Answers
a. The table for the relation is given by the image shown at the end of the answer.
b. The domain and range of the relation are given as follows:
Domain: {0, 1, 2, 3, 4, ...}.Range: {0, 0.75, 1.5, 2.25, ...}.c. The relation is a function, as it value of the input is mapped to a single value of the output.
How to represent the situation?The ratio between the total cost and the number of vehicles is obtained as follows:
k = 3.75/5 = 3/4 = ... = 0.75/1 = 0.75.
Meaning that the situation is modeled by a proportional relationship with a constant of 0.75, and the function is given as follows:
y = 0.75x.
For which:
x is the number of cars.y is the total cost.The domain and range are given as follows:
Domain: {0, 1, 2, 3, 4, ...}. -> possible amounts of cars.Range: {0, 0.75, 1.5, 2.25, ...}. -> possible prices.More can be learned about proportional relationships at https://brainly.com/question/10424180
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Related Questions
In triangle ABC, the measurement of angle A is is greater then the measurement of angle C, then BC> AC is this conditional true? If so, why?
Answers
Using the law of sines, it cannot be affirmed whether the conditional is true or false, as we have no information about the measure of angle B.
What is the law of sines?We suppose a general triangle, for which:
Side with a length of a is opposite to angle of measure A.Side with a length of b is opposite to angle of measure B.Side with a length of c is opposite to angle of measure C.The lengths and the sine of the angles are proportionally related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
The segments in this problem are given as follows:
BC opposite to angle A.AB opposite to angle C.Hence it can be affirmed that:
BC > AB.
As the measure of angle A is greater than the measure of angle C, hence sin(A) > sin(C) and BC > AB, using the proportional relationship.
As for segment AC, we need the measure of angle B, hence nothing can be affirmed.
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What is the probability of tossing a coin and getting heads three times in a row?
What is the chance that the next toss will be heads? What is the chance that the next toss will be tails?
Answers
The probability of tossing 3 heads in a row is P = 0.125, and after that, because the events are independent, the probability of getting heads (or tails) still is p = 0.5
How to find the probability?Assuming that we have a fair coin, we assume that both outcomes have the same probability, so:
P(tails) = 0.5
P(heads) = 0.5
Then the probability of getting heads 3 times in a row, is the product of the probability of getting heads 3 times, this will be:
P(3 heads) = 0.5*0.5*0.5
P(3 heads) = 0.5^3
P(3 heads) = 0.125
Now, after this point, what is the probability of getting heads or tails?
Remember that each toss of the coin is independent of the previous one, so the probability of getting tails still is 0,5, and the same for the probability of getting heads.
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the ratio of boys to girls in the sixth grade is 3 to 5 if there are 45 girls how many students are there in the 6th grade
Answers
Answer: 27 boys
Step-by-step explanation:
There is a rule in math, what you do to one side, you do to the other.
So in this case the ration is 3:5
?:45
As you can see, they multiplied 5 by 9 to get 45, remember the rule, so we do the same.
3 times 9 is 27, so 27 boys
please answer quickly :)
Answers
Answer:
The solution is (-1, 0)-----------------------------------
Given lines:
y = - 2x - 2 and y = x + 1Plot both of the lines using the graphing calculator by adding the equations, then find the graphical solution as the intersection of the lines.
See attached.
The solution is (-1, 0).
(30 points easy) write the equation of side B seat inside AC to determine if the three points could form a right triangle
write the equation of the line for side B C, and side AC, If the points were connected, could this be a right triangle explain why
(use the graph in the photo)
Answers
Answer:
Side BC: y = -2x + 10
Side AC: y = 2x + 4
Yes, these three points could form a right triangle. This is because the slopes of the two lines, Side BC and Side AC, are opposite reciprocals of each other. This means that when the two lines intersect, they will form a right angle.
What is 20% of 80 plus 15% of 30?
Answers
20% of 80 is 16 and 15% of 30 is 4.5, so the sum is 16 + 4.5 = 20.5.
За – 29 = 3(a – 3).
Answers
Answer:
No Solutions
Step-by-step explanation:
Hello!
We can solve for a by isolating the variable.
Solve for a:Distribute: 3a - 29 = 3(a) - 3(3)Simplify: 3a - 29 = 3a - 9Subtract 3a from both sides: -29 = -9Since -29 cannot be equal to -9, there are no solutions for this equation.
A construction company is building a fence that is 1 1/3 miles long. They can building the fence 1/6 Mile every hr. How long to build the
Answers
The length of time to build the fence is 8 hours
How to determine the length of time to build the fenceFrom the question, we have the following parameters that can be used in our computation:
Length of the fence = 1 1/3 miles
Rate of building = 1/6 miles per hour
The length of time to build the fence is then calculated as
Length of time = Length of the fence/Rate of building
Substitute the known values in the above equation, so, we have the following representation
Length of time = (1 1/3 miles)/(1/6 miles per hour)
Evaluate the quotient
This gives
Length of time = 8 hours
Hence, the time taken is 8 hours
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Can someone help? I answered it, but I want second opinions.
Answers
Tim worked for a total of 7 and half hours on Monday and earned $56.25 gross pay.
What is gross pay and net pay?Prior to payroll deductions, earned wages are referred to as gross pay. Employers utilize this amount—$60,000 per year or $25 per hour—when talking to employees about pay. Additionally, the federal and state income tax brackets sometimes refer to gross salary.
The amount of pay that employees get after payroll deductions varies; some may be optional, while others may be required.
Given, On Monday of his time card Tim clocked in at 8:15 am and clocked out at 4:15 pm.
So, The total number of hours she worked is 8 hours, 8:15 to 12:15 is 4 hours, and another four hours.
Also given the time he took for lunch is half an hour.
Therefore, The total hour he worked is 7:30 hours.
He earns $7.5 per hour so his gross pay for Monday is $(7.5×7.5).
= $56.25.
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The distribution of the amount of money undergraduate students spends on books for a term is slightly right-skewed, with a mean of $400 and a standard deviation of S80. If a simple random sample of 100 undergraduate students is selected, what is the probability that these students spend, on average, more than $425 on books?
Answers
The probability that on average these students spend more than $425 on books is given as follows:
0.0009 = 0.09%.
How to obtain the probability using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 400, \sigma = 80, n = 100, s = \frac{80}{\sqrt{100}} = 8[/tex]
The desired probability is one subtracted by the p-value of Z when X = 425, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{425 - 400}{8}[/tex]
Z = 3.125.
Z = 3.125 has a p-value of 0.9991.
1 - 0.9991 = 0.0009 = 0.09%.
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4 times a number decreased by 2 is at most 10
Answers
The statement above can be written as
4n - 2 <= 10.
1. Add two on both sides
4n -2+2 <= 10-2
2. Simplify
4n <= 8
3. Divide by 4 on both sides
4n/4 <= 8/4
4. Simplify
N<= 2
How do I write an equation for this relationship (where y represents the number of blocks and x represents the stage number).
Answers
The equation of the line is y = 4x + 1 , where the slope of the line is m = 4
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the number of blocks be y
Let the stage number be x
Let the first point be represented as P = P ( 1 , 5 )
Let the second point be represented as Q = Q ( 2 , 9 )
Now , the slope of the line between the points be
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 9 - 5 ) / ( 2 - 1 )
Slope m = 4
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 5 = 4 ( x - 1 )
On simplifying the equation , we get
y - 5 = 4x - 4
Adding 5 on both sides of the equation , we get
y = 4x + 1
Therefore , the value of A is y = 4x + 1
Hence , the equation of line is y = 4x + 1
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The triangle flap of an envelope has two sides that are 6 centimeters long and meet at a right angle. How long is the envelope? Round to the 10ths if needed.
Answers
Answer:
Step-by-step explanation:
This is a right triangle that has two equal sides - so it is also isosceles.
It can be solved using Pythagoren Theorem.
a² + b² = c²
In this case a = b
so:
6² + 6² = c²
36 + 36 = c²
72 = c²
[tex]\sqrt{72[/tex] = [tex]\sqrt{c^{2} }[/tex]
8.49 = c
round to 8.5
This is the length of the flap.
Mental Math In a toy store, the ratio of the number of dolls to the number of teddy bears is . If the store has 240 dolls, how many teddy bears are in the store? Use pencil and paper. Describe the mental math steps you use to solve this problem.
Answers
Answer:
Step-by-step explanation:
Dolls:240 Teddy Bears:120
120:240
Please Describe the fraction If Possible.
its 9/16 close to 0, 1/2 or 1 explain
Answers
Answer: It's closer to 1/2
Step-by-step explanation: It's closer to 1/2 and here's why:
So, 1/2 (exact) is 8/16
0 = 0
1 = 16/16
Since 9/16 is the closest to 8/16 or around 1/2 in this case, it'd be about 1/2. I hope this helps!
156x2.2=?????Help fast
Answers
Answer:
343.2
Step-by-step explanation:
156 × 2.2
= (156 × 22)/10
= 3432/10
= 343.2
Victoria needs to earn at least an 85 in College Algebra. Only exam scores are used to calculate her grade. Currently she has scored an 82, 81, and 90 this semester. All that remains is the semester exam, which counts twice (counts as two exam grades). She hopes to make an 85 or higher in the class.
Answers
She would need to make two extra grades of 86 each.
What is the average?Here we can see that the average of the scores that Victoria would need to make is an average score of 85 so as to be able to pull through. In this case, we can see that we have the scores; 82, 81, and 90
Let the scores tat we have to count twice be p each and then we have;
85 = 82 + 81 + 90 + p + p/5
85 = 253 + 2p/5
5(85) = 253 + 2p
p = 5(85) - 253/2
p = 86
Hence, the twice scores that need to be earned for Victoria are both 86.
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Sound waves can be ranked by their intensity, I, given in this formula, where r is the distance from the source of a sound with a power output of P.
[tex]P = 4xr^{2} .[/tex]
Which equation correctly rewrites the formula to solve for I?
A. [tex]I = \frac{P}{4xr^{2} }[/tex]
B. [tex]I = \frac{Pxr^{2} }{4}[/tex]
C. [tex]I = 4Pxr^{2}[/tex]
D. [tex]I = \frac{4P}{xr^{2} }[/tex]
Answers
Answer: C correctly rewrites the formula to solve I
Step-by-step explanation:
Which expression is equivalent to 3/2?
Answers
On solving the provided question we can say that expression which is equivalent form to 3/2 is (5/2-1).
What is Equivalent form ?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Equivalent systems refer to sets of equations with the same solution. We can create an analogous system from a system of two equations by replacing one equation with the total of the two equations or by replacing an equation with a multiple of itself.
When two expressions can be reduced to a single third expression or when one of the expressions can be expressed in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.
The number is 3/2
The expression which is equivalent to 3/2 is (5/2-1)
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y=x-4 and y=4x+2 graph solution of the systems
Answers
Answer:
(-2,-6)
Step-by-step explanation:
we can solve this system of equations with the substitution method because y is already by itself.
since they are both equal to y, we can set both equations equal to each other.
4x+2=x-4
subtract 2 from both sides
4x=x-6
subtract x from both sides
3x=-6
divide both sides by 3
x = -2
now that we know x, we can plug this value into one of the original equations and solve for y.
y=-2-4
y=-6
so on a graph, these two equations will intersect at the point (-2,-6)
An electronics company can spend no more than $4,000 on raw materials for circuit boards. The raw materials cost $10 per ounce for copper and $20 per ounce for silver.
To summarize the situation, a worker writes the inequality:
10c+20s≤4,000 where c is the number of ounces of copper material and s is the number of ounces of silver material.
Which graph's shaded region shows the possible combinations of raw materials the company can buy?
Answers
The given graph's shaded region shows the possible combinations of raw materials the company can buy.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
An electronics company can spend no more than $4,000 on raw materials for circuit boards.
And, The raw materials cost $10 per ounce for copper and $20 per ounce for silver.
Here, The inequality for the given condition is,
⇒ 10c + 20s ≤ 4,000
Where, c is the number of ounces of copper material and s is the number of ounces of silver material.
So, The given graph's shaded region shows the possible combinations of raw materials the company can buy.
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Which equation has two solutions? A. W=-1. B. W=1. C. W=-2. D. W=0
Answers
Answer: An equation has two solutions when it has two distinct values that can be assigned to the variable to make the equation true.
In this case
equation A. W=-1 is a single solution
equation B. W=1 is a single solution
equation C. W=-2 is a single solution
equation D. W=0 is a single solution
So none of the given equations have two solutions. they all have only one solution.
It's worth mentioning that, if the equation is a quadratic equation (in the form of ax² + bx + c = 0) and it has a non-zero discriminant (b² - 4ac) then the equation will have two distinct real solutions.
In this case the equations are not in that form, and also doesn't show any signs of having two solutions.
Step-by-step explanation:
The following is a list of books I read this summer what percent of my books were nonfiction nonfiction equals 8 fiction equals 17
Answers
Answer:
About 47% of books were nonfiction.
The actual percentage includes decimals and it would be this:
%47.0588235294
Find f(g(x)) f(x)= 2x^2-4x-6. G(x)= 2x+7
Answers
if functions f(x) = 2x²-4x-6 and g(x)= 2x+7 then f(g(x)) is 8(x+2)(x+4)
What is a function?A relation is a function if it has only One y-value for each x-value.
Given functions are f(x)= 2x²-4x-6
g(x)=2x+7
We need to find expression of f(g(x))
f(g(x))=f(2x+7)
Now replace x with 2x+7 in f(x)
f(2x+7)=2(2x+7)²-4(2x+7)-6
=2(4x²+49+28x)-8x-28-6
Apply distributive property
=8x²+98+56x-8x-28-6
Add the like terms
=8x²+48x+64
f(g(x))=8(x+2)(x+4)
Hence, if functions f(x) = 2x²-4x-6 and g(x)= 2x+7 then f(g(x)) is 8(x+2)(x+4)
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A new business borrows $320,000 at a yearly simple interest rate of 7%.
The total
amount the company repays for the loan and interest is $678,400. How long did it
take to pay off the loan? Pls help Mee!!
Answers
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 678400\\ P=\textit{original amount deposited}\dotfill & \$320000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years \end{cases} \\\\\\ 678400 = 320000[1+(0.07)(t)] \implies \cfrac{678400}{320000}=1+0.07t\implies \cfrac{53}{25}=1+0.07t \\\\\\ \cfrac{53}{25}-1=0.07t\implies \cfrac{28}{25}=0.07t\implies \cfrac{\frac{23}{25}}{0.07}=t\implies \boxed{16=t}[/tex]
Laura, Tom and Alex share £95 in the ratio 8:7:4 find how much money each of them will receive
Answers
Answer:
Laura: £40Tom: £35Alex: £20Step-by-step explanation:
You want the amount of money each receives if Laura, Tom, and Alex share £95 in the ratio 8:7:4.
Ratio unitsThe total number of ratio units is 8+7+4 = 19, corresponding to a total amount of £95. That makes each ratio unit represent £95/19 = £5.
Multiplying the ratio units by £5, we find the distribution to be ...
Laura : Tom : Alex = £40 : £35 : £20
Answer:
Money received by Laura = 8x = 8x5 = £40
Money received by Tom = 7x = 7x5 = £35
Money received by Alex = 4x = 4x5 = £20
Step-by-step explanation:
Given ,
Laura, Tom and Alex share £95 in the ratio 8:7:4To Find : How much money will each of them receive
Let us take the variable as 'x' to find the money received by them
When we convert it to a equation
8x+7x+4x = 95
19x = 95
x = [tex]\frac{95}{19}[/tex]
x = 5
Money received by Laura = 8x = 8x5 = £40
Money received by Tom = 7x = 7x5 = £35
Money received by Alex = 4x = 4x5 = £20
Hence, the money received by each of them is £40, £35 and £20
Which of the following lines is perpendicular to the line passing through the points (-3, 4) and (-5, 6)?
Answers
The equation of the perpendicular line will be x + y - 5 = 0. Then the correct option is B.
What is the equation of a perpendicular line?Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation of the line passing through (-5, 6) and (-6, 5) will be given as,
(y - 6) = [(5 - 6) / (- 6 + 5)](x + 5)
y - 6 = (x + 5)
y = x + 1
The equation of the line that is perpendicular to the above line is given as,
y = - x + c
The equation of the line is passing through (3, 2)
3 = - 2 + c
c = 5
Then the equation of the perpendicular line will be given as,
y = -x + 5
x + y - 5 = 0
The equation of the perpendicular line will be x + y - 5 = 0. Then the correct option is B.
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The complete question is given below.
Select the answer with the correct number of significant figures for each calculation. 31.580 + 4.26 = 35.8 35.84 35.840
Answers
Answer:
35.84
Step-by-step explanation:
slove system equations
x+y=8
x-y=4
x=? y=?
Answers
Answer:
Step-by-step explanation:
To solve this system of equations, you can use the substitution method.
In this method, you solve one of the equations for one of the variables in terms of the other variable. Then you substitute this expression into the other equation. This will give you a single equation in one variable, which you can solve to find the value of that variable. Finally, you can substitute this value back into one of the original equations to find the value of the other variable.
To solve this system using substitution, we can solve the second equation for y:
y = x - 4
Then, we substitute this expression for y in the first equation:
x + (x - 4) = 8
Combining like terms, we get:
2x - 4 = 8
Adding 4 to both sides, we get:
2x = 12
Dividing both sides by 2, we find that:
x = 6
Now we can substitute this value back into one of the original equations to find the value of y. Let's substitute it into the second equation:
x - y = 4
Substituting 6 for x, we get:
6 - y = 4
Subtracting 6 from both sides, we find that:
y = 2
So the solution to the system of equations is x = 6 and y = 2.
Answer:
x=6, y = 2
Step-by-step explanation:
If you add 2 expressions, 2x = 12, so x = 6.
So the other one y = 2.
The product of 12 and k is 84. Solve for k.
Answers
Answer:
the k is 7
Step-by-step explanation:
12×2=24
12×3=36
12×4=48
12×5=60
12×6=72
12×7=84
Answer:
k = 7
Step-by-step explanation:
The product of 12 and k is 84 [tex]\rightarrow 12k=84[/tex].
[tex]12k = 84 \\ k = \dfrac{84}{12} \\ \boxed{k = 7}[/tex]