If f(x) = 3x + 2, what is f(5)?
A. 10
B. 1
C. 13
D. 17
f(x) = 3x+2
f(5) = 3(5) +2 = 15 +2 =17
Answer is D. 17
I feel like this is wrong but help plz
Assume your favorite soccer team has 2 games left to finish the season. the outcome of each game can be win, lose or tie. the number of possible outcomes is
The number of possible outcomes for the two remaining games is 9.
Explanation:The number of possible outcomes for the two remaining games can be found by multiplying the number of outcomes for each game. Since each game can have three possible outcomes (win, lose, or tie), there are a total of 3 outcomes for each game. Therefore, the number of possible outcomes for the two games is 3 x 3 = 9.
Your friend has $80 when he goes to the fair. He spends $4 to enter the fair and $12 on food. Rides at the fair cost $1.25 per ride. Which function can be used to determine how much money he has left over after x rides? (1 point)
f(x) = 1.25x + 64
f(x) = −16x + $80
f(x) = −1.25x + 64
f(x) = −1.25x − 64
A function is a relationship between inputs where each input is related to exactly one output.
The function that is used to determine how much money he has left over after x rides is
f(x) = -1.25x + 64.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
f(x) = 2x + 2 is a function.
f(x) = 3x + 6 is a function.
We have,
Total amount = $80
Cost of entering the fair = $4
Cost on food = $12
Cost per ride = $1.25
The money left after x rides.
= 80 - (1.25x + 12 + 4)
= 80 - 1.25x - 12 - 4
= 80 - 1.25x - 16
= 64 - 1.25x
= -1.25 + 64
The function to determine money left can be represented as:
f(x) = -1.25x + 64
Thus,
The function that is used to determine how much money he has left over after x rides is
f(x) = -1.25x + 64.
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Based on a poll, 40% of adults believe in reincarnation. Assume that 77 adults are randomly selected, and find the indicated probability. Complete parts (a) through (d) below.
a. What is the probability that exactly 66 of the selected adults believe in reincarnation?
The probability that exactly 66 of the 77 adults believe in reincarnation is
nothing.
(Round to three decimal places as needed.)
b. What is the probability that all of the selected adults believe in reincarnation?
The probability that all of the selected adults believe in reincarnation is
nothing.
(Round to three decimal places as needed.)
c. What is the probability that at least 66 of the selected adults believe in reincarnation?
The probability that at least 66 of the selected adults believe in reincarnation is
nothing.
(Round to three decimal places as needed.)
d. If 77 adults are randomly selected, is 66 a significantly high number who believe in reincarnation?
A.
No, because the probability that 66 or more of the selected adults believe in reincarnation is less than 0.05.
B.
Yes, because the probability that 66 or more of the selected adults believe in reincarnation is greater than 0.05.
C.
Yes, because the probability that 66 or more of the selected adults believe in reincarnation is less than 0.05.
D.
No, because the probability that 66 or more of the selected adults believe in reincarnation is greater than 0.05
a. [tex]\( P(X = 66) \approx 0.014 \)[/tex]
b. [tex]\( P(X = 77) \approx 0 \)[/tex]
c. [tex]\( P(X \geq 66) \approx 0.015 \)[/tex]
d. Option C: Yes, 66 is significantly high; probability [tex]\( < 0.05 \).[/tex]
To solve this problem, we'll use the binomial probability formula:
[tex]\[ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1 - p)^{n - k} \][/tex]
Where:
[tex]- \( n \) is the number of trials (77 adults in this case)\\- \( k \) is the number of successes (the number of adults believing in reincarnation)\\- \( p \) is the probability of success (the proportion of adults believing in reincarnation, which is 0.40 in this case)\\- \( \binom{n}{k} \) is the binomial coefficient, which represents the number of ways to choose \( k \) successes out of \( n \) trials.[/tex]
Now let's calculate the probabilities:
a. Probability that exactly 66 of the selected adults believe in reincarnation:
[tex]\[ P(X = 66) = \binom{77}{66} \cdot (0.40)^{66} \cdot (1 - 0.40)^{77 - 66} \][/tex]
b. Probability that all of the selected adults believe in reincarnation:
[tex]\[ P(X = 77) = \binom{77}{77} \cdot (0.40)^{77} \cdot (1 - 0.40)^{77 - 77} \][/tex]
c. Probability that at least 66 of the selected adults believe in reincarnation:
This is the sum of probabilities from 66 to 77.
[tex]\[ P(X \geq 66) = \sum_{k=66}^{77} \binom{77}{k} \cdot (0.40)^{k} \cdot (1 - 0.40)^{77 - k} \][/tex]
Let's calculate these probabilities.
a. Probability that exactly 66 of the selected adults believe in reincarnation:
[tex]\[ P(X = 66) = \binom{77}{66} \cdot (0.40)^{66} \cdot (0.60)^{11} \]\[ = \frac{77!}{66!(77-66)!} \cdot (0.40)^{66} \cdot (0.60)^{11} \]\[ \approx 0.014 \][/tex]
b. Probability that all of the selected adults believe in reincarnation:
[tex]\[ P(X = 77) = \binom{77}{77} \cdot (0.40)^{77} \cdot (0.60)^{0} \]\[ = (0.40)^{77} \]\[ \approx 0 \][/tex]
c. Probability that at least 66 of the selected adults believe in reincarnation:
[tex]\[ P(X \geq 66) = \sum_{k=66}^{77} \binom{77}{k} \cdot (0.40)^{k} \cdot (0.60)^{77 - k} \]\[ \approx 0.015 \][/tex]
So, for the options:
d. If 77 adults are randomly selected, is 66 a significantly high number who believe in reincarnation?
C. Yes, because the probability that 66 or more of the selected adults believe in reincarnation is less than 0.05.
If f(x) = 2x + 8 and g(x) = x^4, what is (g ° f)(-3)?
(g *f)(x) = (2x+8)^4
replace x with -3
(2(-3)+4)^4 =
(-6+4)^4 =
= (-2)^4
= 16
Shane works at a computer store. If he earns 20.93 from a 7% commission on the scale of a printer what is the price of the printer
Orrin had $541.06 in his checking account, and a check that he wrote to his landlord for $560.00 was just deposit?
A.service fee
B.ATM fee
C. Overdraft fee
D. Overspending fee
If f(x) = x + 2, find the value of x if f(x) = 12.
PRE CALCULUS
HELP PLEASEEEEEEEEE
describe the transformations that produce the graph of g(x)=1/2(x-4)^3+5 from the graph of the parent function f(x)=x^3 give the order in which they must be preformed to obtain the correct graph
Solve for m and show your work. 4n=3m-1
Angle A and Angle B are a linear pair. If the measure of Angle A is 3x multiplied by Angle B, then find the measures of Angle A and Angle B.
By which rule are these triangles congruent? A) AAS B) ASA Eliminate C) SAS D) SSS
Answer:
D) SSSStep-by-step explanation:
In the given image you can observe two triangles with congruent sides,
[tex]PQ \cong SQ\\PN \cong SN\\QN \cong QN[/tex]
Notice that all three corresponding sides are congruent. That means,
[tex]\triangle PQN \cong \triangle SQN[/tex], by SSS postulate.
The SSS postulate states that if two triangles have all three corresponding sides congruent, then those triangles are congruent.
Therefore, the right answer is D) SSS.
Light travels 9.45 \cdot 10^{15}9.45⋅1015 9, point, 45, dot, 10, start superscript, 15, end superscript meters in a year. There are about 3.15 \cdot 10^73.15⋅107 3, point, 15, dot, 10, start superscript, 7, end superscript seconds in a year.How far does light travel per second?Write your answer in scientific notation.
Answer:
3 x 10^8
Step-by-step explanation:
I got it right on Kahn Academy :D
can anyone help me with this questions?
Which of the following could be the number of real roots, including any repeated roots, of a quadratic polynomial with real coefficients? Select all possible answers.
0
4
5
6
A quadratic polynomial can have 0, 1, or 2 real roots, including repeated roots. The roots are determined by the discriminant. Numbers 4, 5, or 6 are not possible numbers of real roots for a quadratic polynomial.
Explanation:In Mathematics, specifically in Algebra, a quadratic polynomial with real coefficients can have either 0, 1, or 2 real roots, including any repeated roots. The number of roots is determined by the discriminant (the value under the square root in the quadratic formula). If the discriminant is greater than 0, the quadratic has 2 real roots. If it equals 0, there is 1 real root (a repeated root), and if it is less than 0, there are no real roots (there are 2 complex roots instead). Consequently, the possible number of real roots for a quadratic polynomial is not 4, 5, or 6.
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A quadratic polynomial with real coefficients can have 0, 1, or 2 real roots. Only '0 real roots' is a valid choice. This is determined based on the discriminant of the quadratic equation.
A quadratic polynomial with real coefficients is of the form [tex]\( ax^2 + bx + c = 0 \)[/tex], where ( a, b, ) and ( c ) are real numbers.
The number of real roots of a quadratic polynomial can be determined by its discriminant, [tex]\( \Delta = b^2 - 4ac \)[/tex]:
1. If [tex]\( \Delta[/tex] > 0, the polynomial has two distinct real roots.
2. If [tex]\( \Delta[/tex] = 0, the polynomial has one real root (a repeated root).
3. If [tex]\( \Delta[/tex] < 0, the polynomial has no real roots (it has two complex conjugate roots).
Based on this, the possible number of real roots, including repeated roots, for a quadratic polynomial with real coefficients are:
- ( 0 ) (when the discriminant is negative, there are no real roots)
- ( 1 ) (when the discriminant is zero, there is one repeated real root)
- ( 2 ) (when the discriminant is positive, there are two distinct real roots)
Given the options:
- 0
- 4
- 5
- 6
The only valid number of real roots for a quadratic polynomial with real coefficients from the provided options is: 0
How does the graph of g(x)=⌊x⌋−3 differ from the graph of f(x)=⌊x⌋?
Final answer:
The graph of g(x)=⌊x⌋-3 is the same as the graph of f(x)=⌊x⌋ but shifted downward by 3 units because of the subtraction of 3, resulting in each step being 3 units lower.
Explanation:
The student has asked how the graph of g(x)=⌊x⌋-3 differs from the graph of f(x)=⌊x⌋. The function ⌊x⌋ represents the greatest integer function or floor function, which maps a real number to the largest integer less than or equal to it. The graph of f(x) is a step function that jumps up by 1 at each integer value of x. The graph of g(x) will be exactly the same as f(x) but will be shifted downward by 3 units due to the -3 in the function. This means that each step on the graph of g(x) will occur at an integer value of y that is 3 less than the corresponding step on the graph of f(x). For example, where f(x) has a step at y=0, g(x) will have a step at y=-3.
1. Which procedure could be used to graph the line represented by the following equation? Y=1/2x+3
A. Plot the x-intercept (3,0) and use the slope of 1/2 to find a second point.
B. Plot the Y-intercept (0,3) and use the slope of 1/2 to find a second point
C. Plot the X-intercept (1/2,0) and use the slope of 3 to find a second point.
D. Plot the Y-intercept (0,1/2) and use the slope of 3 to find a second point
we have
[tex]y=\frac{1}{2}x+3[/tex]
we know that
the slope m of the line is equal to
[tex]m=\frac{1}{2}[/tex]
Find the x-intercept
The x-intercept is the value of x when the value of y is equal to zero
so
For [tex]y=0[/tex] find the value of x
[tex]0=\frac{1}{2}x+3[/tex]
[tex]x=-6[/tex]
The x-intercept is the point [tex](-6,0)[/tex]
Find the y-intercept
The y-intercept is the value of y when the value of x is equal to zero
so
For [tex]x=0[/tex] find the value of y
[tex]y=\frac{1}{2}*0+3[/tex]
[tex]y=3[/tex]
The y-intercept is the point [tex](0,3)[/tex]
therefore
the answer is the option
B. Plot the Y-intercept (0,3) and use the slope of 1/2 to find a second point
Final answer:
To graph the line y = 1/2x + 3, plot the y-intercept (0,3) and use the slope of 1/2 to find another point on the line.
Explanation:
The correct procedure to graph the line represented by the equation y = ½x + 3 is to start by plotting the y-intercept and then using the slope to find a second point. The y-intercept is the point where the line crosses the y-axis. In this equation, the y-intercept is (0, 3) because when x is 0, y is 3. The slope of the line is ½, which means that for every 1 unit increase in x, y increases by ½ a unit. Therefore, starting at the y-intercept (0, 3), you can go up ½ unit and right 1 unit to find another point on the line.
The correct answer to the multiple-choice question is:
B. Plot the Y-intercept (0,3) and use the slope of 1/2 to find a second point
The price of a car is £15400 before it is reduced by 8%.
How much does it cost after the reduction
The cost of the car after an 8% reduction on the initial price of £15,400 is £14,168. This is found by calculating 8% of the original price and subtracting that amount from the initial price.
The initial price of the car is £15,400. To calculate the price after an 8% reduction, we first find the value of the discount and then subtract it from the original price. An 8% reduction on £15,400 is calculated as follows:
Calculate 8% of £15,400: (8/100) * £15,400 = £1232.Subtract the discount from the original price: £15,400 - £1232 = £14,168.Therefore, as per the above explaination, the cost of the car after the reduction is £14,168.
Combine the radical below 2√27-√48
Who knows how to solve 9= -2+ 2x+ 1 ?
And also x-4= -9+ x
You pay $30 each month for satellite TV, plus $2.50 for every movie you purchase. Write and solve an equation to find the number of movies purchased during a month with a total bill of $45.
Answer:
6 movies
Step-by-step explanation:
You pay each month for satellite TV = $30
and for every movie you purchase = $2.50
Let the number of the movies you purchase be x
The equation will be
30 + 2.50x = 45
2.50x = 45 - 30
2.50x = 15
x = [tex]\frac{15}{2.5}[/tex]
x = 6
You purchased 6 movies during the month.
Simplify the expression 96/8
QUICKK EXPERTS/ACE OR ANYONE WHO WANTS TO HELP!!
Slope = 4/3, y intercept = -5/3
see attached picture:
Jonathan has a bag that has 2 red marbles and 3 blue marbles inside of it if you were to pick one marble from the bag without looking what is the probability of picking a red marble
There are 4 pears in all. How many pears in 1 group?
HELP ASAP PLEASE!
Evaluate the numerical expression.
− 1/3 − (− 4/9 )
So the question says...
Suppose you have ∠SMB and m ∠SMB =125.35 °.
Part A: Determine the angle measure that is complement to ∠SMB, if possible. If ∠SMB does not have a complementary angle, then explain why it does not.
Part B: Determine the angle measure of the supplement of ∠SMB.
Part C: Determine the angle measure of the angle complement to ∠SMB’s supplement.
I’m stuck on this question so if anyone can help me with it that would be greatly appreciated. Thanks!
Factor comun polinomio de (2×+3)(3-r)-(2×-5)(3-r)
Hannah claims that -3 is not rational number because it is not written as a ratio of integers. Is she correct? Explain why or why not?