Step-by-step explanation:
2x + 2y = 28 <=====given
x * y = 40 <===given ..... re-arrange to :
y = 40 / x <===substitute this 'y' into the first equation
2x + 2 ( 40/x) = 28 <=====solve for x
2x^2 -28x + 80 = 0
x^2 -14x +40 = 0
(x -10)(x-4) = 0 shows x = 10 or 4 then y = 4 or 10
dimensions 10 and 4 inches
Answer:
4 or 10 inches
Step-by-step explanation:
I added a photo of my solution
Diana uses 30 grams of coffee beans to make a 48 fluid ounces coffee. When guests come,she makes 96 fluid ounces of coffee. How many grams of coffee beans does Diana use when she has visitors?
Diana needs 60 grams of coffee beans to make 96 fluid ounces of coffee for her guests.
What does a percentage formula mean?Determine whether two ratios or fractions are equivalent using the proportion formula. Dividing the provided values will reveal the value that is missing. As an example of the percentage formula: A and d are the extreme terms, while b and c are the mean terms. Hence, b::c: d = a/b = c/d.
We can resolve the issue by using proportions.
The ratio of coffee beans to liquid ounces in Diana's ordinary coffee must first be determined.
48 fluid ounces / 30 grammes
By reducing the numerator and denominator by 6, we may simplify the ratio:
Eight fluid ounces/5 grammes
We can now apply this proportion to determine how many grammes of coffee beans Diana needs to prepare 96 ounces of coffee:
5 grams/8 fluid ounces = 96 fluid ounces x grammes
After cross-multiplying and finding x, we obtain:
x = (96 ounces * 5 grammes) / 8 ounces
x=60 grammes.
In order to prepare 96 fluid ounces of coffee for her visitors, Diana needs 60 grammes of coffee beans.
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a survey of 500 high school students was taken to determine their favorite chocolate candy. of the 500 students surveyed, 139 like snickers, 184 like twix, 181 like reese's peanut butter cups, 129 like snickers and twix, 109 like twix and reese's peanut butter cups, 71 like snickers and reese's peanut butter cups, and 70 like all three kinds of chocolate candy. how many students like at most 2 kinds of these chocolate candies?
433 students like at most two types of these chocolate candies.
A survey of 500 high school students was conducted to determine their favorite chocolate candy.
139 students liked snickers, 184 liked Twix, 181 liked Reese's Peanut Butter Cups, 129 liked Snickers and Twix, 109 liked Twix and Reese's Peanut Butter Cups, 71 liked Snickers and Reese's Peanut Butter Cups, and 70 liked all three types of chocolate candy. So, how many students like at most two types of these chocolate candies?
Step-by-step explanation:
If you use the Principle of Inclusion-Exclusion, you can figure out how many students enjoy two or fewer candies. The PIE formula is as follows:
n(Snickers U Twix U Reese's) = n(Snickers) + n(Twix) + n(Reese's) - n(Snickers ∩ Twix) - n(Snickers ∩ Reese's) - n(Twix ∩ Reese's) + n(Snickers ∩ Twix ∩ Reese's)n(Snickers U Twix U Reese's)
= 139 + 184 + 181 - 129 - 109 - 71 + 70
n(Snickers U Twix U Reese's) = 503
Students who liked two or fewer types of candies can be found by subtracting the number of people who liked all three from the total number of individuals in the study who like any one candy.
503 - 70 = 433 students
Therefore, 433 students like at most two types of these chocolate candies.
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Answer this question. I will give brainlist.
The given diagram represents a right circular cylinder with a base equation of (x - 0)² + (y - 0)² = 7², resulting in an ellipse with an equation of (x - 0)²/4² + (y - 0)²/5² = 1.
The given diagram represents a right circular cylinder with a height of 10 meters and a radius of 7 meters, which means the base of the cylinder is a circle with a radius of 7 meters. The equation of the circle is (x - 0)² + (y - 0)² = 7², where (0, 0) is the center of the circle.
The cylinder has been sliced by a plane that is parallel to the base and 4 meters from the center of the cylinder. This means the distance between the center of the cylinder and the plane is 4 meters.
Mathematically, the equation of the ellipse can be written as (x - 0)²/4² + (y - 0)²/5² = 1, where the center of the ellipse is (0, 0), and the semi-major axis is 5 meters and the semi-minor axis is 4 meters.
So, the given diagram described as a right circular cylinder with a base equation of (x - 0)² + (y - 0)² = 7², sliced by a plane parallel to the base and 4 meters from the center of the cylinder, resulting in an ellipse with an equation of (x - 0)²/4² + (y - 0)²/5² = 1.
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the population of chicago is about 3 million. how does that compare to the total number of dead and wounded in world war i? (give your answer as a fraction)
amy has 3 pound of raisins she didvides the raisins equaly into 12 bags how much puonds of rasins are in each bag :show your work
Answer:
May will have 0.25 pounds per bag.Step-by-step explanation:
We know that
Amy has 3 pounds of raisins.She wants to divide it into 12 bags.To now how many pounds will be in each bag, we have to divide
[tex]3 \ lb \div12 \ bags =0.25 \ lb/bag[/tex]
This means that May will have 0.25 pounds per bag, that is, a quarter pound of raisin in each bag.
If we divide this using the long method, we would have to add a zero to "3", because 3 is less than 12, so we have to transform it from "3" to "30". To be able to do that, we have to add a decimal point to the quotient, and then continue with the division.
out of a random sample of 1000 dutch men, how many would we expect to be taller than 190 cm (rounded to the nearest whole number)?
The number of Dutch men taller than 190 cm is approximately 100.
The proportion of men taller than 190 cm is estimated using the normal distribution.
We'll be using a normal distribution, which requires the mean and standard deviation of the height data.
The percentage of Dutch men who are over 190 cm tall can be estimated using a normal distribution model.
We must first determine the mean and standard deviation of the heights.
For the population mean and standard deviation, we use the following values.
μ = 181 cm (the mean of Dutch men's heights)
σ = 7 cm (standard deviation)We may now convert the height of 190 cm to a z-score, which is a standard score that represents the number of standard deviations from the mean of the distribution.
The z-score is calculated using the following formula: Z = (X - μ) / σ
where X is the height of 190 cm,
μ is the population mean,
and σ is the population standard deviation.
Z = (190 - 181) / 7 = 1.2857
We look up the percentage corresponding to this z-score in the standard normal distribution table.
Using the table, we can see that the percentage of individuals with a z-score greater than 1.2857 is 0.1003.
We will use this percentage to estimate the number of Dutch men over 190 cm tall in a random sample of 1000 men.0.1003 * 1000 = 100.3
The number of Dutch men taller than 190 cm is approximately 100.
To the nearest whole number, we round this up, and the expected number of men taller than 190 cm in a random sample of 1000 Dutch men is 101.
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The graph of a quadratic function with vertex (-3, - 1)
Find the range and the domain.
Therefore the range of the quadratic function with vertex (-3, -1) is y ≥ -1 and the domain is all real number and the Domain is real numbers .
How to the range ?A quadratic function's vertex form is given by:
[tex]y = a(x - h)^2 + k[/tex]
where (h, k) is the parabola's vertex. In this instance, we have:
[tex]h = -3, k = -1[/tex]
So the quadratic function's equation is:
[tex]y = a(x + 3)^2 - 1[/tex]
To determine the function's range, we must first determine the minimum value of y. Because the squared term's coefficient is positive, the parabola opens upwards and the vertex is a minimum point. As a result, the range is:
Range: y ≥ -1
To determine the function's domain, we must first determine the set of all x-values for which the function is defined. Due to the fact that a quadratic function is defined for all real numbers, the domain is:
Domain: All real numbers
So the domain of the quadratic function with vertex (-3, -1) is all real numbers, and its range is y -1.
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a woman is phenotypically normal, but her father had the sex-linked recessive condition of hemophilia, a blood-clotting disorder. if she has children with a man with a normal phenotype, what is the probability that their two sons will both have hemophilia?
The probability that their two sons will both have hemophilia is 0%.
Hemophilia is a sex-linked recessive disorder, which means that it is passed from mother to son. Since the woman does not have the disorder, she does not carry the gene for it and therefore her sons would not be affected by the disorder.
However, her daughters could be carriers of the disorder and could pass it on to their sons.
In order for a son to be affected by hemophilia, his mother must carry the gene for the disorder and the father must also have the gene. If the father does not have the gene, then the son will not have hemophilia.
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miyu is giving out $8$ identical chocolates to her $4$ friends, including dhruv. all possible distributions are equally likely. what is the probability that dhruv gets exactly $1$ chocolate?
Dhruv will most probably admit precisely 1 chocolate if the probability is0.2181 or (21.81%).
What's Probability?Probability refers to eventuality. This area of mathematics examines how arbitrary events be.
First, the total number of ways
= C( 11, 3)
= 11!/ 8! 31
= 11 x 10 x 9/ 3x 2
= 165
Now, If Dhruv gets exactly 1 chocolate there are now 7 chocolate and
3- 1 = 2 bars
So, the number of ways for 1 exactly one chocolate
= C( 9, 2)
= 9!/ 7! 21
= 9 x 8/ 2
= 36 ways
The liability that Dhruv receives exactly one chocolate is now.
= 36/ 165
= 12/ 55
Thus, the probability that Dhruv gets exactly 1 chocolate is 12/55 ≈0.2181 or 21.81%.
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An isosceles right triangle is removed from
each corner of a square piece of paper, as
shown, to create a rectangle. If AB = 12 units,
what is the combined area of the four removed
triangles, in square units?
The combined area of the four removed triangles is 48 sq.units. Answer: 48
We need to find out the combined area of the four removed triangles, in square units. Given: AB = 12 units.
Let's consider the given square, and let's draw an altitude BD and also draw perpendiculars to BD from the three vertices A, C and D.
Let AB = x cm. Area of square = x² sq.cm.
Now, we are cutting a triangle with base x and height x, which is a right-angled triangle. Hence, area of each removed triangle = (1/2) * x * x = (x²/2) sq.cm.
Now, BD = x/√2. Area of rectangle = AB * BD = 12 * 12/√2 = 72√2 sq.cm.
Now, area of 4 triangles = (x²/2) + (x²/2) + (x²/2) + (x²/2) = 2x² sq.cm.
We know that, Area of rectangle = Area of 4 triangles + Area of square => 72√2 = 2x² + x² => 72√2 = 3x² => x² = 24√2 cm² => x = √(24 * 2) cm = √(48) cm = 4√3 * √2 cm.
Area of 4 triangles = 2x² sq.cm = 2 * 24 cm² = 48 sq.cm.
Hence, the combined area of the four removed triangles is 48 sq.units. Answer: 48.
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Complete the table below using what you know about trigonometric ratios for right triangles.
Write your ratios as fractions. A message will appear when you are correct.
(a) The ratio of sin A as a fraction is 63/65, cos A is 16/65 and the tan of angle A is 63/16.
(b) The ratio of sin B as a fraction is 16/65, cos B is 63/65 and the tan of angle B is 16/63.
What is the missing part of the right triangle?The missing parts of the right triangle is calculated using the trigonometry principle as shown below.
For angle A:
opposite side = 63
adjacent side = 16
hypothenuse side = 65
sin A = opp/hypo = 63 / 65
cos A = adj/hypo = 16 / 65
tan A = opp/adja = 63/16
For angle B:
opposite side = 16
adjacent side = 63
hypothenuse side = 65
sin B = opp/hypo = 16 / 65
cos B = adj/hypo = 63 / 65
tan A = opp/adja = 16/63
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Polygon ABCD with vertices at A(1, −1), B(3, −1), C(3, −2), and D(1, −2) is dilated to create polygon A′B′C′D′ with vertices at A′(4, −4), B′(12, −4), C′(12, −8), and D′(4, −8). Determine the scale factor used to create the image.
1/4
1/2
2
4
The scale factor used to create the dilated polygon is 4.
What is scaler factor?
Scale factor is a numerical ratio that describes how much a geometric figure has been enlarged or reduced. It is the ratio of the length of a side, diagonal, or any other linear dimension of the new (dilated) figure to the corresponding dimension of the original figure.
The distance between two points can be calculated using the distance formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.[/tex]
To determine the scale factor, we need to compare the distances between corresponding points in the original and dilated polygons. Let's start by finding the distance between points A and B in the original polygon:
[tex]$d_{AB}=\sqrt{(3-1)^2+(-1+1)^2}=\sqrt{4}=2$[/tex]
Now let's find the distance between corresponding points A' and B' in the dilated polygon:
[tex]$d_{A'B'}=\sqrt{(12-4)^2+(-4+4)^2}=\sqrt{64}=8$[/tex]
To find the scale factor, we divide the corresponding distances:
[tex]$scale\ factor=\frac{d_{A'B'}}{d_{AB}}=\frac{8}{2}=4$[/tex]
Therefore, the scale factor used to create the dilated polygon is 4.
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Spaceship Earth is a major tourist at Epcot. It is a sphere whose volume is
approximately 65, 417 m³. What is the approximate circumference of Spaceship
Earth? Use π = 3. 14. Round to the nearest whole number. Do not label.
The approximate circumference of Spaceship Earth is approximately 138.02 meters.
What is circumference of a circle?A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant. This measurement of a circle's diameter is necessary for someone crossing a circular park or for enclosing a circle. The units for the circumference, which is a linear variable, are the same as those for length.
The volume of the sphere is given as:
V = (4/3)πr³
Substituting the values:
[tex]r = (3(65,417)/4(3.14))^{(1/3)} = 21.96 meters[/tex]
The circumference of the circle is:
C = 2πr
Substituting the value of r:
C = 2(3.14)(21.96) = 138.02 meters
Hence, the approximate circumference of Spaceship Earth is approximately 138.02 meters.
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If the limit as n goes to infinity of the quotient of the absolute value of the quantity a sub n plus 1 times the n plus 1 power of the quantity x minus 7 and the absolute value of the product of a sub n and the nth power of x minus 7 for the power series the summation from n equals 1 to infinity of a sub n times the nth power of the quantity x minus 7, then what is the interval over which the power series converges absolutely? You do not need to consider the endpoints.
In conclusion, the power series converges absolutely over an interval given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex]is a natural number.
The interval over which the power series converges absolutely is given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex] is a natural number.
In other words, for any given N, the series will converge absolutely over the interval \left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n>N.
This means that the series will converge absolutely over a larger interval as N increases, since the terms \frac{\left|a_n+1\right|}{\left|a_n\right|} get closer to 1 for larger values of n.
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During the first year she owned her car, Barbara spent $732 on repairs and maintenance. She spent $1,377 the second year she owned the car. What was the percentage
increase in maintenance and repair costs from the first year to the second year (to the nearest whole percent)?
79%
84%
88%
92%
None of these choices are correct.
There was 88% increase in maintenance and repair costs from the first year to the second year. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
The four fundamental operations, often referred to as "arithmetic operations", are thought to be able to properly represent all real numbers. The mathematical operations quotient, product, sum, and difference come after division, multiplication, addition, and subtraction.
We are given that during the first year she owned her car, Barbara spent $732 on repairs and maintenance and she spent $1,377 the second year she owned the car.
So, the more amount she spent in the second year is obtained using subtraction operation which gives:
⇒ $1,377 - $732
⇒ $645
Now, the percentage increase is
⇒ $645 ÷ 7.32
⇒ 88.11%
Hence, there was 88% increase in maintenance and repair costs from the first year to the second year.
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Which can cover a greater area, 2 quarters, each with a diameter of 1 inch, or 1 half dollar, with a diameter of 1. 2 inches?
The area of the half-dollar coin with a diameter of 1.2 inches is greater.
Both the given objects have a circular shape with a different diameter.
One of the objects is made up of two separate quarters of a circle, each with a diameter of 1 inch.
On the other hand, the second object is one half-dollar coin with a diameter of 1.2 inches.
We will use the formula of the area of a circle that is : A = πr²
Where A is the area of the circle.
π is the constant value (3.14)
r is the radius of the circle.
Let's calculate the area of 2 quarters each with a diameter of 1 inch.
The radius will be half of the diameter.
So, the radius is 1/2 inch for each quarter of the circle.
A = πr²A = π × (1/2)²A = π × 1/4A = 0.7854 square inches.
The total area of both quarters will be = 2 × 0.7854 square inches
The total area of both quarters = 1.5708 square inches
Now, let's calculate the area of the half-dollar coin with a diameter of 1.2 inches.
The radius will be half of the diameter.
The radius of the half-dollar coin = 1.2 / 2 = 0.6 inch
A = πr²A
= π × 0.6²A
= π × 0.36A
= 1.1318 square inches
The half-dollar coin has a greater area as compared to the two quarters of a circle.
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no member of the green party voted for the tax cut. p2) mr jacobs did not vote for the tax cut. c) mr jacobs is a member of the green party.
Answer:
Mr Jacobs did not vote for the tax cut. C - Mr Jacob is a member of the Green Party. Invalid.
Step-by-step explanation:
if adding predictor variables to a regression model never reduces r2, why not just include all the available predictor variables in the model? also, remark on the meaning of r2 adj.
Answer: If adding predictor variables to a regression model never reduces r2, you can include all the available predictor variables in the model, as long as they have a significant correlation with the dependent variable. However, having too many variables in a model may lead to overfitting, resulting in poor model generalization. In addition, some predictor variables may not be useful, while others may be collinear. As a result, it is usually recommended to use a stepwise regression method, which selects the best subset of predictor variables that improve the model's performance, without including irrelevant or collinear variables.r2 adj: R2 adj is the adjusted R2 value of a regression model. R2 adj is a statistical measure of how well the regression model fits the observed data. It is similar to the R2 value, but takes into account the number of predictor variables in the model, in addition to the sample size. The adjusted R2 value increases when a new predictor variable improves the model's fit, but decreases when the new predictor variable does not improve the model's fit or is collinear with other predictor variables.
The adjusted R2 value ranges from 0 to 1, with higher values indicating better model fit.
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To hire an accountant to prepare taxes costs a flat fee and an additional hourty rate. The amount the accountant costs can be modeled by the function A(X) = 140 +
25x, where x represents the number of hours the accountant works to prepare the taxes and 140 represents the flat fee. What is the value of A(215) and its
interpretation?
a A(215) = 3; If the accountant takes 215 hours to prepare the taxes, the cost wil be $2.
b A(215) = 3; If the account takes 3 hours to prepare the taxes, the cost wil be $215.
c A(215) = 5515; If the accountant takes 215 hours to prepare the taxes, the cost wil be $5,515.
d A(215) = 5515; If the accountant takes 5,515 hours to prepare the taxes, the cost will be $215.
Answer: The given function is:
A(x) = 140 + 25x
We need to find the value of A(215), which means we need to substitute x = 215 in the function and simplify:
A(215) = 140 + 25(215)
A(215) = 140 + 5375
A(215) = 5515
Therefore, the correct answer is (c) A(215) = 5515. The interpretation of this result is that if the accountant works for 215 hours to prepare the taxes, the cost will be $5,515, which includes the flat fee of $140 and an additional hourly rate of $25 for each hour worked.
Step-by-step explanation:
The value of A(215) and its interpretation are captured thus:
A(215) = 5515; If the accountant takes 215 hours to prepare the taxes, the cost will be $5,515
What does the function represents?The function given as A(x) = 140 + 25x, represents the total cost of using the services of the accountants for tax computation and preparation, bearing in mind that the 140 means $140 which is the fixed charged irrespective of the number of hours it takes to prepare the tax returns whereas the 25x means that $25 is charged as variable fee for every hour the accountant works on the tax computation
A(x) = 140 + 25x
In this case, A(215) means that 215 hours were made use of by the accountants, hence, to determine the total fees, we simply substitute for x
A(215) = 140+(25*215)
A(215) = 140+5375
A(215)=$5,515
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4. Financial Literacy Tickets to a play cost $10 for
members and $24 for nonmembers. Write an expression
to find the total cost of 4 nonmember tickets and
2 member tickets. Then find the total cost. (Example 6)
H
the total cost of 4 nonmember tickets and 2 member tickets would be $116.
Why it is and what is financial literacy?
The expression to find the total cost of 4 nonmember tickets and 2 member tickets would be:
4($24) + 2($10)
This expression represents the cost of 4 nonmember tickets at $24 each, and 2 member tickets at $10 each.
To find the total cost, we simply need to evaluate this expression using basic arithmetic:
4($24) + 2($10) = $96 + $20 = $116
Therefore, the total cost of 4 nonmember tickets and 2 member tickets would be $116.
Financial literacy is the knowledge and skills required to manage one's personal finances effectively. It encompasses a range of topics, including budgeting, saving, investing, managing debt, understanding financial products such as credit cards and loans, and planning for retirement. Financial literacy also involves an understanding of financial concepts such as interest rates, inflation, and risk management.
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If h = 13 units and r = 6 units, then what is the volume of the cone shown above?
The vοlume οf the cοne is 156π cubic units
What is cοne?A cοne is a three-dimensiοnal geοmetric fοrm with a flat base and a smοοth tapering tip οr end. A cοne is made up οf a cοllectiοn οf line segments, half-lines, οr lines that link the apex—the cοmmοn pοint—tο every pοint οn a base that is in a plane οther than the apex.
Given,
h = 13 units and r = 6 units
We knοw the fοrmula tο determine vοlume οf cοne; that is
(1/3)πr²h
Where r= radius οf the cοne
h= height οf the cοne
We put the value οf h and r in the fοrmula
(1/3)πr²h
= (1/3)π6² *13
=156π cubic units
The vοlume οf the cοne is 156π cubic units
Hence the cοrrect answer is 156π cubic units
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tickets for a raffle cost 5. there were 833 tickets sold. one ticket will be randomly selected as the winner, and that person wins 1400 and also the person is given back the cost of the ticket. for someone who buys a ticket, what is the expected value (the mean of the distribution)?
The expected value (the mean of the distribution) for someone who buys a ticket can be calculated by adding up the total amount of money in the raffle and then dividing that by the number of tickets sold, which in this case in $6.68.
In this scenario, a ticket costs $5. The prize for winning the raffle is $1400 plus the cost of the ticket, which is $5.
The total value of the raffle is equal to the sum of the prize and the total amount of money raised from the tickets. The amount raised from the tickets is the number of tickets sold multiplied by the cost of the ticket.
Therefore, the total value of the raffle is equal to: $1400 + ($5 × 833) = $1400 + $4165 = $5565
The expected value of a ticket is the total value of the raffle divided by the number of tickets sold.
Therefore, the expected value of a ticket is:$5565 / 833 = $6.68
Therefore, the expected value (the mean of the distribution) for someone who buys a ticket is $6.68.
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Cell phone Plan A costs $70 per month and comes with a free $500 phone. Cell phone Plan B costs $50 per month but does not come with a phone. If you buy the $500 phone and choose Plan B, how many months is it until your cost is the same as Plan A's? Let m represent the monthly cost.
Solving a linear equation we can see that the answer is 40 months.
How many months is it until your cost is the same as Plan A's?We know that company A only charges $70 per month, so the cost in dollars after x months is given by the linear equation:
A(x) = 70*x
For company B you need to pay $50 per month plus the $500 phone, so here the cost is:
B(x) =500 + 50*x
We want to find for what value of x we have B(x) = A(x), then we needto solve:
70x = 500 + 50x
70x - 50x = 500
20x = 500
x = 500/20
x = 40
After 40 months the cost will be the same one than in company A.
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Help plis! Need process too
Answer:
Step-by-step explanation:
E
The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a fraction in simplest form. 80
80
24
24
As per the given triangle, the scale factor is 24/5
To identify the scale factor, we can choose two corresponding sides of the triangles and set up a proportion. Let's choose the legs of the triangles. We know that the length of the left leg is 5, and the length of the right leg is 25/4. Therefore, we can write:
5/x = 25/4/12
Here, x represents the length of the corresponding leg of the right triangle. We can simplify this proportion by cross-multiplying:
5 x 12 = (25/4) x (x)
Multiplying both sides by 4/25, we get:
(4/25) x 5 x 12 = x
Simplifying, we get:
x = 24/5
Therefore, the scale factor is 24/5. This means that if we multiply the lengths of any side of the left triangle by 24/5, we will get the corresponding length of the right triangle.
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Complete Question:
The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a fraction in simplest form.
5 and 12, 25/4 and 15
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
8 is subtracted from the cube of a number.
Answer: ChatGPT is acting weird
Step-by-step explanation:
The cube of a number x is represented as x^3, and 8 is subtracted from it.
So, the algebraic expression is:
x^3 - 8
A number is equal to 3 times a smaller number. Also, the sum of the smaller number and 4 is the larger number. The
situation is graphed on the coordinate plane below, where x represents the smaller number and y represents the larger
number.
Which two equations represent the situation?
A. y= 1/3x and y = x-4
B. Y = 1/3x and y= x +4
C. Y= 3x and y= x +4
D. Y= 3x and y = x- 4
Please and thank you! <3
Answer:
3x = y
x + 4 = y
Step-by-step explanation:
Letter C
Projective personality tests are most widely used by which psychological perspective?
Projective personality tests are most widely used by the Psychodynamic perspective.
According to Sigmund Freud's theory of personality, people's personalities are shaped by their unconscious motivations and past experiences. The theory also emphasizes the role of the unconscious mind in human behavior.Projective personality tests are based on this psychodynamic theory, which posits that people's unconscious emotions, thoughts, and desires can reveal much about their personalities. The tests seek to uncover this unconscious content by asking people to interpret ambiguous stimuli.
Projective tests are more effective than self-report measures in discovering unconscious thoughts, desires, and motivations because they bypass a person's defenses. Self-report measures, on the other hand, are more susceptible to response bias or social desirability bias.There are many types of projective personality tests, including the Rorschach Inkblot Test, the Thematic Apperception Test, and the Draw-A-Person Test. Although the reliability and validity of projective tests have been debated in the psychological community, they remain popular in clinical and forensic settings today.
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Lin's job pays $12.50 an hour. She also gets paid $25 per week to cover uniform cleaning and
other expenses. To meet her budget, Lin needs to be paid at least $300 per week.
Answer:
I think it is because 3,500
What is the solution to the system of equations?
A.(7,9)
B.(9,7)
C.(-5,11)
D(11,-5)
Answer:
Step-by-step explanation:
4x - 5y = -17
-4x - 24y = -244
-29y = -261
y = 9
x + 54 = 61
x = 7
(9,7) Option B