Michelle rode her bicycle from her house to school at an average speed of 8 miles per hour. Later that day, she rode from school back home along the same route at an average speed of 12 miles per hour. If the round trip took one hour, how many miles long is the round trip?

Answers

Answer 1

9514 1404 393

Answer:

  9.6 miles

Step-by-step explanation:

Let x represent the round trip distance. Then Michelle's time was ...

  t = distance/speed

  1 = (x/2)/8 +(x/2)/12 = x(1/16 +1/24) = x(3/48 +2/48) = x(5/48)

  48/5 = x = 9.6

The round trip is 9.6 miles.


Related Questions

find the greatest number than divides 45 60 75 without leaving remainder​

Answers

Answer:

15

Step-by-step explanation:

15 is the greatest number that divides 45 60 75 without leaving remainder

Answer:

15

Step-by-step explanation:

Let write the factors of each number:

45: (1,3,5,9,15,45)

60:(1,2,3,4,5,6,10,12,15,20,30,60)

75:(1,3,5,15,15,75).

The greatest common factor is 15. So the answer is 15.

A person's email for one day contained a total of 78 messages. The number of spam
messages was two less than four times the number of other messages. How many of
the email messages were spam?

Answers

Answer:

62 of the email messages were spam

Step-by-step explanation:

Let the number of spam and other messages be s and o respectively.

Total number of messages= 78

s +o= 78 -----(1)

s= 4o -2 -----(2)

Substitute (2) into (1):

4o -2 +o= 78

Simplify:

5o -2= 78

+2 on both sides:

5o= 78 +2

5o= 80

Divide both sides by 5:

o= 80 ÷5

o= 16

Since s +o= 78, s= 78 -o.

s= 78 -16

s= 62

Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. (Enter your answer using interval notation. Round your answers to three decimal places.) 1/((1 + 9x)^4) ≈ 1 − 36x

Answers

Answer:

Part 1)

See Below.

Part 2)

[tex]\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)[/tex]

Step-by-step explanation:

Part 1)

The linear approximation L for a function f at the point x = a is given by:

[tex]\displaystyle L \approx f'(a)(x-a) + f(a)[/tex]

We want to verify that the expression:

[tex]1-36x[/tex]

Is the linear approximation for the function:

[tex]\displaystyle f(x) = \frac{1}{(1+9x)^4}[/tex]

At x = 0.

So, find f'(x). We can use the chain rule:

[tex]\displaystyle f'(x) = -4(1+9x)^{-4-1}\cdot (9)[/tex]

Simplify. Hence:

[tex]\displaystyle f'(x) = -\frac{36}{(1+9x)^{5}}[/tex]

Then the slope of the linear approximation at x = 0 will be:

[tex]\displaystyle f'(1) = -\frac{36}{(1+9(0))^5} = -36[/tex]

And the value of the function at x = 0 is:

[tex]\displaystyle f(0) = \frac{1}{(1+9(0))^4} = 1[/tex]

Thus, the linear approximation will be:

[tex]\displaystyle L = (-36)(x-(0)) + 1 = 1 - 36x[/tex]

Hence verified.

Part B)

We want to determine the values of x for which the linear approximation L is accurate to within 0.1.

In other words:

[tex]\displaystyle \left| f(x) - L(x) \right | \leq 0.1[/tex]

By definition:

[tex]\displaystyle -0.1\leq f(x) - L(x) \leq 0.1[/tex]

Therefore:

[tex]\displaystyle -0.1 \leq \left(\frac{1}{(1+9x)^4} \right) - (1-36x) \leq 0.1[/tex]

We can solve this by using a graphing calculator. Please refer to the graph shown below.

We can see that the inequality is true (i.e. the graph is between y = 0.1 and y = -0.1) for x values between -0.179 and -0.178 as well as -0.010 and 0.012.

In interval notation:

[tex]\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)[/tex]

Fatima purchased a new mattress when it was on sale. The sale price was 27% less than the regular price. If the sale price was $409, what was the original price? (Round your answer to the nearest dollar).

Answers

Answer:

560

Step-by-step explanation:

Let x be the original price

27% off

original price minus discount = new price

x - .27x = new price

.73x = new price

.73x = 409

Divide each side by .73

.73x/.73 = 409/.73

x=560.2739726

To the nearest dollar

x = 560

There are 200 ounces in 6 liters. How many milliliter (ml) are in 6 liters? (How to do in dimensional analysis?)

Answers

9514 1404 393

Answer:

  6000 mL

Step-by-step explanation:

The prefix "milli-" is an SI standard prefix meaning 1/1000. So, 1 mL = (1/1000)L.

When doing dimension changes, you always want to use scale factors that have a value of 1, which is to say the numerator is equal to the denominator. For converting liters to milliliters, the scale factor you want will have mL in the numerator and L in the denominator:

  (1 mL)/(1/1000 L)   or   (1000 mL)/(1 L)

To do your conversion, multiply your liter volume by this factor.

  [tex](6\text{ L})\times\dfrac{1000\text{ mL}}{1\text{ L}}=\dfrac{6\times1000\text{ mL$\cdot$L}}{1\text{ L}}=6000\text{ mL}[/tex]

6 liters is 6000 milliliters.

__

You will notice that the dimensions "L" cancel, which is the point of the exercise.

_____

Additional comment

6 L is closer to 202.884 fluid ounces. The conversion factor is ...

  [tex]\dfrac{128\text{ fl oz}}{231\text{ in}^3}\times\dfrac{1\text{ in}^3}{(0.254\text{ dm})^3}\times\dfrac{1\text{ dm}^3}{1\text{ L}}=\dfrac{128\text{ fl oz}}{3.785411784\text{ L}}\quad\text{exactly}[/tex]

Please help!!! what is x: |6n+7|=8

Answers

Answer:

-5/2, 1/6

Step-by-step explanation:

|6n+7|=8

6n+7=8

n=1/6

6n+7=-8

n=-5/2

Answer:

[tex]n=-\frac{5}{2}[/tex] and [tex]n=\frac{1}{6}[/tex]

Step-by-step explanation:

There is no x variable present in the question, but if you are asking for the value of n, I can help with that.

The absolute value function always results in a positive number, so that means 6n+7 can equal 8 or negative 8, and the absolute value function takes care of the rest. First, we will solve for 6n + 7 equaling 8.

[tex]6n+7=8[/tex]

Subtracting 7 from both sides gets us

[tex]6n=1[/tex]

Dividing by 6 from both sides is equal to

[tex]n=\frac{1}{6}[/tex]

Now we will solve for 6n + 7 equaling negative 8.

[tex]6n+7=-8[/tex]

Subtracting 7 from both sides is equal to

[tex]6n=-15[/tex]

Dividing by 6 from both sides gets us

[tex]n=-\frac{15}{6}[/tex]

Simplifying, we have

[tex]n=-\frac{5}{2}[/tex]

Plz help me find side x and y thanks​

Answers

Answer:

2sqrt3

Step-by-step explanation:

Since this seems to be a 45, 45, 90 triangle, x and y are the same.

The hypoteneuse is always the side lengths *sqrt2

We divide the hypoteneuse by sqrt 2 and get sqrt12

sqrt12 simplified is 2sqrt3

According to the U.S. National Center for Health Statistics, there is a 98% probability that a
20-year-old male will survive to age 30.
(a) Using statistical software, simulate taking 100 random samples of size 30 from this
population.
(b) Using the results of the simulation, compute the probability that exactly 29 of the 30 males
survive to age 30.
(c) Compute the probability that exactly 29 of the 30 males survive to age 30, using the
binomial probability distribution.
(d) Using the results of the simulation, compute the probability that at most 27 of the 30 males
survive to age 30.
(e) Compute the probability that at most 27 of the 30 males survive to age 30 using the
binomial probability distribution.
(f) Compute the mean number of male survivors in the 100 simulations of the probability
experiment. Is it close to the expected value?
(g) Compute the standard deviation of the number of
male survivors in the 100 simulations of the probability experiment. Compare the result to the
theoretical standard deviation of the probability distribution

Answers

Answer:

0.03398 or 3.398%

Step-by-step explanation:

-This is a binomial probability problem.

-Given p=0.24, n=100, the probability that exactly 30 people is calculated as:

Hence, the probability that exactly 30 people have hypertension is 0.03398

Write 55% as a fraction in simplest form

Answers

Answer:

11/20

Step-by-step explanation:

Please help! There is 2 questions in this pic! Thank you so much to whoever helps me

Answers

Answer:

[tex]{ \sf{thats \: it}}[/tex]

absolute value means they answer should be positive
ans |-13-17|=30
|-30|=30

find the h.c.f of 2⁴×3×5²×7,5²×3²×5​

Answers

Answer:

To find the HCF we multiply the numbers in the overlapping quadrant together:

Step-by-step explanation:

josue bought 7 pounds of pretzels at a local wholesaler for $16.80. his friend ricardo bought 5 pounds of pretzels at the supermarket for $12.75. Ricardo thinks he got the better deal because $12.75 is less than $16.80. Is Ricardo's reasoning correct? Explain why or why not.

Answers

(josue) 16.8/7 = $2.4 per lb
(ricardo) 12.75/5 = $2.55 per lb

ricardo is incorrect because if you solve for the price per pound ( price/amount ), josue paid $2.40 for each pound of pretzels while ricardo paid $2.55 per pound. ricardo ended up paying more.

the area of an equilateral triangle of side 8cm is
pls i need answer ASAP
I'll mark brainliest for anyone who can help me​

Answers

Side=a=8cm

[tex]\\ \sf\longmapsto Area=\dfrac{\sqrt{3}}{4}a^2[/tex]

[tex]\\ \sf\longmapsto Area=\dfrac{\sqrt{3}}{4}(8)^2[/tex]

[tex]\\ \sf\longmapsto Area=\dfrac{64\sqrt{3}}{4}[/tex]

[tex]\\ \sf\longmapsto Area=16\sqrt{3}[/tex]

[tex]\\ \sf\longmapsto Area=16\times 1.732[/tex]

[tex]\\ \sf\longmapsto Area=27.7cm^2[/tex]

Which of the following fractions is closest to 0? 5/12 , 2/3, 5/6,3/4

Answers

Answer:

5/12

Step-by-step explanation:

5/12 , 2/3, 5/6,3/4

Get a common denominator of 12

5/12, 2/3 *4/4, 5/6*2/2, 3/4 *3/3

5/12, 8/12, 10/12, 9/12

The numerator closest to 0 is the fraction closest to 0

5/12

The lin 2x - 3y = 4 does not passes through the point :

A) (1/2,-1)

B) (2,0)

C) (1, -2/3)

D) (2,-1)

I would really appreciate it if some helps me with this question!

Answers

Answer:

The choose D (2, –1)

2x-3y=4 —> 3y=2X-4 —> y= 2/3x – 4/3

y=mx+b —> So ; m= 2/3 , b= - 4/3

y-intercept :(0, -4/3)

0=2/3x –4/3 —> 2/3x = 4/3 —> X=2

x-intercept ; (2,0)

By drawing a straight line from point 2 on the x-axis and point -4/3 on the y-axis, the points that are on the axis have been extracted, but the point (2,-1) is not on the axis . :)

I hope it helped you ^_^

Help please:)) 2. When shipping ice cream, melting is understandably a big concern. You will notice that ice cream is not generally packaged in a cube-shaped container. A standard container of ice cream contains 1 L, or 1000 cm3 of ice cream,

a. What would be the optimal dimensions (radius and height) to minimize surface area?

b. What would the surface area be?

C. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.​

Answers

Answer:

a. The radius r = 5.42 cm and the height h = 10.84 cm

b. 553.73 cm²

c. i. Beauty ii. Design

Step-by-step explanation:

a. What would be the optimal dimensions (radius and height) to minimize surface area?

The volume of the standard container is a cylinder and its volume is V = πr²h where r = radius of container and h = height of container.

Since V = 1000 cm³,

1000 cm³ = πr²h  (1)

Now, the surface area of a cylinder is A = 2πr² + 2πrh where r and h are the radius and height of the cylinder.

From (1), h = 1000/πr².

Substituting h into A, we have

A = 2πr² + 2πrh

A = 2πr² + 2πr(1000/πr²)

A = 2πr² + 2000/r

To maximize A, we differentiate A with respect to r and equate to zero to find the value of r at which A is maximum.

So, dA/dr = d[2πr² + 2000/r]/dr

dA/dr = d[2πr²]/dr + d[2000/r]/dr

dA/dr = 4πr - 2000/r²

Equating the equation to zero, we have

4πr - 2000/r² = 0

4πr = 2000/r²

r³ = 2000/4π

r = ∛(1000/2π)

r = 10(1/∛(2π))

r = 10(1/∛(6.283))

r = 10/1.8453

r = 5.42 cm

To determine if this value of r gives a minimum for A, we differentiate dA/dr with respect to r.

So, d(dA/dr)/dr = d²A/dr²

= d[4πr - 2000/r²]/dr

= d[4πr]/dr - d[2000/r²]/dr

= 4π  + 4000/r³

Substituting r³ = 2000/4π into the equation, we have

d²A/dr² = 4π  + 4000/r³ = 4π  + 4000/(2000/4π) = 4π  + 2 × 4π = 4π + 8π = 12π > 0

Since d²A/dr² = 12π > 0, then r = 5.42 cm gives a minimum for A.

Since h = 1000/πr²

h = 1000/π(5.42)²

h = 1000/92.288

h = 10.84 cm

So, the radius r = 5.42 cm and the height h = 10.84 cm

b. What would the surface area be?

Since the surface area, A = 2πr² + 2πrh

Substituting the values of r and h into A, we have

A = 2πr² + 2πrh

A = 2πr(r + h)

A = 2π5.42(5.42 + 10.84)

A = 10.84π(16.26)

A = 176.2584π

A = 553.73 cm²

c. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.​

i. Beauty

ii. Design

4. Eric has 54 yards of fencing to use for a flowerbed. Some possible measurements are
shown below. For which flowerbeds does Eric have enough fencing? Color in all the
possible answers.
A.
length = 30 yards
area = 300 square yards
B.
length = 20 yards
width = 5 yards
C.
width = 12 yards
perimeter = 48 yards
D.
length = 26 yards
width = 22 yards
E.
length = 16 yards
width = 14 yards
F.
width = 9 yards
area = 162 square yard

Answers

Answer:

B,C,F

Step-by-step explanation:

A=L*W

P=2L+2W

P≤54

for A, 2L is already greater than 60

B works as 2W+2L in this case is 50

C states that perimeter is less than 54

D doesn't work, as 2L+2W=96

E doesn't work, see above, P=60

F, area=W*L

162/9=18

L=18

2L+2W=48, so F works

Answer:

trả lời:

B,C,F

Giải thích từng bước:

A = L * W

P = 2L + 2W

Trang ≤54

đối với A, 2L đã lớn hơn 60

B hoạt động như 2W + 2L trong trường hợp này là 50

C nói rằng chu vi nhỏ hơn 54

D không hoạt động, vì 2L + 2W = 96

E không hoạt động, xem ở trên, P = 60

F, diện tích =W*L

162/9=18

L =18

2L + 2W = 48, vì vậy F hoạt động

If x+7 is an even number, is x+11 an even number or odd number?

Answers

Answer:

x + 11 is an even number.

Step-by-step explanation:

Even numbers can only be obtained from the sum of two odd numbers or two even numbers. Since we know that x + 7 is even, x + 11 must be even as well.

Does the point (0, 0) satisfy the equation y = 9x?

Answers

Answer:

yes it does

Step-by-step explanation:

because the equation y=9x does not have a y-intercept (all slopes come in the form y=mx+b -- it can be written differently though) and since there is no 'b' that means the y-intercept is 0. So whenever there is no y-intercept, the slope starts at 0.

A clothing manufacturer purchased 50 yd of cotton and 80 yd of wool for a total cost of $1,330. Another purchase, at the same prices, included 75 yd of cotton and 20 yd of wool for a total cost of $895. Find the cost per yard of the cotton and of the wool.

Answers

Answer:

The cotton is $9 per yard and the wool is $11 per yard

Step-by-step explanation:

Create a system of equations where c is the cost per yard for the cotton and w is the cost per yard for the wool.

50c + 80w = 1330

75c + 20w = 895

Solve by elimination by multiplying the bottom equation by -4:

50c + 80w = 1330

-300c - 80w = -3580

Add these together and solve for c:

-250c = -2250

c = 9

Plug in 9 as c into one of the equations, and solve for w:

50c + 80w = 1330

50(9) + 80w = 1330

450 + 80w = 1330

80w = 880

w = 11

The cotton is $9 per yard and the wool is $11 per yard.

2+4? I am omisha please give me answer​

Answers

Answer:

6

Step-by-step explanation:

2+4 = 6

..............

Answer:

Here is your answer omisha

2+4=6

please helpppp.
Which of these could be the graph of F(x) = In x + 3?

A. Graph A
B. Graph B
C. Graph C
D. Graph D

Answers

Answer:

c

Step-by-step explanation:

Try desmos

The Answer should be graph c

What is the range of the function shown in the graph below?

Answers

Answer:

Step-by-step explanation:

Hey there!

The range is the possible y values, so the range of this graph would be all real numbers less than or equal to -5.

Let me know if this helps :)

Solve this equation for x. Round your answer to the nearest hundredth.
8 = In(x + 3) ​

Answers

Answer:

2977.96 =x

Step-by-step explanation:

8 = In(x + 3) ​

Raise each side to the base of e

e^8 = e^ ln(x+3)

e^8 = x+3

Subtract 3 from each side

e^8  -3 = x+3-3

e^8    -3= x

2977.95798 = x

Rounding to the nearest hundredth

2977.96 =x

Answer:

[tex]\displaystyle x = 2977.96[/tex]

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Algebra II

Natural logarithms ln and Euler's number e

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle 8 = ln(x + 3)[/tex]

Step 2: Solve for x

[Equality Properties] e both sides:                                                                   [tex]\displaystyle e^8 = e^{ln(x + 3)}[/tex]Simplify:                                                                                                             [tex]\displaystyle x + 3 = e^8[/tex][Equality Property] Subtract 3 on both sides:                                                 [tex]\displaystyle x = e^8 - 3[/tex]Evaluate:                                                                                                            [tex]\displaystyle x = 2977.96[/tex]

Find the bases for Col A and Nul​ A, and then state the dimension of these subspaces for the matrix A and an echelon form of A below.
A= 1 3 8 2 7 1 3 8 2 7
2 7 20 6 20 --- 0 1 4 2 6
-3 -12 -36 -7 -19 0 0 0 1 4
3 13 40 9 25 0 0 0 0 0
Start 4 By 5 Table 1st Row 1st Column 1 2nd Column 3 3rd Column 8 4st Column 2 5st Column 7 2nd Row 1st Column 2 2nd Column 7 3rd Column 20 4st Column 6 5st Column 20 3rd Row 1st Column negative 3 2nd Column negative 12 3rd Column negative 36 4st Column negative 7 5st Column negative 19 4st Row 1st Column 3 2nd Column 13 3rd Column 40 4st Column 9 5st Column 25 EndTable
tilde
Start 4 By 5 Table 1st Row 1st Column 1 2nd Column 3 3rd Column 8 4st Column 2 5st Column 7 2nd Row 1st Column 0 2nd Column 1 3rd Column 4 4st Column 2 5st Column 6 3rd Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 1 5st Column 4 4st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 0 5st Column 0 EndTable
A basis for Col A is given by
StartSet nothing EndSet
​(Use a comma to separate vectors as​ needed.)
The dimension of Col A is
3.
A basis for Nul A is given by
StartSet nothing EndSet
​(Use a comma to separate vectors as​ needed.)
The dimension of Nul A .

Answers

Answer:

skip counting by 0

Step-by-step explanation:

skipcount by 0 to get to 100 for the third column.

Answer:

its the first graph

Step-by-step explanation:

I got it right bc im cool like that ig

Let S be a set of linearly dependent vectors in Rn. Select the best statement. A. The set S could, but does not have to, span Rn. B. The set S spans Rn, as long as no vector in S is a scalar multiple of another vector in the set. C. The set S cannot span Rn. D. The set S must span Rn. E. The set S does not span Rn if some vector in S is a scalar multiple of another vector in the set. F. The set S spans Rn, as long as it does not include the zero vector. G. none of the above

Answers

Answer:

The set S could, but does not have to, span Rn   ( A )

Step-by-step explanation:

Assume S is a set of linearly dependent vectors in Rn

The best statement from the options is ; The set S could, but does not have to, span Rn

This is because S could span Rn ( as stated in option c ) but will  not necessary span Rn ( as seen in option D )

Graph the image of this triangle after a dilation with a scale factor of 1/2 centered at (−5, 1).

Answers

View attachment below:

what expression is equivalent to (-7²-x-5)-(3x²+x)

Answers

Answer:

-3x² - 2x - 54

Step-by-step explanation:

(-7²-x-5)-(3x²+x)

-7² - x - 5 - 3x² - x

-49 - x - 5 - 3x² - x

-3x² - x - x - 49 - 5

-3x² - 2x - 54

prove:
sin²A-cos²B=sin²B-cos²A ​

Answers

Step-by-step explanation:

thwashm m GB DC GM 3hka it g feeds ygzdkzyzuzjz indin, mi, hn zbe

Answer:

Solution given:

L.H.S

sin²A-cos²B

we have

sin²A=1-cos²A and Cos²B=1-sin²B

now

replacing value

1-cos²A-(1-sin²B)

open bracket

1-cos²A-1+sin²B

keep together like terms

1-1+sin²B-Cos²A

=sin²B-Cos²A

R.H.S

proved.

Solve the equation below:

5x – 11 = 19
x = 4
x = 6
x = 4.4
x = 1.6


pls answer i need help today

Answers

Answer:

x=6

Step-by-step explanation:

5x - 11 = 19

5x = 30

x = 6

20characters

5x = 19+11 5x = 30 x = 30/5 x = 6

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