The cylinder has base diameter of 6 centimeters and the height, [tex] h [/tex], of 8 centimeters.
Since the base diameter of the cylinder is 6 cm, therefore, it's radius, [tex] r [/tex], will be 3 cm.
Now, we know that the volume, [tex] V [/tex], of such a cylinder will be:
[tex] V=\pi r^2h [/tex]
Plugging in the values given we get the volume to be:
[tex] V=\pi(3)^2\times 8=3.14\times9\times8=226.08 [/tex] [tex] cm^3 [/tex]
Since Rene needs to make 2000 [tex] cm^3 [/tex] of ice and one cylinder's volume is 226.08 [tex] cm^3 [/tex], Rene would need...
[tex] \frac{2000}{226.08}\approx8.846\approx\boldsymbol{9} [/tex] such identical cylindrical containers.
Final answer:
To make 2000 cm3 of ice, Rene would need a minimum of 9 identical containers, given the volume of one container is 226.08 cm3.
Explanation:
To determine the number of identical cylindrical containers needed to make 2000 cm3 of ice, we must first calculate the volume of one container. Given that the diameter of the base is 6 centimeters, the radius (r) is half of that, which is 3 centimeters. We're also given the height (h) of 8 centimeters. We can use the formula for the volume of a cylinder, V = πr2h.
Plugging in the values, we get:
V = 3.14 × (3 cm)2 × 8 cm
which simplifies to V = 3.14 × 9 cm2 × 8 cm = 226.08 cm3.
Now we can divide the total volume of ice Rene wants to make by the volume of one container:
2000 cm3 ÷ 226.08 cm3 = approx 8.85.
Since Rene cannot use a fraction of a container, she would need a minimum of 9 identical containers to make at least 2000 cm3 of ice.
Base your answer to the question on the diagrams shown below.
What is the probability of drawing a red card and then spinning a 1?
Answer: [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
From the given picture, the total number of cards = 5
The number of red card = 2
Thus, the probability of drawing a red card P(red)=[tex]\frac{2}{5}[/tex]
Also, total number of digits on spinner = 8
Number of 1's=4
Thus, the probability of spinning a 1 P( spinning 1)=[tex]\frac{4}{8}=\frac{1}{2}[/tex]
Since both the events of drawing a red card and spinning a 1 are independent events, therefore, the probability of drawing a red card and then spinning a 1=[tex]\text{ P(red)}\times\text{P( spinning 1)}=\frac{2}{5}\times\frac{1}{2}=\frac{1}{5}[/tex]
Iq test scores are normally distributed with a mean of 100 and a standard deviation of 15. find the x-score that corresponds to a z-score of 2.33.
Answer: 134.95 to be exact
you multiply the zscore with the standard deviation and add the mean
The formula for calculating the z-score:
z = (x - μ) / σ
Where
μ - mean
σ = standard deviation
The x-score that corresponds to a z-score of 2.33 is 134.95.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
Iq test scores are normally distributed:
Mean = 100
Standard deviation = 15
z-score = 2.33
The formula for calculating the z-score:
z = (x - μ) / σ
Where
μ - mean
σ = standard deviation
Now,
2.33 = (x - 100) / 15
Multiply 15 on both sides.
2.33 x 15 = x - 100
34.95 = x - 100
Add 100 on both sides.
34.95 + 100 = x
x = 134.95
Thus,
The x-score that corresponds to a z-score of 2.33 is 134.95.
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How many ears of corn would equal to 5 pounds?
Randall bought a bond with a face value of $6000 and a coupon rate of 7.25%. the bond will mature in 5 years. how much interest will he receive semiannually?
Answer:
Face value of bond = $ 6000
Rate of interest =7.25 %
The Bond will mature in 5 years.
If the interest is semiannually , the rate of interest will reduce to half.
So, new rate of interest will be [tex]\frac{7.25}{2}=3.625[/tex]
Formula for simple interest
[tex]=\frac{\text{Principal}\times Rate \times time}{100}[/tex]
Interest after 6 months will be
[tex]=\frac{6000 \times 3.625 \times 1}{100}\\\\=60 \times 3.625\\\\=217.5[/tex]
So, interest that Randall will receive after six months = $ 217.50
What is the name of the polygon if the sum of the measures of its interior angles is 1080°?
Answer:
Octagon
Step-by-step explanation:
It has 8 sides
Books spontaneously catch on fire in temperatures at or above 451, degree Fahrenheit. Write an inequality that is true only for temperatures (t)(t)left parenthesis, t, right parenthesis at which books spontaneously catch on fire.
All ticket for a concert are the same price.
Amy and dan pay £63 altogether for some tickets.
Amy pays 24.50 for 7 tickets.
How many tickets does Dan buy?
To determine how many tickets Dan bought, we calculate the price per ticket from Amy's purchase as £3.50 each. Then we subtract Amy's payment from the total to find Dan's payment of £38.50, and finally, we divide Dan's payment by the price per ticket to find that Dan bought 11 tickets.
The question involves finding out how many tickets Dan bought for a concert, using the total amount paid by both Amy and Dan and the price Amy paid for her tickets.
First, we need to find out the price per ticket from the information provided about Amy's purchase:
Amy pays £24.50 for 7 tickets.
To find the price per ticket, we divide £24.50 by 7:
Price per ticket = £24.50 / 7 = £3.50
Next, we use the total amount paid to find out how much Dan spent:
Total amount paid by Amy and Dan = £63
Amount paid by Amy = £24.50
So, the amount paid by Dan = Total amount - Amount paid by Amy
Amount paid by Dan = £63 - £24.50 = £38.50
To find out how many tickets Dan bought, we divide the amount he paid by the price per ticket:
Number of tickets Dan bought = £38.50 / £3.50
Number of tickets Dan bought = 11 tickets
What is the domain for the piece of the function represented by f(x) = x + 1?
Answer:
All real numbers
Step-by-step explanation:
The domain of the function represented by f(x) = x + 1 is the all real numbers as there is only addition involved in the function so putting any number as input will not lead the function to infinity.
Whats the distance between points C(0, 4), T(-6, -3)
a √(37)
b √(85)
c √(109)
What's the diameter of a cirlce eith an area of 615.75?
There was a sample of 200 milligrams of a radioactive substance to start a study. since then, the sample has decayed by 5.4% each year. let t be the number of years since the start of the study. let y be the mass of the sample in milligrams. write an exponential function showing the relationship between y and t .
The exponential function representing the relationship between the mass y of a radioactive sample in milligrams and t years since the start of the study is y = 200(1 - 0.054)^t.
The student is given a starting mass of a radioactive substance and the percentage of the mass that decays each year. To write an exponential function that models this situation, we consider the initial mass, which is 200 milligrams, and the decay rate, which is 5.4% per year. The relationship between the mass y and the time t in years can be represented by the formula y = 200(1 - 0.054)^t.
Using an exponential decay model, we understand that the amount of substance decreases by a certain percentage each year. To account for this, we raise the base (1 - 0.054) to the power of t, representing the number of years, which gives us the factor by which the original mass has reduced.
A cylindrical tank has a radius of 4.5 ft and an altitude of 14 ft. If a gallon of paint will cover 130 ft squared ft2 of surface, how much paint in gallons is needed to put two coats of paint on the entire surface of the tank? Aswer: To put two coats of paint on the entire surface of the tank, ______ full gallons of pain are needed.
Pratap Puri rowed 14 miles down a river in 2 hours, but the return trip took him 3 and one half hours. Find the rate Pratap can row in still water and find the rate of the current. Let x equals rate Pratap can row in still water and y equals rate of the current. What is the rate that Pratap rows in still water?
Final answer:
By establishing equations based on Pratap's rowing times upstream and downstream, we find that Pratap's rowing rate in still water is 5.5 miles per hour.
Explanation:
Finding Pratap's Rowing Rate in Still Water and the Current Rate
To calculate Pratap Puri's rowing rate in still water and the rate of the current, we need to set up two equations based on the information provided. We know that Pratap rowed 14 miles down a river in 2 hours and the return trip took 3 and a half hours.
Step-by-Step Solution
Let x be the rate at which Pratap can row in still water, and y be the rate of the current.
The downstream speed (with the current) is x + y, and the upstream speed (against the current) is x - y.
Using the formula distance = rate × time, for the downstream trip we have 14 = (x + y) × 2, and for the upstream trip 14 = (x - y) × 3.5.
Simplifying both equations gives us: 7 = x + y and 4 = x - y.
To find x, add the two equations to eliminate y, yielding 11 = 2x, or x = 5.5.
Therefore, Pratap's rowing rate in still water is 5.5 miles per hour.
Please help :)
Solve the system of equations and choose the correct answer from the list of options.
d + e = 1
−d + e = −5
Label the ordered pair as (d, e). (4 points)
(0, 0)
(3, −2)
(−2, 3)
(−3, 0)
(3, -2)
Given equations are
d+e=1
-d+e=-5
We need to find d and e.
What is system of equations?A system of equations is a set of one or more equations involving a number of variables
The system of equations are
d+e=1....(1)
-d+e=-5....(2)
d=1-e (from 1)
Substitute d in (2)
-(1-e)+e=-5
-1+e+e=-5
-1+2e=-5
2e=-5+1
2e=-4
e=-2
Now substitute value of e in (1)
d-2=1
d=1+2
d=3
Therefore the ordered pair for d + e = 1 and −d + e = −5 is (3, -2)
i.e value of d=3 and e=-2
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I NEED UR HELP PLEASE..
Drew ran 5 3/ 8 miles yesterday. Collin ran 8 5/12 miles yesterday. How much farther did Collin run? Choose the correct values to leave your answer as a mixed number. Numbers may be used once or not at all.
Answer:
The correct answer is 3 1/24
Step-by-step explanation:
because I did all the math
Answer:
3 1/24
Step-by-step explanation:
Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Check all that apply.
A. y = –x + 1
B. 3x − 4y = −4
C. 4x − 3y = −3
D. y – 2 = –(x – 4)
E. y + 2 = (x + 4)
If the diameter of a sphere is 12cm, what is its volume to the nearest hundredth
which graph shows the solution set of the compound inequality 1.5x-1>6.5 or 7x+3<-25
Answer:
It's B
Step-by-step explanation:
PLEASE PLEASE HELP ME WITH THESE!!!!
I REALLY NEED HELP AND I WILL AWARD BRAINLIEST FOR WHO IS CORRECT!!!
1. The table below shows the number of cameras sold in each month at the camera shop.
January: 35 cameras were sold
Feb. 21 cameras were sold
Mar. 35 were sold.
April: 55 were sold
May: 73 were sold
Jun. 82 sold
Jul. 85 were sold
Aug. 64 cameras were sold
Sep. 52 sold
Oct. 42 were sold
Nov. 89 were sold
Dec. 125 cameras sold
Use the set of data to answer the question.
The camera shop wants to use the measure of central tendency that expresses how successful they are in selling cameras. Which measure of central tendency should they choose?
A. Mean
B. Interquartile
C. Mode
D. Median
PLEASE HELP PLEASE AND THANK YOU!!!
Over the past week, 34 baby boys were born at the hospital. this was 54% of all babies born. how many girls were born over the past week? (enter numeric value only. if grounding is necessary, round to the nearest whole number
10 - 3(3x - 40) = -9x A)x = -9 B)no solution C)x = 10 D)all real numbers
50 points to answer this for me
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4−x and y = 8−x−1 intersect are the solutions of the equation 4−x = 8−x−1. (4 points)
Part B: Make tables to find the solution to 4−x = 8−x−1. Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 4−x = 8−x−1 graphically? (2 points)
We would graph both equations: y = 4-x and y = 8-x^-1
The point on the graph where the lines cross is the solution to the system of equations.
using a graph tool
see the attached figure N 2
the solutions are the points
(-4.24,8.24)
(0.24,3.76)
Part A. We have two equations: y = 4-x and y = 8-x^-1
Given two simultaneous equations that are both to be true, then the solution is the points where the lines cross. The intersection is where the two equations are equal. Therefore the solution that works for both equations is when
4-x = 8-x^-1
This is where the two graphs will cross and that is the common point that satisfies both equations.
Part B
see the attached table
the table shows that one of the solutions is in the interval [-1,1]
Part C To solve graphically the equation 4-x = 8-x^-1
We would graph both equations: y = 4-x and y = 8-x^-1
The point on the graph where the lines cross is the solution to the system of equations.
using a graph tool
see the attached figure N 2
the solutions are the points
(-4.24,8.24) (0.24,3.76)
The matrix below represents the number of minutes four friends spend driving to each others’ homes each week. A row label represents the friend driving and a column label represents the friend being visited.
Answer:
D - 45
Explanation:
Hope you have a great day!
can someone please solve 5-2x<7
Yo!!!NEED HELP!!!!WILL GIVE BRAIN!!!!!!!
The equation $1.50p + $5.00 = $14.00 shows the total cost of picking p pounds of blueberries at a local blueberry farm. how many pounds of blueberres were picked/
Suppose you are headed toward a plateau 70 m high. If the angle of elevation to the top of the plateau is 60 degrees, how far are you from the base of the plateau?
To find the distance from the plateau's base, use the tangent function with the given height and angle of elevation.
Explanation:We can use trigonometry to determine the distance from the base of the plateau. The vertical height of the table (opposite side) is 70 m, and the elevation angle to the top of the plateau (theta) is 60 degrees. We can use the tangent function to find the distance (adjacent side) from the table's base: tan(theta) = opposite/contiguous. Solving for the space, we get: adjacent = contrasting/tan(theta). Plugging in the values, the distance from the plateau's base is approximately 40 m.
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Would someone Please answer this question please will be thanked and also will pick brainly!! (please be honest)
Find the area of a trapezoid based on the information given below. H=4√2 b1=5√2 b2=3√2