A film shop carrying black and white film and color film has $4000 in inventory the profit on black and white film is 12% and the profit on color film is 21% if all the film is sold and if the profit on color film is $150 less than the profit on blavk and white film how much was invested in each type of film
To solve this problem, set up a system of linear equations based on the total investment and profit conditions given. Solve for the variables representing investment amounts in black and white film and color film. This process demonstrates practical application of algebra in finance.
Explanation:Let's find how much was invested in black and white film and color film at a film shop with a total inventory of $4000, knowing that the profit on black and white film is 12%, the profit on color film is 21%, and the profit on color film is $150 less than the profit on black and white film.
Let x represent the amount invested in black and white film, and y represent the amount invested in color film. According to the problem, we have two equations:
First, rearrange Equation 2 to isolate y: 0.12x - 150 = 0.21y. Then, convert it to y = (0.12/0.21)x - (150/0.21).
Next, substitute the value of y from Equation 2 into Equation 1: x + ((0.12/0.21)x - (150/0.21)) = 4000. Solve this equation for x to find the amount invested in black and white film, then substitute x back into either equation to find y, the amount invested in color film.
This problem involves forming and solving a system of linear equations based on the given profit percentages and the condition that profit on color film is $150 less than the profit on black and white film, demonstrating application of algebra in financial contexts.
(b) how many measurements must be averaged to get a margin of error of ±0.0001 with 98% confidence? (round your answer up to the nearest whole number.)
To find the number of measurements that must be averaged to get a margin of error of ±0.0001 with 98% confidence, you can use the formula for the margin of error.
Explanation:To find the number of measurements that must be averaged to get a margin of error of ±0.0001 with 98% confidence, we can use the formula for the margin of error:
Margin of Error = Z * (Standard Deviation / √(Sample Size))
Given that we want a margin of error of ±0.0001 and a confidence level of 98%, we can find the corresponding Z-value using a standard normal distribution table.
Once we have the Z-value, we can rearrange the formula to solve for the sample size, which represents the number of measurements that must be averaged.
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263,148 what is the value of the digit 6 in this number?
Which of the following sets of points is a direct variation?
(0, 0); (2, 4); (5, 15)
(0, 0); (-1, -2); (1, 2)
(3, 6); (-2, 4); (-1, 2)
(0, 5); (1, 6); (2, 7)
Answer:
(0, 0); (-1, -2); (1, 2) and (0, 5); (1, 6); (2, 7).
Step-by-step explanation:
The set will have a direct variation if each pair is added or subtracted by a common number in each component. You also can see it graphically, if the points form a straight growing line then the set is a direct variation. Then,
In the first set we have
(0,0), (0+2,0+4), (0+2+3, 0+4+11). The behavior is not uniform, then it is not a direct variation.
Second set: (-1, -2); (0,0); (1, 2)
(-1,-2)(-1+1,-2+2), (-1+1+1, -2+2+2). The behavior is uniform and it is increasing, then it is a direct variaton.
Third set:
(-2, 4), (-2+1,4-2), (-2+1+4, 4-2+4). The behavior is not uniform, then it is not a direct variation.
Fourth set:
(0,5), (0+1, 5+1), (0+1+1, 5+1+1). The behavior is uniform and it is increasing, then it is a direct variaton.
jillian bought 1/2 pound of turkey and 1 1/3 pound of cheddar cheese at the deli. both items are on sale for $6 per pound. how much does each turkey cost>
To calculate the cost of the turkey, multiply the weight of the turkey (1/2 pound) by the cost per pound ($6). The total cost for the turkey is $3.
Jillian bought 1/2 pound of turkey and 1 1/3 pounds of cheddar cheese at the deli, with both items on sale for $6 per pound. To find out how much the turkey costs, you need to multiply the weight of the turkey by the cost per pound. Here's how you do it:
Determine the weight of the turkey: 1/2 pound.Multiply the weight of the turkey by the cost per pound: (1/2 pound) x ($6/pound).Calculate the cost: 1/2 x 6 = $3.Therefore, the cost of the turkey is $3.
Theoretically, what would happen if a nation had an unlimited supply of a certain resource?
record the product. use expanded form to help. 5×162=
A movie rental gives a free popcorn to every 15th customer and a free movie rental to every 4th customer. Which customer was the first to win both prizes?
rewrite the following fractions as division problems 7/11 5/2 9/10 7/15
We are given some fractions and we need to write these fractions in terms of division problem.
a)
7/11
There are 7 chocolates and a total of 11 children present at a party.If the chocolates are to be distributed equally among all, then how many chocolates does each get?
b)
5/2
The distance traveled by Xavier is 5 km and the time taken by him is 2 hours.Then find his speed?
c)
9/10
If there are a total of 19 students in a class and the number of girls are 1 more than the number of boys then find the ratio of number of boys to number of girls?
d)
7/15
The are 7 red balls, 2 green balls and 6 yellow balls in a bag.One ball is drawn at random.What is the probability of getting a red ball?
Imagine two lines intersect. How can the properties of linear pairs and vertical angles help to determine the angle measures created by the intersecting lines? Explain.
If you know the measure of one angle in a linear pair, you can find the measure of the other because the sum of the measure of the two angles is 180 degrees. If you know the measure of one angle in a pair of vertical angles, you can find the measure of the other because they are congruent.
Final answer:
Properties of vertical angles and linear pairs allow us to find unknown angles when two lines intersect by employing the facts that vertical angles are equal and linear pairs sum up to 180 degrees.
Explanation:
When two lines intersect, they form two pairs of vertical angles and two pairs of linear pairs. Vertical angles are opposite angles made by intersecting lines and are always equal. So, if one of the vertical angles is known, the opposite angle can be determined because it is congruent. Linear pairs are adjacent angles whose outer arms form a straight line. These linear pairs are supplementary, meaning their sum is 180 degrees. Therefore, if we know one angle of a linear pair, we can find the other by subtracting the known angle from 180 degrees. Understanding these properties allows us to solve for unknown angle measures around the intersection of two lines. For example, if one angle measure in a linear pair is given, we can find the measure of the adjacent angle. Knowing the measure of this adjacent angle, which is also a vertical angle, allows us to determine the measure of the angle vertical to it, as they are equal.
How do you represent any number in an equation?
If 5+6i is a root of the polynomial function f(x),which of the following must also be a root of f(x)
Answer:
5 - 6i must also be a root of f(x)
Step-by-step explanation:
Complex conjugates states that the two complex numbers are conjugates of each other if they have the same real part and their imaginary parts are negatives of each other i.e, the complex conjugate of a + bi is a - bi where i is imaginary.
Conjugate root theorem states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a-bi is also a root of that polynomial.
Given: if 5+ 6i is a root of the polynomial function f(x).
then,
by the conjugate root theorem;
5 - 6i is also be a root of the polynomial f(x).
show the zero property of multiplication using the number 25
In general, the air temperature decreases 12 degrees for every 4,000 feet increase in altitude. If a hiker climbs 3,000 feet by how much can she expect the temperature to decrease?
Trevor had 4 small boxes of raisins to share equally among himself and 2 friends.
How many boxes of raisins would each person receive?
A.
B.
C.
D.
What is 1/7^9 × 1/7^-6
What is the value of log5 125
Answer:
[tex]log_5125=3[/tex]
Step-by-step explanation:
Given : [tex]log_5125[/tex]
We have to find the value of [tex]log_5125[/tex]
Consider the given expression [tex]log_5125[/tex]
Rewrite 125 in power- base form, [tex]125=5^3[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)[/tex]
[tex]\log _5\left(5^3\right)=3\log _5\left(5\right)[/tex]
[tex]=3\log _5\left(5\right)[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1[/tex]
[tex]\log _5\left(5\right)=1[/tex]
[tex]3\log _5\left(5\right)=3[/tex]
Thus, [tex]log_5125=3[/tex]
The value of log_5 125 is 3.
We have,
To find the value of log base 5 of 125, we need to determine the exponent to which we need to raise 5 to obtain 125.
In other words,
What power do we need to raise 5 to in order to get 125.
So,
By evaluating 5³ (5 raised to the power of 3), we find that 5³ = 125.
So, log base 5 of 125 is equal to 3, as log base 5 of 125 = 3.
So,
log base 5 of 125 equals 3 because 5 raised to the power of 3 gives us 125.
Thus,
The value of log_5 125 is 3.
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explain how you could convert a rate of 18000 miles per hour to miles per second
thirty-eight and ninety-seven hundredths kilograms in standard form
Answer:
The answer is 38.97 kilograms.
Step-by-step explanation:
Thirty-eight and ninety-seven hundredths kilograms in standard form is 38.97 kilograms.
Thirty eight is simply 38.
And ninety-seven hundredths means that 97 is written after decimal. This is because when there exists an 'and' in a mathematical number, this means there is a decimal.
So, the answer is 38.97 kilograms.
For the expression below, write an equivalent expression that involves x only. assume x is positive.
Use substitution to determine which of the following points is a solution to the standard form equation below. 2y = 5
Average speed of Car 1 = 45 mph.
Average speed of Car 2 = 65 mph.
Time elapsed between start of Car 1 and start of Car 2 = 18 minutes.
how long until the cars lapse
It will take 40.5 minutes for Car 2 to catch up to Car 1 after its 18-minute head start.
To find out how long it will take for Car 2 to catch up to Car 1, we first need to determine the distance Car 1 travels during the 18-minute head start.
Convert 18 minutes to hours.
18 minutes ÷ 60 minutes/hour = 0.3 hours
Calculate the distance Car 1 travels during the 18-minute head start.
Distance = Speed × Time
Distance = 45 mph × 0.3 hours
Distance = 13.5 miles
Now that we know Car 1 has traveled 13.5 miles when Car 2 starts, we need to find out how long it takes for Car 2 to catch up, which is essentially the time needed to cover this distance at the speed difference between the two cars.
Calculate the relative speed of Car 2 compared to Car 1.
Relative Speed = Speed of Car 2 - Speed of Car 1
Relative Speed = 65 mph - 45 mph
Relative Speed = 20 mph
Calculate the time it takes for Car 2 to catch up.
Time = Distance ÷ Relative Speed
Time = 13.5 miles ÷ 20 mph
Time = 0.675 hours
Convert the time from hours to minutes for better understanding.
0.675 hours × 60 minutes/hour = 40.5 minutes
So, it will take 40.5 minutes for Car 2 to catch up to Car 1 after its 18-minute head start.
If one side of a square notebook measures 20 cm, what is the area of the front cover of the notebook?
One card is drawn at random from the deck of cards shown. Which of the following probabilities is equal to one?
P(even or odd)P(even and odd)P(not yellow)
Answer:
P(Even or ODD) ( .Y .)
Step-by-step explanation:
Divide (8.6 x 108) by (3.2 x 103). Express your answer in scientific notation.
Write three decimals that have a sum of 27.905. Parts of the needed decimals are listed below! thanks!
14. + 8. + 4. = 27.905
there are 220 calories in 4 ounces of beef. how many calories are there in 5 ounces
Final answer:
To find the number of calories in 5 ounces of beef, divide 220 calories by 4 ounces to find the per ounce calorie count and then multiply by 5. The answer is 275 calories for 5 ounces of beef.
Explanation:
To determine the number of calories in 5 ounces of beef, we will first calculate the calories per ounce. Given that there are 220 calories in 4 ounces of beef, we can divide 220 calories by 4 to find the number of calories in 1 ounce.
220 calories ÷ 4 ounces = 55 calories per ounce.
Now, if one ounce of beef has 55 calories, then 5 ounces of beef would have:
55 calories/ounce × 5 ounces = 275 calories.
Therefore, 5 ounces of beef contains 275 calories.
Which number is a prime number??
111
121
131
141
Final answer:
Among the given options, the number 131 is a prime number, as it only has two divisors: 1 and itself.
Explanation:
The student has asked to identify which number among the given options is a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Analyzing the given options:
111 is divisible by 3.
121 is divisible by 11 (11 x 11).
131 is a prime number because it has no divisors other than 1 and itself.
141 is divisible by 3.
Therefore, the correct answer is 131, which is a prime number.
which equation is not true for the solution x = -8
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. n = 4, x = 3, p =
Final answer:
To find the probability of x successes in a binomial distribution, use the binomial probability formula. Substituting the given values into the formula will yield the probability.
Explanation:
To find the probability of x successes in a binomial distribution with n trials and probability of success p, we use the binomial probability formula. The formula is:
P(x) = (nCx) * p^x * (1-p)^(n-x)
Using the given values n = 4, x = 3, and p = ..., we can substitute these values into the formula to calculate the probability.
For example, if p = 0.5, the probability is:
P(3) = (4C3) * 0.5^3 * (1-0.5)^(4-3) = 4 * 0.125 * 0.5 = 0.25