Robert can swim the first 50 meters of a race in 1 minute. Then he slows down by 12 seconds for each of the next 50 meters of a race. How long will it take Robert to swim a 400 meter race?
It takes Robert 13 minutes and 36 seconds to complete a 400 meter swimming race when he swims the first 50 meters in 1 minute and slows down by 12 seconds for each subsequent 50 meters.
Explanation:In this mathematical problem, Robert swims the first 50 meters in 1 minute. He slows down by 12 seconds for each subsequent 50 meters of the race. The total distance Robert needs to swim is 400 meters. The 400 meters is split into eight 50 meter increments.
For the first increment, it takes Robert 1 minute (or 60 seconds). For the next seven increments, Robert swims each in 12 seconds slower than the previous increment.
Therefore, the total time in seconds for Robert to complete the 400 meters swimming race is:
60 + 72 + 84 + 96 + 108 + 120 + 132 + 144 = 816 seconds
This is equivalent to 13 minutes and 36 seconds.
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Of all the rectangles with a perimeter of 168 feet, find the dimension of the one with the largest area
Final answer:
The largest area for a rectangle with a fixed perimeter of 168 feet is achieved by a square, and the dimensions of that square are 42 feet by 42 feet.
Explanation:
To find the dimensions of a rectangle with the largest area given a fixed perimeter, we need to understand that the rectangle with the largest area for a given perimeter is a square.
In this problem, the perimeter is 168 feet, which can be expressed by the formula 2l + 2w = 168, where l is the length and w is the width of the rectangle. Knowing that a square has all four sides equal, we simply divide the perimeter by 4 to get the side length, which gives us l = w = 168/4 = 42 feet.
Therefore, the dimensions of the rectangle with the largest area, which in this case is a square, are 42 feet by 42 feet.
Find three distinct fractions between -7/8 and -4/5
Tony and some friends went to the movies. They bought 4 drinks and 2 tubs of popcorn and spent a total of $32.50 on the food. Each drink cost $3.50 less than a tub of popcorn. Define a variable. Write and equation that can be used to find the cost of one tub of popcorn.
What is 1.5 x 10^-1 in standard form?
Answer:
the answer is .15
Step-by-step explanation:
Select the correct rate of change and y -intercept for the linear function that contains the points (4, 6) and (5, 3). Question 1 options: The rate of change is 3, and the y -intercept is –6. The rate of change is –3, and the y -intercept is 18. The rate of change is −1/3 and the y intercept is 7 1/3 The rate of change is 1/3 and the y intercept is 4 2/3
Use the distributive property in two different ways to find the product of 127 and 32.
Answer and explanation:
Use the distributive property in two different ways to find the product of 127 and 32.
Distributive property says that,
[tex]a(b+c)=ab+ac[/tex]
We have to find product of 127 and 32,
1) Split 127 as 100+27
[tex]127\times32=(100+27)\times 32[/tex]
Apply distributive property,
[tex]127\times32=100\times 32+27\times 32[/tex]
[tex]127\times32=3200+864[/tex]
[tex]127\times32=4064[/tex]
2) Split 32 as 30+2
[tex]127\times32=127\times (30+2)[/tex]
Apply distributive property,
[tex]127\times32=127\times 30+127\times 2[/tex]
[tex]127\times32=3810+254[/tex]
[tex]127\times32=4064[/tex]
Two worded maths questions. Even if you know one answer it would help! Please also give working out if possible.
Answer:
675 litres 80 mLStep-by-step explanation:
1. The total amount of oil in the two tanks at the start is ...
total oil = n + (n +150) + 0 = 2n+150 . . . . litres
The amount of oil in tank C at the end is 1/3 this amount, or
oil in tank C = (total oil)/3 = (2n+150)/3 . . . . litres
The amount pumped into tank C was 500 litres, so we have ...
(2n +150)/3 = 500
2n +150 = 1500 . . . . . . multiply by 3
2n = 1350 . . . . . . . . . . . subtract 150
1350/2 = n = 675 . . . . . divide by the coefficient of n
___
2. Let x represent the amount remaining in container A. Then 4x is the amount in tank B. Before the transfer, the amount in each container was the same, so ...
x +120 = 4x -120 . . . . . A had 120 more than remains; B had 120 less
240 = 3x . . . . . . . . add 120-x
240/3 = x = 80 . . . divide by the coefficient of x
The amount of liquid left in container A is 80 mL.
The function h(t) = –16t2 + 96t + 6 represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet.
Find the distance between the points given. (2, 5) and (6, 8) √(37) 5 √(22)
Answer: The correct option is (B) 5.
Step-by-step explanation: We are given to find the distance between the points (2, 5) and (6, 8).
We will be using the following formula :
DISTANCE FORMULA : The distance between the points (a, b) and (c, d) is given by
[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]
Therefore, the distance between the points (2, 5) and (6, 8) is given by
[tex]D\\\\=\sqrt{(6-2)^2+(8-5)^2}\\\\=\sqrt{4^2+3^2}\\\\=\sqrt{16+9}\\\\=\sqrt{25}\\\\=5.[/tex]
Thus, the required distance between the given points is 5 units.
Option (B) is CORRECT.
"THIS IS A 90 POINT QUESTION"
A) F IS A INCREASING ON THE INTERVAL X < 0
B) F IS A DECREASING ON THE INTERVAL X < 0
C) F IS A INCREASING ON THE INTERVAL 0 < X < 1
D) F IS A DECREASING ON THE INTERVAL 0 < X < 1
E) F IS A INCREASING ON THE INTERVAL 1 < X < 3
F) F IS A DECREASING ON THE INTERVAL 1 < X < 3
G) F IS A INCREASING ON THE INTERVAL X > 3
H) F IS A DECREASING ON THE INTERVAL X > 3
"SELECT ALL THAT APPLY"
Which expression shows how to multiply 5 times 381 by using place value and expanded form
A certain airplane has two independent alternators to provide electrical power. the probability that a given alternator will fail on a one-hour flight is 0.019. (a) what is the probability that both will fail? (round your answer to 4 decimal places.) probability (b) what is the probability that neither will fail? (round your answer to 4 decimal places.) probability (c) what is the probability that at least one fails? (round your answer to 4 decimal places.) probability referencesebook & resources
The probability that both alternators fail is approximately 0.0004, the probability that neither fails is approximately 0.9612, and the probability that at least one fails is approximately 0.0388, all rounded to four decimal places.
(a) The probability that both Alternator will fail is calculated by multiplying the probabilities of each failing:
P(Both Fail) = P(Alternator 1 Fails) x P(Alternator 2 Fails) = 0.019 x 0.019 ≈ 0.000361 = 0.0004 (rounded to four decimal places).
(b) The probability that an alternator does not fail is 1 minus the probability that it fails.
P(Neither Fail) = (1 - P(Alternator Fails))^2 = (1 - 0.019)^2 ≈ 0.9612 (rounded to four decimal places).
(c) To find the probability of at least one alternator failing, we subtract the probability of neither failing from 1:
P(At Least One Fails) = 1 - P(Neither Fail) = 1 - 0.9612 ≈ 0.0388 (rounded to four decimal places)
What is 2x-4y=20 for y
The savings account offering which of these APRs and compounding periods offers the best APY?
4.0784% compounded monthly
4.0798% compounded semiannually
4.0730% compounded daily
Answer:
Option C is correct.
Step-by-step explanation:
The formula is = [tex](1+\frac{r}{n})^{n}-1[/tex]
r = rate of interest
n = number of times its compounded
1. 4.0784% compounded monthly
here n = 12
[tex](1+\frac{0.040784}{12})^{12} -1[/tex] = 1.0403-1 = 0.0403
2. 4.0798% compounded semiannually
here n = 2
[tex](1+\frac{0.040798}{12})^{2} -1[/tex] = 1.0066-1 = 0.0066
3. 4.0730% compounded daily
here n = 365
[tex](1+\frac{0.040730}{12})^{365}[/tex] = 3.328-1 = 2.328
Find the area of the surface. the part of the cylinder y^2+z^2=9 that lies above the rectangle with vertices (0,0),(4,0),(0,2), and (4,2)
To find the area of the surface above the given rectangle, we need to determine the intersection of the cylinder with the plane of the rectangle. The surface area above the rectangle is equal to the area of the rectangle multiplied by the range of the z-coordinate.
Explanation:To find the area of the surface that lies above the given rectangle, we need to determine the intersection of the cylinder with the plane of the rectangle. The equation of the cylinder is y^2+z^2=9, and the vertices of the rectangle are (0,0), (4,0), (0,2), and (4,2). At the x=0 and x=4 cross sections, we can see that the y-coordinate ranges from 0 to 2 and the z-coordinate ranges from -3 to 3. Therefore, the surface area above the rectangle is equal to the area of the rectangle multiplied by the range of the z-coordinate.
The area of the rectangle is (4-0)(2-0) = 8 square units. The range of the z-coordinate is -3 to 3, so the surface area above the rectangle is 8 * (3 - (-3)) = 48 square units.
A rocket is launched with an initial velocity of 360 ft/s. The height of the rocket in meters is modeled by the function shown below, where t is time in seconds. h(t)=‒10t2 + 360t Which statement is true?
A. The rockets maximum height is 324 feet.
B. The rockets maximum height is 3240 feet.
C. In the interval from 9 seconds to 18 seconds, the rocket is descending.
D. The rocket hits the ground in 18 seconds.
John has painted 4/5 of his house the next day he painted 2/3 of what he had left what fraction of the house is left to paint
A major league baseball pitcher throws a pitch that follows these parametric equations:
x(t) = 143t
y(t) = –16t2 + 5t + 5.
Recall that the speed of the baseball at time t is
s(t)=√ [x '(t)]2 + [y ' (t)]2 ft/sec.
What is the speed of the baseball (in mph) when it passes over homeplate?
The speed of the baseball when it passes over the home plate is 97.67 mph.
Given :
[tex]x(t) = 143t[/tex] ---- (1)[tex]y(t) = -16t^2+5t+5[/tex] ---- (2)The distance between the pitcher's plate and the home plate is 60.5 ft.Differentiate the function x(t) and y(t) with respect to t.
[tex]x'(t)=143[/tex]
[tex]y'(t)= -32t+5[/tex] ---- (3)
Now, put the value of x(t) in equation (1).
60.5 = 143t
t = 0.423 sec
Now, put the value of t in equation (3).
[tex]y'(t) = -32(0.423)+5=-8.536[/tex]
Now, [tex]s(t) = \sqrt{(x'(t))^2+(y'(t))^2}[/tex]
[tex]s(t)=\sqrt{143^2+(-8.536)^2}[/tex]
[tex]\rm s(t)=\sqrt{20521.8633} = 143.2545\;ft/sec[/tex]
[tex]\rm s(t) = 97.67 mph[/tex]
Therefore, the speed of the baseball when it passes over the home plate is 97.67 mph.
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Solve the simultaneous equations
5x-4y=19
x+2y=8
please help me with this
Cours hero a simple random sample of 64 8th graders at a large suburban middle school indicated that 89% of them are involved with some type of after school activity. find the 98% confidence interval that estimates the proportion of them that are involved in an after school activity.
a.[0.799, 0.981]
b.[0.699, 0.931]
c.[0.849, 0.854]
d.[0.799, 0.781]
e.[0.719, 0.981] f) none of the above
Final answer:
Using the formula for the confidence interval of a proportion, and after calculating standard error and margin of error, the 98% confidence interval for the proportion of 8th graders involved in after school activities is [0.799, 0.981]. Therefore, option a is correct.
Explanation:
To find the 98% confidence interval for the proportion of 8th graders involved in some type of after school activity, we can use the formula for the confidence interval of a proportion:
CI = ± z * √((p*(1-p))/n), where p is the sample proportion, n is the sample size, and z is the z-score corresponding to the confidence level.
In this case, we have p = 0.89 (since 89% of the sample is involved in after school activities), n = 64, and for a 98% confidence interval, the z-score (from z-tables or statistical software) is approximately 2.33.
First, let's calculate the standard error (SE): SE = √((0.89*(1-0.89))/64) = √((0.89*0.11)/64) = √(0.0989/64) = 0.0392.
Next, calculate the margin of error (ME): ME = z * SE = 2.33 * 0.0392 = 0.09136.
Now we can calculate the confidence interval: the lower limit is p - ME = 0.89 - 0.09136 = 0.79864 and the upper limit is p + ME = 0.89 + 0.09136 = 0.98136.
After rounding to three decimal places, the 98% confidence interval for the proportion is [0.799, 0.981]. Hence, option a is correct.
The shadow of a vertical tower is 50 m long when the angle of elevation of the sun is 35°. find the height of the tower. © k12 inc. 2. an airplane is flying 12,330 feet above level ground. the angle of depression from the plane to the base of a building is 11°. how far must the plane fly horizontally before it is directly over the building?
Salespeople make an average of $1,000 per week. There are nine salespeople. What would the ninth person need to earn for the mean to be $1,000 if the other eight salespeople earned $550, $600, $600, $800, $950, $950, $1,000, and $1,100?
To get an average earnings of $1,000 for all nine salespeople, the ninth salesperson needs to earn $2,450.
Explanation:The subject of this question is mathematics, specifically statistics, and it involves the concept of 'mean' or 'average'. To find out what the ninth person needs to earn to keep the average earn of $1,000, we first need to calculate the total earnings of all nine people. Since the average earnings of a salesperson is $1,000, we multiply $1,000 by 9, which gives us $9,000. Then we need to subtract the sum of the earnings of the first eight salespeople from $9,000 to find out the earnings of the ninth person.
Here is the breakdown with the given figures:
The sum of the earnings of the first eight salespeople is: $550 + $600 + $600 + $800 + $950 + $950 + $1,000 + $1,100 = $6,550Subtract this from the total ($9,000): $9,000 - $6,550 = $2,450So, the ninth person would need to earn $2,450 for the average earnings to remain at $1,000.
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whats the slope of (0,1) and (2,7)
numbers in order from least to greatest. -5.25, 1.002, -5.09
-5.25, -5.09, 1.002
hopes this help please mark me as brainliest. :)
Trina's employer purchased a health insurance plan that cost $550 per month Trina pays $85 toward the plan each month what is the annual value of the employer's contribution
The annual value of the employer's contribution towards Trina's health insurance plan is $5,580.
Here, we have to find the annual value of the employer's contribution, we need to determine how much the employer pays towards the health insurance plan in one month.
Trina's employer purchased a health insurance plan that costs $550 per month, and Trina pays $85 toward the plan each month.
Therefore, the employer's contribution is the difference between the total cost of the plan and what Trina pays:
Employer's contribution = Total cost of the plan - Trina's contribution
Employer's contribution = $550 - $85
Employer's contribution = $465 per month
Now, to find the annual value of the employer's contribution, we multiply the monthly contribution by 12 (since there are 12 months in a year):
Annual employer's contribution = $465 * 12
Annual employer's contribution = $5,580
So, the annual value of the employer's contribution towards Trina's health insurance plan is $5,580.
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David is playing a trivia game where he gains points for correct answers and loses points for incorrect answers. At the start of round 3 his score is −1500 points. During round 3 he answered five 1000 point questions correctly and three 500 points questions incorrectly. What is his score at the end of round 3?
A) −2000
B) −500
C) 2000
D) 3500
Answer:
2000 points
Step-by-step explanation:
Topic: Substraction, Addition and Products
You have to organize the problem, as you can see
at Start of Round 3 David Has: - 1500
During Round 3:
5 Questions: 1000 each correctly
so 5 x 1000 = 5000
3 Questions: - 500 each incorrectly
so 3 x -500 = -1500
at the End of Round 3:
Starting: -1500
During Round 3: 5000 - 1500 = 3500
the end of round 3: -1500 + 3500 = 2000
THe cost of a hamburger is $2.50. Each additional hamburger cost $2.00. Sully wrote this explicit rule to explain the sequence of costs: f(n) = 2 + 2.5(n-1). Using the rule, he found the cost of 12 hamburgers to be 29.50. Is this number correct?
Answer:
Yes, the number is correct.
Step-by-step explanation:
The cost of a hamburger is $2.50.
Each additional hamburger cost $2.00.
Sully wrote this explicit rule to explain the sequence of costs:
[tex]f(n) = 2+2.5(n-1)[/tex]
Using the rule, he found the cost of 12 hamburgers to be 29.50.
Lets check by putting n = 12.
[tex]f(12) = 2+2.5(12-1)[/tex]
= [tex]2+2.5(11)[/tex]
= [tex]2+27.5 [/tex]
= $29.50
So, yes Sully is correct.
Select "Rational" or "Irrational" to classify each number. Rational Irrational 0.25 √ 0.25 √0.33