starting at home, luis traveled uphill to the hardware store for 30 minutes st just 8mph. he then traveled back home along the same path downhill at a speed of 24 mph. what is his average speed for the entire trip from home to the hardware store and back?

Answers

Answer 1

1.
The main formula we use is :

Distance traveled = average Speed * Time,

in short: D = S * T

2.
"luis traveled uphill to the hardware store for 30 minutes at speed 8mph."

we have the speed and the time = 30 min = 1/2 h

so we can find distance:

D=ST=8 (mi/h) * 1/2 (h) = 4 mi

3.
Now we have D, and the speed 24 mph, so we can find the time it takes Luis to travel back home:

D=S*T

T= D/S = 4 (mi) / 24 (mi/h) =1/6 h

4.

The total distance is D+D = 4 +4 = 8 (mi)

the total time is 1/2 +1/6 = 3/6 + 1/6 = 4/6 = 2/3 (h)

So we can find the average speed of the entire trip is:

S=8 / (2/3)= 8* (3/2)=4*3=12 (mph)

Answer : 12 mph

Related Questions

Three counters are used for a board game.If the counters are tossed,how many ways can at least one counter with Side A occur?

Answers

We use the equation for repeated trials written below:

Probability = n!/r!(n-r)! * p^(n-r) * q^r

The p is the probability of getting a side A in one toss. Since a counter has only two side, p = 0.5. The q is the probability of not getting side A in one toss, which is also q = 0.5. Now, r is the number of success per n trials. There are 3 tosses so, n=3. The question is getting "at least 1" counter. So, r=1, r=2 and r=3.

Probability for r=1: 3!/1!(3-1)! * (0.5)^(3-1) * (0.5)^1= 0.375
Probability for r=2: 3!/2!(3-2)! * (0.5)^(3-2) * (0.5)^2= 0.375
Probability for r=1: 3!/3!(3-3)! * (0.5)^(3-3) * (0.5)^3= 0.125

Total probability = 0.375 + 0.375 + 0.125 = 0.875

True or False: The sample size you need to estimate the population distribution should always be at least 10% of the population size.

Answers

Final answer:

False. The sample size needed to estimate the population distribution should not always be at least 10% of the population size.

Explanation:

False. The statement that the sample size needed to estimate the population distribution should always be at least 10% of the population size is not true. The size of the sample needed depends on various factors such as the original population, the level of confidence desired, and the margin of error allowed. For example, if the population is large and diverse, a smaller sample may still provide a reliable estimate of the population distribution. It is important to consider statistical concepts such as normal distribution and sampling techniques when determining the appropriate sample size.

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A total of 504 tickets were sold for the school play. They were either adult tickets or student tickets. There were 54 more student tickets sold than adult tickets. How many adult tickets were sold?

Answers

a + s = 504
s = a + 54

a + (a + 54) = 504
2a + 54 = 504
2a = 504 - 54
2a = 450
a = 450/2
a = 225 <=== adults

a + s = 504
225 + s = 504
s = 504 - 225
s = 279 <=== students

Final answer:

Using algebra, we find that 225 adult tickets were sold out of a total of 504 tickets.

Explanation:

Let's denote the number of adult tickets as x. Since there were 54 more student tickets sold than adult tickets, we can represent the number of student tickets as x + 54. The total number of tickets sold is 504, so we set up the equation x + (x + 54) = 504.

Combining like terms, we get 2x + 54 = 504. Subtracting 54 from both sides gives us 2x = 450. Finally, dividing both sides by 2 gives us x = 225.

Therefore, 225 adult tickets were sold.

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222+203 is rounded up to what?

Answers

[tex]222: 220 \\ 203 = 200 \\ \\ 222 + 203 = 425 \\ 220 + 200 = 420 \\ \\ \\ \\ Good \\ luck \\ on \\ your \\ assignment \\ \\ enjoy \\ your \\ day \\ \\ \\ MeIsKaitlyn :)[/tex]

[tex]Remember [/tex]↓

[tex]1-5[/tex] would rounded [tex]downward [/tex]
[tex]6-9[/tex] would be rounded [tex]upward [/tex]

Sara must plant 340 trees. In the past 6 days Sara planted 204 trees. If she continues at this rate, how many more days will it take her to plant all the trees?

Answers

204/6 = 34 trees a day. 340-204 =136 trees left to plant. 136/34 = 4 4 days

A bird feeder is in the shape of a cylinder. It has a volume of about 100 cubic inches. It has a radius of 2 inches. What is the approximate height of the bird feeder? Use 3.14 for pi

Answers

volume = pi x r^2x h

100 = 3.14 x 2^2 x h

100 =3.14 x 4 x h

100 = 12.56 x h

h = 100/12.56 = 7.9617

the height is approximately 8 inches tall

5. Simplify (15x2 – 24x + 9) ÷ (3x – 3) = ?

Answers

The likelihood is that because we've been told to divide the quadratic by a linear expression, it may perfectly factorize and the linear expression is, in fact, one of the two factors so we can use it to find the other factor by inspection:
3x would have to multiply by 5x to get the 15x² term in the quadratic.
-3 would have to multiply by -3 to get the 9 term in the quadratic.
The second factor would, therefore, be (5x - 3) if the linear divisor is actually a factor. In this case, it is, which we can confirm by expanding.
15x² - 24x + 9 = (3x - 3)(5x - 3)
So:
(15x2 – 24x + 9) ÷ (3x – 3) = 5x - 3

which number produces a rational number when added to 0.5

Answers

Let, the number be x

Therefore, x +0.5= p/q where q is non zero and (p, q) co-prime.

Then, x= -0.5 + (p/q)

now you can substitute any value of p and q to get x.

Answer:

Any rational number.

Step-by-step explanation:

∴ [tex]x+0.5[/tex] is rational if and only if x is rational.

To proveL: we proceed as follows:

Suppose that [tex]x+0.5[/tex] is rational.

Then there are some integers p , q with [tex]q\neq 0[/tex] such that

[tex]x+\frac{1}{2}=\frac{p}{q}[/tex]

Subtract both sides by [tex]\frac{1}{2}[/tex], we get

[tex]x=\frac{p}{q}-\frac{1}{2}=\frac{2p-q}{2q}[/tex] which is rational.

Conversely, if x is rational, then there are integers a,b with b>0 such that [tex]x=\frac{a}{b}[/tex] then we have,

[tex]x+\frac{1}{2}=\frac{a}{b}+\frac{1}{2}=\frac{2a+b}{2b}[/tex] which is also a rational.

A cold front moved in last weekend. In eight hours overnight, the temperature outside dropped from 14 degrees to -10. What was the average temperature change for each hour ?

Answers

[tex]\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -------------------------------\\\\ \begin{cases} x_1=0\\ x_2=8 \end{cases}\implies \cfrac{f(8)-f(0)}{8-0}\implies \cfrac{14-(-10)}{8-0}\implies \cfrac{14+10}{8}\implies \cfrac{3^o}{1hr}[/tex]

A company made 4 million in the second quarter this is 1/3 more then it made in the first quarter and 4/5 of what it made in the third quarter how much did the company make in all 3/4 combined

Answers

In this problem, you have to find the total profit the company made in the three quarters which makes up 3/4 of the whole. In the second quarter, the profit is 4 million. Let x be the profit in the first quarter. Following the description,

4 = (1+1/3)x
x = 3 million

Thus, the second quarter made 5.33 million profit.

For the third quarter, let's assign it to the y variable. Following the description,

4 = (4/5)(y)
y = 5 million

Thus, the total profit is 4 + 3 + 5 = 12 million

Bill's Roast Beef sells 5 times as many sandwiches as Pete's Deli. The difference between their sales is 360 sandwiches. How Many did each sell ?

Answers

b - p = 360
b = 5p

5p - p = 360
4p = 360
p = 360/4
p = 90 <== Pete's deli

b = 5p
b = 5(90)
b = 450 <== Bill's Roast Beef

Answer:

5y-y =360

4y =360

y= 90 sandwiches by Pete's deli

x= 5(90) = 450 sandwiches by Bills Roast Beef

Step-by-step explanation:

the base of this solid crate has an area of 6 square centimeters the height of the crate is 4 meters what is the volume of the crate

Answers

[tex]Area Of Cuboid = length*width*height[/tex]

The length * width is the area of the base, so:

[tex]Area Of Cuboid = base*height = 6 * 4 = 24 meters^3[/tex]

Answer:

2 × 10³ cm³

Step-by-step explanation:

Given data

Area of the base: 6 cm²Height of the crate: 4 m = 4 × 10² cm

Considering the crate is a cuboid, its volume (V) is:

V = length × width × height

Since

area of the base = length × width

We get

V = area of the base × height

V = 6 cm² × 4 × 10² cm

V = 2.4 × 10³ cm³ ≈ 2 × 10³ cm³ (we round off to 1 significant figure)

Find an approximation of the area of the region R under the graph of the function f on the interval [-1, 2]. Use n = 6 subintervals. Choose the representative points to be the left endpoints of the subintervals. f(x) = 7 - x2

Answers

The approximation of the area of the region R under the graph of the function is 18.625 square units.

In this question we must calculate the approximate area ([tex]A[/tex]) below the curve by means of Riemann sums with left endpoints, whose expression is described below:

[tex]A = \Delta x \cdot \Sigma\limits^{n-1}_{i=0} f(a + i\cdot \Delta x)[/tex], for [tex]x \in [a,b][/tex] (1)

[tex]\Delta x = \frac{b-a}{n}[/tex] (2)

Where:

[tex]a[/tex] - Lower bound[tex]b[/tex] - Upper bound[tex]n[/tex] - Number of subintervals[tex]i[/tex] - Index

If we know that [tex]a = -1[/tex], [tex]b = 2[/tex], [tex]n = 6[/tex] and [tex]f(x) = 7 - x^{2}[/tex], then the approximate area is:

[tex]\Delta x = \frac{2-(-1)}{6}[/tex]

[tex]\Delta x = 0.5[/tex]

[tex]A = 0.5\cdot [f(-1) + f(-0.5)+f(0)+f(0.5)+f(1)+f(1.5)][/tex]

[tex]A = 0.5\cdot (6+6.75+7+6.75+6+4.75)[/tex]

[tex]A = 18.625[/tex]

The approximation of the area of the region R under the graph of the function is 18.625 square units.

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Sales tax on an item is directly proportional to the cost of the item purchased. If the tax on a $500 item is $30, what is the sales tax on a $900 item?

Answers

30 / 500 = x / 900....$ 30 tax / 500 item = $ x tax on 900 item
cross multiply
(500)(x) = (900)(30)
500x = 27000
x = 27000/500
x = 54 <===

Answer: $54

Step-by-step explanation:

The equation to show the direct variation in two quantities x and y is given by :-

[tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]

The tax on a $500 item is $30.

Let 'x' be the sales tax on a $900 item.

Then , we have the following equation:-

[tex]\dfrac{x}{900}=\dfrac{30}{500}\\\\\Rightarrow\ x=\dfrac{900\times30}{500}\\\\\Rightarrow\ x=54[/tex]

Hence, the sales tax on a $900 item = $54

Suppose Q and R are independent events. Find P(Q and R) if P(Q) =4/5 and P(R) =4/11

Answers

Since Q and R are independent, this means P(Q and R) = P(Q)*P(R)

P(Q and R) = P(Q)*P(R)
P(Q and R) = (4/5)*(4/11)
P(Q and R) = (4*4)/(5*11)
P(Q and R) = 16/55

Linda deposits $500 into an account that pays simple interest at a rate of 4% per year. How much interest will she be paid in the first 4 years?

Answers

Assuming that she deposits $500 and forgets about it, here is what she would get after 4 years:

Year 1 - $500 * 1.04 = $520
Year 2 - $520 * 1.04 = $540.80
Year 3 - $540.80 * 1.04 = $562.432
Year 4 - $562.432 * 1.04 = $584.92928

Aftere four years. Linda would be paid $84.93

Simplify the expression. 33 • 32 + 12 ÷ 4

Answers

Final answer:

The expression 33 • 32 + 12 ÷ 4 simplifies to 1059.

Explanation:

To simplify the expression 33 • 32 + 12 ÷ 4, we follow the order of operations - performing multiplication and division before addition.

Multiply 33 and 32 to get 1056.Divide 12 by 4 to get 3.

Now we can add the results: 1056 + 3 = 1059.

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richerd works at an ice cream shop. regular cones get two scopes of ice cream and large cones get three scoops. One hot saturday richard scooped 234 regular cones and 156 large cones one scoop of ice cream is 3 ounces a tub of ice cream is 10 pounds how many tubs of ice cream did richerd use to make the cones?

Answers

234 x 2 = 468 scoops

156 x 3 = 468 scoops

468 + 468 = 936 total scoops

936 x 3 = 2808 ounces

16 ounces = 1 pound

2808/16 = 175.5 pounds

175.5/10 = 17.55 tubs

round answer as needed

the length of the hypotenuse is:

6.
12.
36.
[tex]6 \sqrt{3[/tex]

Answers

cos 60° = 1/2
1/2 = 6/x
1/2x=6
x = 6X 2 = 12
The length of the hypothenuse is 12

A figure has a vertex at (5, 2). If the figure has line symmetry about the y-axis, what are the coordinates of another vertex of the figure?

Answers

The answer will be (-5, 2)

Answer:

[tex](-5,2)[/tex]

Step-by-step explanation:

We have been given that a figure has a vertex at (5,2). The figure has line symmetry about the y-axis.

We know that if a figure is symmetric about y-axis, then its x-coordinate changes to opposite sign and y-coordinate remains same.

We can see that x-coordinate of our given point is 5, so x-coordinate of another vertex of the figure would be -5.

Therefore, the point [tex](-5,2)[/tex] is symmetric about y-axis for our given point.

Round to the nearest while decimal 6.7

Answers

If you meant "[tex]whole [/tex]" instead of "[tex]while [/tex]"

Then, [tex]six [/tex] is rounded [tex]1ten[/tex] & [tex]seven[/tex] is rounded to [tex]ten [/tex]

Your answer: [tex]7[/tex]

[tex]good\\luck \\ on \\ your \\ assignment \\ \\ \\ \\ enjoy \\ your \\ day \\ \\ \\ \\ \\ \\ MeIsKaitlyn :)[/tex]

A farmer is going to plant carrots on 5 3/14 acres, corn on 4 23/42 acres and peppers on 2 5/21 acres. If each acre requires 6 bags of fertilizer, how many bags of fertilizer does the farmer need to plant all the acres?

Answers

hmm we do the same as before, you convert the mixed fractions to "improper fractions" by simply making the numerator the product and sum like you saw it

so

[tex]\bf 5\frac{3}{14}\implies \cfrac{5\cdot 14+3}{14}\implies \cfrac{73}{14} \\\\\\ 4\frac{23}{42}\implies \cfrac{4\cdot 42+23}{42}\implies \cfrac{191}{42} \\\\\\ 2\frac{5}{21}\implies \cfrac{2\cdot 21+5}{21}\implies \cfrac{47}{21}\\\\ -------------------------------\\\\ \cfrac{73}{14}+\cfrac{191}{42}+\cfrac{47}{21}\impliedby \textit{our LCD is just 42}\implies \cfrac{3\cdot 73+1\cdot 191+2\cdot 47}{42} \\\\\\ \cfrac{219+191+94}{42}\implies \cfrac{504}{42}\implies \cfrac{12}{1}\implies 12[/tex]

now, that's how many acres the farmer has in total
now, if each acre takes 6 bags of fertilizer, well, you surely know how much that is.

What is the limit for lim x -> 2 int x

Answers

we are asked in the problem to determine the limit of integral of x dx as x approaches to 2. In this case, the first step to do is to integrate first the function. The integral of x dx by the power rule is equal to x^(n+1)/n+1. In this case, since n is equal to 1 from the given, then integral of x dx is equal to x^2/2. To evaluate the limit of x as x approaches to 2, we just have to substitute x by 2, that is
2^2 / 2 equal to 2. Hence the answer to this problem is equal to 2.

One school survey showed that 3 out of 5 students own a pet. Another survey showed that 6 out of 11 students owned a pet. Are these results equivalent? Explain your reasoning.

Answers

no they are not because 3/5 is not equal to 6/11. if they were equal, it would be 6/10

3/5 own a pet means that (0.6) or 60% own a pet
6/11 own a pet means that (0.545) or 54.5% own a pet

Conclusion, in the 1st class more people 60% own a pet whereas in the second class only 54.5% have a pet

A total of 487 tickets were sold for the school play. They were either adult tickets or student tickets. There were 63 fewer student tickets sold than adult tickets. How many adult tickets were sold?

Answers

s=a-63

s+a=487, using s from above in this equation you get:

a-63+a=487 combining like terms

2a-63=487 adding 63 to both sides

2a=550 dividing both sides by 2

a=275

So there were 275 adult tickets sold.

Final answer:

To determine the number of adult tickets sold for the school play, a system of equations is set up and solved, revealing that 275 adult tickets were sold.

Explanation:

To find the number of adult tickets sold for the school play, we need to set up a system of equations based on the information given. Let x represent the number of adult tickets and y represent the number of student tickets. According to the problem, the following two statements are true:

The total number of tickets sold is 487: x + y = 487

There were 63 fewer student tickets sold than adult tickets: y = x - 63

We can substitute the second equation into the first to find the value of x:

x + (x - 63) = 487

2x - 63 = 487

2x = 487 + 63

2x = 550

x = 275

Therefore, 275 adult tickets were sold.

How many millimeters are there in 5 meters?

Answers

1 meter = 1000 mm

so 5 meters = 5 x 1000 = 5,000 millimeters

There are 5000 milimeters in 5 meters because the prefix milli stands for 1000.

What is the slope of a line that passes through the following points (-3,8) and (2,1)

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ 8}})\quad % (c,d) &({{ 2}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-8}{2-(-3)}\implies \cfrac{1-8}{2+3}\implies \cfrac{-7}{5}[/tex]

Hello!

Step-by-step explanation:

Slope: [tex]\frac{Y^2-Y^1}{X^2-X^1}=\frac{rise}{run}[/tex]

[tex]\frac{1-8=-7}{2-(-3)=2+3=5}=\frac{-7}{5}=-\frac{7}{5}[/tex]

Slope is -7/5

Answer is -7/5

Hope this helps!

Thanks!

-Charlie

A marina is in the shape of a coordinate grid. Boat A is docked at (4.2, −2) and Boat B is docked at (−5.2, −2). The boats are ____ units apart. A) 6.2 B) 7.2 C) 9.4 D) 13.4

Answers

The distance between any two points is:

d^2=(x2-x1)^2+(y2-y1)^2

d^2=(4.2--5.2)^2+(-2--2)^2

d^2=(9.4)^2

d=9.4

Answer:

Your answer will be D.

Step-by-step explanation:

I did it on the test and got it correct.

Express the volume of a cone, V, as a function of its radius, r, if the radius is 1/5 of the height.

Answers

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=radius\\ h=height\\ ------\\ r=\frac{h}{5}\implies 5r=h \end{cases}\implies V=\cfrac{\pi r^25r}{3} \implies V=\cfrac{5\pi r^3}{3}[/tex]

In how many different ways can you make exactly 0.75 using only nickles dimes and quarters if you have at least one of each coin?

Answers

There are 18 different ways to make 75 cents

18 different ways to make 75 cents

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