What is the probability of selection for any man in a proportionate random sample, where a sample of 100 will be drawn from a population of 1,000 that is 50% male and 50% female?
A cylindrical shaped vase has the radius of 3cm and a height of 18cm. how much water is needed to fill the vase 3/4 of the way?
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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There are 365,493 blue pens in a warehouse and 549384 black pens how many pens are there in all
Suppose you deposit $5,000 in a savings account that earns 3% annual interest. If you make no other withdrawals or deposits, how many years will it take the account balance to reach at least $6,000? A. 10 years. B. 6 years. C. 7 years. D. 4 years
Find all values of x (if any) where the tangent line to the graph of the given equation is horizontal. HINT [The tangent line is horizontal when its slope is zero.] (If an answer does not exist, enter DNE. Enter your answers as a comma-separated list.) y = −9x2 − 2x
The tangent line is the point that touches a graph at a point.
The value of x at the tangent line to the graph of [tex]\mathbf{y=-9x^2 - 2x}[/tex] is [tex]\mathbf{x = -\frac 19 }[/tex]
The function is given as:
[tex]\mathbf{y=-9x^2 - 2x}[/tex]
Differentiate both sides with respect to x
[tex]\mathbf{y' =-18x - 2}[/tex]
Set the above equation to 0, to calculate the value of x
[tex]\mathbf{-18x - 2 = 0}[/tex]
Collect like terms
[tex]\mathbf{-18x = 2 }[/tex]
Divide both sides by -18
[tex]\mathbf{x = -\frac 19 }[/tex]
Hence, the value of x when at tangent line to the graph of [tex]\mathbf{y=-9x^2 - 2x}[/tex] is [tex]\mathbf{x = -\frac 19 }[/tex]
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What number should I multiply 1 1/4 by to get 7/12
Johns collection contains US, Indian and British stamos. If the stamps ratios of US to Indian stamps is 5 to 2, and the ratio of Indian stamps to British stamps is 5 to 1, what is the ratio of US to British stamps
The ratio of US to British stamps is 25 to 2.
Explanation:To find the ratio of US to British stamps, we need to consider the ratios provided in the question. The ratio of US to Indian stamps is 5 to 2, and the ratio of Indian stamps to British stamps is 5 to 1. We can combine these ratios by multiplying the two ratios together. 5/2 multiplied by 5/1 is equal to 25/2. Therefore, the ratio of US to British stamps is 25 to 2.
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Charlie has 5 times as many stamps as Ryan. They have 1,608 stamps in all. How many more stamps does CHarlie have than Ryan?
A student correctly answers 15 of the first 20 questions on an examination.
What is the value of r, the part of the job that Marina can complete in 1 hour? 0.1 0.4 0.5 0.6
What is the probability that Eric rolls an even number or draws an ace from a standard deck of cards?
PLEASE HELP ASAP DUE IN A DAY What is the unit rate for 768.57 m 41.1 h? Enter your answer, as a decimal, in the box.
The unit rate for 768.57 meters in 41.1 hours is approximately 18.68 meters per hour. This calculation is derived by dividing the distance by the time to find the rate of movement.
To find the unit rate, divide the distance by the time:
[tex]\[ \text{Unit rate} = \frac{\text{Distance}}{\text{Time}} \][/tex]
[tex]\[ \text{Unit rate} = \frac{768.57 \, \text{m}}{41.1 \, \text{h}} \][/tex]
[tex]\[ \text{Unit rate} \approx \frac{768.57}{41.1} \, \text{m/h} \][/tex]
[tex]\[ \text{Unit rate} \approx 18.68 \, \text{m/h} \][/tex]
So, the unit rate is approximately 18.68 meters per hour.
The salaries of the president and the Vice President of a certain country total $562,500 a year. If the president makes $237,400 more than the Vice President , find each of their salaries.
Suppose five construction companies have the ability to build a factory overseas to produce a manufactured good. The marginal cost of building a factory for each construction company is shown in the table below: Producer Marginal Cost Company 1 $1,000,000 Company 2 $1,250,000 Company 3 $1,300,000 Company 4 $1,350,000 Company 5 $1,500,000 If the market price of an overseas factory is $ 1 470 000 , what is the surplus for these five companies?
The surplus for the five companies is amounting to $830,000
What is the surplus for the five companies?Producer Surplus is the difference between the price at which a producer is willing to spend and the price which he is getting from the market for his product.
The minimum price at which a producer is willing to spend is the Marginal Cost of producing that product.Therefore, Producer surplus is Market Price- Marginal CostProducer Marginal Cost Market Price Producer Surpus Company 1 1,000,000 1,470,000 (1,470,000-1,000,000)=470,000
Company 2 1,250,000 1,470,000 (1,470,000-1,250,000)=220,000
Company 3 1,300,000 1,470,000 (1,470,000-1,300,000)=170,000
Company 4 1,350,000 1,470,000 (1,470,000-1,350,000)=120,000
Company 5 1,500,000 1,470,000 (1,470,000-1,500,000)=-30,000
Total producer surplus= 470,000 + 220,000 + 170,000 + -30,000 = 830,000
The surplus for the five companies is amounting to $830,000
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Final answer:
The surplus for Companies 1, 2, and 3 is $470,000, $220,000, and $170,000 respectively, as their marginal costs are less than the market price of $1,470,000. Companies 4 and 5 do not have a surplus since their marginal costs are above the market price. The total surplus is $860,000.
Explanation:
The surplus for the five construction companies based on their marginal costs and the market price of an overseas factory can be calculated as the difference between the market price and the marginal cost for each company. Only the companies that have a marginal cost lower than the market price will experience a surplus. Given that the market price is $1,470,000:
Company 1 has a surplus of $470,000 ($1,470,000 - $1,000,000).
Company 2 has a surplus of $220,000 ($1,470,000 - $1,250,000).
Company 3 has a surplus of $170,000 ($1,470,000 - $1,300,000).
Companies 4 and 5 do not have a surplus because their marginal costs are higher than the market price. The total surplus for the three companies with a surplus is $860,000 ($470,000 + $220,000 + $170,000).
If an article costs a store $7.45 and if it sells the article for $9.95, what percentage (to the nearest tenth) markup is it using?
subtract to find the difference:
9.95 - 7.45 = 2.50
divide 2.50 by cost price to get mark up percentage
2.50 / 7.45= 0.3355
= 33.6 percent to the nearest tenth
Answer:
Markup Percentage is 33.56 %
Step-by-step explanation:
Given: Cost of an article = $ 7.45
Selling price of the article = $ 9.95.
To find: Markup percentage or profit percentage
Clearly Selling price is greater we have profit in this case.
Profit amount = 9.95 - 7.45 = $ 2.50
Profit percentage = [tex]\frac{2.50}{7.45}\times100=33.5570469799=33.56[/tex] %
Therefore, Markup Percentage is 33.56 %
Find the length and width of a rectangle when the width is 4ft. Shorter than the length. The perimeter of the rectangle is greater than 72ft.
A rectangular garden must have an area of 64 square feet. find the minimum perimeter of the garden.
A rectangular garden must have an area of 64 square feet then the minimum perimeter of the garden is 32 feet and this can be determined by using the formula of the perimeter of a rectangle.
Given :
A rectangular garden must have an area of 64 square feet.
The area of a rectangle is given by:
[tex]\rm A =l\times w[/tex]
where 'l' is the length of the rectangle and 'w' is the width of the rectangle.
Given that area of the rectangular garden is 64 square feet that is:
64 = lw
[tex]\rm w = \dfrac{64}{l}[/tex] ---- (1)
Now the perimeter of a rectangle is given by:
P = 2(l + w)
Put the value of w in the above equation.
[tex]\rm P = 2 (l + \dfrac{64}{l})[/tex] ---- (2)
For minimum perimeter differentiate the above equation with respect to the length of the garden.
[tex]\rm P' = 2 - \dfrac{128}{l^2}[/tex]
Now, equate the above equation to zero.
[tex]\rm 0 = 2-\dfrac{128}{l^2}[/tex]
[tex]l^2 = 64[/tex]
[tex]l = 8[/tex]
Now put the value of l in equation (2).
[tex]\rm P = 2(8 + \dfrac{64}{8})[/tex]
P = 32 feet.
A rectangular garden must have an area of 64 square feet then the minimum perimeter of the garden is 32 feet.
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The cost CC (in dollars) of making nn watches is represented by C=15n+85C=15n+85. How many watches are made when the cost is $385?
A Petri dish contains 100 bacteria cells. The number of cells increases 5% every minute. How long will it take for the number of cells in the dish to reach 2000? Use logarithms to solve.
The sum of two positive numbers is 12. what two numbers will maximize the product g
Given two numbers x and y such that:
x + y = 12 ... (1)
from equation (1)
y = 12 - x
Using this value of y, we represent xy as
xy = f(x)= x(12 - x)
f(x) = 12x - x^2
Differentiating the above function:
f'(x) = 12 - 2x
Maximum value of f(x) occurs at point for which f'(x) = 0.
Equating f'(x) to 0 we get:
12 - 2x = 0
2x = 12
> x = 12/2 = 6
Substituting this value of x in equation (2):
y = 12 - 6 = 6
Therefore, value of xy is maximum when:
x = 6 and y = 6
The maximum value of xy = 6*6 = 36
The two numbers that sum up to 12 and maximize the product are 6 and 6.
Let's denote the two numbers by x and y. We know that x + y = 12, and we want to maximize the product P = xy.
First, express y in terms of x,
y = 12 - x
P = x(12 - x)
= 12x - x²
To find the maximum value of P, we can take the derivative of P with respect to x and set it to zero,
dP/dx = 12 - 2x
Set dP/dx to 0: 12 - 2x = 0
x = 6
Since x + y = 12, if x = 6, then y = 12 - 6 = 6.
The two numbers are 6 and 6.
This combination will maximize the product, which is 6 * 6 = 36.
In conclusion, the two numbers that add up to 12 and maximize their product are both 6.
Cameron can display his 12 models cars
Which point on the x-axis lies on the line that passes through point P and is perpendicular to line MN?
(0, 1)
(0, 4)
(1, 0)
(4, 0)
1. Points M and N have coordinates (-4,0) and (4,2), respectively.
Then vector [tex]\overrightarrow{MN}=(4-(-4),2-0)=(8,2)[/tex] is perpendicular to the neede line.
2. Write the equation of line that passes through the point P(2,-4) and is perpendicular to vector [tex]\overrightarrow{MN}=(8,2):[/tex]
[tex]8(x-2)+2(y+4)=0,\\8x-16+2y+8=0,\\8x+2y-8=0,\\4x+y-4=0.[/tex]
3. Find the point on x-axis, that lies on the perpendicular line.
When y=0, then 4x-4=0, x=1 and point (1,0) lies on perpendicular line.
Answer: correct choice is C.
Randy school requires that there are two adult chaperones for every 18 students when the students go on a field trip to the museum if there are 99 students going to the museum how many adult shop around our need it
Which equation can be used to find the answer? A playground with four sides has a perimeter of 52 ft. Three of the sides have lengths of 9 ft, 16 ft, and 19 ft. What is the length of the fourth side? A. s – 9 + 16 + 19 = 52 s =26 26 ft B. s + 9 + 16 + 19 = 52 s = 8 8 ft C. s – 52 = 9 + 16 – 19 s = 58 58 ft D. s – 9 – 16 – 19 = 52 s = 96 96 ft
Option B)s + 9 + 16 + 19 = 52. Solving this gives the fourth side as 8 ft.
To find the length of the fourth side, you need to know the equation that correctly represents the given information. The perimeter of the playground is the sum of all four sides. Therefore, the correct equation to find the fourth side (s) is:
B. s + 9 + 16 + 19 = 52
9 + 16 + 19 = 44.
s + 44 = 52.
s = 52 - 44.
s = 8.
Therefore, the length of the fourth side is 8 ft.
So, the correct option is B. s + 9 + 16 + 19 = 52.
Some luggage pieces have wheels and a handle so that the luggage can be pulled along the ground. Suppose the length from the bottom of the bag to the place on the floor perpendicular to the hand on the bag is 14 inches, and the length of the bag with its handle is 19 inches. At which angle made by the bag and the floor would it be comfortable to roll the bag?
Given point M(0,6),N (5,3), Rc (-7,-5) nd S(-2,-2) determine if MN is congruent to Rs
Two planes which are 3540 miles apart fly toward each other. Their speeds differ by 35 mph. If they pass each other in 4 hours, what is the speed of each?
Final answer:
The speed of the slower plane is 425 mph, and the speed of the faster plane is 460 mph, determined by using the concept of relative speed and algebra to solve the given equation.
Explanation:
To solve the problem of two planes flying towards each other, we need to use the concept of relative speed. We know that the two planes are 3540 miles apart and that they pass each other after 4 hours. The speeds of the planes differ by 35 mph. The relative speed of the two planes combined is the distance divided by the time, so we calculate it as follows:
Relative Speed = Total Distance / Time = 3540 miles / 4 hours = 885 mph
So, if we denote the speed of the slower plane as S mph, the speed of the faster plane will be S + 35 mph. Since their combined speed is the relative speed, we can set up the following equation:
S + (S + 35) = 885
From this equation, we need to find the value of S which represents the speed of the slower plane. We can then add 35 to S to find the speed of the faster plane. Here's how it's done step by step:
Combine like terms: 2S + 35 = 885Subtract 35 from both sides: 2S = 850Divide by 2 to solve for S: S = 425 mphAdd 35 to S to find the speed of the faster plane: 425 + 35 = 460 mphTherefore, the speed of the slower plane is 425 mph and the speed of the faster plane is 460 mph.
10+6 has the same sum as 7+
50% of all the cakes jenny baked were party cakes, 1/5 were fruit cakes and the remainder were sponge cakes. What percentage of cakes were sponge cakes?
If 4f(x)+f(5-x)=x2
What is f(x)?