tex]\log _5\left(5^3\right)=3\log _5\left(5\right)[/tex]

[tex]=3\log _5\left(5\right)[/tex]

[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1[/tex]

[tex]\log _5\left(5\right)=1[/tex]

[tex]3\log _5\left(5\right)=3[/tex]

Thus,  [tex]log_5125=3[/tex]

The value of log_5 125 is 3.

We have,

To find the value of log base 5 of 125, we need to determine the exponent to which we need to raise 5 to obtain 125.

In other words,

What power do we need to raise 5 to in order to get 125.

So,

By evaluating 5³ (5 raised to the power of 3), we find that 5³ = 125.

So, log base 5 of 125 is equal to 3, as log base 5 of 125 = 3.

So,

log base 5 of 125 equals 3 because 5 raised to the power of 3 gives us 125.

Thus,

The value of log_5 125 is 3.

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Use substitution to determine which of the following points is a solution to the standard form equation below. 2y = 5

Answers

2.5=y is the answer to the problem and if its wrong you didn't show me the answers 

explain how you could convert a rate of 18000 miles per hour to miles per second

Answers

You could multiply that fraction by (1 hour / 3,600 seconds) .

               (18,000 mile / 1 hour) x (1 hour / 3,600 second) = 

               (18,000 x 1) / (1 x 3,600)  (mile-hour) / (hour-second) = 

                     (18,000 / 3,600)  (mile / second)  =  5 mile/second
18000 miles / 1 hour)(1 hour / 60 minutes)(1 minute / 60 seconds) =

18000 miles / 3600 seconds =

5 miles / 1 second

5 miles per second

If 5+6i is a root of the polynomial function f(x),which of the following must also be a root of f(x)

Answers

The complex conjugate root theorem states that if a+bi (with a and b being numbers) is a root, then a-bi is also a root. Plugging that in here, this means that 5-6i is also a root

Answer:

5 - 6i must also be a root of f(x)

Step-by-step explanation:

Complex conjugates states that the two complex numbers are conjugates of each other if they have the same real part and their imaginary parts are negatives of each other i.e, the complex conjugate of a + bi is a - bi where i is  imaginary.

Conjugate root theorem states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a-bi is also a root of that polynomial.

Given: if 5+ 6i is a root of the polynomial function f(x).

then,

by the conjugate root theorem;

5 - 6i is also be a root of the polynomial f(x).


Which number is a prime number??

111
121
131
141

Answers

The prime number you are looking for is 141

Final answer:

Among the given options, the number 131 is a prime number, as it only has two divisors: 1 and itself.

Explanation:

The student has asked to identify which number among the given options is a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Analyzing the given options:

111 is divisible by 3.

121 is divisible by 11 (11 x 11).

131 is a prime number because it has no divisors other than 1 and itself.

141 is divisible by 3.

Therefore, the correct answer is 131, which is a prime number.

what is 79.4÷8 what is the answer in decimal form

Answers

79.4 / 8 is;

9.925. Hope this helps you.
Divide 8 into 79.4, either by hand or with a calculator:

9.925            (this is in decimal fraction form)

rewrite the following fractions as division problems 7/11 5/2 9/10 7/15

Answers

7 divided by 11
5 divided by 2
9 divided by 10
7 divided by 15
i hoped helped *3*
Answer with explanation:

We are given some fractions and we need to write these fractions in terms of division problem.

a)

                  7/11

There are 7 chocolates and a total of 11 children present at a party.If the chocolates are to be distributed equally among all, then how many chocolates does each get?

b)

                    5/2

The distance traveled by Xavier is 5 km and the time taken by him is 2 hours.Then find his speed?

c)

                     9/10

If there are a total of 19 students in a class and the number of girls are 1 more than the number of boys then find the ratio of number of boys to number of girls?

d)

                     7/15

The are 7 red balls, 2 green balls and 6 yellow balls in a bag.One ball is drawn at random.What is the probability of getting a red ball?

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The student store sells pencils that have a markup of 120 percent above their wholesale cost of $0.50 each. They also charge sales tax of 8 percent. What is the total cost of a pencil from the student store? Explain why you would make one of the addends a tens number when solving an addition problem. A negative correlation between two variables x and y usually yields a negative p-value for r. a. True b. False Imran and Aubrey were asked to find an explicit formula for the sequence 14,5,-4,-13...Imran said the formula is g(n)=14-9(n-1)Aubrey said the formula is g(n)=14-9nWhich one of them is right?Just IrmanJust AubreyBothNeitherPLEASE HELP ASAP!!! Why are the terms dominant and recessive misleading? What is 1/62/3= to what PLEASE HELPWrite the linear inequality shown in the graph. The gray area represents the shaded region.y 3x + 5y 3x + 5y 3x 5y 3x 5 Which of the following is an example of improved functioning as related to the benefits of muscular strength and endurance training? A.having stronger bonesB.easier to do household choresC.lower blood pressureD.larger lung capacity Describe the characteristics a building had to possess in order to be pleasing, according to the ancient Greeks. What was the purpose of the Federalist Papers? A to explain how the new government would work B to suggest changes needed in the Constitution C to enumerate the powers of Congress D to explain why the Constitution should be opposed Which of the following is not something usually asked when considering a source? Two lines of the same length that rhyme and complete a thought are Which of the following relationships is incorrect?A. Rough ER -- Site of protein synthesisB. Chloroplasts -- site of lipid synthesisC. Cell wall -- Support and protectionD. Nucleus -- holds genetic material (04.02 LC)The graph below shows the numbers of cups of grape juice that are mixed with cups of lemon-lime soda to make servings of grape soda:A graph is shown. The values on the x-axis are 0, 1, 2, 3, 4, 5. The values on the y-axis are 0, 2, 4, 6, 8, 10. Points are shown on ordered pairs 0, 0 and 1, 2 and 2, 4 and 3, 6 and 4, 8. These points are connected by a line. The label on the x-axis is Lemon lime Soda in cups. The title on the y-axis is Grape Juice in cups.What is the ratio of the number of cups of grape juice to the number of cups of lemon-lime soda? Let hh be the set of all points in the second quadrant in the plane v=2v=r2. that is, h={(x,y)x0,y0}h={(x,y)x0,y0}. is hh a subspace of the vector space vv? What two countries have been especially prominent destinations for economic migrants? Most countries in the world have what type of government? A pine tree grows at a rate of 1.5 feet per year. James plants a 2-foot tall pine tree in his yard. How many years will it take for the tree to be at least 14 feet tall? There are four major auto routes from boston to detroit and six from detroit to los angeles. how many major auto routes are there from boston to los angeles via de-troit describe how henry views the british reactions towards petitions made by the colonist Steam Workshop Downloader