For the expressions 3x+4 –2x, and 5x+2x+x the simplified expression after combining like terms is x+4 and 8x.
The given expressions are 3x+4 –2x, and 5x+2x+x
We have to simplify these expressions by combining the like terms
For the expression 3x+4 –2x
We have to combine like terms
x+4
Now for expression 5x+2x+x
Combine the like terms to get
8x
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A group of workers takes 4 1/2 days to plant 5 1/4 acres. What is the unit rate in acres per day?
Write your answer as a fraction or a mixed number in simplest form. Answer would be: 1 1/6
The unit rate for planting is 1 1/6 acres per day.
To find the unit rate, we need to divide the total area planted by the number of days taken to plant it. We can convert the mixed number of days to an improper fraction by multiplying the whole number by the denominator and adding the numerator.
Therefore, 4 1/2 days can be converted to 9/2 days.
Now we can divide the total area of 5 1/4 acres by the number of days it took to plant it, which is 9/2 days. To divide fractions, we invert the second fraction and multiply, so:
5 1/4 ÷ 9/2 = 21/4 ÷ 9/2 = 21/4 x 2/9 = 42/36
We can simplify 42/36 by dividing both the numerator and denominator by their greatest common factor, which is 6.
42/36 = 7/6
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Astronaut Harry Skyes has a mass of approximately 85. 0 kg. What is his weight on Mercury?
Mercury's gravity = 3. 70 m/s^2
The weight of Harry Skyes on Mercury is 32.8 kg, under the condition that Mercury's gravity = 3. 70 m/s².
The weight of astronaut Harry Skyes on Mercury can be evaluated using the formula:
Weight on Mercury = (Weight on Earth / 9.81 m/s²) × 3.7 m/s²
Given that Harry Skyes has a mass of approximately 85.0 kg, his weight on Mercury would be:
Weight on Mercury = (85.0 kg / 9.81 m/s²) × 3.7 m/s²
Weight on Mercury = 32.8 kg
Gravity affects weight severely and causes its change . Objects have mass, which is specified as how much matter an object contains. Weight is known as the pull of gravity on mass. The relation between weight and gravitational pull is such that, when on another celestial body, the difference in gravity would alter a person’s weight.
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19. The functions f and g are defined by f(x) = 2x/x-2 and g(x) = x + 4 respectively. Find
gf.
Answer:
gf(x) = g(f(x)) = (x+4)(2x/x-2) = 2x^2 + 8x - 8
Which of the following expressions can be used to find how many meters it is from Washington, D.C, to Baltimore? Distances: Washington, D.C, and Alexandria, WA = 11 km, Washington, D.C and Baltimore, MD = 57 km, and Washington, D.C and Annapolis, MD = 53 km. Expressions: A. 1000 divided by 57, B. 100 x 57, C. 57 x 1,000, D. 57 divided 1000.
The correct expression to use to find how many meters it is from Washington, D.C., to Baltimore is:
C. 57 x 1,000.
What is expression?An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.
In the given question,
The correct expression to use to find how many meters it is from Washington, D.C., to Baltimore is:
C. 57 x 1,000
Since 1 km equals 1,000 meters, we can convert the distance of 57 km to meters by multiplying it by 1,000. This gives us:
57 km x 1,000 meters/km = 57,000 meters
Therefore, the distance from Washington, D.C., to Baltimore is 57,000 meters.
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Find the value of x.
Applying the Equidistant Chords Theorem, the value of x in the circle given above is calculated as: b. 50.
What is the Equidistant Chords Theorem?The Equidistant Chords Theorem states that If two chords in a circle, or in congruent circles, are equally distant from the center, then the chords are congruent.
The image given reveals that the two chords are equidistant from the center of the circle, therefore:
x = 2(25)
x = 50.
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A consumer group is investigating two brands of popcorn, R and S. The population proportion of kernels that will pop for Brand R is 0. 90. The population proportion of kernels that will pop for Brand S is 0. 85. Two independent random samples were taken from the population. The following table shows the sample statistics. Number of Kernels in Samples Proportion from Sample that Popped Brand R 100 0. 92 Brand S 200 0. 89 The consumer group claims that for all samples of size 100 kernels from Brand R and 200 kernels from Brand S, the mean of all possible differences in sample proportions (Brand R minus Brand S) is 0. 3. Is the consumer group’s claim correct? Yes. The mean is 0. 92−0. 89=0. 3. Yes. The mean is 0. 92 minus 0. 89 equals 0. 3. A No. The mean is 0. 92+0. 892=0. 905. No. The mean is the fraction 0. 92 plus 0. 89 over 2 equals 0. 905. B No. The mean is 0. 92−0. 892=0. 15. No. The mean is the fraction 0. 92 minus 0. 89 over 2 equals 0. 15. C No. The mean is 0. 90+0. 852=0. 875. No. The mean is the fraction 0. 90 plus 0. 85 over 2 equals 0. 875. D No. The mean is 0. 90−0. 85=0. 5
The mean of all possible differences in sample proportions (Brand R minus Brand S) is given by:
mean = pR - pS,
where pR is the population proportion of kernels that will pop for Brand R, and pS is the population proportion of kernels that will pop for Brand S.
Substituting the given values, we get:
mean = 0.90 - 0.85 = 0.05
However, the consumer group claims that the mean of all possible differences in sample proportions is 0.3. This claim is not supported by the calculations above.
Therefore, the correct answer is:
C) No. The mean is 0.90+0.85/2=0.875. No. The mean is the fraction 0.90 plus 0.85 over 2 equals 0.875.
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A shipping container is in the shape of a right rectangular prism with a length of 12 feet, a width of 13. 5 feet, and a height of 15 feet. The container is completely filled with contents that weigh, on average, 0. 47 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?
Answer=1142 lbs
The weight of the component is of length of 12 feet, a width of 13. 5 feet, and a height of 15 feet, and weighs on average 0. 47 pounds per cubic foot is 1142 lbs.
To find the weight of the contents in the container, we need to first find the volume of the container.
The formula for the volume of a right rectangular prism is length x width x height.
So, the volume of the container is:
12 ft x 13.5 ft x 15 ft = 2430 cubic feet
Next, we need to multiply the volume by the weight per cubic foot:
2430 cubic feet x 0.47 lbs/cubic foot = 1141.1 lbs
Rounding to the nearest pound, the weight of the contents in the container is approximately 1142 lbs.
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Check all that are inequalities.
-3 = y
t > 0
-4. 3 < a
g = 5 and one-half
k less-than Negative StartFraction 5 Over 7 EndFraction
x = 1
Anwer: B C E
The inequalities in the given options are: B) t > 0, C) 3 < a, E) k < -5/7, The correct option is B,C,E.
B) t > 0: This represents an inequality because the symbol ">" indicates "greater than." It states that the variable "t" is greater than zero. In other words, it means that "t" has to be a positive number and cannot be zero or negative.
C) 3 < a: This represents an inequality because the symbol "<" indicates "less than." It states that the number 3 is less than the variable "a." In other words, it means that "a" has to be greater than 3 for the inequality to hold true.
E) k < -5/7: This represents an inequality because the symbol "<" indicates "less than." It states that the variable "k" is less than -5/7. In other words, it means that "k" has to be a value smaller than -5/7 for the inequality to be true.
The other options, such as -3 = y, g = 5 and one-half, and x = 1, do not represent inequalities because they either show an equation (equality) or simply assign values to variables without any comparison.
Therefore the correct option is B,C,E.
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A basketball coach thinks that as his team progresses through the season, his players are not scoring as many points as they were in the previous weeks. He uses a table to record the number of points that his team scores for the first ten weeks of the season. First drop down box answers( positive,negative, or no correlation) second drop down box (correct or incorrect)
The correlation between the number of points scored by the basketball team and the weeks of the season is likely negative.
However, without seeing the actual data, it is difficult to determine the exact correlation. As for the coach's statement, it could be either correct or incorrect depending on the actual data. Based on the given information, the basketball coach's observation suggests a negative correlation between the number of weeks into the season and the points scored by his team. Without the actual data, it is impossible to determine if his observation is correct or incorrect.
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Internet Use A survey of U. S. Adults ages 18–29 found that 93% use the
Internet. You randomly select 100 adults ages 18–29 and ask them if they use
the Internet.
(a) Find the probability that exactly 90 people say they use the Internet.
(b) Find the probability that at least 90 people say they use the Internet.
(c) Find the probability that fewer than 90 people say they use the Internet.
(d) Are any of the probabilities in parts (a)-(c) unusual? Explain.
a. The probability that exactly 90 people say they use the Internet is 0.0391
b. The probability that at least 90 people say they use the Internet is 0.1933
c. The probability that fewer than 90 people say they use the Internet is 0.8067
d. The first probability is unusual
How to solve the problems(a) Find the probability that exactly 90 people say they use the Internet.
P(X = 90) = C(100, 90) * (0.93)^90 * (0.07)^10
P(X = 90) ≈ 0.0391
(b) Find the probability that at least 90 people say they use the Internet.
P(X ≥ 90) = P(X = 90) + P(X = 91) + ... + P(X = 100)
To calculate this, we can use cumulative binomial probability:
P(X ≥ 90) ≈ 1 - P(X ≤ 89) ≈ 1 - 0.8067 = 0.1933
(c) Find the probability that fewer than 90 people say they use the Internet.
P(X < 90) = P(X ≤ 89)
P(X < 90) ≈ 0.8067
(d) Are any of the probabilities in parts (a)-(c) unusual? Explain.
A probability is generally considered unusual if it is less than 0.05 or greater than 0.95. Based on the calculated probabilities:
P(X = 90) ≈ 0.0391: This probability is unusual since it is less than 0.05.
P(X ≥ 90) ≈ 0.1933: This probability is not unusual.
P(X < 90) ≈ 0.8067: This probability is not unusual.
So, only the probability of exactly 90 people saying they use the Internet is considered unusual.
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Find the value of each variable. For theâ circle, the dot represents the center.
A four sided polygon is inside a circle such that each vertex of the polygon is a point on the circle. The top and bottom sides of the polygon slowly rise from left to right. The left and right sides of the polygon quickly fall from left to right. The angle measures of the polygon are as follows, clockwise from the top left: "c" degrees, 123 degrees, 92 degrees, and "d" degrees. The arc bounded by the left side of the polygon is labeled 94 degrees. The arc bounded by the right side of the polygon is labeled "b" degrees. The arc bounded by the bottom side of the polygon is labeled "a" degrees.
123 degrees
92 degrees
94 degrees
c degrees
d degrees
b degrees
a degrees
The values of the variables are:
c = 86 degrees
d = 168 degrees
a = 57 degrees
b = 94 degrees
Since the polygon is inscribed in a circle, the opposite angles of the polygon are supplementary. Thus, we have:
The top and bottom angles of the polygon are supplementary to angle "d":
c + 92 + 123 = 180 + d
The left and right angles of the polygon are supplementary to angle "c":
c + 94 = 180, so c = 86
The angle "a" is supplementary to angle "d":
a + 123 = 180 + d
The angle "b" is supplementary to angle "c":
b + 86 = 180
Substituting the values of "c" and solving the system of equations, we get:
d = 168
a = 57
b = 94
Therefore, the values of the variables are:
c = 86 degrees
d = 168 degrees
a = 57 degrees
b = 94 degrees
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Rosemary chooses to attend the University of Houston to earn her degree. Rosemary has $2,500 in her savings and a $1,000 savings bond from her grandparents to use for college. What is the estimated contribution needed from other sources to pay for Rosemary's first year? Display keyboard shortcuts for Rich Content Editor
The estimated contribution for Rosemary's first-year college fee is $6,500 including all her savings and available funds.
Savings of Rosemary = $2,500
Savings from bond = $1000
To calculate the contribution needed for Rosemary from other sources, to pay her college fee, we need to add all the available funds and subtract the money for her college fee.
Let us imagine that the total cost of Rosemary's college = $10,000
Total available funds = $2,500 + $1,000
Total available funds = $3500
The remaining amount needed = $10,000 - $3,500 = $6,500
Therefore, we can conclude that Rosemary would need an estimated contribution of $6,500.
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(15 POINTS) Zachary is an American traveling with a tour group in Southeast Asia.
During a stop in Malaysia, he purchases a souvenir that is priced at 58 Malaysian riggits using his credit card. If the exchange rate that day is USD to MYR = 3. 04, which is the best estimate of the charge Zachary will later find on his credit card statement? (3 points)
$20
$55
$61
$180
The best estimate of the charge Zachary will later find on his credit card statement is $20
The formula to be used is -
Amount in USD = Amount of MYR/Value of one MYR
As, 3.04 MYR is 1 USD performing money conversion of 58 MYR
So, 58 MYR will be = 58/3.04
Divide the values in Right Hand Side of the equation to find the value of MYR in USD
Value in USD = $19.07
Hence, the credit card statement will reflect usage of $20 (since it is the closes correct option and we have been asked the best estimate).
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Segments OT and OV are?
True, The more variables that are deployed to segment a market, the more useful is the resulting segmentation likely to be.
We have,
The factors which are be used to member a request are the segmentation variables. Common variables include demographic, geographic, psychographics and behavioral considerations.
Quantifiable population characteristics, similar as age, gender, income, education, family situation.
The primary ideal of segmentation is to identify guests with analogous attributes, and to find which parts of guests that are seductive from a profit perspective.
Understanding the request segmentation allows marketers to produce a more effective and effective marketing blend.
Hence, True, The more variables that are deployed to segment a market, the more useful is the resulting segmentation likely to be.
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complete question:
The more variables that are deployed to segment a market, the more useful is the resulting segmentation likely ot be.[See p.104]Group of answer choicesTrueFalse
Describe the transformations f(x)= square root 4x
The transformation of f(x) = √(4x) from the parent function g(x) = √(x) includes a horizontal stretch by a factor of 1/4, with no horizontal or vertical shifts.
The function f(x) = √(4x) is a transformation of the parent function, g(x) = √(x). The transformations include a horizontal stretch, a horizontal shift, and a vertical shift. Let's break down each transformation step-by-step:
1. Horizontal Stretch: The factor 4 inside the square root function multiplies the input (x) by 4. This results in a horizontal stretch by a factor of 1/4, meaning the graph is compressed horizontally towards the y-axis.
2. Horizontal Shift: There is no additional value added or subtracted from the input (x), so there is no horizontal shift in this function. The graph remains in its position along the x-axis.
3. Vertical Shift: Similarly, there is no additional value added or subtracted from the output (the entire function), so there is no vertical shift in this function. The graph remains in its position along the y-axis.
This results in the graph of f(x) being compressed towards the y-axis compared to the graph of g(x).
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Suppose that the cost, in dollars, for a company to produce x pairs of a new line of jeans is C(x) = 2300 + 5x + 0.01x2 + 0.0002x? (a) Find the marginal cost function 5 + 0.02x + 0.0006r2 (b) Find C'(100) C'(100) = 11 What does this predict? The exact cost of the 100th pair of jeans. The approximate cost of the 101st pair of jeans. The approximate cost of the 100th pair of jeans. The exact cost of the 101st pair of jeans The exact cost of the 99th pair of jeans. (c) Find the difference between C'(100) and the actual cost of manufacturing the 101st pair of jeans (Round your answer to two decimal places.) $ 3100
The exact cost of the 100th pair of jeans. The approximate cost of the 101st pair of jeans. The approximate cost of the 100th pair of jeans. The exact cost of the 101st pair of jeans The exact cost of the 99th pair of jeans.
The marginal cost function of C(x) = 2300 + 5x + 0.01x2 + 0.0002x is $3100
Process of finding marginal cost:
(a) To find the marginal cost function, we need to take the derivative of the cost function C(x) with respect to x. This gives us:
C'(x) = 5 + 0.02x + 0.0006x^2
So the marginal cost function is:
MC(x) = 5 + 0.02x + 0.0006x^2
(b) To find C'(100), we simply plug in x = 100 into the marginal cost function we just found:
C'(100) = 5 + 0.02(100) + 0.0006(100)^2 = 11
This predicts the exact cost of manufacturing the 101st pair of jeans.
The approximate cost of the 101st pair of jeans can be found by plugging in x = 101 into the original cost function C(x):
C(101) = 2300 + 5(101) + 0.01(101)^2 + 0.0002(101) ≈ $3120.02
The approximate cost of the 101st pair of jeans.
The exact cost of the 100th pair of jeans can be found by plugging in x = 100 into the original cost function C(x):
C(100) = 2300 + 5(100) + 0.01(100)^2 + 0.0002(100) = $3100
Hence the marginal cost is $3100
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Last question :) btw if u can’t tell the equation there is 6x+68
Answer:
The answer for x is 2
z is 100°
Step-by-step explanation:
80=6x+68
6x=80-68
6x=12
divide both sides by 6
6x/6=12/6
x=2
z=?(empty space)
?(empty space)=z
80+z+z+6x+68=360
Note:6x+68=80
80+80+2z=360
160+2z=360
2z=360-160
2z=200
divide both sides by 2
2z/2=200/2
z=100°
please help me with this problem!! Image is attached, 20 points!!
The statement that must be true is the original prices of the refrigerator and the stove were the same. So the answer is option B.
Let x represent the original cost of the refrigerator and y represent the original cost of the stove. The refrigerator's sale price is 0.6x (40% off means paying 60% of the original price), while the stove's sale price is 0.8y (20% off means paying 80% of the original price).
To get the overall discount, multiply the total cost after the discount by the original total cost:
(0.6x + 0.8y) / (x + y)
We want this fraction to equal 0.7 (or 30% off), so we can set up the equation:
(0.6x + 0.8y) / (x + y) = 0.7
Simplifying this equation, we get:
0.6x + 0.8y = 0.7(x + y)
0.6x + 0.8y = 0.7x + 0.7y
0.1x = 0.1y
x = y
Therefore, the statement that must be true to conclude that Alfonso received a 30% overall discount on the refrigerator and stove together is: The original prices of the refrigerator and the stove were the same.
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Use the function f(t) = -16t^2 + 60t + 16 to answer parts A, B, and C.
(Look at the image!)
1) Note that t is either 4 or -0.25 by virtue of the quadratic function.
2) the vertex and line of summer try are t = 1.875. See the attached graph.
How did we arrive at the above conclusion?
First, identify the values of a, b, and c in the equation...
a = -16
b = 60
c = 16
substitute these values into the quadratic formula
t = (-b ± √(b² - 4ac)) / 2a
t = (-60 ± √(60² - 4(-16)(16))) / 2(-16)
t = (-60 ± √(3600 + 1024)) / (-32)
t = (-60 ± √(4624)) / (-32)
t = (-60 ± 68) / (-32)
So, t can be:
t = (-60 + 68) / (-32) = -1/4
or
t = (-60 - 68) / (-32) = 4
2) To find the line of symmetry, we used t = -b/2a
-60/2(-16)
t = 1.875
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Observa las siguientes tablas y analiza los valores que contienen. Después, plantea un problema que pueda resolverse con esos datos, también argumenta por qué una tabla corresponde a la variación lineal y la otra a la variación de proporcionalidad directa.
1 is linear variation and 2 is direct proportionality. In 1 it is linear variation since from the beginning the zeros do not correspond and in 2 if the zeros correspond.
Variation refers to the differences that exist among individuals or groups within a population. These differences can be genetic, environmental, or a combination of both, and can manifest in various traits, such as physical characteristics, behavior, or disease susceptibility.
Genetic variation arises from differences in the DNA sequence among individuals, which can result in different traits being expressed. This variation can occur naturally or be induced by mutations, genetic recombination, or genetic drift. Environmental variation arises from differences in the conditions experienced by individuals or groups, such as differences in climate, nutrition, or exposure to toxins. Environmental variation can also interact with genetic variation to produce complex traits.
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Complete Question:-
Look at the following tables and analyze the values they contain. Then, pose a problem that can be solved with these data, also argue why one table corresponds to linear variation and the other to direct proportional variation.
TABLE 1:
X 0 1 2 3
and 2 17 32 47
TABLE 2:
X 0 1 2 3
AND 0 15 30 45
Question 5 of 5
nguyen has the following cans of soup in his pantry:
•4 cans of chicken noodle soup
• 2 cans of tomato soup
• 3 cans of vegetable soup
•3 cans of potato soup
he randomly chooses a can of soup for lunch. what is the probability that he will choose chicken noodle soup?
a. 1/2
b. 1/4
c. 1/6
d. 1/4
please explain how you got the answer as well
The probability that Nguyen will choose a can of chicken noodle soup is 1/3. Therefore, the correct option is B.
To find the probability, you need to divide the number of favorable outcomes (chicken noodle soup cans) by the total number of possible outcomes (total cans of soup). Hence,
1. Count the total number of cans of soup: 4 chicken noodle + 2 tomato + 3 vegetable + 3 potato = 12 cans in total.
2. Count the number of chicken noodle soup cans: 4 cans.
3. Divide the number of chicken noodle soup cans (4) by the total number of cans (12): 4/12.
4. Simplify the fraction: 4/12 can be simplified to 1/3.
Therefore, the probability of choosing a chicken noodle soup is option B: 1/3.
Note: The question is incomplete. The complete question probably is: Nguyen has the following cans of soup in his pantry: 4 cans of chicken noodle soup; 2 cans of tomato soup; 3 cans of vegetable soup; 3 cans of potato soup. He randomly chooses a can of soup for lunch. What is the probability that he will choose chicken noodle soup? a. ½ b. 1/3 c. 1/6 d. ¼.
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Write an expression for the nth term of the sequence. (Your formula should work for n=1,2,...) 4 5 6 7 5 6 7 8 Need Help? Watch
The nth term of the sequence 4 5 6 7 5 6 7 8 is given by a_n = 3 + (n-1)/2 for odd n and a_n = 4 + (n-2)/2 for even n.
How to find the nth term of a given sequence?To find the nth term of the given sequence, we need to observe the pattern in the sequence. We can see that the sequence consists of two parts:
the first part is a consecutive sequence of integers starting from 4, and the second part is a consecutive sequence of integers starting from 5, where the second part starts right after the first part ends.
So, we can express the nth term of the sequence as follows:
If n is odd, then the nth term is given by:
a_n = 3 + (n-1)/2
If n is even, then the nth term is given by:
a_n = 4 + (n-2)/2
Using this formula, we can find any term of the given sequence by plugging in the corresponding value of n. For example:
When n=1, the first term is 4: a_1 = 4.
When n=6, the sixth term is 6: a_6 = 6.
When n=7, the seventh term is 7: a_7 = 7.
When n=8, the eighth term is 8: a_8 = 8.
Note that this formula works only for n = 1, 2, 3, 4, 5, 6, 7, 8, ... , since the sequence has only 8 terms.
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Madie and Clyde buy another circular plot of land, smaller than the first, on which to plant an orchard. They have set up coordinates as before, with the center of the orchard at (0, 0). They will plant trees at all points with integer coordinates that lie within the orchard, except at (0, 0).
In this orchard, the tree at (5, 12) is on the boundary. What are the coordinates of the other trees that must also be on the boundary? Explain your answer
The coordinates of the other trees that must also be on the boundary are (-5, 12), (5, -12), (-5, -12), (12, 5), (12, -5), (-12, 5), and (-12, -5).
The coordinates of the other trees that must be on the boundary of the circular orchard, given that the tree at (5, 12) is on the boundary and the center of the orchard is at (0, 0) can be determined as follows.
1. Calculate the radius of the orchard using the distance formula:
sqrt((x2-x1)^2 + (y2-y1)^2).
In this case, (x1, y1) = (0, 0) and (x2, y2) = (5, 12).
2. Radius = sqrt((5-0)^2 + (12-0)^2) = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13.
Now, we know the radius of the orchard is 13. To find the other boundary points, we can use the property of circles that states that the points on the boundary are equidistant from the center.
Since the coordinates are integers and symmetric, we can list the other points as follows:
3. The coordinates of the other trees on the boundary are:
(-5, 12), (5, -12), (-5, -12), (12, 5), (12, -5), (-12, 5), and (-12, -5).
These points are also 13 units away from the center, making them equidistant from the center and thus on the boundary of the circular orchard.
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What are measurements less than 435 inches???? Hurry it’s due tomorrow!!!
Any measurement below 435 inches qualifies as a value less than 435 inches.
To find measurements less than 435 inches, you simply need to consider any value below 435 inches. Here's a step-by-step explanation:
1. Understand the question: You are looking for measurements less than 435 inches.
2. Identify the range: The range includes all values below 435 inches.
3. Provide examples: Examples of measurements less than 435 inches can be 400 inches, 350 inches, 250 inches, 100 inches, and so on.
Remember, any measurement below 435 inches qualifies as a value less than 435 inches.
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Help with question in photo please!
Check the picture below.
The original price of a skateboard, not including tax, was $96. Charlie bought the skateboard on sale, and he saved 30% off of the original price. What was the sale price of the skateboard?
A. 66. 00
B. 68. 80
C. 67. 20
D. 28. 80
The answer is (C) 67.20.
Charlie saved 30% off of the original price, which means he paid 70% of the original price.
Let x be the sale price of the skateboard.
We have:
0.7 * 96 = x
x = 67.20
Therefore, the sale price of the skateboard was $67.20.
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420 g of fl our is to be divided into a ratio of 7 : 3 for two different recipes. Find the smaller amount.
After finding the area from the dimensions of the first polygon, find the area of the similar polygon after finding the similarity ratio.
Hi! To find the area of the similar polygon after finding the area of the first polygon and the similarity ratio, follow these steps:
1. Find the dimensions of the first polygon.
2. Calculate the area of the first polygon using the dimensions.
3. Determine the similarity ratio between the first polygon and the similar polygon.
4. Use the similarity ratio to find the corresponding dimensions of the similar polygon.
5. Calculate the area of the similar polygon using the new dimensions.
In your answer: After finding the area from the dimensions of the first polygon, find the area of the similar polygon by determining the similarity ratio and using it to calculate the corresponding dimensions of the similar polygon. Then, calculate the area of the similar polygon using the new dimensions.
To find the area of the similar polygon, you'll need to use the similarity ratio, which compares the corresponding lengths of the sides of two similar figures. Once you have the similarity ratio, you can multiply the area of the first polygon by the ratio squared to get the area of the similar polygon.
Remember, the area of a polygon is found by multiplying the base by the height (or using another appropriate formula depending on the shape of the polygon). So, to summarize, you would first find the area of the first polygon using its dimensions, then use the similarity ratio to find the corresponding sides of the similar polygon, and finally use these sides to find the area of the similar polygon.
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Neave is designing a prize wheel for her school. 200 students will each spin the wheel once. Neave wants the expected number of winners to be 60.
If the wheel is split into 40 equally sized sections, how many sections should be marked “win”
Neave should mark 12 sections as "win" on the prize wheel to achieve the expected number of winners of 60 out of 200 students.
To determine how many sections should be marked "win" on Neave's prize wheel, we need to consider the expected number of winners and the total number of sections on the wheel.
Neave wants the expected number of winners to be 60 out of 200 students. This means that the probability of winning should be 60/200 = 0.3 or 30%.
If the wheel is split into 40 equally sized sections, we can assume that each section has an equal probability of being selected by a student. Therefore, to have a 30% chance of winning, we need to mark a proportionate number of sections as "win".
To calculate the number of sections to mark as "win", we multiply the total number of sections by the desired probability of winning:
40 sections * 0.3 = 12 sections.
It's important to note that the concept of expected value assumes an idealized scenario with perfect randomness. In reality, the actual number of winners may vary due to random chance and individual spin outcomes.
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Using the complex form, find the Fourier series of the function. (30%)
f(x) = 1, 2k -. 25 <= x <= 2k + ,25, k E Z
Answer:
The Fourier series of a periodic function f(x) with period 2L can be expressed as:
f(x) = a0/2 + Σ[n=1 to ∞] (ancos(nπx/L) + bnsin(nπx/L))
where
a0 = (1/L) ∫[-L,L] f(x) dx
an = (1/L) ∫[-L,L] f(x)*cos(nπx/L) dx
bn = (1/L) ∫[-L,L] f(x)*sin(nπx/L) dx
In this case, we have f(x) = 1 for 2k - 0.25 <= x <= 2k + 0.25, and f(x) = 0 otherwise. The period is 0.5, so L = 0.25.
First, we can find the value of a0:
a0 = (1/0.5) ∫[-0.25,0.25] 1 dx = 1
Next, we can find the values of an and bn:
an = (1/0.5) ∫[-0.25,0.25] 1*cos(nπx/0.25) dx = 0
bn = (1/0.5) ∫[-0.25,0.25] 1*sin(nπx/0.25) dx
Since the integrand is odd, we have:
bn = (2/0.5) ∫[0,0.25] 1*sin(nπx/0.25) dx
Using the substitution u = nπx/0.25, du/dx = nπ/0.25, dx = 0.25du/(nπ), we get:
bn = (4/nπ) ∫[0,nπ/4] sin(u) du = (4/nπ) (1 - cos(nπ/4))
Therefore, the Fourier series of f(x) can be written as:
f(x) = 1/2 + Σ[n=1 to ∞] [(4/nπ) (1 - cos(nπ/4))] * sin(nπx/0.25)
for 2k - 0.25 <= x <= 2k + 0.25, and f(x) = 0 otherwise.