Fwam and Eva are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Fwam is gar miles away from the stadium and Eva is 396 miles away from the stadium. Fwam is driving along the highway at a speed of 42 miles per hour and Eva is driving at speed of 65 miles per hour. Let F represent Fwam's distance, in miles, away from the stadium t hours after noon. Let E represent Eva's distance, in miles, away from the stadium t hours after noon. Write an equation for each situation, in terms of t, and determine how far both Fwam and Eva are from the stadium at the moment they are an equal distance from the stadium.
Answers
Fwam and Eva are an equal distance of 69 miles away from the stadium when the time t = 3 hours
Given data ,
The formula for the distance (F) of Fwam from the stadium is:
F(t) = 327 - 42t
Since Fwam is travelling at a 42 mph pace, his distance from the stadium is reducing at a 42 mph rate.
The formula for Eva's separation from the stadium is:
E(t) = 396 - 65t
Eva's distance from the stadium also shrinks at a pace of 65 miles per hour as she drives at a speed of 65 mph.
Set F(t) = E(t) and solve for t to get the time at which Fwam and Eva are equally far from the stadium
On simplifying the equations , we get
327 - 42t = 396 - 65t
Adding 65t to both sides:
65t + 327 - 42t = 396
23t + 327 = 396
Subtracting 327 from both sides:
23t = 396 - 327
23t = 69
Dividing both sides by 23:
t = 69 / 23
t = 3 hours
Hence , at t = 3 hours after noon, both Fwam and Eva are an equal distance of 69 miles away from the stadium.
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The complete question is attached below :
Fwam and Eva are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Fwam is gar miles away from the stadium and Eva is 396 miles away from the stadium. Fwam is driving along the highway at a speed of 42 miles per hour and Eva is driving at speed of 65 miles per hour. Let F represent Fwam's distance, in miles, away from the stadium t hours after noon. Let E represent Eva's distance, in miles, away from the stadium t hours after noon. Write an equation for each situation, in terms of t, and determine how far both Fwam and Eva are from the stadium at the moment they are an equal distance from the stadium.
Related Questions
Solve the equation.
22
= 6
2 =
Answers
Z/2=6
(Multiply both sides by 2)
Z=6*2
Z=12
What is 2x-5y=9 in slope intercept form?
Answers
PLEASE HELP ME SOLVE THIS!!!!
Answers
The meaning of the absolute value of -5.5 is given as follows:
The temperature decreases 5.5 degrees.
What is the absolute value of a number?The absolute value of a number is the number without the signal, for example:
|-2| = |2| = 2.
The number in this problem is given as follows:
-5.5.
Hence:
The negative sign means that the temperature decreased.The absolute value of 5.5 means that the temperature decreased by 5.5 degrees.Hence the second option is the correct option in the context of this problem.
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A jelly bean is selected at random from ajar and is not returned. The jar contains 8 red, 2 green, 4 blue, and 7 pink, jelly beans. Which is the probability of selecting a ed jelly bean on the first draw and a blue jelly bean on the second draw?
Answers
Answer:
There would be a 38% or 8/21 probability of picking a red jelly bean on the first draw and a 20% or 4/20 probability of picking a blue jelly bean on the second.
Step-by-step explanation:
There are 21 jelly beans in total. So on the first draw, there is an 8/21 chance you will get a red jelly bean. If you turn this fraction into a percentage, it is 38%.
Now that a jelly bean is missing, there are 20 jelly beans. There are four blue ones still, so there is a 4/20 chance of getting a blue jelly bean. Turning this ratio into a percent gets you 20%.
I would love a brainliest. I haven't had one yet and it would make my day. Hope this helped you!
The probability of selecting a red jelly bean on the first draw and a blue jelly bean on the second draw is 32/441.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
The jar contains 8 red, 2 green, 4 blue, and 7 pink, jelly beans.
total beans = 8 + 2 + 4 + 7 = 21
So, the probability of selecting a red jelly bean on the first draw and a blue jelly bean on the second draw
= 8/21 x 4 / 21
= 32 /441
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For questions 11-12, divide. Use synthetic division, if possible.
11. (x² +6x²-x² - 5x+1)+(x-2)
12. (x³ +9x² -5x +11)+(x² + 2)
Answers
Question 11 seems to have strange typos in it. Please double-check to make sure it has been typed correctly.
I'm not sure how to answer that one.
----------
I'll focus on Question 12.
The long division scratch work is shown in the image attachment below.
The answer to problem 12 is x+9 remainder -7x-7
Please let me know if you have questions about any step of the polynomial long division process.
A
The bottom of this cylinder, called the
base, has an area of 22 in.² It takes
22 in. of sand to cover the base.
The cylinder has a height of 3 in.
How much sand can the cylinder hold?
B
Which can be used to find the volume of a cylinder?
v=Area of the base + height of the cylinder
V= (Area of the base)2 x height of the cylinder
v=Area of the base x height of the cylinder
V = Area of the base
Answers
Answer: 1) 66 2)
Step-by-step explanation:
1) 22x3=66
2) C
Hope this helps! :)
It's a beautiful fall day! Mari and her friends decide to have a picnic in the park. Each friend is bringing something to eat or drink. Mari is bringing watermelon. Before she leaves her house, Mari cuts a watermelon into 16 equal pieces. At the picnic, she eats 3 pieces of watermelon.What fraction of the watermelon does Mari eat?
Answers
Please help me i need the answer and im so confused just tell me if its a b c or d please
Answers
Answer:
The answer would be option A
Step-by-step explanation:
-14 times 8=-122
The number of runs scored by the Stars for six games is shown below.
4,9, 2, 4, 1,6
If the Stars scored 14 runs in their seventh game, which of the following statements is true?
OA. The mean increases and the median remains the same.
OB. The median increases and the mean remains the same.
OC. The mean and the median both increase.
O D. The median and the mean both remain the same.
Answers
A train moving 50 miles per hour meets and passes a train moving 50 miles per hour in the opposite direction. A passenger in the first train sees the second train pass in 5 seconds. How long is the second train?
Answers
Answer:
The length of the second train is 416.67 meters.
Step-by-step explanation:
mark brainliest
LINES AND ANGLES
Circle the correct answer to each of the following questions. Show your work, if necessary.
1 Which of the following objects is two-dimensional?
a. a pair of dice
b. a basketball
C
tree
d. a circle
Answers
Find the surface area of the cylinder in terms of Pi. The diameter is 14 cm and the height is 18 cm
Answers
The surface area of the cylinder in terms of pi is:
S = pi*301 cm²
how to find the surface?We know that for a cylinder of radius R and height H the surface area is:
S = pi*( 2RH + R²)
Here the height is 18 cm and the diameter is 14cm, then the radius is.
R = 14cm/2 = 7cm
Then the surface area will be:
S = pi*(2*7cm*18cm + (7cm)*7cm)
S = pi*301 cm²
That is the surface area in terms of pi.
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The Sky Train from the terminal to the rental car and long term parking center is supposed to arrive every 8 minutes. The waiting times for the train are known to follow a uniform distribution.
What is the probability of waiting less than 2 minutes and more than 6 minutes?
Answers
The 30th percentile in the uniform distribution is 2.4 min.
The correct option is (b)
Probability :The probability formula is defined as the ratio of favorable outcomes to the ratio of total outcomes. For any event (E), :
P(E)= Number of favorable outcomes/ Number of total outcomes
[tex]\mu=\frac{a +b}{2}[/tex]
[tex]\sigma=\sqrt{\frac{(b-a)^2}{12} }[/tex]
P(x) = 1/ b - a if a < x < b
P(X < a) = 0
and
P(X > b) = 0
In this case, a = 0 and b = 8
The 30th percentile in the uniform distribution, this means that the probability is 0.30. Therefore:
0.3 = [tex]\frac{1}{8-0}.x[/tex]
0.3 (8 -0) = x
2.4 = x
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The given question is incomplete, complete question is :
The Sky Train from the terminal to the rental-car and long-term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution. Find the 30th percentile for the waiting times (in minutes).
a. 2
b. 2.4
c. 2.75
d. 3
Lisa is putting colored 11 light bulbs into a string of lights. There are 3 red light bulbs, 2 yellow light bulbs, and 6 pink light bulbs. How many distinct orders of light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?
Answers
The distinct orders of light bulbs are there if two light bulbs of the same color are considered identical = 4,620
Here, the total number of bulbs = 11
The number of red light bulbs = 3
The number of yellow light bulbs = 2
and the number of pink light bulbs = 6
We know that the formula for the permutation with repetition is:
n! / (n1! × n2! x ... × nk!)
We use this formula to find the required number of light bulbs.
Here, two light bulbs of the same color are considered identical
We divide by 3! in order to adjust for overcounting, because we have 3 red light bulbs.
simmilarly for the 2 yellow light bulbs, we divide with 2!.
and for the 6 pink light bulbs, we divide by 6!
Thus, the total number of distinct orders of bulbs will be:
11! / (3! × 2! × 6!) = 4,620
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Explain how to determine the zeros of g (x) = -(x+2) (x-3) (x-3)
Answers
The zeros of g(x)= -(x+2) (x-3) (x-3) are -2 and 3.
We are given that;
g (x) = -(x+2) (x-3) (x-3)
Now,
To determine the zeros of g(x) = -(x+2)(x-3)(x-3), we need to find the values of x that make g(x) equal to zero. This means that we need to solve the equation:
−(x+2)(x−3)(x−3)=0
To solve this equation, we can use the zero product property, which states that if the product of two or more factors is zero, then at least one of the factors must be zero. Therefore, we can set each factor equal to zero and solve for x:
x+2=0orx−3=0
Subtracting 2 from both sides of the first equation, we get:
x=−2
Adding 3 to both sides of the second equation, we get:
x=3
Therefore, by the given equation the answer will be -2 and 3.
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the lowest common multiple of 36 30
Answers
Answer:
180
Step-by-step explanation:
To find the lowest common multiple (LCM) of 36 and 30, we can use the prime factorization method:First, we can find the prime factorization of each number:36 = 2^2 * 3^230 = 2 * 3 * 5Next, we can take the highest power of each prime factor that appears in either number and multiply them together.The highest power of 2 is 2^2 = 4.The highest power of 3 is 3^2 = 9.The highest power of 5 is 5^1 = 5.Multiplying these together, we get:LCM(36, 30) = 2^2 * 3^2 * 5 = 180Therefore, the lowest common multiple of 36 and 30 is 180.
Answer: 180
Step-by-step explanation:
To find the lowest common multiple (LCM) of two numbers, we need to find the smallest number that is a multiple of both of them.
One way to do this is to find the prime factorization of each number and then take the product of all the prime factors, with each factor occurring as many times as it appears in the factorization of either number.
The prime factorization of 36 is 2^2 × 3^2, and the prime factorization of 30 is 2 × 3 × 5. Therefore, the LCM of 36 and 30 can be found by taking the product of the highest power of each prime factor that appears in either factorization:
LCM(36, 30) = 2^2 × 3^2 × 5 = 180
Therefore, the lowest common multiple of 36 and 30 is 180.
In the figure to the right, you are given a square ABCD. Each of its sides is divided into two segments, such that AE = BF = CG = DH. Prove that quadrilateral EFGH is a square.
First to answer gets brainliest
Answers
Answer:proving that EFGH is a square: points E,F,G,H
separate the sides of the square ABCD into two lines. if AE=BF=CG=DH then
AH=DG=EB=FC and it shows that if we connect the points E,F,G,H to each other with line we will have a square
HAE~EBF~FCG
A bakery sold 107 cupcakes in one day. The head baker predicted he would sell 87 cupcakes that day. What was the percent error of the baker's prediction?
Answers
Answer:
First, we need to calculate the absolute error, which is the difference between the predicted value and the actual value:
Absolute error = |predicted value - actual value| = |87 - 107| = 20
Then, we can calculate the percent error using the formula:
Percent error = (absolute error / actual value) x 100%
Plugging in the values, we get:
Percent error = (20 / 107) x 100% ≈ 18.69%
Therefore, the percent error of the baker's prediction is approximately 18.69%.
IQR of 28 22 15 16 15 13 19 18
Answers
Answer: The IQR of this data set is 5.5
Step-by-step explanation: Ok so first you line the data set up in correct order.
Here's the correct order:
13, 15, 15, 16, 18, 19, 22, 28
Then you find the median and since there's even amount of numbers you add the two numbers in the middle which is 16 and 18 and divide that by 2 which is 17. So the median is 17. Then you split the data set into halves. The first quartile is 15 and the third quartile is 20.5. Then to find the IQR, you would minus 20.5 - 15 = 5.5. Hope this helps!
The equation of a line is y= -2/7x + 3/7. What is the slope of a line perpendicular to this line?
Answers
The slope of the line perpendicular to the line is m = ( 7/2 )
Given data ,
The equation of the given line is y = -2/7x + 3/7.
Now , it is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
The slope of the given line is -2/7, which means that for any line perpendicular to this line, the slope would be the negative reciprocal of -2/7.
So , m = ( 7/2 )
Hence , the slope of the perpendicular line is = 7/2
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Cindy has a new job offer but will need a new car for the job. After planning a budget, they determine that they can afford to pay at most $215 per month for a 6-year car loan. If an annual percentage rate of 2.1% is available to finance the car loan, calculate the value of the most expensive car loan that Cindy can afford. Round to the nearest whole
number
Answers
The value of the most expensive car loan that Cindy can afford is $13,712
We are given that;
Amount= $215
Percentage= 2.1%
PMT = 215 i = 0.021 / 12 = 0.00175 (the annual interest rate divided by 12 months) n = 6 × 12 = 72 (the number of months in 6 years)
Now,
The formula for the present value of an annuity is:
PV = PMT × (1 - 1/(1 + i)^n) / i
where:
PV = present value PMT = payment amount i = interest rate per period n = number of periods
Plugging these values into the formula, we get:
PV = 215 × (1 - 1/(1 + 0.00175)^72) / 0.00175 PV = 215 × (1 - 0.888) / 0.00175 PV = 215 × 0.112 / 0.00175 PV = 13,712
Therefore, by the percentage the answer will be $13,712.
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Carl went grocery shopping. He weighed his apples and they have a mass of 2450g. He measured the mass of the pineapple and found it was 3547g. How much more mass does the pineapple have?
Answers
The pineapple has 1097g more mass than the apples.
We have,
The difference between two values is the result of subtracting one value from the other.
In this case, we want to find the difference between the mass of the pineapple and the mass of the apples.
To do this, we subtract the mass of the apples from the mass of the pineapple.
The equation for this is:
Pineapple mass - Apple mass = Difference
Substituting the given values:
3547g - 2450g = 1097g
Therefore,
The pineapple has 1097g more mass than the apples.
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Jerry had 35 big stickers and 20 small stickers at first. He exchanged 10 small stickers for 5 big stickers. What percentage of his sticker are big stickers in the end?
(1) 10% (2) 20% (3) 40% (4) 80%
Answers
Answer:
80%
Step-by-step explanation:
After all the trade he got 50 stickers
40 Big
10 small
50 stickers is 100%
40B stickers is ??
WE multiply 40 by 100 then divide by 50
so 80%
To find the percentage of big stickers, we can use the following formula:
Percentage of big stickers = (Number of big stickers ÷ Total number of stickers) x 100%
Plugging in the numbers, we get:
Percentage of big stickers = (40 ÷ 70) x 100%
Percentage of big stickers = 57.14%
Therefore, the closest answer to the percentage of big stickers in the end is (4) 80%.
Given f(x) = 7 - 4x and f(x) = 27, what is the value of x?
Answers
Answer: x = -5
Step-by-step explanation:
Answer:
x=-5
7 - 4 * (-5)
Negative times a negative equals a positive
-4*-5=20
7+20=27
In circle R, find arc length of arc GH
Answers
The length of the arc GH is 13.3 cm
What is length of an arc?The length of an arc is the distance that runs through the curved line of the circle making up the arc.
The length of an arc is expressed as;
l = tetha/360 × 2πr
tetha = R
R = 360-( 170+80)
R = 360-250
R = 110°
l = 110/360 × 2 × 3.14 × 6.4
l = 4787.2/369
l = 13.3 cm (1.dp)
therefore the length of the arc GH is 13.3 cm
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Sarah's bird feeder holds 1/2 of a cup of birdseed. Sarah is filling the bird feeder with a scoop that holds 1/4 of a cup. How many scoops of birdseed will Sarah put into the feeder?
Answers
The number of scoops of birdseed Sarah puts in the feeder n = 2
Given data ,
Let the number of scoops of birdseed Sarah puts in the feeder be n
While utilizing a scoop that can contain 1/4 cup of birdseed, Sarah's bird feeder holds 1/2 cup of birdseed. We must divide the capacity of the bird feeder by the capacity of the scoop to determine how many scoops Sarah will add to the feeder.
On simplifying the equation , we get
1/2 ÷ 1/4 = n
n = 1/2 x 4/1
n = 4/2
n = 2 scoops
Hence , the equation is solved and n = 2
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Victoria wants to figure out if she can run faster than
an elephant. She reads that an elephant can run 100
yards in 20 seconds. She knows she can run 60 feet in
10 seconds. Victoria says, "Since 60/10 = 6 and 100/20 = 5,
my speed is faster than an elephant's!" Does her
statement make sense? Explain why or why not.
20
Answer and explanation:
Answers
Victoria's statement that her running speed is faster an elephant's does not make sense because it is based on the comparison of unlike units of measurement.
How the above conclusion is reached:Elephant's running speed = 100 yards in 20 seconds
= 5 yards per second (100 ÷ 20)
Units of Measurement:1 yard = 3 feet
5 yards = 15 feet (5 x 3)
The elephant's running speed = 15 feet per second.
Victoria's running speed = 60 feet in 10 seconds
= 6 feet per second (60 ÷ 10)
Thus, we conclude that the elephant's running speed is 15 feet per second, while Victoria does 6 feet per second, making her claim untrue.
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Jake and Rafael are training for a bike race. Jake is a beginner and starts by riding up a hill with a 7.9° incline. Rafael is more experienced and rides up a hill with an 18.3° incline. If Jake and Rafael ride 100 ft., how much more horizontal distance did Jake cover?
Responses
4.1 ft.
4.1 ft.
9.6 ft.
9.6 ft.
17.7 ft.
17.7 ft.
19.2 ft.
Answers
The horizontal distance more that Jake was able to cover, given the incline, would be A.4.1 ft.
How to find the horizontal distance ?We can find the horizontal distance that both Jake and Raphael covered .
Jake's distance was:
cos ( 7.9 ° ) = adjacent / 100
adjacent = 100 x 0.989
adjacent = 98.9 ft
Rafael's distance was :
cos ( 18. 3° ) = adjacent / 100
adjacent = 100 x 0.951
adjacent = 95.1 ft
The difference and the distance covered in addition by Jake would be:
= 98. 9 - 95. 1
= 3. 8 ft
The closest option is 4. 1 ft.
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Jessica wants to make a ramp using a board so that she can ride her bike onto the front porch. The ramp must reach from the ground to the floor of the porch, which is 212
ft above the ground. Jessica has decided that the ramp cannot have an incline of more than 35°.
What length board should Jessica buy if she uses the maximum angle of incline?
Enter your answer in the box. Round only your final answer to the nearest tenth
Answers
Length of board should Jessica buy is 4.4 feets.
Step-by-step explanation:
Height of the ramp =
Distance of the porch from the ground = x
Inclination of the ramp,θ = 35°
In triangle ABC,
AB =
AC = x
θ = 35°
According trigonometric ratios:
Length of board should Jessica buy is 4.4 feets.
The length of one of the legs of a right triangle is 17. The lengths of the other two sides are consecutive integers. Use the Pythagorean theorem to solve for the smaller of the two missing sides (the second leg).
Answers
The value of the smaller of the two missing sides (the second leg) is,
⇒ 144 units
We have to given that;
The length of one of the legs of a right triangle is 17.
And, The lengths of the other two sides are consecutive integers.
Hence, Let the smallest of the other legs be x,
And, the hypotenuse be x + 1.
So, By using the Pythagorean theorem as;
⇒ 17² + x² = (x + 1)²
⇒ 289 + x² = x² + 1 + 2x
⇒ 2x = 288
⇒ x = 144
Thus, The value of the smaller of the two missing sides (the second leg) is,
⇒ 144 units
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