The expression for the total time is:
T = (324/34x).
How to get the expression?He does 18 laps in total.
8 laps at a rate of 3x10 laps at a rate of x.The average rate for the whole 18 laps is the average of the rates (taking in account the number of laps made with each) so we get:
average rate = (8/18)*3x + (10/18)*x = (34x/18)
This means that he does (34x/18) laps per hour.
Then, the time needed to do 18 laps is:
T = (18/(34x/18)) = (324/34x).
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6. A circle has a circumference whose length is 25pi . Find the length of an arc whose
central angle is 90°.
Answer:
So, A 90° central angle cuts off an arc which has length 90/360 = 1/4 of the circumference. Therefore, length of arc = (1/4)(25π) = 25π/4.
Step-by-step explanation:
espero te sirva
a regular polygon has 33 sides find the size of each interior angle
Answer:
169.09 degrees
Step-by-step explanation:
Interior Angle of a polygon with 33 sides = (n-2) x 180/n degrees = (33-2) x 180/33 degrees = 169.09 degrees
33 sides
to find:the size if each interior angle.
solution:[tex] \frac{360}{33} [/tex]
[tex] = 10.91[/tex]
[tex]180 - 10.91[/tex]
[tex] = 169.09[/tex]
[tex] \frac{169.09}{33} [/tex]
[tex] = 5.12[/tex]
hence, the size of each interior angle is 5.12°
Determine the probability of having 1 girl and 3 boys i a 4 child family assuming boys and girls are equally likely
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Im glad i could help out.
Leaf U. Allone needs to borrow $120,000 from his local bank for the home he is buying. The bank offers a 30 year mortgage at an APR of 6.5%.
A) How many monthly payments would it take to pay off the 30 year loan?
B) What is her monthly payment on the 30 year loan?
C) What is the total paid to the bank over 30 years?
D) How much of that is interest?
Answer:
A) It would take 360 monthly payment to pay of the 30-year loan.
B) Her monthly payment would be $650.
C) The total paid back to bank over 30 years would be $234,000
D) The total amount of interest was $114,000 (95% interest back to the bank after 30 years).
Step-by-step explanation:
6.5 percent *120000 =
(6.5:100)*120000 =
(6.5*120000):100 =
780000:100 = 7800
6.5% of 120,000 is 7,800.
Every year Leaf U. Allone has to pay $7,800 to the bank.
12 months in a year.
7,800 ÷ 12 = $650
Every month Leaf U. Allone has to pay $650 to the bank.
Over 30 years of paying 7,800
Multiply 7,800 * 30
= $234,000
To find the interest,
subtract 120,000 from 234,000
= $114,000 in interest.
Meaning the home value went up.
Zach's step counter tracked how many steps he took each day for a week. Number of steps 2,000 4,000 6,000 8,000 10,000 What was Zach's median number of steps?
Answer: 8,000
Step-by-step explanation: Did it on IXL
1. The final scores from the last five games of two basketball teams are given.
Jumping Jackrabbits: 70, 65, 72, 80, 73
Leaping Lizards: 61, 47, 70, 63, 54
(a) Determine the MAD of each data set. In your work, show the mean and the absolute deviation of
each data value in each set.
(b) Compare and interpret the MADs in context of the situation.
Answer:
Using it's concept, it is found that:
a) For the Jumping Jackrabbits, the MAD is of 3.6 and for the Leaping Lizards, the MAD is of 6.8.
b) Due to the higher value of the MAD, the Leaping Lizards have less consistent scores than the Jumping Jackrabbits.
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the number of observations.The mean absolute deviation(MAD) of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.Item a:
For the Jumping Jackrabbits, the mean and the MAD are given by:For the Jumping Jackrabbits, the MAD is of 3.6 and for the Leaping Lizards, the MAD is of 6.8.
M = (70 + 65 + 72 + 80 + 73)/5 = 72
MAD = (|70 - 72| + |65 - 72| + |72 - 72| + |80 - 72| + |73 - 72|)/5 = 3.6.
For the Leaping Lizards, the mean and the MAD are given by:
M = (61 + 47 + 70 + 63 + 54)/5 = 59
MAD = (|61 - 59| + |47 - 59| + |70 - 59| + |63 - 59| + |54 - 59|)/5 = 6.8.
For the Jumping Jackrabbits, the MAD is of 3.6 and for the Leaping Lizards, the MAD is of 6.8.
Item b:
Due to the higher value of the MAD, the Leaping Lizards have less consistent scores than the Jumping Jackrabbits.
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Find the arc length of the semicircle.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
Answer:
18.852
Step-by-step explanation:
Formula to find the arc of semi circle is :
Arc length = π r
Given that,
diameter ⇒ 12
So, the radius will be,
Radius ⇒ 12 / 2
⇒ 6
Let us solve now.
Arc length = π r
= 3.142 × 6
= 18. 852
Can somebody help me with this it's the last question and i'm somehow very confused
Pls pls pls pls help po
HELP A marble paperweight shaped similar to a prism weighs 0.2 lb. How much does a similarly shaped marble paperweight weigh if its length, width, and height are tripled?
5.4 lb
0.6 lb
0.8 lb
1.8 lb
Answer:
0.6 lbs
0.2 ×3=0.6
explanation
Trust
Mr. Marsh plans to tile the floor in his 6-foot by 8-foot front hall. If each tile is an 8-inch square. what is the minimum number of tiles needed to cover the floor?
The division is one of the four fundamental arithmetic operations. The number of tiles that will be needed to cover the entire area of the hall is 864.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
The area of the hall with dimensions 6 feet by 8 feet are:
[tex]\rm \text{Area of the hall} = 6 feet \times 8foot =48\ feet^2[/tex]
The area of the tile is 8 square inches, therefore, the area of tile in square feet can be written as,
[tex]\rm \text{Area of the tile} = \dfrac8{12 \times 12}\ feet^2[/tex]
Noe, the number of tiles needed to tile the complete area of the hall is,
[tex]\text{Number of tiles needed} = \dfrac{\text{Area of the hall}}{\text{Area of the tile}}\\\\\\\text{Number of tiles needed} = \dfrac{48}{\frac8{12 \times 12}} = \dfrac{48 \times 12 \times 12}{8} = 864[/tex]
Hence, the number of tiles that will be needed to cover the entire area of the hall is 864.
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Anna surveyed 300 of the students in her school about their favorite color. 186 students said their favorite color was red. What percentage of the surveyed students said their favorite color was red
Answer:
62 %
Step-by-step explanation:
186 out of 300
186/300 = .62 this represents 62%
HELP ME PLEASEEE URGENT I’ll mark the brainiest!!
216.66
169π-100π=69π
69*3.14= 216.66
How did u find 12? Because In my answer choices it doesn’t have 12
Answer:
Salamat sa puntosStep-by-step explanation:
filipino akoYou want to bake a 20" diameter pizza. Give exact answers.
a. What should be the circumference of the pan?
b. What is the area of the pizza?
c. If you cut the pizza into 8 congruent slices, what is the area of one slice?
d. What is the length of the crust of one slice?
Step-by-step explanation:
pizza = circle
the area of a circle is
pi×r²
r = radius (half of the diameter). in our case 20/2 = 10".
the circumference of a circle is
2×pi×r
again, r = radius.
in our case that gives us
a.
2×pi×r = 2×pi×10 = 20×pi = 62.83185307... "
b.
the area of the pizza is
pi×10² = 100×pi = 314.1592654... in²
c.
it is 1/8 of the whole area, of course.
314.1592654... / 8 = 39.26990817... in²
d.
it is 1/8 if the whole circumference, of course.
62.83185307... / 8 = 7.853981634... "
Given the points M = (8, 4, –3) and N = (–12, 6, –7), find Vector M N. in component form.
Vector M N = LeftAngleBracket 4, negative 10, 10 RightAngleBracket.
Vector M N = LeftAngleBracket negative 4, 10, negative 10 RightAngleBracket.
Vector M N = LeftAngleBracket 20, negative 2, 4 RightAngleBracket.
Vector M N = LeftAngleBracket negative 20, 2, negative 4 RightAngleBracket.
Considering the points M and N, the vector MN is component form is given by:
MN = [-20, 2, -4]
How to find a vector given two end-points?
The vector is given by the subtraction of the coordinates of the endpoint by the coordinates of the start point.
In this problem, for vector MN, we have that:
The endpoint is N = (–12, 6, –7).The start point is M = (8, 4, –3).Hence:
MN = N - M = [-12 - 8, 6 - 4, -7 - (-3)] = [-20, 2, -4]
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Answer:
D on edge ( MN = (-20, 2 , -4)
Step-by-step explanation:
Help! I got it wrong the first time
Answer:
The correct correspondence is B.
The annual number of burglaries in a town rose by 50% in 2012 and fell by 10% in 2013. hence the total number of burglaries increased by 40% over the two year period.
a. by what percent has the number of burglaries actually changed in the two-year period?
b. by what percent would the crime have to decrease in the second year in order for the change over the two-year period to actually be a 40% increase?
Answer:
a) 35%
b) 6.67%
Step-by-step explanation:
a) The annual number of burglaries in 2012 would be 150% and since in 2013, it fell by 10%:
10% of 150 is 15 so 150-15 = 135%.
The actual percentage increase of burglaries is 135% - 100% = 35% not 40%.
b) In the second year, the percentage would have to decrease by 10% of the initial 150% so [tex]\frac{10}{150}[/tex] = [tex]\frac{1}{15}[/tex] which as a percentage would be 6.66666....% or 6.67%.
The number of burglaries actually changed in the two-year period will be 35% and the crime have to decrease in the second year in order for the change over the two-year period to actually be a 40% increase will be 6.7%
BurglariesIt is act of breaking and entering a dwelling at night to commit a felony such as theft.
How to solve this problem?The steps are as follow:
Let us assume that the annual number of burglaries in 2011 are 100. After that there is 50% increase in 2012 so the number of burglaries will be: 100(1.50) = 150.Burglaries after the 10% reduction in 2013 would be: 150(.90) = 135So there will be change in burglaries over the two-year period = (135 / 100) - 1 = 35% To know how much burglaries would have to reduce in order to have a 40% change in burglaries we would be using the following formula:(x - 100) / 100 = 0.40
x - 100 = 40
x = 140
Change in burglaries over the two-year period to have 40% increase = (140 / 150) - 1 = 6.7%So, burglaries after the 10% reduction in 2013 would be 35% and change in burglaries over the two-year period to have 40% increase will be 6.7%.
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the sides of a triangle are 54,31,and 69. use the phone ythagorean theorem to determine if the triangle is right acute or obtuse.
Answer:
obtuse
Step-by-step explanation:
a² + b² = c²
Let's use the two shorter sides as legs.
a² + b² = 31² + 54² = 961 + 2916 = 3877
c = √3877 = 62.2655...
For the triangle to be a right triangle, the third side would have to have a length of 62.2655. The actual length of the third side is 69. 69 is greater than 62.3, so the angle between the sides 31 and 54 must be greater than 90°. Therefore the triangle is an obtuse triangle.
28/100 = ?/10 + 8/100. this is the second time i asked i need help on my work
Answer:
2/10
Step-by-step explanation:
28/100 - 8/100 = 20/100 = 2/10
find the mean, median and mode of the following data set: 8, 12, 15, 3, 7, 10, 15
8, 12, 15, 3, 7, 10, 15
to find:mean, median and mode.
solution:mean:to find mean you'll have to add all of the numbers and divide by the number of numbers in the data set.
[tex] \frac{(8 + 12 + 15 + 3 + 7 + 10 + 15)}{7} [/tex]
[tex] = \frac{70}{7} [/tex]
[tex] = 10[/tex]
median:to find median you'll have to order the numbers either in descending or ascending, and find the number in the middle.
[tex]3 \: 7 \: 8 \: 10 \: 12 \: 15 \: 15[/tex]
=10
mode:most frequently occurred number is the mode.
[tex] = 15[/tex]
What is the vertex of f(x)=x2−8x+15 ?
Answer:
(4,-1)
i strongly believe that is the answer, pls mark as brainlist
5(x - 20) = 1/2 (4x + 4)
Show your work
Help
Answer: 334
Step-by-step explanation: Find the steps in the file
Answer:
34
Step-by-step explanation:
1. Expand 5(x - 20):
Use the distributive property to distribute 5 to x and -205x - 100
2. Expand [tex]\frac{1}{2} (4x + 4)[/tex]:
Use the distributive property to distribute [tex]\frac{1}{2}[/tex] to 4x and 42x + 2
3. Add 100 to both sides:
5x - 100 = 2x + 2
5x - 100+100 = 2x + 2+100
5x = 2x + 102
4. Subtract 2x from both sides:
3x = 102
5. Divide both sides by 3:
x = 34
hope this helps!
a - 1 = 70; a = 71 solution or not a solution??
solution
hope it helps...!!!
The exam scores in Bryan's class are Normally
distributed with a mean of 88 points and a standard
deviation of 1.5 points.
Exam Scores
83.5 85 86.5 88 89.5 91 92.5
Score
Which statements are true? Check all that apply.
□ About 16% of all exam scores are less than 86.5
points.
About 16% of all exam scores are greater than 89.5
points.
About 68% of the test scores fall between 85 and 91
points.
About 84% of all exam scores are less than 89.5
points.
About 84% of all exam scores are greater than 89.5
points.
0
Using the Empirical Rule, it is found that the correct statements are given by:
About 16% of all exam scores are less than 86.5 points.About 16% of all exam scores are greater than 89.5 points.About 84% of all exam scores are less than 89.5 points.What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.We also have to consider that the normal distribution is symmetric. Then, alog with the mean of 88 and standard deviation of 1.5, the correct statements are given by:
About 16% of all exam scores are less than 86.5 points(more than 1 standard deviation below the mean, the percentage, considering the symmetry, is 0.5 x 32 = 16%).About 16% of all exam scores are greater than 89.5 points, due to the same explanation as above.About 84% of all exam scores are less than 89.5 points, as the percentage is 50%(all below the mean) + 50% x 68%(one standard deviation above the mean) = 84%.More can be learned about the Empirical Rule at https://brainly.com/question/24537145
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Answer:
Step-by-step explanation:
Fill in the correct values in the statements.
About 68% of the observations will fall within
⇒ 1.5 points of the mean of
⇒ 88 points.
About
⇒ 95% of the observations will fall within 3 points of the mean.
About 99.7% of the observations will fall within
⇒ 4.5 points of the mean.
Consider the function
f(x) = x² ln(x)
Find the second derivative and use it to calculate f''(1). Type your answer in the space below.
Answer:
y'=(1/x^2-3/x^4)*(1+15x^2)+(-2/x^3+12/x^5)(x+5x^3)
Step-by-step explanation:
We know that (x2)′=2x and that (ln(x))′=1x, soOr, putting x in evidence
You're really good at investing
Answer:
What do you mean by "You are really good at investing" ?
Step-by-step explanation:
Christine exercises more than 40 minutes per day.
Use t to represent Christine's amount of exercise (in minutes per day).
Answer:
t=40+
Step-by-step explanation:
I couldn't really tell what you meant by that question
what is the area of the figure
Answer:
Explanation:
So you want to start by finding the area of the big square.
We know the width of the big square is 60cm. The length of the big square is
19
+
24
+
13
=
56
Big square
A
r
e
a
=
L
⋅
W
=
56
⋅
60
=
3360
Now let’s find the little square inside the bigger square. We see from the picture that the width is 34 and the length is 24cm. Using the same formula, we can find the area of the little square.
Little square
A
r
e
a
=
L
⋅
W
=
24
⋅
34
=
816
The area is enclosed in the area of the big square minus the area of the little square.
3360
−
816
=
2544
So the area enclosed is
2544
c
m
2
Step-by-step explanation:
The cost of a first-class postage stamp in 1962 was 4. In 1999 it is 33. The cost was (and is) growing exponentially. What was the growth rate? What will be the cost of a first-class postage stamp in 2010?
Answer:
The growth rate was 5.87%
Step-by-step explanation:
Time interval is t=1999−1962=37 yearsInitial cost in 1962 was a=4 unit Final cost in 1999 was y=33 unit Exponential growth function :y=a(1+r)t;a>0,r>0,ris rate of growth in decimal form.y=a(1+r)tor33=4(1+r)37 or(1+r)37=334or(1+r)37=8.25 , taking log on bothsides we get, 37log(1+r)=log(8.25) orlog(1+r)=log(8.25)37orlog(1+r)≈0.24769(1+r)=100.24769or1+r≈1.0587∴r=0.0587 orr%=0.0587⋅100≈5.87%The growth rate was 5.87% [Ans]