Answer:
No.
[tex]\text{Average rate} = \dfrac{\text{Total distance}}{\text{Total time}} = \dfrac{r_{1}t_{1} + r_{2}t_{2}}{t_{1} + t_{2}}\\\\= \text{50.91 mi/h}[/tex]
Step-by-step explanation:
First leg: d = r₁t₁
Second leg: d = r₂t₂
r₁t₁ = r₂t₂
Total distance: 2d = r₁t₁ + r₂t₂
Total time: t = t₁ + t₂
1. Equation for average rate
[tex]\text{Average rate} = \dfrac{\text{Total distance}}{\text{Total time}} = \dfrac{r_{1}t_{1} + r_{2}t_{2}}{t_{1} + t_{2}}[/tex]
2. Average rate
Since r₁t₁ = r₂t₂,
[tex]t_{1} = \dfrac{r_{2}t_{2}}{r_{1}} = \frac{40}{70}t_{2} = \frac{4}{7}t_{2}\\\\\text{Average rate} = \dfrac{2r_{2}t_{2}}{\frac{4}{7}t_{2} + t_{2}} = \dfrac{2 \times 40t_{2}}{\frac{4t_{2}+ 7t_{2}}{7}}= 80t_{2} \times\frac{7}{11t_{2}} = \dfrac{560}{11}\\\\= \textbf{50.91 mi/h}[/tex]
We cannot say truthfully that the average rate is 55 mi/h.
The average rate of a body is the total distance travelled divided by the total time.
The cheetah runs at an average rate of 50.91mph, not 55mph
Let
[tex]d \to[/tex] distance
[tex]r \to[/tex] average rate
[tex]t \to[/tex] time
Given that:
[tex]d = r_1t_1 = r_2t_2[/tex]
So, we have:
[tex]r_1 = 70[/tex]
[tex]r_2 = 40[/tex]
The average rate (r) is calculated as follows:
[tex]r = \frac{Total\ Distance (D)}{Total\ Time (T)}[/tex]
Where:
[tex]D=d + d[/tex]
[tex]D = r_1t_1 + r_2t_2[/tex]
and
[tex]T =t_1 + t_2[/tex]
So, the average rate is:
[tex]r =\frac{r_1t_1 + r_2t_2}{t_1 + t_2}[/tex]
Recall that:
[tex]D = r_1t_1 + r_2t_2[/tex]
[tex]r_1t_1 = r_2t_2[/tex]
Make [tex]t_2[/tex] the subject
[tex]t_2 = \frac{r_1t_1}{r_2}[/tex]
Substitute values for [tex]r_1[/tex] and [tex]r_2[/tex]
[tex]t_2 = \frac{70t_1}{40}[/tex]
So, we have:
[tex]r =\frac{r_1t_1 + r_2t_2}{t_1 + t_2}[/tex]
[tex]r = \frac{70t_1 + 40 \times \frac{70t_1}{40}}{t_1 + \frac{70t_1}{40}}[/tex]
[tex]r = \frac{70t_1 + 70t_1}{t_1 + \frac{70t_1}{40}}[/tex]
[tex]r = \frac{140t_1}{t_1 + \frac{70t_1}{40}}[/tex]
Factor out t1
[tex]r= \frac{140t_1}{t_1(1 + \frac{70}{40})}[/tex]
[tex]r = \frac{140}{(1 + \frac{70}{40})}[/tex]
[tex]r = \frac{140}{\frac{40+70}{40}}[/tex]
[tex]r= \frac{140}{\frac{110}{40}}[/tex]
Rewrite as:
[tex]r = \frac{140 \times 40}{110}[/tex]
[tex]r = 50.91mph[/tex]
Hence, the cheetah's average rate is 50.91mph, not 55mph
Read more about distance, average rates and time at:
https://brainly.com/question/22457482
what is the sum of (2x - 6) + (4x - 4)
Answer:
6x - 10
Step-by-step explanation:
2x + 4x = 6x
6 + 4 = 10
6x - 10
What is the equation of a line with a slope of six and passes through the coordinates 0,1
Answer:
y = 6x + 1
Step-by-step explanation:
Use the point slope equation:
y - y1 = m( x - x1 )
y - 1 = 6 ( x - 0)
y - 1 = 6x
y = 6x + 1
Please help me and Thank you
Q3. Explain any one congruency Property with real world example
Which pair of angles are vertical angles?
Answer:
angles 1 and 4, and angles 2 and 3
Answer:
1 and 4, 2 and 3
Step-by-step explanation:
Does this actually seem difficult? If you're in High school, because i'm in Middle school and I can answer this question.
Have a feeling it’s 3X am i correct ??
Answer:
D
Step-by-step explanation:
The volume of a cube can be found by multiplying together all of the side lengths by each other, or:
[tex]x\cdot x \cdot x=x^3[/tex]
Therefore, the correct answer is D. Hope this helps!
Answer:
D. x^3.
Step-by-step explanation:
The volume = length*width*height
= x * x * x
= x^3.
When you use the distance formula you are calculating the length of the _____ of a right triangle
Answer:
hypotenuse
Step-by-step explanation:
When you use the distance formula you are calculating the length of the hypotenuse of a right triangle.
When using the distance formula, you are making a right triangle whose hypotenuse connects two given points.
Answer: The blank would be hypotenuse if I’m not mistaken!
Need help please help me
Answer:
0.000000207 in scientific notation = 2.07 × 10^-7
Remember it has to have one number before the decimal.
8.2 * 10^-7 in standard form = 0.00000082
YOu have to move the decimal back.
In the first box the answer is 2.07 × 10^-7.
In the second box the answer is 0.00000082.
Lakesha is taking three of her friends to see the latest movie. Each ticket is $5.50, and she is paying for all four tickets. How much money does Lakesha need to bring to pay for all of the tickets? A. $16.50 B. $22.00 C. $49.50 D. $55.00
Answer: $22
Step-by-step explanation:
$5.50 * 4 = 22
Answer:
B. $22.00
Step-by-step explanation:
The expression you need to set up is 5.5 times 4, since she needs to pay 4 tickets and each is $5.50. After you multiply, you should get 22, which is the answer.
Which words or variables mean OUTPUT? Select all possible answers. help me out
a. domain
b .range
c .x
d .y
e. f(x)
no jk drtyguhiytr5tyguhigyft fyguhijk
Answer:
1232
Step-by-step explanation:
13/91= 176/x
1/7=176/x
x= 176*7
x= 1232 bass
HELP ME OUT! A student dissolves 1 gram of sugar in 10 grams of water. She then determines the mass of the solution. What is the mass of the dissolved sugar and water?
Answer:
The mass of the dissolved sugar and water is 11 g.
Step-by-step explanation:
When a substance is dissolved in another, they are mixed together forming a new one, therefore the new substance's mass must be the same as the sum of the individual mass of each substance mixed, because there are no leaks. In this case, there are two substances being mixed, the water which have a mass of 10 grams and the sugar which have a mass of 1 gram, therefore the final solution's mass must be equal to 11 g.
Please look at photo and solve for y
Answer:
y = 45
Step-by-step explanation:
70 and y + 25 are corresponding angle and corresponding angles are equal when we have parallel lines cut by a transversal
70 = y+25
Subtract 25 from each side
70-25 = y
45 = y
[tex]answer \\ y = 45 °\\ solution \\ y + 25 = 70(being \: corresponding \: angles) \\ or \: y = 70 - 25 \\ y = 45 °\\ hope \: it \: helps[/tex]
solve for x. 7(x-3)+3(4-x)=-8
Answer:
x=1/4
Step-by-step explanation:
1.distribute the 7 and 3 into parentheses
2. combine like terms
3. add 9 on both sides
4. divide both sides by 4
x=1/4
hope this helped!
Answer:
x = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
7(x-3)+3(4-x)= -8
Expand 7(x-3) and 3(4-x)
i.e. 7x-21+12-3x= -8
4x-9=-8
Collect like terms
4x= -8+9
4x= 1
x = [tex]\frac{1}{4}[/tex]
Hope this helps!!!
(20 POINTS AND BRAINLIEST)
The Timothy Edwards Matinee Program has a one time fee of $25 to join the bowling club. It then costs $6 each time the club goes bowling.
a) Write an equation in slope-intercept form for the cost y of joining the club and going on x bowling trips.
b) Sarah wants to join and go bowling 10 times. How much will she pay?
c) Tyler wants to join the club and go bowling 7 times. How much will he have to pay?
Answer:
a) The equation is y = 6x + 25 since the 25 is the initial fee.
b) We plug in 10 for x. 6 * 10 + 25 = $85.
c) We plug in 7 for x and get 6 * 7 + 25 = $69.
Answer:
see below
Step-by-step explanation:
a) y = 6x + 25 (because the 25 is the initial fee)
b) x = 10, so:
= 6 * 10 + 25
= $85
c) x = 7, so:
= 6 * 7 + 25
= $69
Hope this helps!
Aubrey's parents are signing her up for summer camps. If there are 5 weeklong camps to choose from, in how many orders can they select 3 of the camps to sign her up for?
Answer:
This can be done in a total of 10 ways
Step-by-step explanation:
This is a selection problem.
What we are trying to do is to properly select 3 week long camps from the total 5. we are looking for the number of ways in which we can do this.
Now, since this is a selection problem, the proper mathematical term and approach to use is the COMBINATION
Mathematically, having r items to pick from a total n, the number of ways to do this is nCr ways
which is mathematically equivalent to;
n!/(n-r)!r!
now applying this to the problem at hand, what we have is 5C3
= 5!/(5-3)!3! = 5!/2!3! = (5 *4)/2 = 20/2 = 10 ways
Raj’s farmhouse is 1245km away from hiswarehouse. Daily he drivesa certain distance and then his friend Rohantakes aturn to drive his carfor 412km distance to reach thewarehouse.(a)What distance does Raj drivedaily?
Answer:
Step-by-step explanation:
Subtract the distance driven by Rohan from the total distance
Distance driven by Raj = 1245 - 412
= 833 km
what does it mean by bisecting angles
Answer: A line that splits an angle into two equal angles.
Step-by-step explanation: ("Bisect" means to divide into two equal parts.)
Bisecting angles: A line that splits an angle into two equal angles.
There are 200 carpenters in a crew. On a certain day, 150 were present. What percent showed up for work?
what is the answer to -2x- x +8
Answer:
[tex]x=\frac{8}{3}[/tex]
Step-by-step explanation:
I don't know if this has an =0 at the end, but I assume it does.
This is how you would work it out:
[tex]-2x-x+8=0\\-3x=-8\\x=\frac{-8}{-3} \\x=\frac{8}{3}[/tex]
The floor of the cage measures 11 yardyard wide by 66 feetfeet long. One bag of shavings covers 55 square feetfeet. How many bags will HarperHarper have to buy to cover the floor of the cage? Explain.
Answer:
3 3/5 bags
Step-by-step explanation:
We have to find the surface area of the floor of the cage first.
The cage measures 1 yard wide by 6 feet long.
1 yard = 3 feet
The floor of the cage is rectangular, so, the surface area of the floor of the cage is therefore:
3 * 6 = 18 square feet
One bag of shavings covers 5 square feet.
To find the number of bags we need to cover the floor, we divide the surface area of the floor by the number of bags per square feet.
The number of bags needed for the floor of the cage is therefore :
18 / 5 = 3 3/5 bags
Florence Tyler invests $5000 in a 1-year CD that earns interest at an annual rate of 4% compounded monthly. The amount per $1.00 is 1.040742. What is the interest earned?
Answer:
$203.71
Step-by-step explanation:
Given;
Principal = $5,000
The amount per $1.00 is given as 1.040742
The total amount earned is equal to the product of the principal and the amount per dollar.
A = Principal × amount per dollar
Substituting the values;
A = $5000 × 1.040742
A = $5203.71
Interest earned = Total amount earned - principal
Interest earned = $5203.71 - $5000
Interest earned = $203.71
Can I get help with this?
Answer:
Around 13.7
Step-by-step explanation:
The cosine of an angle in a right triangle is equivalent to the length of the adjacent side divided by the length of the hypotenuse. In this case, this means:
[tex]\cos 70= \dfrac{x}{40} \\\\x=40\cdot \cos 70\approx 13.7[/tex]
Hope this helps!
the triangle bounded by the lines y = o, y = 2x
and y = -0.5x + k with k positive is equal to 80 square untits find k
Answer
k = 3.575.
Step-by-step explanation:
Which graph represents the function f(x) = 1/x+3
-2
Answer:
Step-by-step explanation:
To eliminate ambiguity please use parentheses when typing a function like this one. I'm going to assume that you meant
f(x) = 1 / (x + 3) - 2
Start with the graph of y = 1/x. Its vertical asymptote is the line x = 0. The graph never touches the x-axis.
Translating the entire graph 3 units to the left will give you the function
h(x) = 1 / (x + 3).
Translating the above graph 2 units down will give you the desired function g(x) = 1 / (x + 3) - 2.
Answer:
Graph B on Edge2022.
Have a great day.
A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $80 million after 4 years, while profits increased $60 million per year. Select the correct graph of this function. A B C D
Step-by-step explanation:
Given a point (4,80) and a slope, m = 60, these can be used to formulate the equation of the graph. Using the point-slope formula:
y - y1 = m(x - x1)
y - 80 = 60(x - 4)
y - 80 = 60x - 240
y = 60x -160
Taking the x and y-intercepts:
At y = 0
0 = 60x - 160
x = 2.7
At x = 0
y = 60(0) - 160
y = -160
The answer is A. Hope this helps ✌️
What’s the cosine of U?
Step-by-step explanation:
The cosine of U is equal to the adjacent side divided by the hypotenuse.
cos(U) = 28/53
You can simplify it from there.
Can anyone one give me the answer for this??!! Please hurry up to
Answer:
N=6
Step-by-step explanation:
As the answer is 6 and we already have 3 so the other half is 3. Half of 6 is three so n=6
Please help someone……………………
Answer:
I think it's number one
Step-by-step explanation:
Macy’s was offering a Memorial Day sale. The price of a shirt is now $21.25. The original price was $25. What is the percent of change from the original to the sale price?
Answer:
The original price drops by 15%.
Step-by-step explanation:
What was the drop in price? To answer that, subtract $21.25 from $25, which results in $3.75.
Now compare $3.75 to the original price, $25, through division, as follows:
$3.75
-------------- * 100% = 15%
$25
The original price drops by 15%.
