Answer:
The decimal form is 0.8 and the simplified fraction of 80% is 4/5
Step-by-step explanation:
abc is a right triangle with ab=ac. bisector of <a meets bc at d. prove that bc = 2ad.
Answer:
Let ac=ab=5
With this, bc= 5√2
Step-by-step explanation:
So to find ad, Let ad be x
5√2=(2)(x)
(5√2/2)= x
This proves that bc=2ad
students at day camp are decorating circles for placemats
Answer: Your welcome!
Step-by-step explanation:
The students can decorate the circles for placemats in a variety of ways. They can use paint, markers, fabric, or any other creative material of their choice. They can also add images, shapes, and words to the circles. They could even attach ribbons or other decorations to the circles to create a unique design. The possibilities are endless!
The width of a rectangle is 2 cm less than its length. The perimeter of the rectangle is 16 cm. What are the dimensions of the rectangle?
Answer:
Width=3 cm
Length=5 cm
Ward finances $20,000 to purchase a car. If he gets a 2. 5% interest rate regardless of loan length, how much interest will Ward save if he finances the $20,000 for 3 years rather than 5 years? A) $1,000 B) $10,000 C) $333. 33 D) $3,333. 33.
The total amount of interest will Ward save if he finances car the $20,000 for 3 years rather than 5 years is $1000.
What is simple interest?Simple interest is the amount charged on the principal amount with a fixed rate of interest for a time period. Simple interest calculated only on the principal amount.
The formula for the simple interest can be given as,
\(I=\dfrac{Prt}{100}\)
Here, (I) is the interest amount earned on the principal amount of (P) with the rate of (r) in the time period of (t).
Ward finances $20,000 to purchase a car. The rate of interest is 2.5% regardless of loan length. The interest amount of the car for three years is,
\(I_3=\dfrac{20000\times2.5\times3}{100}\\I_3=1500\)
The interest amount of the car for five years is,
\(I_3=\dfrac{20000\times2.5\times5}{100}\\I_3=2500\)
The amount of interest Ward save,
\(C=2500-1500\\C=1000\)
Thus, the total amount of interest will Ward save if he finances car the $20,000 for 3 years rather than 5 years is $1000.
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A student would like to estimate the proportion of students at his school who have lunch during period 4. To do so,
he selects a random sample of 40 students and finds that 30% of them have period 4 lunch. Later, he goes to the
guidance office and finds that of the 380 students at this school, 25% of them have period 4 lunch. Which of the
following properly describes the number, 25%?
sample
statistic
population
parameter
Yeah
Answer:
D
As we are getting the 25% from the whole population of 380 students, therefore this is a population proportion which is a parameter. Note that we get parameter from population and statistic from the sample.
Step-by-step explanation:
The property parameter describes the number, 25% because 25% from a population of 380 students, this is a population proportion that may be used as a metric option (D) parameter is correct.
What are population and sample?It is described as a collection of data with the same entity that is linked to a problem. The sample is a subset of the population, yet it is still a part of it.
We have:
Number of samples = 40
30% of them have period 4 lunch.
Total population = 380
25% of them have period 4 lunch.
Because we're collecting 25% from a population of 380 students, this is a population proportion that may be used as a metric.
We collect parameters from the population and statistics from the sample.
Thus, the property parameter describes the number, 25% because 25% from a population of 380 students, this is a population proportion that may be used as a metric option (D) parameter is correct.
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Donnie deli man delivered 595 box lunches for the robotics convention. There were 20 more turkey sandwiches then roast beef. There were twice as many roast beef has PB&J. How many of each type of BoxLunch did Donnie delivered?
Answer:
250 turkey sandwiches were delivered.
There were 230 roast beef delivered.
115 PB&J were delivered.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
x is the number of turkey sandwiches.
y is the number of roast beef.
z is the number of PB&J.
Donnie delivered 595 box lunches
This means that \(x + y + z = 595\)
There were 20 more turkey sandwiches then roast beef.
This means that \(x = y + 20\)
There were twice as many roast beef has PB&J.
This means that \(y = 2z\).
So in the second equation, we have that \(x = 2z + 20\)
Replacing this in the first equation:
\(x + y + z = 595\)
\(2z + 20 + 2z + z = 595\)
\(5z = 575\)
\(z = \frac{575}{5}\)
\(z = 115\)
115 PB&J were delivered.
\(x = 2z + 20 = 2*115 + 20 = 250\)
250 turkey sandwiches were delivered.
\(x = y + 20\)
So
\(y = x - 20 = 250 - 20 = 230\)
There were 230 roast beef delivered.
if the tangent line to y = f(x) at (4, 2) passes through the point (0, 1), find f(4) and f '(4).
If the tangent line to y = f(x) at (4, 2) passes through the point (0, 1), then f'(4) = 1/4 and f(4) = 2.
Let's assume that the tangent line to y = f(x) at (4, 2) passes through the point (0, 1). We need to find f(4) and f '(4).
Given that f'(x) is the slope of the tangent line, let's find the slope of the tangent line using the given data:
Let (x1, y1) = (4, 2) and (x2, y2) = (0, 1).The slope of the tangent line (m) can be determined by using the slope formula as follows: `(y2-y1)/(x2-x1)`m = `(1-2)/(0-4)`m = `(1/4)`
Therefore, the slope of the tangent line is 1/4. We can then determine f'(4) by equating it to the slope of the tangent line. We get: f'(4) = m = 1/4
Next, let's find the equation of the tangent line using the point-slope form of the equation of a line. We have:
m = 1/4 and (x1, y1) = (4, 2).
Therefore, the equation of the tangent line is: y - y1 = m(x - x1)
Substituting the values, we get: y - 2 = (1/4)(x - 4)y - 2 = (1/4)x - 1y = (1/4)x + 1
The function y = f(x) passes through (4, 2). Substituting the values, we get:2 = (1/4)(4) + c
Simplifying, we get:2 = 1 + c
Therefore, c = 1.Substituting c into the equation, we get: y = (1/4)x + 1
Therefore, f(x) = (1/4)x + 1. Hence, f(4) = (1/4)(4) + 1 = 2.
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The angle facing the shortest length in a triangle is
A. A right angle
B. An acute angle
C. An opposite angle
D. The smallest angle
Answer: To be honsest i think it is C.) "Opposite angle" because the shortest side is always opposite the smallest interior angle.
What is the equation of a line perpendicular to this line x+4y=-2
Step-by-step explanation:
solve for y
x-4y =24
-4y = 24-x
y = x/4 - 6 slope = 1/4, the coefficient of the x term
a perpendicular line has the negative inverse, change the sign and flip the fraction upside down to get -4/1 or -4
y=-4x + b. plug in the point x=-2, y=7 to calculate b the y intercept
7=-4(-2) + b
b = 7-8 =-1
y=-4x -1 is the perpendicular line through (-2,7)
general equation in slope intercept form is y=mx +b. m=-4, b=-1
Danae is choosing between two jobs. One job pays an annual bonus of $1,500 plus $120 per day worked. The second job pays an annual bonus of $2,500 plus $110 per day worked. Which equation can be solved to determine after how many days, d, Danae would make the same amount of money regardless of the job she chooses?
O 120d + 110d = 1,500 + 2,500
O 120 + 110 = 1,500d + 2,500d
• 120d + 1,500 = 110d + 2,500
• 120d + 2,500 = 110d + 1,500
Answer: 120d + 1500 = 110d + 2500
Solution: The first 1500 + 120d
The second 2500 + 110d
So. 120d + 1500 = 110d +2500
Given point Y is between X and Z, where XY = 12 and XZ = 48, What is YZ?
Answer: 36
Step-by-step explanation:
XZ=XY+YZ
48=12+YZ
48-12=12-12+YZ
YZ=48-12
YZ=36
a student committee has 6 membersâ€""4 undergraduate and 2 graduate students. a subcommittee of 3 members is to be chosen randomly so that each possible combination of 3 of the 6 students is equally likely to be selected. what is the probability that there will be no graduate students on the subcommittee?
The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.
The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in
(4 choose 3) = 4 ways.
The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in
(6 choose 3) = 20 ways.
Therefore, the probability that there will be no graduate students on the subcommittee is:
Number of subcommittees with only undergraduate students / Total number of possible subcommittees
= 4 / 20
= 1/5
= 0.2
So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.
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Determine the sum of the interior angles of an 18-gon, in degrees.
Which of the following types of harm resulting from technological innovations can engineers be held most morally blameworthy? O Foreseen harms O Foreseeable harms O Unforeseen harms O Unforeseeable harms
Engineers can be held most morally blameworthy for foreseeable harms resulting from technological innovations, engineers have a responsibility to anticipate the potential consequences of their work,
and to take steps to mitigate those consequences. If they fail to do so, and their work results in harm, they can be held morally blameworthy. When engineers develop new technologies, they have a responsibility to consider the potential consequences of their work.
They need to think about how their technology could be used, and whether it could be used to harm people or the environment.
They also need to consider how their technology could be misused, and what steps they can take to prevent misuse.
If engineers fail to consider the potential consequences of their work, and their work results in harm, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.
For example, engineers who develop new weapons systems have a responsibility to consider the potential consequences of their work. They need to think about how their weapons could be used,
and whether they could be used to kill or injure innocent people. They also need to consider how their weapons could be misused, and what steps they can take to prevent misuse.
If engineers fail to consider the potential consequences of their work, and their weapons are used to kill or injure innocent people, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.
It is important to note that engineers cannot be held morally blameworthy for unforeseeable harms. This is because they did not have the opportunity to anticipate the harm, and they could not have taken steps to prevent it.
For example, engineers who develop new medical treatments cannot be held morally blameworthy if the treatments have unforeseen side effects. This is because the engineers did not have the opportunity to anticipate the side effects, and they could not have taken steps to prevent them.
In conclusion, engineers can be held morally blameworthy for foreseeable harms resulting from technological innovations.
This is because they have a responsibility to anticipate the potential consequences of their work, and to take steps to mitigate those consequences.
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A boy is mowing a rectangular lawn 40ft long and 30ft wide. He has cut all of it except for a rectangle that is 20ft long and 15ft wide. What fractional part of the lawn remains uncut?
Answer:
1/4
Step-by-step explanation:
Find the area of the full rectangle:
=> 40 x 30 = 1200
Find the area of the uncut part:
=> 20 x 15
=> 300
Make these numbers as a fraction.
=> 300 / 1200
=> 3/12
=> 1/4
So, 1/4 part remains uncut.
The fractional part of the lawn remains uncut is 1/4
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Given that A boy is mowing a rectangular lawn 40ft long and 30ft wide. He has cut all of it except for a rectangle that is 20ft long and 15ft wide.
To Find the area of the full rectangle:
40 x 30 = 1200
To Find the area of the uncut part:
= 20 x 15
= 300
Now Make these numbers as a fraction;
=> 300 / 1200
=> 3/12
=> 1/4
Therefore, 1/4 part remains uncut.
Hence, The fractional part of the lawn remains uncut is 1/4.
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Which angle is formed by EA−→
and EG−→−?
Select all that apply.
Answer:
Step-by-step explanation:
\(\angle 2,\angle AEG, \angle GEB\)
Help pls with probability tasks.
1.In the class, there are 14 girls and 9 boys. Let's consider event A - there are at least two girls in the class who were born in the same month. Event A is...
A. an impossible event
C. an elementary event
B. a certain event
D. impossible to determine
2.There are 75 parts in the box, each labeled with a number from 1 to 75. Among these parts, 10 are defective. Let's consider event B - taking out a part with the number 10 from the box. Event B is...
A. an impossible event
B. a certain event
C. an elementary event
D. impossible to determine
3.Out of 25 shots, 20 hit the target. The relative frequency of hits is...
A. 5/25
B. 5/20
C. 25/20
D. 20/25
4.In a certain month, 43 boys and 57 girls were born. The relative frequency of boys born in that month is...
A. 43/57
B. 57/43
C. 43/100
D. 57/100
5.There are twelve balls in a jar, labeled with numbers from 1 to 12. The probability that drawing a ball will result in a number divisible by 3 is...
A. 1/12
B. 1/4
C. 1/3
D. 1/2
6.The probability that a part is of good quality is 0.75. Calculate the probability that it is not of good quality.
A. 0.25
B. 1
C. 0.75
D. 0.25/0.75
7.Two coins are flipped. The probability that at least one coin lands heads up is...
A. 0.25
B. 0.5
C. 0.75
D. 1
8.A fair die is rolled. The probability of rolling a 2 is...
A. 1/6
B. 5/6
C. 1/3
D. 2/3
9.From a deck of cards containing 36 cards, one card is drawn. Calculate the probability that the drawn card is a spade.
A. 1/4
B. 1/6
C. 1/9
D. 1/36
10.There are 2 white and 8 black marbles in a bag. Calculate the probability of randomly selecting a white marble.
A. 1/5
B. 1/4
C. 3/4
D. 1/36
11.Two dice are rolled. Calculate the probability that the sum of the numbers rolled is 5.
A. 1/36
B. 1/9
C. 5/36
D. 1/6
12.Jānis usually throws a ball into the basket with a probability of 0.68. Calculate how many times he will throw the ball into the basket if he makes 50 throws.
A. 8
B. 16
C. 34
D. 0.44
13.Two dice are rolled. The probability that at least one of them shows 4 points is...
A. 1/6
B. 1/9
C. 11/36
D. 1/3
14.A worker regulates two independent machines. The probability of needing to regulate the first machine within an hour is 0.8, and for the second machine it is 0.7. Calculate the probability that both machines need to be regulated within an hour.
A. 0.44
B. 0.56
C. 0.2
D. 0.3
15.Targets are arranged in two concentric rings with radii R and 4R. It is known that a shot hit the target. Calculate the probability that the shot hit the smaller ring.
A. 1/4
B. 1/3
C. 1/16
D. 1/9
16.In a lottery with 20 tickets, 4 tickets are winning tickets. Ilze buys one ticket. Calculate the probability that her ticket is a winning ticket.
A. 1/4
B. 1/5
C. 1/20
D. 4/5
17.Two friends meet. Calculate the probability that both of them were born on a Saturday.
A. 1/7
B. 2/7
C. 2/49
D. 1/49
18.A student has learned 7 out of 8 questions. In a test, two of these questions will be included. Calculate the probability that the student knows both of these questions.
A. 7/8
B. 49/56
C. 42/64
D. 3/4
19.There are 4 cards in an envelope labeled with the letters A, P, S, E. Successively, three cards are drawn from the envelope without replacement. Calculate the probability that the cards are drawn in the order A, P, E.
A. 1/6
B. 1/12
C. 1/24
D. 3!/4!
20.Two dice are rolled simultaneously. Calculate the probability that the sum of the numbers rolled is 14.
A. 1
B. 14/36
C. 1/36
D. 0
Step-by-step explanation:
Event A is a certain event because with 14 girls and only 12 months in a year, by the pigeonhole principle, there must be at least two girls who were born in the same month.
Event B is an elementary event because there is only one part labeled with the number 10 out of 75 parts in the box, so the probability of drawing that part is 1/75.
The relative frequency of hits is calculated by dividing the number of hits by the total number of shots. In this case, it is 20/25.
The relative frequency of boys born in that month is calculated by dividing the number of boys born by the total number of births. In this case, it is 43/100.
There are four balls labeled with numbers divisible by 3 (3, 6, 9, and 12) out of twelve balls in total. So the probability of drawing a ball with a number divisible by 3 is 4/12 = 1/3.
The probability that a part is not of good quality is equal to 1 minus the probability that it is of good quality. In this case, it is 1 - 0.75 = 0.25.
The probability that at least one coin lands heads up is equal to 1 minus the probability that both coins land tails up. The probability that both coins land tails up is (1/2) * (1/2) = 1/4. So the probability that at least one coin lands heads up is 1 - 1/4 = 3/4.
A fair die has six equally likely outcomes when rolled. So the probability of rolling a 2 is 1/6.
A deck of cards containing 36 cards has four suits: clubs, diamonds, hearts, and spades. Each suit has nine cards, so there are nine spades in the deck. So the probability of drawing a spade is 9/36 = 1/4.
There are two white marbles and ten marbles in total in the bag. So the probability of randomly selecting a white marble is 2/10 = 1/5.
There are four ways to roll two dice and get a sum of five: (1,4), (2,3), (3,2), or (4,1). Each outcome has a probability of (1/6) * (1/6) = 1/36. So the probability that the sum of the numbers rolled is five is 4 * (1/36) = 1/9.
If Jānis throws a ball into the basket with a probability of 0.68 and he makes 50 throws, we can expect him to throw the ball into the basket about 0.68 * 50 = 34 times.
The probability that at least one die shows four points when two dice are rolled can be calculated as one minus the probability that neither die shows four points: P(at least one die shows four points) = = 1 - P(neither die shows four points) = 1 - P(first die does not show four points) * P(second die does not show four points) = 1 - (5/6) * (5/6) =11/36
If two events are independent, then the probability that both events occur simultaneously can be calculated as the product of their probabilities: P(both machines need to be regulated within an hour) = = P(first machine needs to be regulated within an hour) * P(second machine needs to be regulated within an hour) =0.8 *0.7 =0.56
15.The area of a circle is proportional to the square of its radius so if we consider each ring as a target then their areas will be proportional to R^2 and (4R)^2 respectively. The ratio between these areas will be R^2 : (4R)^2 = R^2 :16R^2 =1:16 So if we consider each unit area as having an equal chance to be hit then we have: P(the shot hit the smaller ring)= Area(smaller ring)/(Area(smaller ring)+Area(larger ring))=1/(16+1)=1/17
16.There are four winning tickets out of twenty tickets in total in a lottery so if Ilze buys one ticket then her chance to get a winning ticket will be: P(Ilze’s ticket is a winning ticket)= Number of winning tickets / Total number of tickets=4/20=1/5
17.The day on which someone was born can be any day from Monday to Sunday with equal chances so if we consider two friends then: P(both friends were born on Saturday)=P(first friend was born on Saturday)P(second friend was born on Saturday)=(1/7)(1/7)=1/49
18.The student knows seven out of eight questions so if two questions are included in a test then his chance to know both questions will be: P(the student knows both questions)= Number of ways to choose two known questions / Number of ways to choose any two questions=(7 choose 2)/(8 choose 2)=21/28=3/4
19.There are four cards labeled with letters A,P,S,E so if three cards are drawn successively without replacement then there will be: Number of ways to draw three cards=Number of ways to draw first cardNumber of ways to draw second cardNumber of ways to draw third card=432=24 The only way for these cards to be drawn in order A,P,E will be if they are drawn successively as A,P,E so: P(the cards are drawn in order A,P,E)=Number of ways for cards to be drawn in order A,P,E / Number of ways for any three cards to be drawn=1/24
20.Two dice have six faces each so when they are rolled simultaneously there will be: Number of possible outcomes=Number of faces on first dieNumber of faces on second die=66=36 None of these outcomes will result in a sum equal to fourteen so: P(the sum of numbers rolled equals fourteen)=0
I need help with 5 X 5 pls!
Answer:
it's 25
nwhhehshhjeheb
the answer is 25 just do 5 plus 5 plus 5 plus 5 plus 5
WHOEVER HELPS ME ON THIS WILL GET BRAINLIEST
Answer:
7.8
Step-by-step explanation:
The diameter is the full length across a circle. The radius is always half the diameter. if you divide 15.6 by 2 (to get half), we get 7.8. If this does not answer the question, let me know so I can edit
What is the area of a trapezoid and why
Answer:A=a+b/2h
Step-by-step explanation:A trapezoid is a quadrilateral with only one pair of opposite sides that are parallel. We must take the average of the bases and then multiply by the height. That means that we need to add the bases together and divide by 2. Then we will multiply by the height.
Answer:
Area= (a+b) X h
2
Step-by-step explanation:
Area of a trapezoid is the average of the bases multiplied by the altitude
A line includes the points (0,-7) and (n, -8) has a slope of -1/6. What is the value of n?
Answer:
n = 6.
Step-by-step explanation:
The slope of the line = (y2 - y1) / (x2 - x1) where the 2 points are (x1, y1) and (x2, y2).
So, (-8 - (-7)) / (n - 0) = -1/6
-1/n = -1/6
n = 6.
find the p-value (to two significant digits) for the following test. h0: μ ≤ 0, h1: μ > 0, σ = 1, z = 1.5 hint: the population follows the standard normal distribution.
The p-value for the given test is approximately 0.067, rounded to two significant digits. This was calculated by finding the area to the right of z=1.5 under the standard normal distribution.
It is given that Null hypothesis: H0: μ ≤ 0, Alternative hypothesis: H1: μ > 0, Population standard deviation: σ = 1, Test statistic: z = 1.5
To find the p-value, we need to calculate the probability of observing a z-value of 1.5 or greater under the null hypothesis. Since the population follows the standard normal distribution, we can use a standard normal table or a calculator to find this probability.
Using calculator, we can find that the area to the right of z = 1.5 is approximately 0.0668 (rounded to four decimal places).
Since this is a one-tailed test with the alternative hypothesis in the right tail, the p-value is equal to the area in the right tail beyond the observed z-value. Therefore, the p-value for the test is approximately 0.067 (rounded to two significant digits).
So, the p-value for the given test is 0.067 (rounded to two significant digits).
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Which is equivalent to
64 ^1/4?
O 24/4
O4
O 16
O 16/4
Answer: \(\sqrt[4]{64}\)
Step-by-step explanation:
\(64^{\frac{1}{4} }= \sqrt[4]{64}\)
The total surface area of a cube is 96 cm2. Find its volume.
(1) 256 cm3
(2) 64 cm3
(3) 16 cm3
4) 4 cm3
Answer:
The answer is B or number (2)64 cm3.
Hope that's work for you.Answer:
64 cm3
Step-by-step explanation:
trust i'm a doctor
Given x^2−4y^2−16z^2=4 (a) Rewrite into standard form and name/identify the type of surface. (b) Find the equations of the traces of the surface in the following planes (write "None" if no trace). Sketch and name the type of trace obtained. (i) xz-plane (ii) xy-plane (iii) trace in the planes x=±4 (c) Sketch an accurate representation of the surface including traces and intercepts (z-axis pointing up).
The standard form of the hyperboloid is \(\frac{1}{4}x^2-y^2 - 4z^2 = 1\).
The type of trace on xz and xy planes is hyperbola. The trace on x=4 plane does not exist.
A hyperboloid is a quadratic surface, that is, a surface defined as the zero set of a polynomial of degree two in three variables.
Given equation: \(x^2 - 4y^2 - 16z^2 = 4\\\\\)
Standard form: \(\frac{1}{4}x^2-y^2 - 4z^2 = 1\)
Type of surface = hyperboloid
On xz plane,
name of trace = hyperbola
equation : \(\frac{1}{4} x^2 - 4 z^2 = 1\)
(y and z are interchangeable in image as graph is two dimensional only with z axis pointing up)
On xy plane,
name of trace = hyperbola
equation : \(\frac{1}{4} x^2 - y^2 = 1\)
where, A hyperbola is an open curve with two branches, the intersection of a plane with both halves of a double cone.
On x=4 plane,
name of trace = does not exist
equation : \(y^2+4z^2 = 0\) (imaginary roots only)
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The cost to make each T-shirt is $10. You estimate that you will
sell 50 shirts. If you want to make a profit of at least $250, what
price will you charge for these T-shirts? Show your solution in two
different ways.
The price per T-shirt should be at least $15 to achieve a profit of $250.
To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.
Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.
Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.
Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.
Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.
By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.
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What is the right translation of these expressions and equations? (with solution)
1. 7 - 2m
2. 3( m + 2) = 15
3. 5m - m(2 - m)
Answer:
7 - 2m can be translated to "7 minus two times m" or "the difference between 7 and twice m".
3(m + 2) = 15 can be translated to "three times the sum of m and 2 is equal to 15" or "the product of 3 and the sum of m and 2 is 15".
To solve the equation, we can start by distributing the 3 on the left side:
3(m + 2) = 15
3m + 6 = 15
Then, we can subtract 6 from both sides:
3m + 6 - 6 = 15 - 6
3m = 9
Finally, we can divide both sides by 3:
3m/3 = 9/3
m = 3
Therefore, the solution to the equation 3(m + 2) = 15 is m = 3.
5m - m(2 - m) can be translated to "5m minus the product of m and the difference between 2 and m" or "the difference between 5m and m times the quantity 2 minus m".
To simplify the expression, we can use the distributive property to expand the second term:
5m - m(2 - m) = 5m - 2m + m^2 = m^2 + 3m
Therefore, the simplified expression is m^2 + 3m.
What is the mode for the data set? 49, 47, 46, 40, 48, 41, 44, 49, 45, 42, 43
Answer:
49
Step-by-step explanation:
The mode is the number that appears most often in a set of data. In this case, 49 appears twice while all the other numbers only appear once.
(20 points) Two players have to simultaneously decide how much to contribute to the provision of a public good. If Player 1 contributes x and Player 2 contributes y, then the payoff to Player 1 is 2(x+y+xy)-x² and payoff to Player 2 is 2(x+y+xy)-2y². (a) (10 points) Find and draw the best response functions of both players. (b) (10 points) Find the Nash equilibrium of this game.
(a) The best response functions for both players are:
Player 1's best response function: x = 1 - y
Player 2's best response function: y = 1 - x
(b) The Nash equilibrium of this game is when both players contribute half of the maximum possible contribution, which is 0.5.
To find the best response functions, we need to determine the strategies that maximize the payoffs for each player given the other player's strategy.
For Player 1, the payoff function is 2(x + y + xy) - x². To find the best response, we maximize this function with respect to x while assuming y is fixed. Taking the derivative of the payoff function with respect to x and setting it to zero, we get:
∂(2(x + y + xy) - x²)/∂x = 2 + 2y - 2x = 0
Simplifying this equation, we find:
2x = 2 + 2y
x = 1 + y
x = 1 - y (rearranging the equation)
This is the best response function for Player 1.
Similarly, for Player 2, the payoff function is 2(x + y + xy) - 2y². Maximizing this function with respect to y while assuming x is fixed, we differentiate and set it to zero:
∂(2(x + y + xy) - 2y²)/∂y = 2 + 2x - 4y = 0
Simplifying the equation, we find:
2y = 2 + 2x
y = 1 + x
y = 1 - x (rearranging the equation)
This is the best response function for Player 2.
To find the Nash equilibrium, we need to find the values of x and y where both best response functions intersect. Solving the simultaneous equations x = 1 - y and y = 1 - x, we find the Nash equilibrium point at x = y = 0.5.
The best response functions for both players in this game are Player 1's best response function: x = 1 - y and Player 2's best response function: y = 1 - x. The Nash equilibrium occurs when both players contribute half of the maximum possible contribution, which is x = y = 0.5.
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) Kadence has $50 in her bank account. Then, she bought a new shirt that cost $33. She then deposited x dollars into her account to bring her balance to $28. What is the value of x?
Answer:
The value of X is $5
Step-by-step explanation:
Step-by-step explanation:
We have $50 - $33 + $x = $28.
=> $17 + $x = $28
=> $x = $11
Therefore Kadence deposited $11 into her account.
The value of x is 11.