Aliza needs to run at a rate faster than 8.8 feet per second in order to exceed her fastest time in a race. After running for 15 minutes, her coach determines that she is running at an average rate of 5.8 miles per hour. He converts the average rate to feet per second as shown below:
He concludes that she is not running fast enough to exceed her fastest time.
Answers
Answer:
Check: He used an incorrect time ratio converting hours to minutes
Check: He incorrectly concluded that she is not running fast enough
Do not check: His units do not cancel
Do not check: He used an incorrect distance ratio converting miles to feet
Do not check: He cannot determine her average rate in miles per hour after only 15 minutes
Step-by-step explanation:
You're welcome bud :)
Related Questions
Find the complex conjugate of the given number -1+4i
Answers
1. Lisa is working with the system of equations x + 2y = 7 and 2x ‒ 5y = 5. She multiplies the first equation by 2 and then subtracts the second equation to find 9y = 9, telling her that y = 1. Lisa then finds that x = 5. Thinking about this procedure, Lisa wonders:
There are lots of ways I could go about solving this problem. I could add 5 times the first equation and twice the second or I could multiply the first equation by ‒2 and add the second. I seem to find that there is only one solution to the two equations but I wonder if I will get the same solution if I use a different method?
What is the answer to Lisa’s question? Explain.
2. Does the answer to the first question change if we have a system of two equations in two unknowns with no solutions? What if there are infinitely many solutions?
Answers
Answer:
1. Yes
2. Yes
Step-by-step explanation:
1. Lets test Lisa's different solution. Lets times 5 to the first equation:
[tex]5\cdot{x}+10\cdot{y}=35[/tex]
and 2 times the second equation:
[tex]4\cdot{x}-10\cdot{y}=10[/tex]
lets add the two equations:
[tex]9\cdot{x}=45[/tex]
[tex]x=5[/tex]
The second method is multiplying the first equation by -2:
[tex]-2\cdot{x}-4\cdot{y}=-14[/tex]
and add the second equation:
[tex]-9\cdot{y}=-9[/tex]
[tex]y=1[tex]
Substitute into equation 1:
[tex]x+2\cdot{1}=7[/tex]
[tex]x=5[/tex]
The answer to Lisa's question is yes she wull get the same solution if she uses a different method.
2. Yes, The answer would change if the same amout of x and y values are the same and therefore we cannot solve for x and y. If there was infinitely many solutions we would have quadratic equations.
TRUE OR FALSE: The number 532 has 2 significant digits.
Select one:
True
False
Answers
A boat traveled 280 miles downstream and back. The trip downstream took 7 hours. The trip bck took 14 hours. Find the speed of the boat in still water and the speed of the current.
Answers
bearing in mind that the trip over, upstream, is the same distance as back, 280 miles.
if say, the boat has a speed rate of say "b", and the current has a speed rate of "c", so, when the boat was going upstream, it really wasn't going "b" fast, it was going "b-c" fast, because the stream is subtracting speed from it, because is going against the stream.
And when the boat was going downstream, is not going "b" fast either, is going "b+c" because, since it's going with the current, the current's rate is adding speed to it.
[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ Downstream&280&b+c&7\\ Upstream&280&b-c&14 \end{array} \\\\\\ \begin{cases} 280=7(b+c)\implies \frac{280}{7}=b+c\\ 40=b+c\implies 40-c=\boxed{b}\\ -------------\\ 280=14(b-c)\implies \frac{280}{14}=b-c\\ 20=b-c\\ ----------\\ 20=\left( \boxed{40-c} \right)-c \end{cases} \\\\\\ 20=40-2c\implies 2c=40-20\implies c=\cfrac{20}{2}[/tex]
what's the speed of the boat? well, 40 - c = b.
John runs every day. The number of miles that he runs varies per day. Write a variable expression to show John's total miles for three days."
Answers
T = x + y + z
A total of 252 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold?
Answers
Students= 2x
Adults= x
Total=3x
3x=252
x= 252/3
=84
Thus, number of adult tickets sold is 84
The number of adult ticket sold are 28.
What is a ticket ?"a piece of paper or card that shows you have paid for a journey, or that allows you to enter a theatre, cinema, etc."
Let, the number of student ticket be x
Let, the number of adult ticket be y
So, [tex]x = 2y[/tex]
And Given,
Total number of tickets are 252
So, [tex]x+y = 252[/tex]
[tex]2y + y = 252\\3y = 252 \\y = 28[/tex]
Hence, the adult tickets sold are 28.
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How many solutions are possible for the equation 5(x-3)=7x-2(x+1)
Answers
5(x-3) = 7x - 2(x+1)
5x - 15 = 7x -2x - 2
5x -13 = 5x
-13 = 0
So, there is no solution.
Hope this helped!
What is the area, in square millimeters, of a right triangle with a hypotenuse of 68 millimeters and a leg of 60 millimeters?
Answers
x² + 60² = 68²
x² + 3600 = 4624
x² = 1024
x = √1024
x = 32 = length of the other side
A = (1/2)(32) (60) = 960 mm²
What is m∠M ?
Enter your answer in the box.
Answers
Answer: We can find the measurement of the angle M using that the sum of the interior angles in any triangle is equal to 180°, then:
m<M=98°
Solution:
m<M=(3x-16)°
To find m<M we need "x".
m<N=x°
m<O=(x+6)°
The sum of the interior angles of any triangle is equal to 180°:
m<M + m<N + m<O = 180°
Replacing the angles:
(3x-16)° + x° + (x+6)° = 180°
We have one equation with one variable "x", then we can solve for x. Adding the terms:
(3x-16+x+x+6)°=180°
3x-16+x+x+6=180
Adding similar terms:
5x-10=180
Adding 10 both sides of the equation:
5x-10+10=180+10
5x=190
Dividing both sides of the equation by 5:
5x/5=190/5
x=38
Then:
m<M=(3x-16)°
Replacing x by 38 in the formula above:
m<M=(3(38)-16)°
m<M=(114-16)°
m<M=98°
You roll a six sided dice four times, what is the probability of rolling four sixes?
Answers
6×6×6×6
6×6=36
36×6=216
216×6=1296
1/1296
Find the value of x that makes lines u and v parallel
Answers
34x - 2 + 11x +2 = 180
If consecutive interior angles are supplementary then the 2 lines are parallel
Directed line segment AB has endpoints A(2,3) and B(8,15). Point P has coordinated P(6,11). What ratio does P partition AB into?
Answers
collinear.
Calculate the length of AP (as a).
a = √[(6 - 2)² + (11 - 3)²]
= 8.9443
Calculate the length of BP (as b).
b = √[(8 - 6)² + (15 - 11)²]
= 4.4721
Calculate ratio a/b.
a/b = 8.9443/4.4721 = 2
Therefore P partitions AB in a 2:1 ratio so that AP = 2*BP.
Answer: 2:1 ratio.
Which of the following shows the correct order of the numbers below? (1/2) 2 , , 0.45
Answers
Hope I helped :)
Ten times the sum of half a number x and 4 is 7?
Answers
Divide both sides by ten
(x/2)+4 = 7/10
Then -4 on both sides
x/2=-3 3/10
mutiple both sides by 2
x= -6 6/10
x= -6.6
Simplify the trigonometric expression. Show your work.
1/1+sin theta + 1/1-sin theta
Answers
[tex] \dfrac{1}{1+sin(\theta)} + \dfrac{1}{1-sin(\theta)} \\\\ \dfrac{1-sin(\theta) + 1+sin(\theta)} {1-sin^2(\theta) }}\\\\ = \dfrac{2} {cos^2(\theta)} [/tex]
trigonometric identites
1. D
2. B
3. tangent identity
4. A
5. B. 2sec2 therma.
(also, the answer above me is NOT correct. the asnwer was 2sec2 therma.
A rectangle has a perimeter of 112 centimeters. if the length of the rectangle is 3 times its width, find the dimensions of the rectangle.
Answers
4x=56
x=14
length=42
width=14
nine less than the product of ten and a number d is eleven
Answers
Add 9 to both sides.
10d = 20
Divide both sides by 10.
d = 2
The answer is d = 2.
What is the slope of the line that passes through points (5,0) and (10, 0)? How do you know?
Answers
The Richter scale is used to measure the magnitude of an earthquake. The magnitude, R, is given by the earthquake. Determine the amount of energy released be an earthquake of magnitude of 7.5.
It says simplify so it is written in the form b = log a.
Answers
B)[tex]6.05=0.65log(0.39E) Subtracted 1.45 from~ both~ sides~ of~ equation. 9.31=log(0.39E) Divided each side by 0.65. [/tex]
C) [tex]9.31=log(0.39E) 10^(9.31)=0.39E E=5.24*10^9 kilowatt hours[/tex]
Amount of energy released during Earthquake is [tex]5.23*10^{6} kilowatt[/tex]
The Richter scale is used to measure the magnitude of a earthquake. The magnitude R is,
[tex]R=0.65log(0.39E)+1.45[/tex] E is the energy (measured in kilowatt-hours) released by the earthquake.
Given that, R = 7.5
Substituting the value of R into above equation.
[tex]7.5=0.65log(0.39E)+1.45\\\\7.5-1.45=0.65log(0.39E)\\\\6.05=0.65log(0.39E)\\\\9.31=log(0.39E)\\\\0.39E=10^{9.31}\\\\E=\frac{10^{9.31} }{0.39} \\\\E=5235225499watt\\\\E=5.23*10^{6} kilowatt[/tex]
Thus, Amount of energy released is [tex]5.23*10^{6} kilowatt[/tex]
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Which expression is the correct translation of the following word phrase?
"3 multiplied by the sum of a number and 5"
Answer choices:
A) 5X+3
B)3X+5
C)X+(3)(5)
D)3(X+5)
I think the answe is B ,but I think it could be A as well ,but I just need toconfirm if I'm correct or not.Thanks in advance:).
Answers
The parentheses would make it multiplication
The word sum means add
A number was unknown, so we will label it as "x"
So, let's see what we're working with here!
If you chose "Option A" the question would be "five multiplied by a number and the sum of 3" (that doesn't give you the right answer"
For B. same thing with option A
For "Option C" its not asking you "a number with sum of three times five"
So, this leaves "Option D." as your answer because 3 is getting multiplied by the sum of some number and five
Good luck on your assignment and enjoy your day!
~MeIsKaitlyn:)
The correct translation of the word phrase '3 multiplied by the sum of a number and 5' is option D) 3(X+5).
Explanation:The correct translation of the word phrase '3 multiplied by the sum of a number and 5' is option D) 3(X+5).
In this expression, the number is represented by X. The sum of the number and 5 is represented by (X+5). Multiplying 3 by the sum gives us 3(X+5).
If the area of the outer square is 4x2, then the area of the inner square is
Answers
Final answer:
The area of the inner square is x squared. This is determined by the rule that the ratio of areas of similar figures is the square of the scale factor, with the larger square having dimensions and area four times that of the smaller square.
Explanation:
Considering a larger square with an area of 4x², and given that the dimensions of this square are twice that of a smaller square, we can derive the area of the smaller square by understanding the relationships between the scale factor and the area of similar figures. If Marta's original square has a side length of 4 inches, doubling the dimensions gives a side length of 8 inches for the larger square.
The scale factor for the sides is 2, but when considering area, the scale factor is squared. Consequently, the area of the larger square, which is 8 inches by 8 inches, will be 64 square inches. This area is four times larger than the area of the smaller square, which is 16 square inches (4 inches x 4 inches). Thus, the rule that the ratio of areas of similar figures is the square of the scale factor applies. The area of the inner square would be equivalent to the area of the outer square divided by 4, which in our case, with an outer square area of 4x², leads to an inner square area of x².
In angle abc , m angle A =x , m angle B =2x+2, m angle C = 3x+4.what is value x
Answers
x + 2x + 2 + 3x + 4 = 180
6x + 6 = 180
6x = 174
x = 29
You want to make five-letter codes that use the letters A, F, E, R, and M without repeating any letter. What is the probability that a randomly chosen code starts with A?
Answers
there are 5 letters used for the code.
The probability of A being first the number of A’s which can be picked (1) over the total number of letters that can be picked (5).
The probability of A being first is 1/5
1/5 = 0.2
Answer:
Correct answer for plato
Step-by-step explanation:
C. 0.20
Miss violet is buying granola bars for her students. she already has 16 granola bars in her desk and needs a total of 100 bars. they are sold in packs of 12. how many more boxes of granola bars does she need to purchase for her students?
Answers
please Sara recorded the height of the ocean at low tide, with respect to sea level, for four days. Time Low Tide (inches) Monday a.m. −4 Monday p.m. −6 Tuesday a.m. −3 Tuesday p.m. −1 Wednesday a.m. 0 Wednesday p.m. 2 Thursday a.m. −1 Thursday p.m. −3 What is the average height of the ocean at low tide with respect to sea level? Enter your answer in the box.
Answers
Answer:
-2
Step-by-step explanation:
The averge of low tide is of -2 inches
The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool?
The height of the water increases 2 inches per minute.
The height of the water decreases 2 inches per minute.
The height of the water was 2 inches before any water was added.
The height of the water will be 2 inches when the pool is filled.
Answers
Example: In minute 2 it was 8 inches, in minute 4 it was 12 inches. (12-8=4)
This means that if the height of the water is increased by 4 inches for 2 minutes, then for 1 minute is increased 4/2=2 inches.
The following statement best describes how the slope relates to the height of the water in the pool:
The height of the water increases 2 inches per minute.
The correct statement describes how the slope relates to the height of the water in the pool is,
The height of the water increases by 2 inches per minute.
Given that,
The slope of the line through the points is 2.
And, the slope relates to the height of the water in the pool.
Here, a table for the height of the water in a pool is shown.
Since the slope of the line through the points is 2.
Hence, It means that,
if the height of the water is increased by 4 inches for 2 minutes, then for 1 minute is increased,
4/2 = 2 inches.
So, the correct statement is,
The height of the water increases by 2 inches per minute.
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How do I round 123834392 to the nearest thousand
Answers
To round to the nearest thousand, take apart the number so that you only have x thousand.
4,392
Now, take the second highest number (hundred) and if it is 1-4 then it stays the same. If it's 5+, then it would go up one. In this case, since the hundreds place is 3, the number would stay the same.
Y is between points J and A. JA=17 and YA=3.
What is JY?
Enter your answer in the box.
JY =
Answers
we know that
[tex]JA=JY+YA[/tex]
solve for JY
[tex]JY=JA-YA[/tex]
in this problem we have
[tex]JA=17\ units\\YA=3\ units\\JY=?[/tex]
substitute the values in the formula above
[tex]JY=17-3[/tex]
[tex]JY=14\ units[/tex]
therefore
the answer is
[tex]JY=14\ units[/tex]
Answer:
JY = 14
Step-by-step explanation:
Given : Y is between points J and A.
and JA = 17 and YA = 3.
We have to find the length of JY.
Since, Y is between points J and A.
So, JA = JY + YA
Substitute, JA = 17 and YA = 3.
We have,
17 = JY + 3
Solve for JY, we have,
JY = 17 - 3 = 14
Thus, JY = 14
A six-sided number cube is labeled with the numbers 1–6, one number on each face. Each number is used exactly once. How many possible outcomes exist when the cube is rolled two times?
Answers
Answer:
36
Step-by-step explanation:
When the cube is rolled two times
Let (a,b) denote a possible outcome of rolling the cube twice , with a the number on the top of the first roll and b the number on the top of the second roll
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
There are 36 possibilities for (a,b).
It can be obtained from the multiplication principle: there are 6 possibilities for a, and for each outcome for a, there are 6 possibilities for b.
So, the total number of outcomes (a,b) is [tex]6 \times 6 =36[/tex]
Hence the total number of possible outcomes is 36
When the cube is rolled two times, there are a total of 36 possible outcomes.
Use the concept of probability defined as:
Probability is the ratio of:
The number of favorable outcomes to the total number of outcomes for an event's taking place.
Given that,
A six-sided number cube is used, with numbers 1-6 labeled on each face.
Each number is used exactly once on the cube.
The cube is rolled two times.
The objective is to determine the number of possible outcomes when rolling the cube two times.
To find the number of possible outcomes when a six-sided number cube is rolled two times:
Use a simple principle called the multiplication principle.
Since there are six possible outcomes for each roll,
The total number of outcomes for rolling the number cube two times is found by multiplying the number of outcomes for each roll together.
So, if you roll the number cube two times,
There would be 6 outcomes for the first roll and 6 outcomes for the second roll.
Multiplying them together gives us a total of 36 possible outcomes.
Hence,
The answer is 36 possible outcomes when the cube is rolled two times
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Please help:
[tex]5^{x-1} + 5 [/tex] x [tex]0.2^{x-2} = 26[/tex]
When I tried it, I got up until canceling the 5s and getting x - 1 - x - 2 = 21
What did I do wrong?