Volume of the cylinder is 3696 m²
Step-by-step explanation:
Step 1: Calculate volume of the cylinder using the formula V = πr²h⇒ V = 22/7 × 14² × 6 = 3696 m²
Ashley has a sprinkler that has several varieties of coverage. The quarter circle sprinkler head sprays water a distance of up to 20 feet from the lead. What area will be covered by the spray of the quarter-circle sprinkler head to the nearest square foot?
Answer:
314 square feet
Step-by-step explanation:
we know that
The area that will be covered by the spray of the quarter-circle sprinkler head, is equal to the area of a quarter circle with radius of 20 feet
so
The area of a quarter circle is
[tex]A=\frac{1}{4}\pi r^{2}[/tex]
we have
[tex]r=20\ ft[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]A=\frac{1}{4}(3.14)(20)^{2}=314\ ft^2[/tex]
The area covered by the quarter-circle sprinkler head to the nearest square foot is 314 square feet.
To find the area covered by the quarter-circle sprinkler head, we need to calculate the area of a quarter circle with a radius of 20 feet. The formula for the area of a circle is [tex]\( A = \pi r^2 \), where \( r \)[/tex] is the radius. Since we are dealing with a quarter circle, we will take [tex]\( \frac{1}{4} \)[/tex] of the full circle's area.
Given that the radius [tex]\( r \)[/tex] is 20 feet, the area of the full circle would be:
[tex]\[ A_{\text{full circle}} = \pi \times (20 \text{ feet})^2 \] \[ A_{\text{full circle}} = \pi \times 400 \text{ square feet} \] \[ A_{\text{full circle}} = 400\pi \text{ square feet} \][/tex]
Now, to find the area of the quarter circle, we divide the full circle's area by 4:
[tex]\[ A_{\text{quarter circle}} = \frac{1}{4} \times 400\pi \text{ square feet} \] \[ A_{\text{quarter circle}} = 100\pi \text{ square feet} \][/tex]
Using the value of [tex]\( \pi \)[/tex] as approximately 3.14159, we get:
[tex]\[ A_{\text{quarter circle}} \approx 100 \times 3.14159 \text{ square feet} \] \[ A_{\text{quarter circle}} \approx 314.159 \text{ square feet} \][/tex]
Rounding to the nearest square foot, the area covered by the quarter-circle sprinkler head is 314 square feet.
What number is 7 hundreds 1 tens 12 ones
Answer:
.712
Step-by-step explanation:
Answer:
i think the answer is 722
decimal and integers are both classified as ______ numbers
Answer:whole numbers
Step-by-step explanation:
You can buy 5 cans for green beans at the Village Market for $3.70. You can buy 10 of the same cans of beans at Sam’s club for $6.30. Which place is the the better buy?
Answer:
Sams club
Step-by-step explanation:
3.70/5= $.74 per can
6.30/10=$.63 per can
If a number is divisible by 3 and 5 then it is divisible by 15
Answer:
Yes!
Step-by-step explanation:
Besides 15 and one, 3 and 5 are the greatest common factors of 15. Those numbers are therefore divisible by any product of 15.
Example:
45
45/3 = 15
45/5 = 9
45/15 = 3
Answer:
Yes it is
Step-by-step explanation:
Since the multiplication of 3 and 5 will give 15
I.e 3 × 5 = 15
Then any number that can be divided by 3 and 5, can also be divided by 15.
Find two consecutive even integers whose sum is 30
Answer:
14 & 16
Step-by-step explanation:
30÷2=15
15+15=30, so we can make the conclusion...
14+16=30
Find the missing number
45-9=46-
The answer is 10 because 45-9 is 36, so 46-x must be 36, which would result in 10
You want to draw an enlargement of a design that is printed on a card that is 5 in. by 6 in. You will be drawing this design on an piece of paper that is 8.5 in. by 11 in. What are the dimensions of the largest complete enlargement you can make?
Answer:
The dimensions of the largest enlargement are
[tex]8\frac{1}{2}\ in\\10\frac{1}{5}\ in[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the scale factor is the ratio of its corresponding sides
step 1
Divide 8 1/2 by 5
[tex]8\frac{1}{2}=\frac{8*2+1}{2}=\frac{17}{2}\ in[/tex]
so
[tex]\frac{17}{2}/5=1.7[/tex]
step 2
Divide 11 by 6
so
[tex]\frac{11}{6}=1.83[/tex]
step 3
Find the largest complete enlargement
The scale factor is the smaller of the two previous values
so
The scale factor is 1.7
The dimensions are
[tex]5(1.7)=8.5=8\frac{1}{2}\ in[/tex]
[tex]6(1.7)=10.2=10\frac{1}{5} \ in[/tex]
The largest complete enlargement of the original 5 in by 6 in design that can be made on an 8.5 in by 11 in paper has dimensions of 8.5 in by 10.2 in, determined by the limiting width dimension and maintaining the aspect ratio.
Explanation:The question involves finding the dimensions of the largest complete enlargement of a design with an original size of 5 in. by 6 in. onto a piece of paper that is 8.5 in. by 11 in. To determine the largest complete enlargement, we must consider the scale factor that will allow the design to fit within the dimensions of the larger paper while maintaining the aspect ratio of the original design.
To maintain the aspect ratio, the scale factor for width and height must be the same. We compare the ratio of the widths and the heights of the original and target sizes to find the limiting dimension:
For width: 8.5 in / 5 in = 1.7For height: 11 in / 6 in = 1.833...Since the scale factor for the width (1.7) is less than the scale factor for height, the width is the limiting factor. Thus, we can enlarge the original design by a factor of 1.7 to fit the paper. Now, we calculate the enlarged dimensions:
Width: 5 in * 1.7 = 8.5 inHeight: 6 in * 1.7 = 10.2 inThe largest complete enlargement of the design that can be made on an 8.5 in by 11 in paper will have dimensions of 8.5 in by 10.2 in.
10. A student studied 18 hours in 7 days, if he wants to study average 2 hours each day for 14 days. How many hours he needs to study for next 7 days?
Answer:
2 x 14 = 28
28 - 18 = 10
He needs to study for 10 hours that week or, about one and half hours per day.
29+x+41=90 and 113-y=90
29+x+41 = 90
x+70 = 90 ..... combine like terms
x+70-70 = 90-70 .... subtract 70 from both sides
x = 20 answer---------------------------------------
113 - y = 90
113 - y = 90 - 113 ... subtract 113 from both sides
-y = -23
y = 23 answerMultiply simplest form
Answer:
4 [tex]\frac{8}{9}[/tex]
Step-by-step explanation:
2 [tex]\frac{1}{5}[/tex] × 2 [tex]\frac{2}{9}[/tex]
[tex]\frac{11}{5}[/tex] × [tex]\frac{20}{9}[/tex] = [tex]\frac{220}{45}[/tex] = 4 [tex]\frac{8}{9}[/tex]
WILL GIVE BRAINLIEST!!!! Which of the values for x and y make the equation 2x + 3y + 4 = 15 true? (4 points) x = 6, y = 3 x = 3, y = 5 x = 6, y = 4 x = 1, y = 3
2x + 3y + 4 = 15
2(1) + 3(3) + 4 = 15
2 + 9 + 4 = 15
11 + 4 = 15
15 = 15
x = 1 and y = 3
Hope this helps! ;)
Answer: The correct answer choice is D.
Step-by-step explanation: I will show all the work done for each answer choice so it is more clear.
First Answer Choice's Work:
2(6) + 3(3) + 4
12 + 9 + 4
12 + 9
21
21 + 4
25.
Second Answer Choice's Work:
2(3) + 3(5) + 4
6 + 15 + 4
21 + 4
25.
Third Answer Choice's Work:
2(6) + 3(4) + 4
12 + 12 + 4
24
24 + 4
28.
Fourth Answer Choice's Work:
2(1) + 3(3) + 4
2 + 9 + 4
11
11 + 4
15.
Therefore, the correct answer choice is D.
I need help please and thank you
(A AND B ARE NOT ANSWERS THEY ARE SEPARATE PROBLEMS)
Answer:
Part a) Wayne's savings before he spent $28 was $31.08
Part b) Stef's savings after she spent $28 was $9.29
Step-by-step explanation:
Part a)
Let
x ----> original amount of Wayne's savings
y ----> original amount of Stef's savings
we know that
Original ratio
[tex]\frac{x}{y}=\frac{5}{6}[/tex]
[tex]x=\frac{5}{6}y[/tex] ----> equation A
After spending $28 each
[tex]\frac{x-28}{y-28}=\frac{1}{4}[/tex]
Multiply in cross
[tex]4x-112=y-25\\y=4x-112+25[/tex]
[tex]y=4x-87[/tex] ----> equation B
substitute equation A in equation B
[tex]y=4(\frac{5}{6}y)-87[/tex]
solve for y
[tex]\frac{20}{6}y-y=87[/tex]
[tex]\frac{7}{3}y=87[/tex]
[tex]y=37.29[/tex]
Find the value of x
[tex]x=\frac{5}{6}(37.29)=31.08[/tex]
so
The original amount of Wayne's savings was $31.08 and the original amount of Stef's savings was $37.29
therefore
Wayne's savings before he spent $28 was $31.08
Part b) Find Stef's savings after she spent $28
Subtract $28 from the original savings
so
$37.29-$28=$9.29
therefore
Stef's savings after she spent $28 was $9.29
A pack of cinnamon-scented pencils sells for $5.00. What is the sales tax rate if the total cost of the pencils is $5.40?
Answer:
The sales tax rate is 5%
Given:
Sales price = 5.00
Total amount paid = 5.25
Sales tax value = Total amount paid - sales price
= $5.25 - $5.00
Sales tax value = $0.25
Sales tax rate = Sales tax / Sales price
= 0.25/5
Sales tax rate = 0.05 or 5%
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Thanks to taskmasters.
Step-by-step explanation:
A pair of shoes is priced $35.99, but is on sale for 20% off.What is the sale price of the shoes
Answer: $7.20
Step-by-step explanation:
20% equals 1/5 and 35.99 divided by 1/5 is 7.198 now round to the nearest tenth and you got 7.20.
Which of the following will lower your interest rate?
Answer:points
Step-by-step explanation:
Solve the equation for y plz -1.2y-4.2y=-3.78
Answer:
y=0.7
Step-by-step explanation:
-1.2y-4.2y=-3.78
Simplify:
-5.4y=-3.78
5.4y=3.78
3.78/5.4=0.7
y=0.7
6x-y=8
7x-y=9
Solve linear systems by Multiplying first
Find the tenth term in the sequence: 12, 10, 8, ...
Answer:
-6
Step-by-step explanation:
12, 10, 8, 6, 4, 2, 0, -2, -4, -6
Subtracting two each time
Answer:
-6
Step-by-step explanation:
It subtracts 2 each time in the sequence.
The first term is 12.
You subtract 2 ten times to get to the tenth number in this sequence. 10*2 = 20. 12-20 = -6
2. If the whole bar is 3 units long, what is the length of the shaded part of the bar? Write a multiplication
equation for the diagram, and then solve.
Answer:
The length of the shaded part is [tex]\frac{9}{4}[/tex]
Step-by-step explanation:
The original figure, which you may have unintentionally missed to add, is attached below.
From the figure, it is easy to figure out that:
The whole bar is 3 units long.The bar has 4 total parts.The shaded region has 3 parts.So, the ratio of shaded parts to total parts will be: [tex]\frac{3}{4}[/tex]
In order to determine length of the shaded part, just multiply the ratio of the shaded parts to total parts by the total length of the bar.
So,
[tex]\frac{3}{4} \times3=\frac{9}{4}[/tex]
Therefore, the length of the shaded part is [tex]\frac{9}{4}[/tex]
Keywords: ratio, length
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Answer:
see the explanation
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The fraction of the shaded part is equal to divide the number of shaded parts divided by the total number of parts
so
Let
x ----> the number of shaded parts
y ----> the total number of parts
we have
x=3, y=4
so
[tex]\frac{3}{4}[/tex]
To find out the length of the shaded part, multiply the fraction of the shaded parts by the total length of the bar
so
[tex]\frac{3}{4}(3)=\frac{9}{4}=2.25\ units[/tex]
The total price of a bag of peaches varies directly with the cost per pound. If 3 pounds of peaches cost $3.60, how much would 5.5 pounds cost?
A: $1.20
B: $6.60
C: $6.00
D: $1.96
Step-by-step explanation:
Given , the total price of a bag of peaches varies directly with the cost per pound. If 3 pound of peaches cost $3.60.
Therefore,
[tex]{\textrm{beg of peaches}}\propto{\textrm{cost}}[/tex]
[tex]\Leftrightarrow {\textrm{beg of peaches}}= {\textrm{k cost}}[/tex].......(1) [ k is a constant]
cost = $3.60 when beg of peaches = 3 pounds
[tex]3 = 3.60 k[/tex]
[tex]\Leftrightarrow k = \frac{3}{3.60}[/tex]
[tex]\Leftrightarrow k = \frac{1}{1.20}[/tex]
Therefore the equation (1) becomes
[tex]{\textrm{beg of peaches}}=\frac {cost}{1.20}[/tex]
[tex]\Leftrightarrow {\textrm{beg of peaches}}\times 1.20={cost}[/tex]
When beg of peaches = 5.5 pound
[tex]cost = 5.5 \times 1.20[/tex]
[tex]\Leftrightarrow cost = 6.60[/tex]
Therefore the cost of 5.5 pound of peaches is $ 6.60.
Bryan has a summer job of unloading fruit crates. Last week he unloaded 243 crates. This week he unloaded 361. How many more did Bryan unload this week than last week?
Answer:
The answer is 118
Step-by-step explanation:
In order to solve this you need to subtract this weeks, to last weeks.
361 - 243 = 118.
Hope this helps :)
Bryan unloaded 118 more crates this week than last week.
Explanation:To find out how many more crates Bryan unloaded this week than last week, we can subtract the number of crates unloaded last week from the number of crates unloaded this week.
So, to find the difference, we subtract 243 from 361:
= 361 - 243
= 118
Therefore, Bryan unloaded 118 more crates this week than last week.
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Max spent 35 minutes doing research on the internet. She finished at 7:10 P.M. At what time did max start her reserch
Answer:
6:35
Step-by-step explanation:
Answer: 6:35
Step-by-step explanation:
7:10 take 10 from 35 and you get down to 7:00 and then subtract 25 from 7:00 and get your answer
Apply the distributive property to factor out the greatest common factor 70-40p
Answer:
10(7-4p)
Step-by-step explanation:
Donato is 6 feet 2 inches tall. His sister is 68 inches tall. Donato is how many inches taller.
6 inches taller
Step-by-step explanation:
There’s 12 inches in a foot. So 12•6 is 72 then plus another 2 then you get 74. Then subtract 74 by 68 and you get 6
Answer:
Step-by-step explanation: since 1 foot =12 inches then we multiply 12*6=72 inches +2 inches =74 inches therefore Donato is 74 inches which is obviously bigger than 64 inches so we subtract 74-64=10
As a result ,Donato is 10 inches taller than his sister
Decide whether 3(x-2)+5 and 3x+1 are equivalent expressions. explain how you know.
Answer:
Not equivalent
Step-by-step explanation:
Let,
3(x-2) + 5 = 3x + 1
By Multiplying
3x - 6 + 5 = 3x + 1
3x - 1 = 3x + 1
So, the expressions are not equal
PLSSSSS HELP What is the period of the function f(x)=sin1/6x ? π/6 12/π 6π 1/6
the answer is 12pi
just took the quiz :)
The period of the function is 12π, the correct option is B.
What is the period of a function?The period of a function is the distance in which the graph repeats itself.
For a trigonometric function, the length of one complete cycle is called the periodic function.
For the function
y = a sin (bx + c)
Here,
a is the amplitude,
b is the period of the sine curve, and
c is the phase shift of the sine curve
The amplitude is the height of the curve.
The coefficient of b = 1, for a period of 2π
To find the period of the sine curve for any coefficient b,
Divide 2π by the coefficient of b to get the new period of the curve.
The coefficient b and the period of the sine curve have an inverse relationship,
As b gets smaller, the length of one cycle of the curve gets bigger. Similarly, on increasing the value of b, the period will decrease.
The function is y = sin1/6x
The period of the function is,
= 2π / ( 1/6)
= 12π
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Manuela works as a security guard. She makes $15 per hour. Her employers deduct $125 from her weekly check to cover insurance and takes. If Manuela receives at least $205 in her weekly paycheck, what is the feast number of hours she works in a week show steps.
Manuela works at least 22 hours in a week.
Step-by-step explanation:
Given,
Per hour salary of Manuela = $15
Amount deducted = $125
Amount received = $205
Let,
x be the number of hours per week.
Per hour salary * Number of weeks - Amount deducted ≥ Amount received
[tex]15x-125\geq 205\\15x\geq 205+125\\15x\geq 330[/tex]
Dividing both sides by 15
[tex]\frac{15x}{15}\geq \frac{330}{15}\\x\geq 22[/tex]
Manuela works at least 22 hours in a week.
Keywords: inequality, division
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5. Name the property the equation illustrates.
an elephant eats about 2500 pounds of food in 10 days. About how muck food does an elephant eat in 1000 days
Final answer:
An elephant that eats about 2500 pounds of food in 10 days would eat approximately 250,000 pounds in 1000 days. You find this by dividing 2500 pounds by 10 to get a daily consumption rate and then multiply that rate by 1000 days.
Explanation:
If an elephant eats about 2500 pounds of food in 10 days, to find out how much food it eats in 1000 days, you should first calculate how much it eats per day and then multiply that number by the total number of days (1000). To find the daily food consumption, you divide the total food consumed in 10 days by the number of days:
2500 pounds ÷ 10 days = 250 pounds per day.
Now multiply the daily consumption by 1000 days to find the total amount for that period:
250 pounds per day × 1000 days = 250,000 pounds.
So the elephant would eat approximately 250,000 pounds of food in 1000 days.