a) The proportion of male Internet users who use social networking is approximately 0.6747, and the proportion of female Internet users who use social networking is approximately 0.7358.
b) The difference in proportions is approximately -0.0611.
c) The standard error of the difference is approximately 0.0181.
d) The 95% confidence interval for the difference between these proportions is (-0.096, -0.026).
To calculate the standard error of the difference and find a 95% confidence interval for the difference between the proportions, we can use the formulas for proportions and their differences.
Let \(p_1\) be the proportion of male Internet users who use social networking, and \(p_2\) be the proportion of female Internet users who use social networking.
a) Proportion for male Internet users: \(p_1\) = 517/766 = 0.6747
Proportion for female Internet users: \(p_2\) = 692/941 = 0.7358
b) Difference in proportions: \(p_1 - p_2\) = 0.6747 - 0.7358 = -0.0611
c) The standard error of the difference (SE) can be calculated using the formula:
\(SE = \sqrt{(p_1(1-p_1)/n_1) + (p_2(1-p_2)/n_2)}\)
Where \(n_1\) and \(n_2\) are the sample sizes for male and female Internet users, respectively.
For male Internet users: \(n_1\) = 766
For female Internet users: \(n_2\) = 941
Plugging in the values, we have:
\(SE = \sqrt{(0.6747(1-0.6747)/766) + (0.7358(1-0.7358)/941)}\)
d) To find the 95% confidence interval for the difference between these proportions, we can use the formula:
\(CI = (p_1 - p_2) \± (Z * SE)\)
Where Z is the critical value corresponding to a 95% confidence level. For a large sample size, Z is approximately 1.96.
CI = (-0.0611) ± (1.96 * SE)
CI = -0.0611 ± 0.0355
CI = (-0.096, -0.026)
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three friends ate at restaurant. They ordered nachos for S19 95 and jalapeno poppers. Each friend paid $9.73, not including sales tax or tip, which was 1/3 of the total determine the cost of the jalapeno poppers
The total cost of a Jalapeno is $ 9.24
Three friends ate at a restaurant and ate nachos for $19.95 and jalapeno poppers.
Three of them paid $9.73 each
So the total amount of money paid by three friends = 3×9.73
= 29.19
Now we have to calculate the cost of jalapeno poppers
Therefore we have,
Total amount of money paid = cost of nachos + cost of jalapeno poppers
29.19 = 19.95 + cost of jalapeno poppers
The cost of jalapeno poppers =29.19 - 19.95
= $9.24
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Answer: The cost is $9.24 for the peppers.
Step-by-step explanation: Just do math.
The linear equation y−3=4(x+5) is in what form
Answer: 4x − y = -23
Step-by-step explanation:
Cameron worked as a salesperson at an electronics store and sells phones and phone accessories. Cameron earns a $11 commission for every phone he sells and a $2. 50 commission for every accessory he sells. On a given day Cameron made a total of $361 in commission from selling a total of 56 phones and accessories sold.
The number of phones sold is 26 and the number of accessories sold is 30.
What is a Linear equation:An equation is said to be linear if the maximum power of the variable is usually 1. A linear equation with one variable has the standard form Ax + B = 0. In this case, x is the variable and A is the coefficient of x, and B is a constant.
In mathematical problems, 'x' stands for unknown value or quantity. Here we use the Linear equation concept to solve the problem.
Given that
Cameron earns an $11 commission for every phone he sells and a $2. 50 commission for every accessory he sells.
On a given day Cameron made a total of $361 in commission from selling a total of 56 phones and accessories sold.
Let x and y be the number of phones and accessories
Given that
Cameron made a total of $361 in commission
=> 11x + 2.5y = 361 ----- (1)
Total number of phones and accessories sold
=> x + y = 56
Multiply by 11
=> 11x + 11y = 616 ----- (2)
Do (2) - (1)
=> 11x + 11y - ( 11x + 2.5y) = 616 - 361
=> 11x + 11y - 11x - 2.5y = 255
=> 8.5y = 255
=> y = 255/8.5
=> y = 30
Substitute y = 30 in x + y = 56
=> x + 30 = 56
=> x = 26
Therefore,
The number of phones sold is 26 and the number of accessories sold is 30.
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Which graph or equation represents a nonproportional relationship?
A
On coordinate plane A, a line goes through points (negative 2, 0) and (0, 1).
B
On coordinate plane B, a line goes through points (0, 0) and (2, negative 2).
C
0.375x
D
y = StartFraction 5 Over 9 EndFraction x
A
B
C
D
The graph that does not represents a proportional relationship is: A (see image attached below).
What is a Proportional Relationship?A proportional relationship has a constant, which is uniform and is defined in the equation y = kx, as k. This means a relationship that is proportionate will have an equation in that form.
For a proportional graph, the line must pass through the point of origin which is denoted by the ordered pair, (0, 0).
Therefore, from the options given, the option B represents a proportional relationship because it contains (0, 0), while option C and D takes the form of y = kx.
Therefore, option A does not represent a proportional relationship.
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functions f and g are defined as
f(x) = 5x² - 10x + 7
where x > 1
g(x) = 7x - 6
Find fg(2)
Explain if the triangles below are congruent or not and explain why you think that.
In this picture, we have the triangles with two common sides and one common angle. However, they are not congruent, as they do not follow any of the congruence theorems. The congruence theorem with two sides and an angle is the SAS(Side-Angle-Side). However, the angle has to be the angle between the two sides, which does not happen in this case.
Use the Chain Rule to find the indicated partial derivatives. w = xy + yz + zx, x = r cos(θ), y = r sin(θ), z = rθ; ∂w/∂r , ∂w/∂θ when r = 8, θ = π/2
By using the chain rule, we find the partial derivatives as ∂w/∂r = 8 + 4π and ∂w/∂θ = 4π when r = 8 and θ = π/2, respectively.
The partial derivatives ∂w/∂r and ∂w/∂θ of the function w = xy + yz + zx can be found using the Chain Rule. The first step is to express the variables x, y, and z in terms of r and θ.
Given that x = r cos(θ), y = r sin(θ), and z = rθ, we substitute these expressions into the function w.
The partial derivative ∂w/∂r represents the rate of change of w with respect to r while keeping θ constant. To find this derivative, we differentiate each term of the function w with respect to r, treating θ as a constant.
The derivative of xy with respect to r is y (since x is multiplied by a constant r), the derivative of yz with respect to r is z, and the derivative of zx with respect to r is x.
Therefore, ∂w/∂r = y + z + x.
The partial derivative ∂w/∂θ represents the rate of change of w with respect to θ while keeping r constant. To find this derivative, we differentiate each term of the function w with respect to θ, treating r as a constant.
The derivative of xy with respect to θ is x (since y is multiplied by a constant r), the derivative of yz with respect to θ is 0 (since z does not depend on θ), and the derivative of zx with respect to θ is z.
Therefore, ∂w/∂θ = x + z.
To evaluate these partial derivatives at the point (r, θ) = (8, π/2), we substitute these values into the expressions obtained above.
Thus, ∂w/∂r = y + z + x = 8sin(π/2) + 8π/2 + 8cos(π/2) = 8 + 4π and ∂w/∂θ = x + z = 8cos(π/2) + 8π/2 = 0 + 4π = 4π.
Therefore, ∂w/∂r = 8 + 4π and ∂w/∂θ = 4π when r = 8 and θ = π/2.
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At a furniture manufacturer, worker a can assemble a shelving unit in 5 hours. worker b can assemble the same shelving unit in 3 hours. which equation can be used to find t, the time in hours it takes for worker a and worker b to assemble a shelving unit together? rate (shelving units per hour) time (hours) fraction completed worker a one-fifth t worker b one-third t 5 t 3 t = 1 one-fifth t minus one-third t = 1 one-fifth t one-third t = 1 5 t minus 3 5 = 1
If they work together, they need 15/8 hours to assemble one shelving unit.
What does work mean in math?
In summary, work is done when a force acts upon an object to cause a displacement. Three quantities must be known in order to calculate the amount of work. Those three quantities are force, displacement and the angle between the force and the displacement.According to tittle, we know worker A can assemble a shelving unit in 5 hours , which means worker A can finish 1/5 of work in 1 hour . And worker B can finish 1/3 of work in 1 hour.
If A & B work together , they will spend the same time t to assemble only one shelving .
That means, 1/5t + 1/3 t = 1 (equation)
1/5 t is worker A's workload during time t , 1/3 t is worker B workload.
So, 1/5 t + 1/3t = 1 is the answer
⇒ 5t + 3t = 15
⇒ t = 15/8 hours
If they work together, they need 15/8 hours to assemble one shelving unit.
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Answer:
Letter C is the correct answer or 1/5 t + 1/3t = 1
Find the midpoint of the line segment with the given endpoints (6,6) and (-9,2)
1.(7.5,2)
2.(-24,-2)
3.(6,-3.5)
4.(-1.5,4)
A recipe for fruit punch is 3 parts orange juice to 2 parts apple juice. Jim mixes 180 ml of orange juice with 120 ml of apple juice.
Has Jim made the fruit punch correctly? Explain your answer.
PLEASE HELP ASAP
which is the correct curve for y=3/x
What is b) please help I will give 5 points or even all of them. PLEASE PLEASE PLEAS HELP!!!!!
Answer:
A
Step-by-step explanation:
If we evaluate 3/x at x=1, we get 3/1 = 3.
The only one that showed that is graph A, and we can further check by evaluating other points, such as when x = 1/2, y = 6, and that's shown on graph A.
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Graph A, correctly represents the function y = x/3.
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
From the table of y = 3/x,
The value of (x, y) are (0.5, 6), (1, 3), (2, 1.5), (3, 1) and (4, 0.75).
Now, Observe graphs A, B, and C.
Graph A, when x = 0.5, y = 6, when x = 1 y = 3 so graph A matches with our table.
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If someone is estimating a sample average for the purposes of inference about a single mean, how much better is a sample size of 1000 than a sample size of 10? The standard deviation will be 10 times smaller. The variance will be 900 times smaller. O The variance will be 10 times smaller. The standard deviation will be 100 times smaller.
The statement "The variance will be 10 times smaller. The standard deviation will be 100 times smaller" is correct.
When estimating a sample average for the purpose of inference about a single mean, increasing the sample size provides more precise and reliable estimates. The precision of an estimate is determined by the variability of the data, which is measured by the variance and standard deviation.
When comparing a sample size of 1000 to a sample size of 10, increasing the sample size by a factor of 100 (from 10 to 1000) results in a decrease in the variability of the data. Specifically:
The variance is inversely proportional to the sample size. Increasing the sample size by a factor of 100 reduces the variance by a factor of 100 (10^2), making it 100 times smaller.
The standard deviation is the square root of the variance. Therefore, increasing the sample size by a factor of 100 reduces the standard deviation by a factor of 10 (10^0.5), making it 10 times smaller.
Hence, a sample size of 1000 is expected to provide estimates with 10 times smaller variance and 100 times smaller standard deviation compared to a sample size of 10. This indicates that larger sample sizes generally lead to more precise and reliable estimates.
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quadrilateral g'r'a'm is a translation of quadrilateral gram describe the translation
The translation is described as -
(x, y) → (x + 10, y + 2).
What is the difference between upward, downward, leftwards and rightwards translation?Upward translation : [k] units = When the upward translation take's place then, each point will have its y - coordinate shifted upwards by +k units.Downward translation : [k] units = When the downward translation will take place then, each point will have its y - coordinate shifted downwards by -k units.Leftward Translation : [k] units = When the leftward translation will take place then, each point will have its x - coordinate shifted by -k units to the left.Rightward Translation : [k] units = When the rightward translation will take place then, each point will have its x - coordinate shifted by +k units to the rightGiven is that quadrilateral G'R'A'M' is a translation of quadrilateral GRAM.
Translation along the {x} - axis would be → x + {6 - ( - 4)} → (x + 10).Translation along the {y} - axis would be → y + {4 - 2} → (y + 2).The translation rule will be : (x, y) → (x + 10, y + 2).Therefore, the translation is described as -
(x, y) → (x + 10, y + 2).
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Linda uses the simple interest formula to calculate the interest fee on her recent loan. Her interest rate is 5%.What value will Linda use for r, interest rate, in her calculation?
Since the interest rate is 5%. She needs to express the percentage as a decimal.
In order to do it, she needs to divide 5 by 100, so:
\(\frac{5}{100}=0.05\)Answer:
r = 0.05
assume a simple model with only two countries: the united states and germany, and two goods: beer and motorcycles. suppose that the opportunity cost for the united states to produce 1 beer is 3 motorcycles and the opportunity cost for germany to produce 1 beer is 1/2 motorcycles. which of the following statements is true
The statement opportunity cost for Germany to produce 1 beer is 1/2 motorcycles is true.
The German economy would be better off if it produced beer and traded motorcycles with the US.
Germans would benefit from specializing in producing beer and engaging in trade with the United States since their opportunity cost is lower (1/2 is less than 3).
A country is said to be having a comparative advantage in producing a good if it can produce it at a lower opportunity cost. Germany has a lower opportunity cost in producing beer so it has a comparative advantage in making beer.
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what is the equation in standard form of the line that passes through the point (1,24) and has a slope of (-3/5)
y = -3/5x - 123/5 is slope-intercept form .
What is an explanation of the slope-intercept form?
A line's equation can be written in the slope-intercept form so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are immediately visible. This form is frequently known as the y = mx + b form.Point = ( 1,24 )
slope = -3/5
the equation in standard form of the line that passes through the point
y - y₁ = m ( x - x₁)
y - 24 = -3/5 ( x - 1)
5 (y - 24) = -3( x - 1 )
5y - 120 = -3x + 3
5y = -3x + 3 + 120
5y = -3x + 123
y = -3/5x - 123/5
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Match each polynomial in the first column with a factoring technique in the second column. If none of the techniques can be used to factor the polynomial, select none.
The factorization case for each polynomial is listed below:
Sum and product Grouping Perfect square trinomial Difference of two squares None GCFHow to identify the factorization case of a given polynomial
In this problem we find six cases of polynomials, whose factorization case must be found. Now we proceed to show and indicate what kind of factorization case is used for each polynomial:
Case 1: z² + z - 90 (Sum and product)
z² + z - 90
z² - (- 10 + 9) · z + (- 10) · 9
(z + 10) · (z - 9)
Case 2: x² - 4 · x + 6 · x - 24 (Grouping)
x² - 4 · x + 6 · x - 24
x · (x - 4) + 6 · (x - 4)
(x + 6) · (x - 4)
Case 3: 16 · x² + 24 · x · y + 9 · y² (Perfect square trinomial)
16 · x² + 24 · x · y + 9 · y²
(4 · x + 3 · y)²
Case 4: 49 · x² - 100 · y² (Difference of two squares)
49 · x² - 100 · y²
(7 · x - 10 · y) · (7 · x + 10 · y)
Case 5: 121 · m² + 64 (None)
Case 6: 8 · x³ · y² + 4 · z³ (GCF)
8 · x³ · y² + 4 · z³
4 · (2 · x³ · y² + z³)
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1). A researcher randomly selects and interviews fifty male and fifty female teachers. i. systematicii. convenienceiii. randomiv. stratifiedv. cluster2). Solve the absolute-value inequality.|8−x|≥5
The researcher randomly selected and interviewed fifty male and fifty female teachers can be categorized as:
iii. random - The selection of teachers is done randomly, without any specific criteria or pattern.
To solve the absolute-value inequality |8 - x| ≥ 5, we can consider two cases:
Case 1: (8 - x) ≥ 5
To solve this inequality, we have:
8 - x ≥ 5
-x ≥ 5 - 8
-x ≥ -3 (multiplying by -1 and reversing the inequality)
x ≤ 3 (dividing by -1 and reversing the inequality)
Case 2: -(8 - x) ≥ 5
To solve this inequality, we have:
-8 + x ≥ 5
x ≥ 5 + 8
x ≥ 13
Combining the solutions from both cases, we have:
x ≤ 3 or x ≥ 13
So, the solution to the absolute-value inequality |8 - x| ≥ 5 is x ≤ 3 or x ≥ 13.
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The sum of 3 and a number is between -2 and 17.
Answer:
The number, x = { -5 < x < 14}
This means x is any integer between -5 and 14
Step-by-step explanation:
From the statement, let the number be x
3 + x = y; y = { -2 < y < 17}
This means that y is any integer between -2 and 17
Therefore, x = y - 3
Subtract 3 from the limits of y
i.e. -2 - 3 = -5 and 17 - 3 = 14
Hence, x = { -5 < x < 14}
Last year Murkthar earned £18,900. This year Murkthar now earns £19750.50. Calculate his percentage increase
Step-by-step explanation:
First, you need to take away £18,900 from £19750.50 and the answer is £850.5 but it's not yet finished.
Formula:
increase/original money=850.50/18900 *100
Work it on your calculator and you'll get an answer. That will be the real answer.
Consider one mathematical idea from the course that you have found beautiful, and explain why it is beautiful to you. Your answer should: (1) explain the idea in a way that could be understood by a classmate who has taken classes X and Y but has not yet taken this class and (2) address how this beauty is similar to or different from other kinds of beauty that human beings encounter.
One beautiful mathematical idea is the concept of the Golden Ratio. The Golden Ratio is a mathematical ratio that is approximately equal to 1.618. It can be found in various natural and artistic phenomena, such as the proportions of the human body and the dimensions of famous artworks like the Parthenon. The beauty of the Golden Ratio lies in its aesthetic appeal and harmonious proportions, which can be appreciated by individuals from different backgrounds.
The Golden Ratio is a mathematical concept that can be understood by considering the relationship between two quantities. It is the ratio of the larger quantity to the smaller quantity, and this ratio is approximately equal to 1.618. This ratio has been observed in various natural and artistic contexts, which adds to its beauty. For example, the proportions of the human body, such as the ratio of the height to the navel compared to the navel to the floor, are often close to the Golden Ratio. Similarly, famous artworks, such as the Parthenon in Athens, exhibit dimensions that are related to the Golden Ratio.
The beauty of the Golden Ratio is similar to other kinds of beauty that humans encounter in the sense that it evokes a sense of harmony, balance, and aesthetic appeal. It demonstrates the presence of underlying mathematical principles that govern patterns and proportions in the natural and artistic world. This beauty can be appreciated by individuals regardless of their mathematical background, as it appeals to our innate sense of visual harmony and proportion. The elegance of the Golden Ratio lies in its ability to bridge mathematics and aesthetics, showcasing the interconnectedness between these domains of human experience.
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if you are traveling at 60 mph you will travel almost the length of a football field in how many seconds
Time taken to cross the field will be 3.36 seconds.
What does physics mean by speed?Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path. In other words, velocity is a vector, whereas speed is a scalar value. There are four different types of speed. constant speed, varying speed, an average rate, instantaneous speed.
Solution,
Given,
speed=60 mph
length of football field=0.056 miles
time taken to cross it = distance/speed
time=0.056/60=0.00093 hour = 3.36 seconds.
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Use the Pythagorean Theorem to find the missing side of the right triangle:
Answer:
9.165
Step-by-step explanation:
Pythagorean Theorem implies a^2 + b^2 =c^2
AC= hypotenus
AB= 4
CB= ?
10^2=4^2+CB^2
CB= √10^2-4^2
= 9.165
Find the volume of a right circular cone that has a height of 18.1 in and a base with a diameter of 18.7 in. Round your answer to the nearest tenth of a cubic inch.
Answer: 1657.0 in^3
Step-by-step explanation:
The formula for the volume of a right circular cone is: V = π*r^2*(h/3).
Therefore, plugging in 18.1 for "h" and 9.35 for "r" (this is half of the diameter) yields the answer.
There are 9 out of 25 students in science class who passed the test and 4 out of 16 in history. What is the percentages of students in each class that passed the test?
Answer: 36% passed the science test, while 25% passed the history test.
In order to find a percentage we divide our two know numbers
Science Class- 9/25 is a fraction with / standing for divided by. 9 divided by 25 is .36 This means 36% of the class passed the science test.
History Class- 4/16 is a fraction with / standing for divided by. 4 divided by 16 is .25 This means 25% of the class passed the science test.
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Redbox rents out both video games and movies. They charge $2 for each video game and
$1 for each movie rented. Last week the total number of rentals was 114 and the machine
made a total of $177. How many movies and games were rented? What are the two
equations we can make? One is about the price, the other is the total rentals.
Answer:
1x + 2y = 177 (price)
x + y= 114 (rentals)
Step-by-step explanation: x= movies y= video games
Answer:
56
Step-by-step explanation:
add and then multiply
Determine the period.
Answer:
shopkeeper sells a book at INR 960 for a profit of 20% and another book at INR 720 for a loss of 10%. Find the total profit/loss of the shopkeeper
What is the positive difference between the sum of the first 15 positive even numbers and the sum of the first 15 positive odd numbers
The positive difference between the sum of the first 15 positive even numbers and the sum of the first 15 positive odd numbers is 15.
We are supposed to find out the positive difference between the sum of the first 15 positive even numbers and the sum of the first 15 positive odd numbers. That means we need to find the sum of the first 15 positive even numbers and the sum of the first 15 positive odd numbers separately and then find their positive difference.
Step 1: Calculation of the sum of the first 15 positive even numbers: Even numbers are multiples of 2 and first 15 even numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30. The sum of the first 15 positive even numbers is equal to (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 + 28 + 30). The sum can be calculated as follows :sum of the first 15 positive even numbers = 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 + 28 + 30= 240
Step 2: Calculation of the sum of the first 15 positive odd numbers: Odd numbers are not multiples of 2 and first 15 odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29. The sum of the first 15 positive odd numbers is equal to (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29). The sum can be calculated as follows: sum of the first 15 positive odd numbers = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29= 225
Step 3: Calculation of positive difference between the sum of the first 15 positive even numbers and the sum of the first 15 positive odd numbers: We have found that the sum of the first 15 positive even numbers is 240 and the sum of the first 15 positive odd numbers is 225. Thus, the positive difference between the sum of the first 15 positive even numbers and the sum of the first 15 positive odd numbers is equal to the absolute difference between 240 and 225.Positive difference = |240 - 225|= 15. Thus, the positive difference between the sum of the first 15 positive even numbers and the sum of the first 15 positive odd numbers is 15.
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250 people at acorn lake 25 are counselors, what % are couns
Answer:
10%
Step-by-step explanation:
250/25 is 10%
Answer:
10%
Step-by-step explanation:
hope this helps. . . <3
good luck! UwU
Original price of a car $7,800.00 discount: 30%
Step-by-step explanation:
Disclaimer* this is what my tutor has taught me and answers could differ*
A 30% of $7,800-
10% of $7,800= 7,800/10= 780
30% of $7,800= 780*3= 2,340
so
$7,800 - $2,340 = $5,460
Hope this helped!
Let me know if there is a mistake in this!