Final answer:
The range of a relation is the set of all possible y-values. For the given table, the range is -3, 0, 1, 2, and 3, which corresponds to answer D.
Explanation:
You're asking to identify the set of numbers that makes up the range in the given relation. The range of a relation refers to all the possible values of y that you can get when you input various values of x. For your table, the y-values are -3, 0, 1, 2, and 3. So, the range is the set of these y-values. Therefore, the correct answer is D. -3, 0, 1, 2, 3.
In general, to find the range, you look at all the second numbers in the ordered pairs of a relation or function. When plotted on a graph, this shows the dependence of y on x.
Four hot air balloons each descend 295 feet per minute for 7 minutes. Find the total change in altitude for all 4 balloons.
The total change in altitude for all 4 balloons is
nothing feet.
Answer:
"total change in altitude for all 4 balloons is 8260 feet"
Step-by-step explanation:
295 feet per minute, so in 7 minutes:
Descend (for 7 minutes) = 295 * 7 = 2065 feet
This is for a single balloon.
So for 4 balloons, this would be:
2065 * 4 = 8260 feet in total
So, total change in altitude for all 4 balloons is 8260 feet
13 feet in 5 steps unit rate
2.6 feet per step is the answer
y = (x + 3)^2 -4 and identify the axis of symmetry
Answer:
Step-by-step explanation:
the line for equation : x = - 3
simplify the given expression
expression:1
9(2+ 7f)
expression:2
6•7-3^2•9+4^3
show your work
Answer:
Expression: 1 ⇒ 18 + 63 f
Expression: 2 ⇒ 25
Step-by-step explanation:
* Lets revise at first the order of operations
- The order of these operations is:
# Parenthesis
# Exponents
# Multiplication and Division which comes first from left to right
# Addition and Subtraction which comes first from left to right
- There is a word made from the first letter of each operation
PEMDAS to remember the order of operations
* Lets solve the problem
# Expression: 1
∵ 9(2 + 7 f)
- To simplify this expression multiply the bracket by 9
∵ 9(2 + 7 f) = 9 × 2 + 7 f × 9
∵ 9 × 2 = 18
∵ 7 f × 9 = 63 f
∴ 9(2 + 7 f) = 18 + 63 f
* Expression: 1 ⇒ 18 + 63 f
# Expression: 2
∵ 6 × 7 - 3² × 9 + 4³
- At first simplify exponent
∵ 3² = 9 and 4³ = 64
∴ 6 × 7 - 3² × 9 + 4³ = 6 × 7 - 9 × 9 + 64
- Solve the multiplication first
∵ 6 × 7 = 42
∵ 9 × 9 = 81
∴ 6 × 7 - 3² × 9 + 4³ = 42 - 81 + 64
- Solve 42 - 81 first because it comes first from left to right
∵ 42 - 81 = - 39
∴ 6 × 7 - 3² × 9 + 4³ = - 39 + 64
- Add them
∵ - 39 + 64 = 25
∴ 6 × 7 - 3² × 9 + 4³ = 25
* Expression: 2 ⇒ 25
A set of bivariate data was used to create a least squares regression line. Which of the following is minimized by the line
A) the sum of the residuals
B) the sum of the squared residuals
C) the sum of the absolute value of the residuals
D) the influence of outliers
E) the slope
Answer:
B) The sum of the squared residuals
Step-by-step explanation:
Least Square Regression Line is drawn through a bivariate data(Data in two variables) plotted on a graph to explain the relation between the explanatory variable(x) and the response variable(y).
Not all the points will lie on the Least Square Regression Line in all cases. Some points will be above line and some points will be below the line. The vertical distance between the points and the line is known as residual. Since, some points are above the line and some are below, the sum of residuals is always zero for a Least Square Regression Line.
Since, we want to minimize the overall error(residual) so that our line is as close to the points as possible, considering the sum of residuals wont be helpful as it will always be zero. So we square the residuals first and them sum them. This always gives a positive value. The Least Square Regression Line minimizes this sum of residuals and the result is a line of Best Fit for the bivariate data.
Therefore, option B gives the correct answer.
The only correct option that is minimized by the least squares regression line is;
Option B; the sum of the squared residuals.
We want to find the correct option that minimizes the line. Let's look at the options ;
Option A; This statement is not correct because If you do a summation of the residuals, you would get a value of 0.
Option B; Since error needs to be minimized so that the line is a close to the points as possible and as seen above that the sum of the residuals is zero. Then before we sum them, we need to first of all square the residuals which will always give a positive value. Thus, since the Least Square Regression Line minimizes the sum of residuals, then this option is correct.
Option C; This option is wrong because the sum of the absolute values of the residuals is not a method for in creation of least squares regression line
Option D; This option is wrong because the influence of outliers has nothing to do with the topic in question.
Option E; This option is wrong too because slope has nothing to do with the topic in question.
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what is the point slope form of a line with slope 3 that contains the point (2, 1)
Answer:
y - 1 = 3(x - 2)
y - 1 = 3x - 6
y = 3x - 5
Answer:
The point slope form of the line is y-1=3(x-2).
Step-by-step explanation:
If a line passes through a points [tex](x_1,y_1)[/tex] with slope m, then the point slope form of the line is
[tex]y-y_1=m(x-x_1)[/tex] .... (1)
where, m is slope.
It is given that the slope of a line is 3 and it passes through the point (2,1).
Substitute m=3, [tex]x_1=2\text{ and } y_1=1[/tex] in equation (1), to find the point slope form of the line.
[tex]y-(1)=(3)(x-(2))[/tex]
[tex]y-1=3(x-2)[/tex]
Therefore the point slope form of the line is y-1=3(x-2).
Write an equation of the line passing through each of the following pairs of points. a (−10, 4), (2, −5)
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 10, 4) and (x₂, y₂ ) = (2, - 5)
m = [tex]\frac{-5-4}{2+10}[/tex] = [tex]\frac{-9}{12}[/tex] = - [tex]\frac{3}{4}[/tex], thus
y = - [tex]\frac{3}{4}[/tex] x + c ← is the partial equation of the line
To find c substitute either of the 2 given points into the partial equation
Using (2, - 5), then
- 5 = - [tex]\frac{3}{2}[/tex] + c ⇒ c = - 5 + [tex]\frac{3}{2}[/tex] = - [tex]\frac{7}{2}[/tex]
y = - [tex]\frac{3}{4}[/tex] x - [tex]\frac{7}{2}[/tex] ← equation of line
3. Noah is helping to collect the entry fees at his school's sports game. Student entry
costs $2.75 each and adult entry costs $5.25 each. At the end of the game, Diego
collected $281.25.
Select all equations that could represent the relationship between the number of
students, s, the number of adults, a, and the dollar amount received at the game.
A. 281.25 – 5.25a = 2.75s
B. a = 53.57 - 13:25
C. 281.25 -5.25s = a
D. 281.25 +2.75a = s
E. 281.25 +5.25s = a
281.25-5.25a=2.75
step by step:
so you divide the total amount by two and you get 140.62
then you divide that by 5.25 and you get 26.78
plug that into a and you get 140.62
then you take the remainder which is 140.62 and you divide that by 2.75
which is 51.13 and that will be your number for s
and at the end you should get the remainder of 140.62
then you multiply 140.62 by 2 and you get were you started and thats how you check your answer
Select all equations that could represent the relationship between the number of
number ofstudents, s, the number of adults, a, and the dollar amount received at the game.
The equations that could represent the relationship between the number of students, s, the number of adults, a, and the dollar amount received at the game is 281.25 – 5.25a = 2.75s
let
student fee = $2.75
Adult fee = $5.25
Total income = $281.25
Number of students = s
Number of adults = a
The equation:
Total income = (student fee × Number of students) + (Adult fee × Number of adults)
281.25 = (2.75 × s) + (5.25 × a)281.25 = 2.75s + 5.25a281.25 - 5.25a = 2.75sA. 281.25 – 5.25a = 2.75s
True
B. a = 53.57 - 13:25
Not true
C. 281.25 -5.25s = a
Not true
D. 281.25 +2.75a = s
Not true
E. 281.25 +5.25s = a
Not true
Therefore, the equations that could represent the relationship between the number of students, s, the number of adults, a, and the dollar amount received at the game is 281.25 – 5.25a = 2.75s
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Between 10 pm and 7:45 am the water level in a swimming pool decreased by 13/16 inch. Assuming the constant rate how much did it drop each hour
Answer:
[tex]\frac{1}{12} [/tex] inches per hour .
Step-by-step explanation:
Between 10 pm and 7:45 am there are 9 hours and 45 minutes i.e. [tex]9+\frac{45}{60} =\frac{39}{4}[/tex] hours
The water level in a swimming pool decreased by amount in [tex]\frac{39}{4}[/tex] hours = [tex]\frac{13}{16}[/tex] inches
The water level in a swimming pool decreased by amount in 1 hour:
= [tex]\frac{\frac{13}{16}}{\frac{39}{4}}[/tex] inches
= [tex]\frac{13}{16} \times \frac{4}{39}[/tex] inches
= [tex]\frac{1}{4} \times \frac{1}{3}[/tex] inches
= [tex]\frac{1}{12} [/tex] inches
Hence it drop by [tex]\frac{1}{12} [/tex] inches each hour .
How much did it drop each hour is 0.08333 inches/hour
First step is to calculate the Decrease
Decrease = 13/16 inches
Decrease=0.8125 inches
Second step is to calculate the time interval
From 10 pm to 7:45 hours will be 9.45 hours
Time interval= (9 + 45/60) hours
Time interval=9.75 hours
Now let determine How much did it drop each hour
0.8125/9.75 inches/hour
=0.08333 inches/hour
Inconclusion How much did it drop each hour is 0.08333 inches/hour
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f(x) = 10x – 4
What is the inverse for this?
Answer:
Step-by-step explanation:
f(x) = 10x – 4
10x = f(x)+4
x = f(x)/10 + 2/5
the inverse is y = x/10 + 2/5
Saleem says 45 × 32 is the same as (45 × 3) + (45 × 2). Explain Saleem’s error using words, numbers, and/or pictures.
Answer:
[tex]45\times 32 \neq (45\times 3) + (45\times 2)[/tex]
Step-by-step explanation:
First we will evaluate the value of the expressions.
[tex]45\times 32 = 1440[/tex]
[tex](45\times 3) + (45\times 2) = 225[/tex]
Hence, Saleem made an error in the evaluation of product of 45 and 32.
Saleem did a mistake in placing the values that is in 32, 3 is at ten's place so he should have multiplied 45 by 30 instead of 3.
The product can be evaluated in a correct manner as:
[tex](45\times 30) + (45\times 2) = 1350 + 90 = 1440[/tex]
6.
Tickets to a basketball game cost $1.50
o a basketball game cost $1.50 for students and $3.25 for adults. The
school made $752.25 and sold 358 tickets. How many student and how many
adult tickets were sold?
Answer: Adult tickets = 123
Student tickets = 235
Step-by-step explanation:
Let x represent the number of adult tickets sold and
let y represent the number of student tickets sold
Then create two equations: Quantity & Cost
Cost: 3.25x + 1.50y = 752.25
Qty: x + y = 358
I am going to solve the system using the substitution method.
You can also solve using the elimination method.
Since x + y = 358
then y = 358 - x
Substitute y in the Cost equation with 358 - x and solve for x
3.25x + 1.50(358 - x) = 752.25
3.25x + 537 - 1.50x = 752.25
1.75x + 537 = 752.25
1.75x = 215.25
x = 123
Now substitute x with 123 into the Quantity equation to solve for y
x + y = 358
123 + y = 358
y = 235
For the function f(x) = 6x - 8, identify the values of f(o), f(1/2), and f(-2).
O 8; -5; 4
O -8; -11; -20
O 8; -11; 4
© -8; 15; -20
Answer:
-8, -5, -20.
Step-by-step explanation:
f(0) = 6(0) - 8 = -8
f(1/2) = 6(1/2) - 8 = -5
f(-2) = 6(-2) - 8 = -20.
[tex]\text{Hello there!}\\\\\text{You're plugging in the values 0, 0.5, and -2 to x}\\\\\text{Plug them into the equation:}\,\,f(x) = 6x - 8\\\\\text{Solve:}\\\\f(x) = 6(0) - 8\\\\\boxed{f(x)=-8}\\\\f(x) = 6(0.5) - 8\\\\f(x) = 3 - 8\\\\\boxed{f(x)=-5}\\\\f(x) = 6(-2) - 8\\\\f(x)=-12-8\\\\\boxed{f(x)=-20}\\\\\text{Those three solutions will be your answer}\\\\\large\boxed{\text{Answer:}\,\,-8;-5;-20}[/tex]
Write an equation that can be used to find the area of any 10 square floor tiles
Write the equation of the line with the given slope and y-intercept. Undefined slope, (0,-6)
Answer:
y = -6
Step-by-step explanation:
The y intercept is when x equals 0 , and as you can see in the coordinate, the x is zero so the y is -6. Since the slope is undefined, the answer is y=-6. I know that seems confusing, but when the slope is undefined, it just means that it is a straight line.
4y + 9 = - 4y - 7. Please explain to me how to do it.
You want to keep the variable on the left and number on right.
So, we need to get rid of 9 and -4y. Let's start with 9.
4y+9=-4y-7
Subtract nine from both sides.
4y=-4y-16
Now add 4y on both sides.
8y=-16
Finally, divide both sides by 8 to get y=-?.
8y/8=-16/8
Therefore, the answer is y=-2.
solve the equation. -x/3=27
Answer:
x=-81
Step-by-step explanation:
Multiply both sides of the equation by 3 to eliminate the fraction on the left side.
[tex]-x/3(3)=27(3)[/tex]
[tex]-x=81[/tex]
Divide both sides by -1 to isolate x on the left side of the equation
[tex]-x/-1=81/-1\\x=-81\\[/tex]
Answer:
x = - 81.
Step-by-step explanation:
Given : [tex]\frac{-x}{3} = 27[/tex].
To find : solve the equation.
Solution: We have given
[tex]\frac{-x}{3} = 27[/tex].
On multiplying both sides by 3
-x = 27*3.
On dividing both sides by -1.
x = - 81.
Therefore, x = - 81.
Peter has been saving his loose change for several days. When he counted his quarters and dimes, he found they had a total value of $13.10. The number of quarters was 15 more than 3 times the number of dimes. How many quarters and how many dimes did Peter have?
it wont give me the answer.. i have to pay for it, and my homework is due in 3 hours...HELP?
Answer: Dimes: 11
Quarters: 48
Step-by-step explanation:
48/4= 12.00
11•0.10= 1.10
12+1.10= 13.10
what is the gcf of 25 and 14
Find the sum or difference in simplest form 1 3/7 + 10 6/7
Answer:
[tex]12\frac{2}{7}[/tex]
Step-by-step explanation:
we have
[tex]1\frac{3}{7} +10\frac{6}{7}[/tex]
step 1
Convert mixed number to an improper fraction
[tex]1\frac{3}{7}=\frac{1*7+3}{7}=\frac{10}{7}[/tex]
[tex]10\frac{6}{7}=\frac{10*7+6}{7}=\frac{76}{7}[/tex]
step 2
Substitute in the expression above and find the sum
[tex]\frac{10}{7}+\frac{76}{7}=\frac{86}{7}[/tex]
Convert to mixed number
[tex]\frac{86}{7}=\frac{84}{7}+\frac{2}{7}=12\frac{2}{7}[/tex]
What is the degree of the polynomial 5a^6bc^2+8d^5+7e^6f^2-10g^4h^7
Final answer:
The degree of the polynomial 5a⁶bc²+8d⁵+7e⁶f²-10g⁴h⁷ is 11, determined by the highest sum of exponents in any term of the polynomial, which is found in the term -10g⁴h⁷.
Explanation:
The degree of a polynomial is the highest exponent of its variables when it is expressed in standard form. To find the degree of the given polynomial 5a⁶bc²+8d⁵+7e⁶f²-10g⁴h⁷, we look at each term individually and sum the exponents of the variables within that term. The terms of the polynomial are:
5a⁶bc² with a degree of 6 + 1 + 2 = 9
8d⁵ with a degree of 5
7e⁶f² with a degree of 6 + 2 = 8
-10g⁴h⁷ with a degree of 4 + 7 = 11
Comparing the sums of the exponents, we see that the term -10g⁴h⁷ has the highest sum which is 11. Therefore, the degree of the given polynomial is 11.
The diameter of a circle is 5 kilometers. What is the area?
Answer:
[tex]\large\boxed{A=6.25\pi\ km^2\approx19.625\ km^2}[/tex]
Step-by-step explanation:
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
We have the length of a diameter d = 5 km
We know: d = 2r. Therefor r = 5km : 2 = 2.5 km.
Substitute:
[tex]A=\pi(2.5)^2=6.25\pi\ km^2[/tex]
If you want an approximation, then
[tex]\pi\approx3.14\to A\approx(6.25)(3.14)=19.625\ km^2[/tex]
Hey!
-----------------------------
Formula: A = πr²
Diameter: d / 2 = r
-----------------------------
Solution:
A = (3.14)(2.5)²
A = (3.14)(6.25)
A = 19.625km.
-----------------------------
Answer:
The area of the circle is 19.625km. or 6.25π km.
-----------------------------
Hope This Helped! Good Luck!
A 5-pound bag of apples costs $3.50. Use this rate to complete the table to identify equivalent ratios, then answer the questions. Pounds 5 15 Cost ($) 0.70 3.50 7 Apples cost $ per pound.
Are my answers correct?
Answer:
1lb to $0.70, 5lb to $3.50, 10lb to $7, 15lb to $10.50
Step-by-step explanation:
Turn your ratios into fractions and place them near each other. you multiply across then divide with the remaining number.
inverse of y= x-6/x+5
as you would already know, we start off to gettting any inverse of any expression by doing a quick switcheroo on the variables and then we solve for "y".
[tex]\bf y = \cfrac{x-6}{x+5}\implies \stackrel{\textit{quick switcheroo}}{x = \cfrac{y-6}{y+5}}\implies x(y+5)=y-6\implies xy+5x=y-6 \\\\\\ xy+5x+6=y\implies 5x+6=y-xy\implies 5x+6=\stackrel{\textit{common factor}}{y(1-x)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{5x+6}{1-x}=\stackrel{f^{-1}(x)}{y}~\hfill[/tex]
Which is bigger 0.305 or 0.350
Answer:
0.350 is bigger
Step-by-step explanation:
Answer:
0.305
Step-by-step explanation:
When working with decimals, it would be the smaller number that is bigger. .305 is bigger because .305 is 305 points away from 0 and .350 is 350 points away from 0!!
Hope this helps!!!
-Unicorns110504
Starting from the same place, Karina walks due west and Lucas walks due east. On the number line, 0 represents their starting point, negative values represent the distance traveled west and positive values represent the distance traveled east. All values are given in feet. How many feet apart are Karina and Lucas on the number line? Enter your answer in the box.
Answer:
The answer is 480
Step-by-step explanation:
When F(x)=-3 What is X
175,000
In Scientific notation
Answer:
1.75*10 to the power of 5
Step-by-step explanation:
start by moving the decimal over until only one number is in front of the decimal. this is because in scientific notation a number can't be higher than 9.
check how many places you move the decimal over (5). 1.75000 needs to be simplified (since that's the point of scientific notation) and can be simplified to 1.75.
the answer is 1.75 multiplied by ten to the power of digits the decimal moved (5) so the answer is 1.75*10 to the power of 5
175,000 in scientific notation is 1.75 × [tex]10^5[/tex].
To express the number 175,000 in scientific notation, follow these steps:
Move the decimal point in the number to the position after the first non-zero digit. For 175,000, this is 1.75.
Count the number of places the decimal point has moved to determine the exponent of 10. In this case, the decimal point moves 5 places to the left.
Combine the number obtained in the first step with the power of 10 determined in the second step. Thus, 175,000 in scientific notation is 1.75 × [tex]10^5[/tex].
This provides a concise representation of the number.
given: f(x)=3 - x; g(x) = -2x find f[g(2)]
Answer:
7
Step-by-step explanation:
To calculate f(g(2)) evaluate g(2) then evaluate f(x) for this value
g(2) = - 2(2) = - 4, then
f(- 4) = 3 - (- 4) = 3 + 4 = 7
If two planes are perpendicular to the same line, then
•
.
•
•
A. they form a straight line
B. they are perpendicular to each other
C. they are parallel
D. not enough information
Answer:
option c) they are parallel !!
Step-by-step explanation:
If two lines are perpendicular to the same line that is they both make 90° with the same line have difference in their angle 0° with respect to the same line , and line having difference in their angle as 0° are parallel to each other !