Answer:
Step-by-step explanation:
To fill the entire vase:
pi(3)^2(18)= 508.9 cubic centimeters
To fill vase 3/4 of the way:
3/4= .75
So then you take what it takes to fill the vase (508.9) and multiply that by .75 which equals 381.70 cubic centimeters.
3/4 of the volume of water needed to fill the vase is 162π cm^3.
To find how much water is needed to fill the vase 3/4 of the way, we first need to calculate the volume of the vase and then determine 3/4 of that volume.
The formula to calculate the volume of a cylinder is:
[tex]Volume = \pi * radius^2 * height[/tex]
Given:
Radius (r) = 3 cm
Height (h) = 18 cm
Volume of the entire vase:
[tex]Volume = \pi * (3 cm)^2 * 18 cm\\Volume = \pi* 9 cm^2 * 18 cm\\Volume = 162\pi cm^3[/tex]
Now, to find 3/4 of the volume, multiply the total volume by 3/4:
[tex]3/4 * 162\pi cm^3 = 3 * 54\pi cm^3 = 162\pi cm^3[/tex]
So, 3/4 of the volume of water needed to fill the vase is 162π cm^3.
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The planet Mercury orbits around the sun at 29.74 miles per second. How many miles will mercury travel in 1 minute?
A pound of raisins costs $2.00, and a pound of almonds costs $5.00. Six pounds of a trail mix contains 2 more pounds of raisins than almonds. What is the cost of the 6 pounds of trail mix? $7.00 $18.00 $24.00 $42.00
Answer:
18 just took the test
Adding Rational Expressions
Show work please. thank you
Using polar coordinates, evaluate the integral ∫∫rsin(x2+y2)da where r is the region 16≤x2+y2≤81.
The value of the integral is: πcos(16)- πcos (81)
What are polar coordinates?The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a from a reference point and an angle from a reference direction.
Given:
∫∫ r sin(x²+y²)dA and 16≤x²+y²≤81.
Now,
x =rcosϕ
y=rsinϕ
I=r
Find the integration limits:
ϕ∈[0,2π]
16≤x²+y²≤81
16≤r² cos² Ф + r²sin² Ф≤81
16≤r²≤81
4≤r≤9
So, r∈[4,9]
Now,
∫∫ r sin(x²+y²)dA=
= [tex]\int\limits^9_4 {dr} \int\limits^{2\pi}_0 {rsin \;(r^{2}) } \, d\phi[/tex]
=2π [tex]\int\limits^9_4 {rsin \;(r^{2}) } \, dr[/tex]
Let r² = u
2rdr=du
Also, limit will change from 16 to 25.
5→25
4→16
So,
= π[tex]\int\limits^{81}_{16} {sin \;(u) } \, du[/tex]
=−π|cos (u)∣[tex]^{81}_{16}[/tex]
= πcos(16)- πcos (81)
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Jake walks a mile to work. If Jake has already walked two-fifths of a mile, how many more feet must he walk to get to work?
1 mile = 5280 feet
5280 * 3/5 = 3168 feet more to go
I need help Asap!! Please!!
Line v passes through point (6, 6) and is perpendicular to the graph of y = 34x – 11. Line w is parallel to line v and passes through point (–6, 10). Which is the equation of line w in slope-intercept form?
Answer:
y = -1/34 . x + 167/17
Step-by-step explanation:
The slope-intercept form of a linear equation is:
y = m.x + b
where,
m is the slope
b is the y-intercept
Line v is perpendicular to the graph of y = 34 x - 11. If 2 lines are perpendicular, the slope of one is the inverse and opposite of the other. Then, the slope of v is -1/34.
Line w is parallel to line v. When 2 lines are parallel, they have the same slope.
The equation of w is:
y = -1/34 . x + b
Lines b passes through the point (-6, 10). We can replace this ordered pair in the previous equation to find the value of b.
10 = -1/34 . (-6) + b
b = 167/17
The equation of w is:
y = -1/34 . x + 167/17
In the scale used on a blueprint, 1/4 inch represents 3 feet. On the blueprint, what is the length of a room with an actual length of 24 feet.
If g'(3)=8 and h'(-3)=6, find f'(-3) for f(x)=-3g(x)-2h(x)+3
Elise is measuring the angles of a triangle. She measures the first two and gets 30° and 100°. What should be the measure of the third angle?
A) 50°
B) 60°
C) 130°
D) 230°
The measure of the third angle is 50 degrees for the given triangle. The correct answer would be an option (A).
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbolΔ.
Let x be the measure of the third angle.
As we know that the sum of interior angles in the triangle is always 180 degrees.
So, as per the given question, we have
30° + 100° + x = 180°
130° + x = 180°
x = 180° - 130°
Apply the subtraction operation, and we get
x = 50°
Thus, the measure of the third angle is 50 degrees.
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Eugene earns $17 per hour tutoring athletes at Brooklyn University.
A. if Eugene tutored for 12 hours just last month, how much money did she earn this month?
B. if Eugene tutor for 19.5 hours last month, how much money did she earn last month?
Answer:
A) $204 B) $331.50
Step-by-step explanation:
For both scenarios, you just multiply the amount of hours worked by the amount per hour to find the total amount made.
Eugene earned $204 by tutoring for 12 hours and $331.50 for 19.5 hours, calculated by multiplying the number of hours by her hourly rate of $17.
Eugene earns money by tutoring athletes at Brooklyn University. The amount she earns can be calculated by multiplying the number of hours she tutors by the hourly rate.
Part A Calculation
For 12 hours of tutoring:
Amount Earned = Hourly Rate imes Hours Tutored
Amount Earned = $17/hour imes 12 hours
Amount Earned = $204
Part B Calculation
For 19.5 hours of tutoring:
Amount Earned = Hourly Rate imes Hours Tutored
Amount Earned = $17/hour imes 19.5 hours
Amount Earned = $331.50
find two numbers the quotient is between 67÷4
Use the regression line for the data in the scatter plot to answer the question. On average, how many more goals will a player score for every additional hour of practice?
A. )1/2 of a goal
B. )3/4of a goal
C.) 1 goal
D.) 4/3 goals
Answer:
Step-by-step explanation:
Given is a scatter plot and the regression line using least squares.
We are required to find out how many more goals a player will score for every additional hour of practice.
In other words, we are to find the slope of the regression line.
By taking two points on the line we can find slope of the line.
(1.5,2) and (6.5,6) are points on the line
Find slope using two point formula
Slope = [tex]\frac{y2-y1}{x2-x1} =\frac{6-2}{6.5-1.5} \\=\frac{4}{5}[/tex]
near slope is 3/4
Hence answer is option b.
On average, the goals a player scores for every additional hour of practice will be 3/4.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
We need to find out how many more goals a player will score for every additional hour of practice.
In other words, we have to find the slope of the regression line.
By taking two points on the line we can find the slope of the line.
Lets (1.5,2) and (6.5,6) are points on the line
So, the slope will be
Slope = y-y₁ / (x-x₁)
= 6- 2 / 6.5 - 1.5
= 4/5
Thus, the near slope is 3/4. Option B is correct.
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5 x 70 = 5 x _____ tens
= ____tens = _____
The perimeter of a rectangle is 99 inches. It’s width is 11 inches. What is the length of the rectangle? Solve algebraically and arithmetically.
What is 571,951 in written form
How many times can you put 555555 in 52222854
A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, and 2 mangos. imagine you stick your hand into the refrigerator and pull out a piece of fruit at random. what is the sample space for this process?
Mrs. Santos is buying binders for the students in her class. She determined that 15 binders would cost $22.50.If all of the binders cost the same amount, which statement is true?
It will cost $12 for 18 binders.
It will cost $20 for 30 binders.
It will cost $42 for 28 binders.
It will cost $48 for 48 binders.
Answer:
Option C It will cost $42 for 28 binders
Step-by-step explanation:
Mrs. Santos determined that 15 binders would cost = $22.50
Therefore, 1 binder would cost = $1.50
Now we calculate each statement :
a. 18 binders will cost $12
= 18 × $1.50 = $27.00 (not correct)
b. 30 binders will cost $20
= 30 × $1.50 = $60.00 (not correct)
c. 28 binders will cost $42
28 × $1.50 = $42.00 (Correct)
d. 48 binders will cost $48
48 × $1.50 = $72.00 (not correct)
Option C It will cost $42 for 28 binders would be correct.
what does u stand for and could you make your answer a little clearer please?
simplify each expression -(5p+3)
Answer:
-5p-3
Step-by-step explanation:
use the distributive property
A disc jockey must allow time for 24 minutes of commercials every hour, along with 4 minutes for news, 3 minutes for weather, and 2 minutes for public-service announcements. If each record lasts and average of 3 minutes, how many records per hour can the DJ play?
3/4 of a number is 27, what's the number? I'm asking what is the blank in
3/4 x something over 1 that would reduce to 27
If a dilation is applied to a triangle, then the image must be _____
Answer: I believe it would be "larger or smaller triangle" due to when dilation is applied it mostly only changes the size of the figure but never changing its shape. Hope this helps :)
Please help me with this problem.
The diagram shows the floor plan of a one-bedroom apartment. Find the area of the living room in square feet. Round to nearest square foot.
The area of the living room is approximately 238 square feet.
To find the area of the living room, we need to multiply its length by its width.
First, let's convert the dimensions from feet and inches to feet. We have:
Length: 12 feet + 4 inches = 12 + 4/12 = 12.33 feet
Width: 19 feet + 4 inches = 19 + 4/12 = 19.33 feet
Now, we can multiply the length and width to find the area:
Area = length × width = 12.33 feet × 19.33 feet = 238.1289 square feet
Rounding to the nearest whole square foot, the area of the living room is approximately 238 square feet.
Please help me with this problem.
The diagram shows the floor plan of a one-bedroom apartment. Find the area of the living room in square feet. Round to nearest square foot.
The dimensions of living room are 12' 4" x 19' 4"
On rounding off to nearest feet we get the area of the living room as 238 ft²
In the figure it is given that the dimensions of the living room are 12' 4" x 19' 4". This means that the dimensions are:
12 ft 4 in x 19 ft 4 in
To get the area in feet, we need to convert the dimensions into feet. This can be done by using the conversion factor that 1 foot = 12 inch
So, 12 ft 4 in can be converted into feet as follows:
[tex]12\ \text{ft}\ 4\ \text{in} = 12\ \text{ft}\ + \frac{4}{12}\ \text{ft} = 12.333\ \text{ft}[/tex]
19 ft 4 in can be converted into feet as follows:
[tex]19\ \text{ft}\ 4\ \text{in} = 19\ \text{ft}\ + \frac{4}{12}\ \text{ft} = 19.333\ \text{ft}[/tex]
Now to calculate the area we multiply the dimensions of the living room (as the living room is a rectangle and area of rectangle is product of its length and breadth):
[tex]area = 12.333 \times 19.333 =238.433889[/tex] ft²
On rounding of to nearest feet we get the area as 238 ft². So, the area of the living room is 238 ft²
James built a small electric car and recorded the distance it traveled. The table below shows the distance traveled (n) during the first 4 seconds after starting (f). Elapsed Time (seconds) Distance Traveled (feet) 1 6.2 2 12.4 3 18.6 4 24.8 Which of the following equations represents the relationship between the distance traveled and the elapsed time? f = 6.2 + n n = 6.2 + f f = 6.2n n = 6.2f
Answer:
Answer: n = 6.2 f
Step-by-step explanation:
so you only know the answer
Complete the inequality statement. 2/7___5/14
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=
What does it mean to say that a shape has an area of 8 square inches?
Final answer:
To say a shape has an area of 8 square inches means the shape covers 8 units of square inches. For similar shapes, the area comparison is the square of their scale factor; hence, if one shape's dimensions are twice another's, its area is four times larger.
Explanation:
When it is said that a shape has an area of 8 square inches, it means that the surface enclosed by the shape covers 8 units of square inches. In other words, you could fit 8 squares, each measuring 1 inch by 1 inch, inside the shape without overlapping or leaving any space inside the shape uncovered. To understand how the area of similar shapes compares, we can look into the problem involving two squares.
Marta has one square with a side length of 4 inches. A similar square has dimensions that are twice as large, meaning its side lengths are 8 inches. The area of the smaller square can be calculated as 4 inches x 4 inches, which equals 16 square inches. The area of the larger square would be 8 inches x 8 inches, resulting in 64 square inches. The ratio comparing the two areas is 64:16, which simplifies down to 4:1. This shows that the larger square's area is four times greater than that of the smaller square.
An area of 8 square inches means the shape covers a space equivalent to eight 1-inch by 1-inch squares.
To say that a shape has an area of 8 square inches means that the amount of space enclosed within the boundaries of the shape is equivalent to the area of eight 1-inch by 1-inch squares. Imagine a piece of graph paper where each small square is 1 inch by 1 inch.If the shape could be perfectly copied onto the graph paper, you would find that it covers eight of those squares.For example, an area of 8 square inches could be visualized by a variety of shapes: a rectangle measuring 2 inches by 4 inches or even an irregular shape that neatly fits inside the same area.In mathematics, there are various ways to calculate the area depending on the shape. For regular shapes like rectangles and circles, formulas are often used. But the fundamental idea of area — the measure of the space inside a shape — remains the same.One option in a roulette game is to bet $2 on red. (There are 18 red compartments, 18 black compartments, and two compartments that are neither red nor black.) If the ball lands on red, you get to keep the $2 you paid to play the game and you are awarded $2. If the ball lands elsewhere, you are awarded nothing and the $2 that you bet is collected. Find the expected payback for this roulette game if you bet $2 on red.
The expected payback for betting $2 on red in a roulette game is -$0.62. This indicates an expected average loss, making it not a profitable bet.
Explanation:The expected payback for betting $2 on red in a roulette game is -$0.62. This means that on average, you would expect to lose 62 cents per game if you play this game repeatedly over a long string of games. The expected value indicates an expected average loss, so it is not a profitable bet.
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