Going from point A to point B, the cheetah traveled at an average rate of 70 mph. Returning to point A, the cheetah traveled at an average rate of 40 mph. Can we say that this cheetah’s average rate was 55 mph? The average rate for the trip is equal to the total distance traveled divided by the total time traveled. The following equations represent the distance traveled on each leg of the trip. First leg of trip: d=r_1 t_1 Second leg of trip: d=r_2 t_2 Write an equation for the average rate for the trip. Remember, the cheetah runs from point A to point B and back to point A.
Answers
Answer:
No.
\(\text{Average rate} = \dfrac{\text{Total distance}}{\text{Total time}} = \dfrac{r_{1}t_{1} + r_{2}t_{2}}{t_{1} + t_{2}}\\\\= \text{50.91 mi/h}\)
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
\(\text{Average rate} = \dfrac{\text{Total distance}}{\text{Total time}} = \dfrac{r_{1}t_{1} + r_{2}t_{2}}{t_{1} + t_{2}}\)
2. Average rate
Since r₁t₁ = r₂t₂,
\(t_{1} = \dfrac{r_{2}t_{2}}{r_{1}} = \frac{40}{70}t_{2} = \frac{4}{7}t_{2}\\\\\text{Average rate} = \dfrac{2r_{2}t_{2}}{\frac{4}{7}t_{2} + t_{2}} = \dfrac{2 \times 40t_{2}}{\frac{4t_{2}+ 7t_{2}}{7}}= 80t_{2} \times\frac{7}{11t_{2}} = \dfrac{560}{11}\\\\= \textbf{50.91 mi/h}\)
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
\(d \to\) distance
\(r \to\) average rate
\(t \to\) time
Given that:
\(d = r_1t_1 = r_2t_2\)
So, we have:
\(r_1 = 70\)
\(r_2 = 40\)
The average rate (r) is calculated as follows:
\(r = \frac{Total\ Distance (D)}{Total\ Time (T)}\)
Where:
\(D=d + d\)
\(D = r_1t_1 + r_2t_2\)
and
\(T =t_1 + t_2\)
So, the average rate is:
\(r =\frac{r_1t_1 + r_2t_2}{t_1 + t_2}\)
Recall that:
\(D = r_1t_1 + r_2t_2\)
\(r_1t_1 = r_2t_2\)
Make \(t_2\) the subject
\(t_2 = \frac{r_1t_1}{r_2}\)
Substitute values for \(r_1\) and \(r_2\)
\(t_2 = \frac{70t_1}{40}\)
So, we have:
\(r =\frac{r_1t_1 + r_2t_2}{t_1 + t_2}\)
\(r = \frac{70t_1 + 40 \times \frac{70t_1}{40}}{t_1 + \frac{70t_1}{40}}\)
\(r = \frac{70t_1 + 70t_1}{t_1 + \frac{70t_1}{40}}\)
\(r = \frac{140t_1}{t_1 + \frac{70t_1}{40}}\)
Factor out t1
\(r= \frac{140t_1}{t_1(1 + \frac{70}{40})}\)
\(r = \frac{140}{(1 + \frac{70}{40})}\)
\(r = \frac{140}{\frac{40+70}{40}}\)
\(r= \frac{140}{\frac{110}{40}}\)
Rewrite as:
\(r = \frac{140 \times 40}{110}\)
\(r = 50.91mph\)
Hence, the cheetah's average rate is 50.91mph, not 55mph
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Related Questions
Jaylin solved this equation from the card sort:
15 – 7x= 3 + 5x
12 – 7x= 5x
12 = 12x
1= x
Is this correct?
Answers
Find the 50th term of this arithmetic sequence
6, 13, 20, 27 ...
Answers
Answer:
349
Step-by-step explanation:
\(a_{n} = a_{1} + (n - 1)d\)
n = 50 \(a_{1}\) = 6 d = 13 - 6 = 7
\(a_{50}\) = 6 + (50 - 1)(7)
= 6 + 49(7)
= 6 + 343
= 349
Answer:
formula as mentioned above...
Step-by-step explanation:
N=50,a=6,d=difference between no. that is 8
so,
x50=6+8(50-1)
x50=6+8(49)
x50=6+392=398 Answer
hope it helps....
please write 50 on the correct position of N as drawn in picture
A shipping container will be used to transport several 120-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 12400 kilograms have already been loaded into the container. Which inequality can be used to determine x, the greatest number of
120-kilogram crates that can be loaded onto the shipping container?
Answers
Inequality can be used to determine x, the greatest number of 120-kilogram crates that can be loaded onto the shipping container is 8000 + 120C <= 27500
What is inequality?An inequality is a relationship that allows us to contrast two or more mathematical expressions.
Knowing that;
Each carton weighs 120 kg.
The container's maximum weight when loaded is 27500 kg.
Weight of the container as it is currently loaded: 8000 kg
Now that we have merged, we have;
Solution
because 8000 grams have already been loaded kilograms
into the container
each crate weighs 120 kilograms.
so 8000 + 120C <= 27500
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Jamie bought a total of 20 pounds of grass seed at the nursery for $168. He paid $9 per pound for Kentucky bluegrass and $6 per pound for Tall Fescue. Which system of equations can be used to find the amount x (in pounds) of Kentucky bluegrass and the amount y (in pounds) of Tall Fescue Jamie purchased?
Determine the number of pounds of Kentucky bluegrass and the number of pounds of Tall Fescue that Jamie purchased from the problem above.
Answers
Answer:
D) x + y = 20
9x + 6y = 168
Step-by-step explanation:
x, y, is in pound, the weight
$168 is money, $9, $6
thankss for the point and i appreciate if mark my answer as brainliest <3
Answer:
x + y = 209x + 6y = 168Step-by-step explanation:
Given:
Amount of grass seed = 20 poundsx pounds of Kentucky bluegrass for $9, it sums to 9xy pounds of Tall Fescue for $6, it sums to 6yTotal amount spent = $168Required equations:
x + y = 209x + 6y = 168The slope of line ℓ
is greater than 0 and less than 1. Write an inequality for the slope of a line perpendicular to ℓ
.
Answers
By properties of perpendicular lines and algebra properties, the slope of the line perpendicular to line ℓ is represented by m' > 1.
How to represent an inequality associated with a line perpendicular to another line
Let m be the slope of a line, in accordance with analytic geometry, the slope of line perpendicular to the first one is equal to m' = - 1 / m. The statement can be summarized by the following inequality:
0 < m < 1
Then, by algebra properties for inequalities we find that that slope for the perpendicular line is:
0 < m · m⁻¹ < m⁻¹
0 < 1 < m⁻¹
1 < m⁻¹
- m⁻¹ > 1
- 1 / m > 1
m' > 1
The slope of the line perpendicular to line ℓ is represented by m' > 1.
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"Solve. Show all steps needed to solve the problem. If it is a fraction problem, the answer must be a fraction (not a decimal)."
-1/3(x+24)=10
Answers
Answer:
x=-54
Step-by-step explanation:
-1/3(x+24)=10
Remove the parentheses
-1/3x-8=10
Add 8 to both sides
-1/3x=18
Multiply both sides by 3
-x=54
Divide by -1
x=-54
Here are the coordinates of rectangle PLAY: (-11,20), (-11,-3), (-1,20), (-1,-3). Find the Area of this rectangle.
Answers
Answer:
230 unit^2
Step-by-step explanation:
\(From\ the\ information\ provided\ we\ know\ the\ coordinates\ of\ points:\\P(-11,20),L(-11,-3),A(-1,20),Y(-1,-3)\\Hence,\\PL =AY= 20+3=23\ units\\PY=LA=11-1=10\ units\\Hence,\\As\ we\ know\ that:\\Area\ of\ a\ rectangle=Length*BreadthArea\ of\ rectangle\ PLAY=23*10\\=230\ unit^2\)
DUE BY 11:59 PM!!
HELP GREATLY APPRECIATED!!
Answers
Answer:
Step-by-step explanation:
1. There are only 4 numbers including 5 that follow the "five or more" requirment, and the probability of spinning it once is 4/8, or 1/2. (The total sections is 8) Then we multiply 1/2 and 1/2 together to get the "two times in a row" requirement done. (1/2)*(1/2)= 1/4 is the probability.
2. There are two values on the spinner that are a multiple of 3, 3 itself and 6. Again, the total amount of numbers/sections is 8, so the probability of spinning a multiple of three is 2/8 or 1/4. The probability of spinning an odd number is 4/8 or 1/2. (1/2)*(1/4)=1/8 is the probability.
3. The probability of spinning one odd number is 1/2, and so we multiply 1/2 by itself four times. (1/2)*(1/2)*(1/2)*(1/2)=1/16 is the probability.
4. There are 6 numbers greater than two on the number wheel not including two itself. So the probability of that is 6/8, or 3/4. Then we multiply 3/4 by itself 3 times as it asks. (3/4)*(3/4)*(3/4)*(3/4)=81/256 is the probability.
Note that I am not really sure about the answer myself, but I hope that this can help in some way. Good luck! :)
Find the measure of the arc or angle indicated.
Answers
Answer: The correct is 114
Step-by-step explanation: Hope this helps
A square field has 3844 m² of land what is the width of the field?
Answers
a = one side of a square
The area of a square = a^2
In our problem,
Area = 3844 m^2
a = ?
Let's plug our values into the area equation.
3844 m^2 = a^2
Take the square root of both sides
62 m = a
The width of the field is 62 meters
I dont understand how to do this, looking for someone who can help
Answers
Write the inequality for the situation.
The number g is greater than 25
Answers
Answer:
g > 25
I hope this helps you :D
Is this what you mean?
I WILL GIVE BRAINLIEST
For which equation is x = 5 a solution
A. 2 + x = 3
B. 3x = 15
C. x/2 = 10
D. x - 7 = 12
Answers
Answer:
B
Step-by-step explanation:
too easy
Answer:
B
Step-by-step explanation:
Trust me
Please help, thank you!
Answers
Answer:
Vertical Asympote, but I might be wrong, haven't done this math in years
Find the distance between points P(7,9) and Q(2, -3) to the nearest tenth.
12
14
26
13
Answers
Answer:
I think 26. pls give me brainliest.
Which similarity statements describe the relationship between the two triangles? Check all that apply.
Answers
Answer:
umm is there a diagram for this?
anwerr: sys
There are 4 red marbles and 3 blue marbles in a bag. Once a marble is drawn it is not replaced. Find the probability of drawing two red marbles in a row.
Answers
Answer:
2/7
Step-by-step explanation:
4 red marbles and 3 blue marbles in a bag = 7 marbles
P(red) = red/total = 4/7
No replacement
3 red marbles and 3 blue marbles in a bag = 6 marbles
P(red) = red/total = 3/6 = 1/2
P(red, no replacement, red) = 4/7 * 1/2 = 2/7
5/7 - 3/2 in simplest form HELP ASAP
Answers
\( \frac{5}{7} \: - \: \frac{3}{2} \)
First, we find the lowest common denominator which is "14", we put it in the common numerator.\( \frac{10 \: - \: 21}{14} \)
We subtract the numbers.\( \boxed{ \bold{- \frac{11}{14} }}\)
MissSpanish\(\boldsymbol{\sf{\dfrac{5}{7}-\dfrac{3}{2} }}\)
The least common multiple of 7 and 2 is 14. Convert 5/7 and 3/2 to fractions with like denominators.
\(\boldsymbol{\sf{ \dfrac{5\times2}{7\times2}-\dfrac{3\times7}{2\times7} \ \ \to \ \ \ Simplify }}\)
\(\boldsymbol{\sf{\dfrac{10}{14}-\dfrac{21}{14} }}\)
Since 10/14 and 21/14 have the same denominator, subtract their numerators to subtract them.
\(\boldsymbol{\sf{\dfrac{10-21}{14} \ \ \to \ \ \ Subtract}}\)
Subtract 21 from 10 to get −11.
\(\red{\boxed{\boldsymbol{\sf{-\frac{11}{14} }}}} \ \ \to \ \ \boldsymbol{\sf{Answer}}\)
{ Pisces04 }What is the slope of the line y = 20x?
Answers
Answer:the slope is 20
Step-by-step explanation:
Answer:
m=20
Step-by-step explanation:
The line is in point slope form, or
y=mx+b
where m is the slope and b is the y-intercept
For the equation
y=20x
20 and x are being multiplied. The number being multiplied by x is the slope, therefore the slope is 20
Find the x- and y-intercepts of the graph of 4x-4y=324x−4y=32. State each answer as an integer or an improper fraction in simplest form.
Answers
Answer:x-intercepts (5,0)
y-intercepts (0,-5)
Step-by-step explanation: To find the x-intercept substitute in 0 for y and solve for x. to find the y-intercept subsitute 0 for x and solve for y
An object is traveling at a steady speed of 9 4/5 mi/h. How long will it take the object to travel 2 1/5 miles? First round to the nearest integer to find the estimated answer. Then find the exact answer.
Answers
Answer:
Time taken by the object = 14 minutes
Step-by-step explanation:
Speed of an object = \(9\frac{4}{5}\) miles per hour ≈ 9.8 miles per hour
Distance covered by the object = \(2\frac{1}{5}\) miles ≈ 2.2 miles
Formula to calculate the distance in the time 't' is,
Time taken by the object = \(\frac{\text{Distance traveled}}{\text{Speed of the object}}\)
= \(\frac{2.2}{9.8}\)
= 0.2245 hours
= 13.47 minutes
≈ 14 minutes
Therefore, distance traveled by the object to cover 2.2 miles = 14 minutes.
Donna wants to wrap a shipping box shaped like a rectangular prism. The box is 28 inches tall and has a square base with sides that each measure 4 inches how much paper will she use.
Answers
Answer:
the paper use by her is 112
Step-by-step explanation:
The computation of the paper use is shown below:
= Height of the box × sides
= 28 inches × 4 inches
= 112
Hence, the paper use by her is 112
Therefore the same would be considered and relevant too
Compute the partial sums S2, S4 and S6 of the following sequence.1/64 + 1/256 + 1/576 + 1/1024
Answers
The partial sums S2, S4, and S6 of the sequence are 0.0195 (approx), 0.0204 (approx), and 0.0229 (approx), respectively.
The given sequence is 1/64 + 1/256 + 1/576 + 1/1024 + ...
To find the partial sums, we need to add up the first 2, 4, and 6 terms of the sequence.
S2 = 1/64 + 1/256 = 5/256 = 0.0195 (approx)
S4 = 1/64 + 1/256 + 1/576 + 1/1024 = 47/2304 = 0.0204 (approx)
S6 = 1/64 + 1/256 + 1/576 + 1/1024 + 1/1600 + 1/2304 = 317/13824 = 0.0229 (approx)
Therefore, the partial sums S2, S4, and S6 of the sequence are 0.0195 (approx), 0.0204 (approx), and 0.0229 (approx), respectively.
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factorize: (2a+b)^3+(a+2b)^3
Answers
Answer:
9(a+b) x (a²+ab+b²)
Step-by-step explanation:
expand the brackets collect like terms remove the brackets collect like terms factorise reorder the terms multiplyA 4-h club held a canned food drive. On Wednesday they collected 63 cans which was 21% of the total cans collected during the food drive for the table to show a number of cans liked on Thursday and FridayWednesday [21/63Thursday [46/??]Friday [33/??
Answers
Let x be the number of cans that are 100% of the total cans collected.
\(\begin{gathered} 63\to21\text{percent} \\ x\to100\text{percent} \\ \Leftrightarrow \\ \frac{63}{21}=\frac{x}{100} \\ \Rightarrow x=300 \end{gathered}\)Thus, 300 cans were collected in total.
1) Thursday
Remember that 46%=0.46; then, the 46% of 300 is
\(300\cdot0.46=138\)138 cans were collected on Thursday.
2) Friday
33%=0.33, then
\(300\cdot0.33=99\)99 cans were collected on Friday.
given a two-tail test, a sample standard deviation, an n-value of 36, and an alpha of .05, find the critical value.
Answers
To find the critical value for a two-tail test with a sample standard deviation, an n-value of 36, and an alpha of 0.05, you will need to use the t-distribution table (as the population standard deviation is not given). However, since you have only provided the sample standard deviation and not its actual value, I cannot calculate the specific critical value for you.
Here are the general steps to find the critical value:
1. Calculate the degrees of freedom: df = n - 1 = 36 - 1 = 35
2. Divide the alpha (0.05) by 2 for a two-tail test, resulting in 0.025 in each tail.
3. Look up the t-value corresponding to the degrees of freedom (35) and the given alpha level (0.025) in the t-distribution table.
4. The t-value you find in the table is your critical value.
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C has four congruent sides.
5. Four quadrilaterals are described.
• Quadrilateral
• Quadrilateral
diagonals.
Quadrilateral
L has two pairs of parallel sides and congruent
T has at least one pair of parallel sides that are
congruent.
Quadrilateral Z has exactly one pair of parallel sides that are
congruent. The other pair of sides are congruent.
Show
Select all of the statements that MUST be true based on the given
information.
Base angles of Quadrilateral T are congruent.
Base angles of Quadrilateral Z are congruent.
□ Opposite angles of Quadrilateral C are congruent.
□ Opposite angles of Quadrilateral L are congruent.
Answers
The statements which must be true from the given statements are :
Base angles of Quadrilateral Z are congruent.
Opposite angles of quadrilateral C are congruent.
Opposite angles of quadrilateral L are congruent.
Consecutive angles of quadrilateral Z are congruent.
Consecutive angles of quadrilateral L are congruent.
Opposite angles of quadrilateral C are supplementary.
Opposite angles of quadrilateral T are supplementary.
Given are,
Quadrilateral C has 4 congruent sides.
So this must be a square and thus all angles are equal which is equal to 90°.
Opposite angles are thus congruent.
Opposite angles of a quadrilateral is always supplementary.
Quadrilateral L has two pairs of parallel sides and congruent diagonals.
So it must be a rectangle or a square.
So, opposite angles are congruent, each equal to 90 degrees.
Also, consecutive angles are equal, since each angle equal to 90°.
Quadrilateral T has at least one pair of parallel sides that are also congruent.
If at least one pair of parallel sides are congruent, then the other pair of sides are also parallel and congruent.
S it can be rectangle, square, parallelogram or rhombus.
If it is parallelogram or rhombus, base angles will not be equal.
Opposite angles are supplementary.
Quadrilateral Z has exactly one pair of parallel sides that are not congruent. The other pair of sides are congruent.
This must be an isosceles trapezium.
Base angles of an isosceles trapezium are equal and thus congruent.
So consecutive angles are congruent.
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Which of the following sets of coordinates is one the line represents by the equation y = -3x + 7? Explain how you got the answer.
A. (1,10)
B. (1, -4)
C. (3, -2)
D. (2, -1)
Answers
The coordinate (3, -2) will be a solution to the given equation since it lies on the line.
Equation of a lineA line is defined as the shortest distance between two points. The equation of a line is described by the linear equation y = mx + b
Given the equation y = -3x +7, in order to determine the coordinate that represents a solution, we will substitute the value of x and check if we are going to get the corresponding y-value.
For the coordinate (1, 10)
y = -3(1) +7
y = 4
Hence (1, 10) is not a solution
For the coordinate (1, -4)
y = -3(1) +7
y = 4
Hence (1, -4) is not a solution
For the coordinate (3, -2)
y = -3(3) +7
y = -2
Since the equivalent y-value is -2, hence the coordinate (3, -2) is a solution.
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If a function is differentiable then it is continuous.
Answers
The statement "If a function is differentiable, then it is continuous" is generally true. In summary, if a function is differentiable at a point, it must also be continuous at that point.
Differentiability is a stronger condition than continuity. If a function is differentiable at a point, it means that it has a derivative at that point, indicating the existence of a well-defined tangent line.
A key property of differentiability is that it implies continuity. In other words, if a function is differentiable at a point, it must also be continuous at that point.
On the other hand, a function can be continuous without being differentiable. Continuous functions have no abrupt jumps, holes, or vertical asymptotes in their graphs. However, they may have corners, cusps, or vertical tangents, which prevent them from being differentiable at those points. Therefore, while differentiability guarantees continuity, continuity does not necessarily imply differentiability.
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Complete question - Write the conserve and contrapositive of the following statement- "If a function is differentiable then it is continuous."
pls answer. On a coordinate plane, a line with a 90-degree angle crosses the x-axis at (negative 4, 0), turns at (negative 1, 3), crosses the y-axis at (0, 2) and the x-axis at (2, 0). What is the range of the function on the graph? all real numbers all real numbers less than or equal to –1 all real numbers less than or equal to 3 all real numbers less than or equal to 0
Answers
Range: All real numbers greater than or equal to 3. The Option C.
What is the range of the function on the graph formed by the line?To find the range of the function, we need to determine the set of all possible y-values that the function takes.
Since the line crosses the y-axis at (0, 2), we know that the function's range includes the value 2. Also, since the line turns at (-1, 3), the function takes values greater than or equal to 3.
Therefore, the range of the function is all real numbers greater than or equal to 3.
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