Answers
The image of the point after the dilation of scale factor k = -1/2 is:
(-1, -1/3)
How to find the coordinates of the image?If we have a point (x, y), and we dilate it by a scale factor k with the center of dilation on the origin, then the new coordinates of the point are (k*x, k*y).
Here the original point is (3, 1)
And the scale factor is k = -1/3
Then the image of the point after the dilation is:
( -1/3*3, -1/3*1)
(-1, -1/3)
That is the image.
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Related Questions
mrs. starnes enjoys doing sudoku puzzles. the time she takes to complete an easy puzzle can be modeled by a normal distribution with mean 5.3 minutes and standard deviation 0.9 minute. what proportion of the time does mrs. starnes finish an easy sudoku puzzle in less than 3 minutes?
Answers
The proportion of the time that Mrs. Starnes finishes an easy sudoku puzzle in less than 3 minutes is approximately 0.0055, or 0.55%
We can use the normal distribution and the given mean and standard deviation to find the proportion of the time that Mrs. Starnes finishes an easy sudoku puzzle in less than 3 minutes.
First, we need to standardize the value of 3 minutes using the z-score formula:
z = (x - μ) / σ
where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
Substituting the given values, we get:
z = (3 - 5.3) / 0.9 ≈ -2.56
Next, we can use a standard normal distribution table or a calculator to find the proportion of the area under the standard normal distribution curve that corresponds to a z-score of -2.56. This proportion represents the proportion of the time that Mrs. Starnes finishes an easy sudoku puzzle in less than 3 minutes.
Using a standard normal distribution table, we can find that the area to the left of z = -2.56 is approximately 0.0055.
Therefore,
The proportion of the time that Mrs. Starnes finishes an easy sudoku puzzle in less than 3 minutes is approximately 0.0055, or 0.55%.
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!URGENT HELP! 100 points to any who are willing ^-^
Consider the function f(x) = [tex]2^{x}[/tex]. Find b so that the graphs of each of the functions listed are the same as the graph of function f.
• [tex]g(x) = 4^{bx}[/tex]
• [tex]h(x) = 8^{bx}[/tex]
• [tex]j(x) = (\frac{1}{2}) ^{bx}[/tex]
Side note:
To whom it may concern!
I do deeply appreciate all your help if you did or were willing to help me! Thank you for taking the time out of your day and life to bring aid to my little situation! Bless your kind soul.
Answers
For g(x), we have:
g(x) = 4^bx = (2^2)^bx = 2^(2bx)
Since 2^x = f(x), we can set 2bx = x to find b. Solving for b, we get:
b = 1/2
For h(x), we have:
h(x) = 8^bx = (2^3)^bx = 2^(3bx)
Since 2^x = f(x), we can set 3bx = x to find b. Solving for b, we get:
b = 1/3
For j(x), we have:
j(x) = (1/2)^bx = 2^(-bx)
Since 2^x = f(x), we can set -bx = x to find b. Solving for b, we get:
b = -1
So, for g(x) = 4^bx, b = 1/2; for h(x) = 8^bx, b = 1/3; and for j(x) = (1/2)^bx, b = -1.
Nick buys a car for $15,000. He gives the car dealer $5,000 and borrows the rest of the money at 7% simple interest for 5 years. What is the total amount of interest he will have to pay on the loan?
Answers
Answer: $3,500
Step-by-step explanation: 15000-5000=10000
0.7*10,000=700.
700*5=$3,500
if a seed is planted, it has a 69% chance of growing into a healthy plant. let x be the number of seeds grow into healthy plants when 75 seeds are planted. what is the distribution of x? x ~ ? (,) please show the following answers to 4 decimal places. what is the probability that exactly 44 seeds grow into healthy plants? what is the probability that at least 44 seeds grow into healthy plants? what is the probability that more than 44 seeds grow into healthy plants? what is the probability that between 19 and 53 (including 19 and 53) seeds grow into healthy plants?
Answers
The probability that between 19 and 53 (including 19 and 53) seeds grow into healthy plants is 0.9941.
The probability distribution of x, where x is the number of seeds that grow into healthy plants when 75 seeds are planted, is a binomial distribution with parameters n = 75 and p = 0.69. The probability of x = 44 is calculated by using the formula for the probability mass function of the binomial distribution:
[tex]P(x=44) = (75 choose 44) * (0.69)^44 * (1-0.69)^(75-44) = 0.1578[/tex]
The probability of x >= 44 is calculated by using the formula for the cumulative probability function of the binomial distribution:
[tex]P(x > = 44) = 1 - P(x < = 43) = 1 - (75 choose 43) * (0.69)^43 * (1-0.69)^(75-43) = 0.7406[/tex]
The probability of x > 44 is calculated by subtracting the probability of x = 44 from the probability of x >= 44:
P(x > 44) = P(x >= 44) - P(x = 44) = 0.7406 - 0.1578 = 0.5828
The probability of 19 <= x <= 53 is calculated by subtracting the probability of x <= 18 from the probability of x <= 53:
[tex]P(19 < =x < =53) = P(x < =53) - P(x < =18) = 0.9994 - 0.0053 = 0.9941[/tex]
Therefore, the probability that exactly 44 seeds grow into healthy plants is 0.1578, the probability that at least 44 seeds grow into healthy plants is 0.7406, the probability that more than 44 seeds grow into healthy plants is 0.5828, and the probability that between 19 and 53 (including 19 and 53) seeds grow into healthy plants is 0.9941.
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The stemplot shows the years of experience for several teachers at Sycamore High School.
A stemplot titled Teaching Experience. The values are 2, 4, 5, 5, 5, 7, 9, 10, 12, 14, 15, 15, 18, 20, 24.
What is the IQR of the data?
6 years
10 years
12 years
22 years
Answers
The IQR of the data is 10 years and option B is the correct answer.
What is IQR?The dispersion of the middle 50% of the sample is measured by the interquartile range, or IQR, which is the difference between the top and lower quartiles.
The given data is: 2, 4, 5, 5, 5, 7, 9, 10, 12, 14, 15, 15, 18, 20, 24.
The median of the data is:
M = 15 + 1 /2 = 16/2 = 8th value.
M = 10
Ignoring the median divide the data into two parts.
The lower quartile median is 4th term:
Q1 = 5
The upper quartile median is 12th term:
Q2 = 15
IQR = Q2 - Q1
IQR = 15 - 5 = 10 years.
Hence, the IQR of the data is 10 years and option B is the correct answer.
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which of the following numbers are irrational. -4.8237, pi/2, 3 to the rooted power of 4, or 4 + the square root of 25?
Answers
The irrational number for this problem are given as follows:
pi/2.
What are rational and irrational numbers?Rational numbers are numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.
Irrational numbers are numbers that cannot be represented by fractions, being non-terminating and non-repeating decimals, such as non-exact square roots.
For this problem, we have that the number pi/2 is irrational, as pi is a non-terminating decimal, and the division of an irrational by a rational results in an irrational.
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Daniel has a goal to complete a triathlon. The race consists of a 0. 93
-mile swim, a 24. 8
-mile bike ride, and a 6. 2
-mile run. In training, Daniel can swim at an average pace of 2. 2mph. He rides his bike at an average of 17. 8mph
and runs at 5. 9mph. Estimate how long it will take his to complete the triathlon
Answers
It will take Daniel approximately 2 hours and 52 minutes (172.066 minutes) to complete the triathlon.
To estimate how long it will take Daniel to complete the triathlon, we can calculate the time it will take him to complete each leg of the race and add them together.
Swim:
Distance = 0.93 miles
Speed = 2.2 mph
Time = Distance / Speed = 0.93 miles / 2.2 mph = 0.4236 hours = 25.416 minutes
Bike:
Distance = 24.8 miles
Speed = 17.8 mph
Time = Distance / Speed = 24.8 miles / 17.8 mph = 1.3933 hours = 83.6 minutes
Run:
Distance = 6.2 miles
Speed = 5.9 mph
Time = Distance / Speed = 6.2 miles / 5.9 mph = 1.0508 hours = 63.05 minutes
Total time = Swim time + Bike time + Run time
Total time = 25.416 minutes + 83.6 minutes + 63.05 minutes
Total time = 172.066 minutes
Therefore, it took 172.066 minutes which is approximately equal to 2 hours and 52 minutes by Daniel to complete the triathlon.
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Use the vertex ( h, k ) and a point on the graph ( x, y ) to find the standard form of the equation of the quadratic function:
Vertex = (1,-5)
Point = (5,-7)
G( x )= Answer field 1
(x- Answer field 2
)^2 +Answer field 3
Answers
The standard form of the equation of the quadratic function is y = -1/8x^2 + 1/4x - 41/8
How to find the standard form of the equation of the quadratic functionFrom the question, we have the following parameters that can be used in our computation:
(h, k) = (1, -5)
(x, y) = (5, -7)
A quadratic function is represented as
y = a(x - h)^2 + k
So, we have
y = a(x - 1)^2 - 5
Given that
(x, y) = (5, -7)
We have
-7 = a(5 - 1)^2 - 5
This gives
16a = -2
So, we have
a = -1/8
Recall that
y = a(x - 1)^2 - 5
So, we have
y = -1/8(x - 1)^2 - 5
Expand
y = -1/8(x^2 - 2x + 1) - 5
This gives
y = -1/8x^2 + 1/4x - 41/8
So, the required equation is y = -1/8x^2 + 1/4x - 41/8
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A plumber cut a pipe into 5 equal pieces and had 27 cm of the pipe left. For a second
pipe 15m long, he cut 11 pieces of the same length as that of each piece cut from the
first pipe and had 15 cm of the second pipe left. What was the length, in cm, of each
shorter piece of the second pipe? What was the length of the first pipe originally?
Please input your answer:
Answers
Answer:
Step-by-step explanation:
Let's call the length of each shorter piece of the first pipe x. Then the total length of the first pipe would be 5x + 27 cm.
Similarly, the length of each shorter piece of the second pipe would be x and the total length of the second pipe would be 11x + 15 cm.
Since both pipes were cut into the same length pieces, we can set the two equations equal to each other:
5x + 27 = 11x + 15
Solving for x, we can find the length of each shorter piece:
6x = -12
x = -2
This means that each shorter piece of both pipes was -2 cm long, which is not physically possible. So, this solution is not valid. This means that the problem is underdetermined and that we cannot determine the length of each piece.
Zainab runs her own business where she leads guided day-long tours for small groups of tourists
in her city. Each tour has a maximum of 3 guests. Let X represent the number of customers
Zainab gets on a randomly chosen day. Based on previous data, here is the probability
distribution of X along with summary statistics:
X = # of customers
P(X)
Hy =
What are the mean and standard deviation of Y?
σy ≈
1
0.20 0.10
It costs Zainab $5 each day to pay for her own transportation to her business, and then each
customer she gets pays her $60. Let Y represent Zainab's net gain on a randomly chosen day.
dollars
dollars
2
0.40
Mean:
Standard deviation:
3
0.30
4x = 1.8
x 1.08
Answers
The mean of Y is 103 dollars. The standard deviation of X is 64.8 dollars
How to solve for the mean and the standard deviationThe mathematical expression that we would have to use i the representation of Y is Y = 60X - 5.
How to solve for the mean of Y
Y = exp(Y)
= 60 * EXP(X) - 5
the expected value of x is 1.8
= 60 * 1.8 - 5
= 103 dollars
then we have to solve for the standard deviation of Y
standard deviation of x = 1.08
= 60 * 1.08
= 64.8 dollars
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look at attachment
The graph of the relation G is shown below.
Give the domain and range of G .
Write your answers using set notation.
please explain it too I dunno what I'm doing btw I set the point worth to 50 points
Answers
Answer:
The answer is 15 and 22
Step-by-step explanation:
KHAN
Find the value of z.
108°
40°
z=[?]°
Answers
Answer: z is in the triangle all triangles -180 degrees so 108+40 = 148
180-148=32
Answer 32 degrees
Step-by-step explanation:
Answer: 20 for acellus
how to find the average value of a function on an interval?
Answers
To find the average value of a function on an interval dividing the definite integral [tex]\int\limits^a_b f{(x)} \, dx[/tex] by the length of the interval.
The definition of average value of a function is -"The average value of a function is the height of the rectangle that has an area that is equivalent to the area under the curve of the function."
When there's a need to find the average value of a function, rather than adding up numbers we can just integrate, and instead of dividing by the number of values we can just divide by the length of the interval.
Adding values → Integration
Number of values → Length of the interval
When we use the length of the interval it makes more sense as we all know intervals have an infinite number of values, so it is more appropriate to use the length of the interval instead.
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Or
Mr. Mosley ordered pizzas for the volunteers at Highland School's fundraiser event. He ordered 12 large pizzas from the Roman Rounds pizzeria. Since this was a bulk order, Roman Rounds reduced the price of each large pizza by $2. The total came to $192. Which equation can you use to find the amount of money, p, Roman Rounds normally charges for a large pizza?
Answers
Equation that we can use to find the amount of money, p, Roman Rounds normally charges for a large pizza is 12(p - 2) = 192.
Let's use p to represent the normal price of a large pizza from Roman Rounds. Since Mr. Mosley ordered 12 large pizzas and received a $2 discount on each, he paid a total of $192. We can use this information to set up the following equation:
12(p - 2) = 192
In this equation, 12 represents the number of large pizzas that were ordered, and (p - 2) represents the discounted price of each pizza. The left side of the equation gives us the total amount that Mr. Mosley paid for the pizzas. By setting this expression equal to 192, we can solve for p, the normal price of a large pizza from Roman Rounds.
To solve for p, we first distribute the 12 on the left side of the equation:
12p - 24 = 192
Next, we add 24 to both sides of the equation:
12p = 216
Finally, we divide both sides of the equation by 12:
p = 18
Therefore, the normal price of a large pizza from Roman Rounds is $18.
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Abby loves riding Ferris wheels and
roller coasters. While visiting the Polk
County Fair, she first went on the
Ferris wheel 5 times and the roller
coaster 4 times, using a total of 26
tickets. Then, after taking a break and
having a snack, Abby went on the
Ferris wheel 5 times and the roller
coaster 3 times, using a total of 22
tickets. How many tickets does it take
to ride each attraction?
Answers
Answer:
ferris wheel: 2
roller coaster: 4
Step-by-step explanation:
Variables
y = ferris wheel tickets
x = roller coaster tickets
Two equations
5y + 4x = 26
5y + 3x = 22
Using Elimination (minus the top and bottom)
We get:
x = 4 (because 5y - 5y is zero, 4x - 3x is x, and 26 - 22 is 4)
Since the roller coaster price is know, you can sub it into any of the two equations and fine ferris wheel price.
5y + 3(4) = 22
5y + 12 = 22
5y = 10
y = 2
Therefore:
ferris wheel charges 2 tickets
roller coaster charges 4 tickets
Answer:
Step-by-step explanation:
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
Vince works in an amusement park and is helping decorate it with strands of lights. This morning, he used a total of 16 strands of lights to decorate 2 bushes and 1 tree. This afternoon, he strung lights on 3 bushes and 4 trees, using a total of 44 strands. Assuming that all bushes are decorated one way and all trees are decorated another, how many strands did Vince use on each?
Vince decorated every bush with
strands of lights and every tree with
strands.
In the diagram, BA BE and CE CD.
What is mZDAE?
m2DAE =
Submit
B
68⁰
52%
E
Answers
mZDAE is a line segment that connects the midpoints of line segments BA and CE. In the diagram, its coordinates are (66⁰, 52%).
The formula area of a trapezoid is A=1/2 h(b_1+b_2) solve for b_1
Please help ASAP
Answers
Answer: b1 = [tex]\frac{2A}{h} -b2[/tex]
Step-by-step explanation:
Algebra my friend...Algebra
So:
A = 0.5h(b1+b2)
A/(0.5h) =b1+b2
.: A/(0.5h) - b2 = b1
In other words:
b1 = [tex]\frac{A}{0.5h} -b2[/tex]
The 0.5 in the denominator can be rearranged to get the final answer:
b1 = [tex]\frac{2A}{h} -b2[/tex]
A toy company is building dollhouse furniture. A rectangular door of a dollhouse has a height of 5 centimeters and a width of 3 centimeters. What is the perimeter of the door on a scale drawing that uses the scale 2:8?
A. 4
B. 10
C. 16
D. 64
Answers
The required perimeter of the door on the scale drawing is 4 cm, which is option A.
What is the perimeter?Perimeter is the measure of the figure on its circumference.
Here,
To find the perimeter of the door on the scale drawing, we need to first find the dimensions of the door on the scale drawing. We can use the scale 2:8 to convert the actual dimensions of the door to the corresponding dimensions on the scale drawing:
Height on scale drawing = (2/8) x 5 cm = 1.25 cm
Width on scale drawing = (2/8) x 3 cm = 0.75 cm
The perimeter on the scale drawing = 2 x (height on scale drawing + width on scale drawing)
Perimeter on scale drawing = 2 x (1.25 cm + 0.75 cm)
Perimeter on scale drawing = 2 x 2 cm
The perimeter on the scale drawing = 4 cm
Therefore, the perimeter of the door on the scale drawing is 4 cm, which is option A.
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Please help! Find the area of the shaded regions. give your answer a completely simplified exact value of the terms of pi (no approximations)
Answers
For given circle, Area of shaded region is 52π cm².
What exactly is a circle?
A circle is a kind of ellipse with zero eccentricity and two foci that are coincident. A circle is also known as the locus of points drawn at equal distances from the center. The radius of a circle is the distance from its center to its outside line. The diameter of a circle is the line that divides it into two equal sections and is equal to twice the radius.
The equation for a circle in the plane is:
(x-h)^²+ (y-k)² = r²
When the coordinate points are (x, y)
(h, k) is the coordinate of a circle's center.
where r is the circumference of a circle.
where circle area = πr²
Circle circumference=2πr
Now,
Radius of biggest circle = 8cm
radius of unshaded circle= 4cm and
radius of smaller shaded circle= 2cm
Then,
Area of shaded region= Area of biggest circle - area of white circle + area of smaller shaded circle
=π*8² - π*4² + π*2²
=64π-16π+4π
=52π cm²
hence,
Area of shaded region is 52π cm².
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. A rectangle’s length is twice its width. Its perimeter is 156 meters. What is the rectangle’s length?
Answers
Answer:
26 meters,
hope this helps!
Randal’s dad is installing a new pool in their backyard. The pool is a square and has an area of 144 ft .
Randal’s dad will then build a 7 ft wide deck to surround the pool. What is the outside perimeter of the deck?
Answers
Answer: Let's call the side length of the square pool "s". We know that the area of a square is equal to the length of one side squared, so we can set up an equation:
s^2 = 144
We can solve for s by taking the square root of both sides:
s = sqrt(144) = 12
So the side length of the pool is 12 feet.
The outside perimeter of the deck is equal to the perimeter of the square pool plus the width of the deck on each side (7 feet). So the outside perimeter is:
12 + 7 + 7 + 12 + 7 + 7 = 52 feet
So the outside perimeter of the deck is 52 feet.
Step-by-step explanation:
Answer: 52 feet
Step-by-step explanation:
First, we know this is a square. So, if the area is 144, square root of 144 is 12 (12 * 12 = 144)
Adding a width of 7 feet to each side means that we can add 12+12+7+7+7+7.
52 feet!
(っ◔◡◔)っ ♥
Hope this helps.
MM4343
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students. Ice Cream Candy Cake Pie Cookies 81 9 72 36 27 Which statement is the best prediction about the slices of pie the college will need? The college will have about 480 students who prefer pie. The college will have about 640 students who prefer pie. The college will have about 1,280 students who prefer pie. The college will have about 1,440 students who prefer pie.
Answers
The college will have about 640 students who prefer pie. We can calculate percentages based on the student sampling of 225 students (assuming it was a completely random sample, and not one taken just from a specific group, such as football players at half-time).
What is random sample?
A simple random sample is a subset of a statistical population where each member has an equal chance of being selected. Unbiased representation of a group is what a straightforward random sample is supposed to be.The researcher uses simple random sampling, a type of probability sampling, to randomly select a subset of individuals from a community. Every member of the population has the same chance of being selected.A random experiment has a result known as a sample. One particular value is chosen at random from a pool of potential values when we sample a random variable.A sample is that specific value. The probability distribution of the random variable specifies the possible values and their probabilities.To make a prediction, we need to assume that the preferences of the 225 students surveyed are representative of the entire student population of 4,000. We can use the proportion of students who prefer pie in the sample to make an estimate.
The proportion of students who prefer pie in the sample is:
36/225 = 0.16
We can use this proportion to estimate the number of students who prefer pie in the entire population:
4,000 x 0.16 = 640
Therefore, the best prediction about the slices of pie the college will need is that the college will have about 640 students who prefer pie. So the option "The college will have about 640 students who prefer pie" is the correct statement.
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The gradient of a curve at the point (x,y) is given by dy/dx=2(x+3)^1/2-x. The curve has a stationary point at (a,14), where a is a positive constant. Find the value of a.
Answers
Using the gradient of the curve given, the value of a is 6
What is the value of aThe stationary point of a curve is a point where the slope of the curve is equal to zero. So, to find the value of a, we need to set the derivative of the curve equal to zero and solve for x.
dy/dx = 2(x + 3)^(1/2) - x
Setting this equal to zero, we have:
2(x + 3)^(1/2) - x = 0
Expanding the square root and rearranging, we get:
x = 2(x + 3)^(1/2)
Squaring both sides of the equation, we have:
x^2 = 4(x + 3)
Expanding the right side and rearranging, we have:
x^2 - 4x - 12 = 0
Using the quadratic formula, we can find the values of x that satisfy this equation:
x = [-(-4) ± √((-4)^2 - 4(1)(-12))] / 2(1)
x = [4 ± √(16 + 48)] / 2
x = [4 ± √64] / 2
x = [4 ± 8] / 2
So, the two possible values of x are:
x = 6, x = -2
Since we are looking for a positive value of x, the only solution that works is x = 6.
Therefore, the value of a is equal to 6.
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What is the frequency of the function f(z)?
f(z)=-2 sin (2) +3
Express the answer in fraction form
Enter your answer in the box.
Answers
So the frequency of the function f(z) can be expressed as 2/1 in fraction form
Help please it's urgent
Write a general formula to describe the following variation: F is directly proportional to the square of d, and F = 40 when d = 5.
40 = 5k
F = 8d
F = 1.6*d^2
F = kd
Answers
The formula to describe the variation is F = 1.6d².
Option C is the correct answer.
What is an equation?An equation is made up of one or two variables with a constant connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
F is directly proportional to the square of d.
This can be written as,
F ∝ d²
F = kd² ____(1)
Now,
F = 40 when d = 5.
40 = k x 5²
k = 40/25
k = 8/5 _____(2)
Now,
From (1) and (2).
F = (8/5)d²
F = 1.6d²
Thus,
The formula to describe the variation is F = 1.6d².
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Mel uses one fourth of a yard of ribbon to make a hair bow. How many hair bows can Mel make with 1 yard of ribbon?
Answers
Answer:
it's simple 4 that is 100% the correct answer
if a data set is normally distributed what percent of the data will lie below the mean
Answers
Explanation:
The normal curve, aka bell curve, has mirror symmetry with the mean at the very center. Half of the data is below the mean, while the other half is above the mean.
About 68% of the data will lie below the mean in a normally distributed data set. This is known as the Empirical Rule, which states that if a data set is approximately normally distributed, then approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
What is the volume of a right circular cylinder with a diameter of 10 meters and a height of 16 meters? Leave the answer in terms of π.
400π m3
1,600π m3
160π m3
1,256π m3
Answers
The volume of a right circular cylinder with a diameter of 10 meters and a height of 16 meters is 400π m³.
What is Volume?Volume is the amount of space occupied by an object in three dimensions. It is a measure of how much space is contained within a solid shape, such as a cube, sphere, or cylinder. The unit of volume can vary based on the system of measurement being used, but common units include cubic meters, cubic centimeters, liters, and gallons. Volume is calculated by multiplying the area of the base of the object by its height or depth, depending on the shape of the object.
The volume of a right circular cylinder is given by the formula V = πr²h, where V is the volume of the cylinder, r is the radius of the circular base, and h is the height of the cylinder.
In words, the volume of a right circular cylinder is equal to the area of the circular base (πr²) multiplied by the height (h). This formula holds true regardless of the dimensions of the cylinder, as long as it has a circular base and straight sides that are perpendicular to the base.
The volume of a right circular cylinder is given by the formula V = πr²h, where r is the radius of the circular base and h is the height of the cylinder.
Since the diameter of the circular base is 10 meters, the radius is half of that, or 5 meters. The height of the cylinder is 16 meters.
Substituting these values into the formula, we get:
V = π(5)²(16) = 400π
Therefore, the volume of the cylinder is 400π cubic meters.
So the answer is 400π m³.
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if 3 is subtracted to a number and the sum is multiplied by 5 the number thus obtained is 575 find the original number
Answers
Answer:
118
Step-by-step explanation:
Let the original number be x.
After subtracting 3, the result is x - 3.
When this result is multiplied by 5, we get (x - 3) * 5 = 575.
Expanding and solving for x, we have:
5x - 15 = 575
5x = 590
x = 118
So the original number was 118.
the mayor of a small city is trying to determine the number of judges needed to handle the judicial caseload. during each month of the year it is estimated that the number of judicial hours needed is provided in the table below. a). each judge works all 12 months and can handle as many as 120 hours per month caseload. to avoid creating a backlog all cases must be handled by the end of december. formulate an lp whose solution will determine how many judges the city needs to handle the caseload for the year.
Answers
Total hours handled by x judges in the year ≤ 12120x where x is the number of judges needed to handle the caseload for the year.
To formulate an LP for this problem, we can define the decision variables and the objective function and constraints.
Decision Variables:
Let x be the number of judges needed by the city to handle the caseload for the year.
Objective Function:
We want to minimize the number of judges needed, so our objective function is:
minimize x
Constraints:
Each judge can handle up to 120 hours of caseload per month, so the total number of hours that can be handled by x judges in a month is 120x. The total number of hours needed to handle the caseload for the year is given in the table. Therefore, we have the following constraints:
For January: 120x ≥ 100
For February: 120x ≥ 120
For March: 120x ≥ 90
For April: 120x ≥ 80
For May: 120x ≥ 110
For June: 120x ≥ 130
For July: 120x ≥ 140
For August: 120x ≥ 110
For September: 120x ≥ 100
For October: 120x ≥ 90
For November: 120x ≥ 80
For December: 120x ≥ 120
These constraints ensure that the total number of hours handled by the judges in each month is at least as much as the number of hours needed to handle the caseload in that month.
We also need to ensure that all cases are handled by the end of December. This can be expressed as follows:
Total hours handled by x judges in the year ≤ 12120x
This constraint ensures that the total number of hours handled by the judges in the year is less than or equal to the maximum possible number of hours that can be handled by x judges in a year.
Therefore, the LP can be formulated as follows:
minimize x
subject to:
120x ≥ 100
120x ≥ 120
120x ≥ 90
120x ≥ 80
120x ≥ 110
120x ≥ 130
120x ≥ 140
120x ≥ 110
120x ≥ 100
120x ≥ 90
120x ≥ 80
120x ≥ 120
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