Answer:
The surface area of the sphere is 86525.84 square yards
Step-by-step explanation:
The widest circle of the sphere has the same radius of the sphere
Use the circumference of the circle to find its radius, then use it to find the surface area of the sphere
The formula of the circumference of the circle is C = 2π r
The formula of the surface area of the sphere is SA = 4π r²
∵ The circumference of the widest circle is 521.24 yards
∴ C = 521.24
- Equate the formula of the circumference by it
∴ 2π r = 521.24
∵ π ≈ 3.14
∴ 2(3.14) r = 521.24
∴ 6.28 r = 521.24
- Divide both sides by 6.28
∴ r = 83 yards
Now use the formula of the surface area of the sphere to find it
∵ The radius of the sphere = the radius of the widest circle
∴ The radius of the sphere is 83 yards
∵ SA = 4π r²
- Substitute r by 83 and π by 3.14
∴ SA = 4(3.14)(83)²
∴ SA = 86525.84
The surface area of the sphere is 86525.84 square yards
Round to 2 SF
0.00706
please
The rounded number is 0.01.
To round 0.00706 to 2 significant figures, we first need to identify the non-zero digits and any zeros between them. The non-zero digits in this number are 7 and 6. There are no zeros between them.
Since the second significant digit is 6, which is greater than or equal to 5, we round the first significant digit up. Therefore, the rounded number is 0.01.
Here is a table of the rounding rules:
| Digit to the right of the last significant digit |
| Less than 5 | Round the last significant digit down |
| 5 or greater | Round the last significant digit up |
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Pay Periods a
Due Apr 10, 20:
D Question 4
10 pts
Last season, LeBron James played 74 games. He was paid $31 for the season.
a) How much does that mean he earned per game? Round to the nearest cent.
b) He played a total of 2,796 minutes in the season. What was his pay per minute?
Round to the nearest cent.
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Answer:
¢42 per game
¢1.11 per minute
Step-by-step explanation:
Please refer to the attached image for explanations
LeBron James earns approximately $0.42 per game and $0.01 per minute based on the given salary and total games and minutes played for the season.
The student has asked two questions about calculating earnings per game and per minute for LeBron James, based on a given salary for a season and the total number of games and minutes played.
To calculate the earnings per game, we divide the total salary for the season by the number of games played. If LeBron James was paid $31 for the season and played 74 games, his earnings per game would be: $31 ÷ 74 games = $0.4189 per game, which rounds to $0.42 per game to the nearest cent.
For the earnings per minute, we divide the total salary for the season by the total number of minutes played. With $31 for the season and 2,796 minutes played, his pay per minute would be: $31 ÷ 2,796 minutes = $0.0111 per minute, rounding to $0.01 per minute to the nearest cent.
Determine ƒ(a + h) for ƒ(x) = 2x3.
ƒ(a + h) = 2(a3 + 3a2h + 3ah2 + h3)
ƒ(a + h) = 8(a3 + 3a2h + 3ah2 + h3)
ƒ(a + h) = 8(a3 + h3)
ƒ(a + h) = 2(a3 + a2h + ah2 + h3)
Answer:
ƒ(a + h) = 2(a^3 + 3a^2h + 3ah^2 + h^3)
Step-by-step explanation:
Put (a+h) in place of x and "simplify" the expression.
f(x) = 2x^3
f(a +h) = 2(a +h)^3 = 2(a^3 +3a^2h +3ah^2 +h^3) . . . . matches 1st choice
_____
It helps to know the expansion of a binomial:
(a +b)^3 = a^3 +3a^2b +3ab^2 +b^3
Even if you don't, you can multiply it out.
(a +b)^3 = (a +b)(a^2 +2ab +b^2) = a^3 +2a^2b +ab^2 +a^2b +2ab^2 +b^3
= a^3 +3a^2b +3ab^2 +b^3
Rhada has a 3-pound bag of clay. Her craft project requires 3 oz of clay for each batch of 4 ornaments.
If she uses all of the clay, how many ornaments can she make?
Answer:
64
Step-by-step explanation:
The first thing we should know is the equivalence between pound and ounce.
1 pound equals 16 ounces. Which means that Rhada has a total of:
3 * 16 = 48 ounces of clay.
We are told that for every 3 ounces of clay you can make 4 ornaments., therefore:
48 * 4/3 = 64 ornaments
Which means that you can with the amount of clay you have can make 64 ornaments.
Answer:
64
Step-by-step explanation:
Sam is stacking cans of vegetables at the store his shelf is 10 in tall and 10in wide and the cans are 4 in tall and each has a volume of 50.24in how many cans will fit on the shelf?
Answer:
7 cans
Step-by-step explanation:
-The number of cans that can be fitted is obtained by dividing the volume of the shelf by the volume of an individual can.
-Volume of the shelf is calculated as below:
[tex]V_{shelf}=lwh\\\\=10\times10\times4\\\\=400\ in^3[/tex]
#We then divide by the volume of a can:
[tex]No \ of \ cans=\frac{V_{shelf}}{V_{can}}\\\\=\frac{400}{50.24}\\\\=7.96\approx 7\ cans[/tex]
We round down since the 8th can cannot properly fit.
Hence, only 7 cans will fit in the shelf
A shelf that is 10 inches tall and 10 inches wide can fit up to 4 cans of vegetables.
To determine how many cans of vegetables fit on Sam's shelf, we need to compare the dimensions of the shelf with the dimensions of the cans. Given:
Shelf height: 10 inchesShelf width: 10 inchesCan height: 4 inchesCan volume: 50.24 cubic inchesWe assume we stack the cans upright, which is the most common arrangement in a shelf. Each can occupies a 4-inch height. Therefore, we can stack:
10 inches / 4 inches = 2.5 cans
Since we cannot have half a can, we round down to 2 cans high. The shelf width allows for:
10 inches / 4 inches = 2.5 cans wide
Again, rounding down, 2 cans wide. Since we only have shelf dimensions in height and width (depth isn't mentioned, we'll assume a single layer in depth), the total number of cans that fit is:
2 (height) x 2 (width) = 4 cans
in a wildlife preserve, a random sample Of the population of 150 raccoons was caught and weighed. The results, Given in pounds, were 17 19 20 21 23 27 28 28 28 and 32. Jean made the inference the average weight of the raccoon population is 25 pounds is the statement reasonable?
Answer:
It is not reasonable
Step-by-step explanation:
We have a population of 150 and the person takes 10 data from the raccoons, if we take the average of these values, we are left with:
(17 +19 +20 +21 +23 +27 +28 +28+ 28 + 32) / 10 = 24.3
Therefore the inference of the average weight is to approximate up to 25.
This is NOT correct, since it cannot be approximated in this way first and also that the sample is not representative. 10 sample data of 150, which is the population, will give results with a very large margin of error and with a minimum level of confidence.
Therefore it is not reasonable.
Answer:
No
Step-by-step explanation:
Here we have the weights as follows
17, 19, 20, 21, 23, 27, 28, 28, 28, 32
Sum = 243 pounds
Sample size = 10
Which gives the average as 243/10 = 24.3
Therefore, since the average is a point estimate, and measure of central tendency, to give the average rounded up in error will impact on the description of the data as the average is closer to 24 than to 25.
0.694 rounded to the nearest hundredth is
0.694 rounded to the nearest hundredth remains 0.69 because the third digit after the decimal is 4, which is less than 5.
The question asks for 0.694 to be rounded to the nearest hundredth.
To round to the nearest hundredth, you look at the third digit after the decimal point.
If this digit is 5 or greater, you round the second digit after the decimal up.
In this case, the third digit is 4, which is less than 5.
Therefore, when rounding 0.694 to the nearest hundredth, it remains 0.69.
Joseph and Wilson each started out at their own houses and are biking towards each other. Joseph started out first, and has already gone 10 kilometers. He bikes at a constant speed of 7 kilometers per hour. Wilson just left, and rides at 9 kilometers per hour. When the boys meet halfway between their houses, they will continue to the park together. How far will each boy have ridden to meet the other halfway? How long will that take?
Joseph and Wilson will each have ridden 45 kilometers to meet halfway, and it will take each of them 5 hours to do so.
Joseph and Wilson are biking towards each other. Joseph has already traveled 10 kilometers and is moving at a constant speed of 7 kilometers per hour. Wilson has just started and rides at a speed of 9 kilometers per hour. To determine how far each boy will have ridden to meet halfway and how long that will take, we need to use the relation between distance, speed, and time.
Let's assume the total distance between their houses is 2d kilometers. Meeting halfway means each boy will cover d kilometers. We already know Joseph has covered 10 kilometers, so he has d - 10 kilometers left to travel. Since Wilson just started, he has the entire d kilometers to cover.
The time it will take for each to travel the remaining distance can be calculated using the formula:
Time = Distance ÷ Speed
For Joseph:
Time = [tex]\frac{d - 10}{ 7}[/tex]
For Wilson:
Time = [tex]\frac{d }{ 9}[/tex]
Since they meet halfway at the same time, the times for each to travel the remaining distance must be equal.
[tex]\frac{d - 10}{ 7} = \frac{d }{ 9}[/tex]
By solving this equation cross-multiplying, we get:
9(d - 10) = 7d
9d - 90 = 7d
2d = 90
d = 45
Each boy will ride for 45 kilometers to meet halfway. Joseph has already covered 10 kilometers, so he will ride an additional 35 kilometers (45 km - 10 km).
Now to find out how long it will take:
For Joseph:
Time = 35 ÷ 7 hours = 5 hours
For Wilson:
Time = 45 ÷ 9 hours = 5 hours
So, both boys will have ridden for 5 hours to meet each other halfway.
A parabola opening up or down has vertex (0,0) and passes through (4,2). Write it’s equation in vertex form
The equation of the parabola opening up or down with a vertex at the origin and passing through the point (4,2) is y = 0.125x².
Explanation:The equation of a parabola in vertex form is represented by y = a(x-h)² + k, where (h, k) is the vertex of the parabola, and 'a' is a coefficient that determines the direction and steepness of the parabola.
Since the vertex of the parabola in this case is at the origin (0, 0), the equation simplifies to y = ax²
We know the curve passes through the point (4,2), so we can substitute these values into the equation 2 = a(4)², which simplifies to 2 = 16a. Solving for 'a' gives us a = 2/16 or a = 0.125.
Thus, the equation of the parabola is y = 0.125x²
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The equation of a parabola with vertex at (0,0) passing through (4,2) is y = (1/8)x². This is derived by using the vertex form and solving for 'a'.
Equation of a Parabola in Vertex Form
The equation of a parabola in vertex form is given by:
y = a(x - h)² + k, where (h, k) is the vertex.
In this case, the vertex of the parabola is at (0, 0), so the equation simplifies to:
y = ax²
Since the parabola passes through the point (4, 2), we can substitute this point into the equation to find the value of 'a':
Substitute x = 4 and y = 2:
2 = a(4)²
2 = 16a
Solve for 'a': a = 2/16 = 1/8
Therefore, the equation of the parabola in vertex form is: y = (1/8)x²
If the area of circle b is 1/5 the area circle a What is the area of circle b
Answer:
(Area of circle a)/5
Step-by-step explanation:
(Area of circle b) = (1/5)* (Area of circle a)
What is the area of circle a? There is not enough given information
Answer:
area of circle a/5
Step-by-step explanation:
The equation: 1/5(a) = b
multiply 1/5(a)
We get the area of circle a/5
Caroline took a math test and got 19 out of 25 questions correct. What percent of the questions did she answer correctly? What percent did she answer incorrectly?
Answer:
She got a 76
Step-by-step explanation:
All you have to do is divide 19/25. You'll get your answer. Hope you understand. If you have any concerns, contact me! Also, a fraction is a division problem! The number on the top goes first!
What is 19+11+77-2/10? for math points
Answer: 19 + 11 = 30 + 77 = 107 - 2/10 = 106.8
If you're confused by the fraction just do 2 divided by 10 and you should get 0.2.
So, instead of doing 2/10 you can do:
19 + 11 = 30 + 77 = 107 - 0.2 = 106.8
Have a good day!
Caitlin plays on her school basketball team and scored 1/4 of the total points during the first three games. Her team scored 38 points the first game, 45 points the second game, and 49 points the third game. How many points total did Caitlin score during the first three games
Answer:
33 Points
Step-by-step explanation:
We can figure out that the total number of points scored by the team is 38+45+49=132. Since we know that Caitlin scored 1/4 of these total points, and 1/4 of 132=33, then she scored 33 points during the first three games.
I believe one of the answers is D, but i cant find any other ones. Can someone check my work and make sure i am correct? thank you!
Answer:
sqrt(15)/ sqrt(3)
sqrt(5)
sqrt(25)/ sqrt(5)
Step-by-step explanation:
Sqrt(100)/sqrt(20)
We know sqrt(a)/sqrt(b) = sqrt(a/b)
Sqrt(100/20)
sqrt(5)
sqrt(100)/sqrt(20)
10 / sqrt(4) sqrt(5)
10/2 sqrt(5)
5/ sqrt(5)
Rewriting 5 as sqrt(25)
sqrt(25)/ sqrt(5)
We can also look at
sqrt(15)/ sqrt(3)
We know sqrt(a)/sqrt(b) = sqrt(a/b)
sqrt(15/3)
sqrt(5)
There are 3 choices that are equal to sqrt(100)/ sqrt(20)
The cost, C, to produce b baseball bats per day is modeled by the function. What number of bats should be produced to keep costs at a minimum
Answer:
60
Step-by-step explanation:
Take the function's first derivative
C'(b) = 0.12b -7.2
7.2 = 0.12b
b = 7.2 / 0.12
b = 60
Second derivative test
C''(b) = 0.12 (+).
for all values of b, the graph will be concave downwards, therefore is value is confirmed to be a minimum
?/6 < 1/2 whats the missing number
Answer:
The missing number is either 1 or 2.
1/6 and 2/6 are both less than 1/2.
a = 7, b = ?, c = 14
you gave us nothing to go off of..no details or anything i was gonna say 7 until i realized b has no values
To get an A average in George's math class, he must get at least
I an 80% on his last math test. Which inequality represents the score George must get on his test?
A. x > 80 B. x < 80 C.x> 80 D. x < 80
Answer:
b or d
Step-by-step explanation:
they have the same answers bruh
A person wants to place pavers to make a new backyard patio. The patio will measure 4 2/3 yards by 5 1/3 yards. If the pavers are each 1 square foot and cost $1.20 each, how much will the pavers cost?
Answer:
$268.80
Step-by-step explanation:
#first convert the patio's dimensions to feet:
[tex]1 \ Yd= 3 \ ft\\\\4\frac{2}{3}\times 3=14\ ft\\\\5\frac{1}{3}\times 3=16\ ft[/tex]
#We now calculate the patio's area in sq ft:
[tex]A=lw\\\\=14\times 16\\\\=224\ ft^2[/tex]
#To determine the total cost of the pavers, we multiply by the cost per sq foot;
[tex]Cost=Area \times Cost/sq \ ft\\\\=224\times 1.2\\\\=268.80[/tex]
Hence, the pavers cost a total of $268.80
The square prism has a base length of 2 ft. Which describes the cross section of the prism that is perpendicular to the base? please help
Answer: Cross-Section of the prism perpendicular to base is equal to base area so the base area is equal to 2*2=4 ft^2
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
help someoneee!!!!
ill give a brainliest
Answer:
-13.5
Step-by-step explanation:
-4/3w=18
You would need to get the w by itself on one side so the easiest way to do so would be to divide both sides my -4/3.
This would give you an answer of w= -27/2 or w= -13.5
Describe a way in which the diagram above illustrates the unique plane postulate.
A.
Planes r and s intersect at line AB
B.
There is exactly one line, m, through points B and D.
C.
There is exactly one plane, s, through points A, B, and C.
D.
Plane rcontains points A and B and line /.
please hurry
Deshawn invests $5,000 in a savings account that earns 6% annual interest, compounded continuously. How long will it take to double his money?
It will take about 11.55 years to double his money.
Important information:
Principal value = $5,000Rate of interest = 6% compounded continuously.Continuous compound interest:The formula for the amount in continuous compound interest is:
[tex]A=Pe^{rt}[/tex]
Where A is the amount, P is the principal, r is the rate of interest and t is time in years.
Substitute [tex]A=10000, P=5000,r=0.06[/tex].
[tex]10000=5000e^{0.06t}[/tex]
[tex]\dfrac{10000}{5000}=e^{0.06t}[/tex]
[tex]2=e^{0.06t}[/tex]
Taking ln on both sides, we get
[tex]\ln 2=\ln e^{0.06t}[/tex]
[tex]\ln 2=0.06t[/tex]
[tex]\dfrac{\ln 2}{0.06}=t[/tex]
[tex]t=11.55245[/tex]
[tex]t\approx 11.55[/tex]
Therefore, it will take about 11.55 years to double his money.
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Evaluate 8a - 1 + 0.5b when a = 1/4 and b = 10
Answer:
6
Step-by-step explanation:
8(.25)-1+.5(10)
2-1+5
1+5
6
What is the area of the shaded region of the diagram use a value pi= 3.14 and round your answer to two decimal places.
A. 19.23
B. 9.81
C. 1.57
D. 9.42
Answer:
The answer is 9.42, Yash :) ~Anusri
Step-by-step explanation:
Basically, you can set up two proportions (one for each concentric circle).
x/25pi=45/360 will get you an area of 9.81 for the smaller circle and x/49pi=45/360 will get you an area of 19.4225 for the larger circle. Subtract those and get 9.42.
Have fun Yash
To find the area of the shaded region, subtract the area of the smaller circle from the area of the larger circle.
Explanation:To find the area of the shaded region, we need to subtract the area of the smaller circle from the area of the larger circle.
The formula to find the area of a circle is pi * r^2, where pi is approximately 3.14 and r is the radius of the circle.
Let's assume the radius of the larger circle is 4 units and the radius of the smaller circle is 3 units. The area of the larger circle is 3.14 * 4^2 = 50.24 square units, and the area of the smaller circle is 3.14 * 3^2 = 28.26 square units.
Therefore, the area of the shaded region is 50.24 - 28.26 = 21.98 square units.
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PLEASE HELP
4x^2+2x=7
Solve By Completing the Square
Please show steps!
Answer:
Step-by-step explanation:
The given quadratic equation is expressed as
4x² + 2x = 7
The first step is to divide both sides of the equation by 4. It becomes
4x²/4 + 2x/4 = 7/4
x² + x/2 = 7/4
The next step is to add the square of half of the coefficient of x to both sides of the equation. It becomes
x² + x/2 + (1/4)² = 7/4 + (1/4)²
(x + 1/4)² = 7/4 + 1/16
(x + 1/4)² = 29/16
Taking square root of both sides of the equation, it becomes
x + 1/4 = ±√29/4
x = - 1/4 ± √29/4
x = (- 1 + √29)/4 or x = (- 1 - √29)/4
x = (- 1 + 5.385)/4 or x = (- 1 - 5.385)/4
x = 1.09625 or x = - 1.59625
brooke has scores of 84,72,90,87, and 95 on her first five quizzes. After taking the sixth quiz, brookes mean score increased. what could be brookes sixth quiz score?
Answer:
Any number above 85.6
Step-by-step explanation:
To calculate the mean you add all of the scores together then divide by how many scores you added
So in this case you would add 84 + 72 + 90 + 87 + 95 = 428
Then you would Divide 428 by five because you are adding 5 numbers
428/5 = 85.6
It says the score increased so as long as then score is greater than 85.6 it is an option.
Answer:
90, 86, 89, and 92
Step-by-step explanation:
Basically anything above 85.6
Find an equation equivalent to r=7csc theta in rectangular coordinates and describe the graph of the equation
Answer: B. Y=7 straight horizontal line
Step-by-step explanation:
Answer:
B : y = 7 straight horizontal line
Step-by-step explanation:
On edge
Which side lengths form a right triangle?
Answer:
It B and C
Step-by-step explanation:
the equation in Pythagorean theorem is a^2+b^2=c^2
so the answer for B would be 5^2*5^2=50,which is correct sine 5^2=25,and 25+25=50
The answer for C would be like 9^2+12^2=225
the square root of 225 is 15 which is correct.
but A is wrong because 5^2+6^2=31 is wrong.
Answer:
its A and C
Step-by-step explanation:
khan academy
A cruise left port A and traveled towards port B 225 km away. After 1.5 hours of travel, the cruise was stopped for a half an hour and then it had to increase its speed by 10 km/hour in order to reach port B on time. Find the original speed of the cruise.
Answer:
50
Step-by-step explanation:
v = the original speed of the cruise
d = 225 km the distance passed
t = d/v = 225/v the total time of the travel
v*1.5 + (v + 10)(d/v - 1.5 - 0.5) = d (using the formula distance = speed*time)
1.5v + (v + 10)(225/v - 2) = 225
Look at the images to see the solved equation