The equation 4y = x represents a direct variation. This type of relationship between variables implies that the ratio between x and y is constant. In this specific example, the constant of variation is 0.25.
Explanation:Yes, the given equation 4y = x is a representation of direct variation. Direct variation in mathematics refers to a situation where the ratio of two variables is constant. In a direct variation equation the form is y = kx, where k is the constant of variation. Here, you can rewrite 4y = x as y = x/4 or y = 0.25x, so the constant of variation is 0.25. It's important to note that a direct variation has no y-intercept, it always passes through the origin (0,0) which is the case in this equation.
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Th local park has 4 bike racks. Each bike rack can hold 15 bikes. There are 16 bikes in the bike racks. What expression shows the total number of empty spaces in the bike racks?
PLZ HELP!!!!! D: D: IM FAILING PLZ HELP ;cccc
A trucking company determined that the distance traveled per truck per year is normally distributed, with a mean of 30 thousand miles and a standard deviation of 10 thousand miles. complete parts (a) through (c) below.
a. nbsp what proportion of trucks can be expected to travel between 18 and 30 thousand miles in a year?
To solve this problem, we have to make use of the z statistic. The formula for z score is:
z = (x – u) / s
where x is the sample value = 18,000 to 30,000, u is the sample mean = 30,000, and s is the standard deviation = 10,000
at x = 18,000
z = (18,000 – 30,000) / 10,000 = - 1.2
at x = 30,000
z = (30,000 – 30,000) / 10,000 = 0
So find for the P at values of z = -1,2 and z = 0.
P (z = - 1.2) = 0.1151
P (z = 0) = 0.5000
The proportion in between is the difference:
P (18,000 < x < 30,000) = 0.5000 – 0.1151 = 0.3849
So about 38.49% can be expected to travel 18,000 to 30,000 miles in a year
Using z-scores and the normal distribution, we can calculate that approximately 38.49% of trucks can be expected to travel between 18 and 30 thousand miles in a year.
Explanation:This problem involves the normal distribution in mathematics, particularly statistics. Given that the distance travelled per truck per year is normally distributed, we can calculate the proportion of trucks that may be expected to travel between 18 and 30 thousand miles in a year using z-scores.
The first step is to calculate the z-scores for the two distances we are concerned with. The z-score is a measure of how many standard deviations an element is from the mean. Given a mean of 30 thousand miles and a standard deviation of 10 thousand miles, the z-score for 18 thousand miles is (18 - 30) / 10 = -1.2, and the z-score for 30 thousand miles is (30 - 30) / 10 = 0.
You then need to find the area between these two scores on a standard normal distribution table, which gives you the proportion of trucks likely to travel this distance. Looking up -1.2 and 0 in a standard normal table gives us values of 0.1151 and 0.5000 respectively. The difference between these two areas (0.5000 - 0.1151) is 0.3849, or 38.49% when expressed as a percentage. Thus, we can expect approximately 38.49% of trucks to travel between 18 and 30 thousand miles in a year.
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Translate the phrase to mathematical language. Then simplify the expression.
Subtract 81 from −55.
What is a numerical expression for the phrase?__
(Do not simplify.)
Simplify the expression.__
Jerry lost his credit card and instead of reporting it right away, he decides to continue looking for it believing he could find it. Some time passes and after two weeks, he logs into the account activity page of his credit card and sees a recent $500 internet purchase that was made by someone else. At that moment, he calls to report his card stolen. How much of this $500 charge is Jerry at risk for having to pay?
Jerry did not report his lost credit card right away believing that he could find it. Fraudulent transactions were made on his account and he is responsible to pay the maximum amount of $50 under the Fair Credit Billing Act (FCBA).
how to convert 8.6 into mixed numbers
F(x, y) = y3/x, p(1, 3), u = 1 3 2i + 5 j (a) find the gradient of f.
what is -8 3/4 + -11 1/3
scuba diver is swimming 30 feet below sea level . A hand glider passes over the position of the scuba diver. The hand glider is 215 ft above sea level.
draw a number line to represent the distance between the scuba diver and the hand glider (include sea level at zero feet)
what is the decimal of 77/200?
Deanna has 80 books in her collection. If 60% of the books are fiction, how many of the books are nonfiction?
if 60% is fiction, then 40% are non fiction
80 x 40% =
80 x 0.40 = 32
32 books are nonfiction
The average American consumes about 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will 50 Americans consume in one week? Round to the nearest hundredth.
Three years ago, Marry was three times as old as his brother. Five years from now he will be twice as old as his brother. How is Marry now?
Larry mixed 15 grams of salt with 210 grams of a 5% salt solution in water. What is the percent of salt in his new solution?
Answer:
11.33%
Step-by-step explanation:
Amount of salt which Larry has to mix= 15 grams
In 210 gm of salt solution, content of salt= 5%
Amount of salt in salt solution= 5 % of 210 grams
Amount of salt in salt solution= [tex]\frac{5}{100}[/tex] of 210 grams
Amount of salt in salt solution= [tex]\frac{21}{2}[/tex]
Amount of salt in salt solution= 10.5 grams
Now the 15 grams of salt have to mix with 5% of salt solution
Total amount of salt= 15+ 10.5
Total amount of salt = 25.5 gram
Total amount of salt solution=15+ 210= 225 grams
Percentage of salt in new solution=[tex]\frac{amount of new salt}{ amount of new solution}[/tex] ×100
Percentage of salt in new solution=[tex]\frac{25.5}{ 225}[/tex] ×100
Percentage of salt in new solution= 0.13333×100
Percentage of salt in new solution= 11.33% (approx)
Hence, the correct answer is 11.33%
select the graph that represents the given set a={(1,2),(2,3),(3,4),(4,5)
Without graphing, tell which statements are true for the graph of the function y = x2 + 2.
I. All points on the graph are above the origin.
II. All points on the graph have positive x-values.
III. All points on the graph have positive y-values.
Statements (... and ...) are true. Statement (...) is true because x^2 is non-negative for all values of x, so the minimum value of x^2 is 0. Thus, the minimum y−value for the function is (...) and the lowest point on the graph is (0, ...), which is above the origin. Statement (...) is true because the lowest point on the graph is (0, ...) so all other points have a y−value that is greater than (...) and must be positive.
Statements I and III are true as per the defined function y=x^2+2. The graph of this function would have all points above the origin and all points would have positive y-values. Statement II is incorrect as x can take both negative and positive values.
Explanation:Considering the three statements given, only the statements I and III are true. This is because for the function y = x^2 + 2, all points on the graph are above the origin and all points on the graph have positive y-values.
Statement I is true because the function x^2 is non-negative for all values of x, which means that the minimum value of x^2 is 0. As a result, the minimum y−value for the function is 2 when x=0 and the lowest point on the graph is (0, 2), which is indeed above the origin.
Statement III is true because the lowest point on the graph is (0, 2) and since 2 is positive all other points have a y−value that is greater than 2 and therefore must be positive. Statement II is not true as x can take both negative and positive values in the function y=x^2+2.
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How many different pairs of numbers with a difference of 12
A cafe only sells two types of sandwiches, turkey, and steak. The cafe charges $4 for turkey sandwiches and $6 for steak sandwiches. Last month, the cafe sold $4524 worth of sandwiches. The cafe sold a total of 925 sandwiches.
How many turkey sandwiches did they sell?
Answer:
They sold 513 turkey sandwiches.
Step-by-step explanation:
Let t be the number of turkey sandwiches and s be the number of steak sandwiches.
With these variables, we can create equations for the totals they've given us:
Total sandwiches = [tex]t+s=925[/tex]
Total income = [tex]4t+6s=4524[/tex]
Now we can solve the system for the number of turkey sandwiches and steak sandwiches
Isolate t for [tex]t+s=925[/tex] => [tex]t=925-s[/tex]Substitute [tex]t=925-s[/tex] into [tex]4t+6s=4524[/tex][tex]4\left(925-s\right)+6s=4524[/tex]
Solve for s[tex]3700-4s+6s=4524\\3700+2s=4524\\3700+2s-3700=4524-3700\\2s=824\\\frac{2s}{2}=\frac{824}{2}\\s=412[/tex]
For [tex]t=925-s[/tex] substitute s = 412[tex]t=925-412\\t=513[/tex]
They sold 513 turkey sandwiches and 412 steak sandwiches.
An interior angle and an exterior angle are adjacent. The interior angle measures 84°. What is the measure of the exterior angle?
The measure of the exterior angle is
What is Exterior Angle?External angles are those that run parallel to a polygon's inner angles but are located outside of it. The sum of the two internal opposed angles determines the size of an outside angle.
We have,
The interior angle measures 84°.
We know that
Exterior angle + interior angle = 180
Exterior angle = 180 - Interior angle
Exterior angle = 180 - 84
Exterior angle = 96
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how to solve an equation for x with natural log of x
A logarithmic equation involving natural logarithms can be solve by taking the exponent of both sides
How to solve a natural logarithmic equation for x
To solve an equation involving the natural logarithm of x, you generally follow these steps:
Isolate the natural logarithm termExponentiate both sidesSolve for x: After removing the natural logarithm, solve the resulting equation for x.Take for instance, the equation is of the form
2 + ln(x) = 7
Isolate the natural logarithm
ln(x) = 5
Take the exponent of both sides
So, we have
[tex]x = e^5[/tex]
Evaluate the exponent
x = 148.41
Hence, the logarithmic equation solved for x is x = 148.41
Jason bought 5 movie tickets and a bag of popcorn Jeremy bought 2 movie tickets they spent 54$ total. If the popcorn cost 5$, how much did each movie ticket cost?
What is the interquartile range of 4 5 7 9 10 14 16 24
Answer:
The answer is 9
Step-by-step explanation: ? i did the the tetst or whatever and 9 is the correct answer.
YOUR WELCOME :}
x+29=−11
what does X equal
When hired at a new job selling jewelry, you are given two pay options:
Option A: Base salary of $16,000 a year, with a commission of 7% of your sales
Option B: Base salary of $25,000 a year, with a commission of 2% of your sales
In order for option A to produce a larger income, you would need sell at least $_______ of jewelry each year
You are required to sell a minimum of 180,001 of jewelry each year.
Given that,
The base salary is $16,000 per year and there is a 7% commission on sales for option A. The base salary is $25,000 per year and there is a 2% commission on sales for option B.Also, let us assume the sales be xBased on the above information, the following expression should be made:
16,000 + 0.07x > 25,000 + 0.02x
0.07x - 0.02x > 25,000 - 16,000
0.05x > 9000
x > 9000 ÷ 0.05
x > 180,000
Therefore we can conclude that you are required to sell a minimum of 180,001 of jewelry each year.
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Which of the following is a sample of the population of bookstores on the West Coast of the United States? I. All book stores in California II. Randomly selected children's book stores III. Internet book stores A. I only B. II only C. I and III D. III only E. I and II
Answer:
It would be I - All bookstores in California
Step-by-step explanation:
Internet book stores and random children's bookstores do not specify that they're on the West Coast and could be taken from anywhere
Determine whether the fractions -4/5, -4/6, -4/7, and -4/8 are arranged in order from least to greatest. explain
The median for the given set of 6 ordered data values is 32.5.
9, 12, 25, _, 41, 48
What is the missing value?
Suppose a parabola has a vertex (5,-3) and also passes through (6,1). Write the equation of the parabola in vertex form
The equation of the parabola with vertex (5, -3) and passing through (6, 1) in vertex form is y = [tex]4(x - 5)^2 - 3.[/tex]
To write the equation of a parabola in vertex form, we use the formula:
y = [tex]a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola. Given the vertex (5, -3) and a point (6, 1) the parabola passes through, we can plug these values into the equation to find a.
For the point (6, 1):
[tex]1 = a(6 - 5)^2 - 3[/tex]
[tex]1 = a(1)^2 - 3[/tex]
4 = a
So, the equation of the parabola in vertex form is:
y = [tex]4(x - 5)^2 - 3[/tex]
How to find the derivative of functions: y=(5x+7)(x+5)^3
A rectangular floor is 24 feet long and 9 feet wide. What is the area of the floor in square yards?