For the function f(x) = -2x² + 12x - 4, we can find the outputs for specific inputs. When x = 3, the output is 14. When x = -4, the output is -84. When x = 0, the output is -4.
For finding the equation of a line passing through given points, the equation can be determined using the slope-intercept form, y = mx + b.
To determine the outputs of the function f(x) = -2x² + 12x - 4 for specific inputs, we substitute the given values of x into the function and calculate the corresponding outputs.
a) For x = 3: f(3) = -2(3)² + 12(3) - 4 = -18 + 36 - 4 = 14.
b) For x = -4: f(-4) = -2(-4)² + 12(-4) - 4 = -32 - 48 - 4 = -84.
c) For x = 0: f(0) = -2(0)² + 12(0) - 4 = 0 - 0 - 4 = -4.
Moving on to finding the equation of lines passing through given points:
7) The points given are (-5,2) and (5,4). We can calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Substituting the coordinates, we have m = (4 - 2) / (5 - (-5)) = 2 / 10 = 1/5. Using the slope-intercept form, y = mx + b, we can substitute one of the given points and the slope to solve for b. Let's use the point (5,4): 4 = (1/5)(5) + b. Simplifying, we find b = 4 - 1 = 3. Therefore, the equation of the line is y = (1/5)x + 3.
The points given are (-3,8) and (1,-4). Calculating the slope, m = (-4 - 8) / (1 - (-3)) = -12 / 4 = -3. Again, using the slope-intercept form, we substitute the point (1,-4) and the slope: -4 = (-3)(1) + b. Solving for b, we find b = -1. Hence, the equation of the line is y = -3x - 1.
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a hotel manager asked each guest that checked in on may 15th if they were more likely to use the hotel pool, exercise room, or neither. identify the sampling method used.
a. voluntary response.
b. stratified
c. convenience
d. systematic
The sampling method used in this scenario is c. convenience sampling.
Convenience sampling involves selecting individuals who are readily available and easily accessible. In this case, the hotel manager asked each guest that checked in on May 15th about their preferences. The manager likely approached the guests based on convenience, as they were already present at the hotel.
Convenience sampling is a quick and convenient way to gather information, but it may introduce bias since the sample may not accurately represent the larger population. It's important to note that convenience sampling may not provide a representative sample and may not yield generalizable results.
The other sampling methods are not applicable in this case. Voluntary response sampling is a type of non-probability sampling in which individuals volunteer to participate in a study. Stratified sampling is a type of probability sampling in which the population is divided into groups (strata) and then a random sample is selected from each group. Systematic sampling is a type of probability sampling in which every nth individual is selected from the population.
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Simplify
x + (-3) + 5 -2x
Answer:
- x + 2
Step-by-step explanation:
Step 1:
x + ( - 3 ) + 5 - 2x Equation
Step 2:
x - 3 + 5 - 2x Open Parenthesis
Step 3:
- x - 3 + 5 Subtract
Answer:
- x + 2 Add
Hope This Helps :)
Answer:
-x+2 is the final answer
Step-by-step explanation:
you first do with the brackets and deduce
f(x)=-2x + 2, find f(6)
Answer:
-10
Step-by-step explanation:
f(6)=-2(6)+2
f(6)=-12+2
f(6)=-10
Answer:
f(6) = - 10
Step-by-step explanation:
-2(6)+2
-12+2
= -10
12.8
-4
Evaluate the expression:
HEY CAN YALL PLS ANSWER DIS RQ
Answer:
B
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Is the equation shown proportional? y=1.2x
Answer:
yes
Step-by-step explanation:
A proportional equation is of the form
y = kx and the constant of proportionality is k
y = 1.2x is proportional
.(2n + 4) + 6 = –9 + 4(2n + 1)?
Answer:
n = 5/2
Step-by-step explanation:
(2n + 4) + 6 = -9 + 4(2n + 1)
2n + 4 + 6 = -9 + 8n + 4
2n + 10 = 8n - 5
15 = 6n
n = 5/2
Hope this helps!
Twice the sum of consecutive numbers n and n+1 is 510. What is the smaller number and the larger number?
Answer:
n is smaller, n + 1 is larger
Step-by-step explanation:
First, make the equation.
2(n + n+1) = 510
Then, simplify.
2(2n + 1) = 510
Distribute.
4n + 2 = 510
Solve.
n = 127
The smaller number is n (127) and the larger number is n + 1 (128).
Answer:
the correct answer is the smaller number is:127 and the bigger number is:128
Step-by-step explanation:
Four friends are saving money to go on a vacation together. The table shows how much each has saved so far.
Friend
Part of Money Saved
Gabrielle
85%
Savanna
0.9
Katrina
4/5
Susan
5/6
Arrange the numbers in order from least to greatest.
Answer:
Katrina = 0.8
Susan = 0.833
Gabrielle = 0.85
Savannah = 0.9
Step-by-step explanation:
Change to decimal
Gabrielle = 85%
= 85/100
= 17/20
= 0.85
Savannah = 0.9
= 9/10
= 0.9
Katrina = 4/5
= 0.8
Susan = 5/6
= 0.833
Arrange from least to greatest
Katrina = 0.8
Susan = 0.833
Gabrielle = 0.85
Savannah = 0.9
solve x/-4 ≥ –1, show your work
Answer:
x≤4
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
−1/4
x≥−1
Step 2: Multiply both sides by 4/(-1).
(4−1)*(−14x)≥(4−1)*(−1)
Answer:
1. multiply both sides of the equality by -4 and flip the equality sign
that makes the problem: -4×x/-4 >_ -4×(-1)
2.since you multiplied -4 the divisor cancels and you are left with : x<_ -4×(-1)
multiplying 2 negatives makes it a positive so now you get x<_4
4. A plumber charges $75 for a house call plus $45 per hour, h. If he charged $210 for the plumbing work, which equation would represent the situation to find how many hours of work he did? I A. $210 = $75h +S45 B. $210 = $45h +$75 C. $210h = $75 +545 D. 575 = 5210 + 545h
Answer:
B
Step-by-step explanation:
Four wrestlers made a pact to lose some weight before their wrestling competition. Campbell lost 6 pounds, Alex lost 5 pounds, and Eric lost 9 pounds. If their average weight loss was 7 pounds each, over a 3-week period of time, how many pounds did Rock lose?
Answer:
8lb
Step-by-step explanation:
6+5+9=20
28-8=20
28/4=7
average=mean
Calculate the angle of inclination, to the nearest tenth of a degree, of a road with a grade of 19%. a.79.0° b.79.2° c.10.8° d.11.0°.
The angle of inclination of a road with a grade of 19% is approximately 10.8 degrees, which is calculated by using the inverse tangent formula in trigonometry.
The correct answer is C).
Explanation:The angle of inclination, or grade, in terms of percentage, represents the rise (vertical distance) over the run (horizontal distance). The measure of the angle of inclination in degrees can be found by using the inverse tangent (tan-1) formula in trigonometry. To be specific, if a road has a 19% grade, it means for every 100 units (meters, feet, etc.) of horizontal distance, there is a 19 unit rise in vertical distance.
An angle θ can be calculated using tan-1(rise/run) = tan-1(19/100).
When you compute this, θ equals approximately 10.8 degrees.
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How do I find the perimeter for a double headed arrow
Answer:
The perimeter is the measure or length of the outline of an object or a shape.
The perimeter of the double headed arrow is,
= 7.9 cm + 7.9 cm + 5.1 cm + 5.1 cm + 5.1 cm + 5.1 cm + 1.2 cm + 1.2 cm + 1.2 cm + 1.2 cm.
= 2 × 7.9 cm + 4 × 5.1 cm + 4 × 1.2 cm.
= 15.8 cm + 20.4 cm + 4.8 cm.
= 41 cm.
Step-by-step explanation:
Suppose that 20% of voters are in favor of certain legislation- A large number n of voters are polled and a relative frequency estimate £3111} for the above proportion is obtained. a) Use the Chebyshev inequality to determine 1101? many voters should be polled in order that the probability is at least 0.95 that fan) differs from 0.20 by less than 0.02. b} Use central limit theorem to determine how many voters should be polled in order that the probability is at least 0.95 that £311: 11} differs from 0.20 by less than 0.02.
A. To ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02, at least 7976 voters should be polled.
b. We find the z-score corresponding to a cumulative probability of 0.95 to be approximately 1.96.
n > 2401
a) Using the Chebyshev inequality, we can determine the minimum number of voters that should be polled to ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02.
The Chebyshev inequality states that for any random variable X with mean μ and standard deviation σ, the probability of X deviating from the mean by k standard deviations is at least 1 - 1/k^2.
In this case, we want the relative frequency estimate to deviate from 0.20 by less than 0.02, which means we want the difference to be within 0.02 standard deviations of the mean. Since the relative frequency estimate is a sample proportion, its standard deviation can be approximated by sqrt(p(1-p)/n), where p is the true proportion (0.20) and n is the sample size.
We can set up the inequality as follows:
1 - 1/k^2 ≥ 0.95
Solving for k:
1/k^2 ≤ 0.05
k^2 ≥ 1/0.05
k^2 ≥ 20
Taking the square root of both sides:
k ≥ sqrt(20)
k ≥ 4.47
To ensure that the difference between the relative frequency estimate and 0.20 is within 0.02, we need k standard deviations to be less than 0.02. So, we have:
k * sqrt(p(1-p)/n) < 0.02
4.47 * sqrt(0.20(1-0.20)/n) < 0.02
Simplifying:
sqrt(0.20(1-0.20)/n) < 0.02/4.47
sqrt(0.16/n) < 0.00448
0.4/sqrt(n) < 0.00448
sqrt(n) > 0.4/0.00448
sqrt(n) > 89.29
n > 89.29^2
n > 7975.84
Therefore, to ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02, at least 7976 voters should be polled.
b) Using the central limit theorem, we can determine the minimum number of voters that should be polled to ensure that the probability is at least 0.95 that the sample mean differs from 0.20 by less than 0.02.
According to the central limit theorem, the sample mean follows a normal distribution with mean μ and standard deviation σ/sqrt(n), where σ is the population standard deviation (unknown in this case), and n is the sample size.
To ensure that the difference between the sample mean and 0.20 is within 0.02, we can set up the following inequality:
z * (σ/sqrt(n)) < 0.02
Since the population standard deviation σ is unknown, we can use a conservative estimate by assuming the worst-case scenario, which is p(1-p) = 0.25. Therefore, σ = sqrt(0.25) = 0.5.
Using the standard normal distribution table, we find the z-score corresponding to a cumulative probability of 0.95 to be approximately 1.96.
1.96 * (0.5/sqrt(n)) < 0.02
0.98/sqrt(n) < 0.02
sqrt(n) > 0.98/0.02
sqrt(n) > 49
n > 49^2
n > 2401
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Which Who is the general form of the equation of the circle shown X2 plus Y2 plus 4X minus 2Y -4 equals zero
The general form of the equation of the circle is[tex]x^2 + y^2 + 4x - 2y - 4 = 0[/tex]. The general form of the equation of a circle is given by
[tex](x - h)^2 + (y - k)^2 = r^2[/tex] where (h, k) represents the center of the circle, and r represents the radius.
To rewrite
[tex]x^2 + y^2 + 4x - 2y - 4 = 0[/tex]
into the general form, we need to complete the square on x and y terms. So, we will start by grouping the x and y terms separately as shown below:
[tex]x^2+ 4x + y^2 - 2y - 4 = 0[/tex]
Rearranging terms, we have
[tex](x^2 + 4x) + (y^2 - 2y) = 4[/tex]
Now, we complete the square on the x-term as follows:
[tex](x^2 + 4x + 4) + (y^2 - 2y) = 4 + 4= 8[/tex]
Simplifying, we have
[tex](x + 2)^2+ (y - 1)^2 = 8[/tex]
which is in the general form of the equation of a circle as required. Therefore, the center of the circle is (-2, 1) and its radius is
[tex]\sqrt{8} = 2\sqrt{2} .[/tex]
The standard form of a circle is
[tex](x-a)^2 + (y-b)^2 = r^2[/tex]
, where the center is (a, b) and the radius is r. In order to derive the general form of a circle, we square the terms on the left-hand side to get [tex]x^2 + 2ax + a^2 + y^2 + 2by + b^2 = r^2.[/tex]
By rearranging the terms, we arrive at
[tex]x^2 + y^2 + 2ax + 2by + (a^2 + b^2 - r^2) = 0[/tex].
The coefficients of x and y in this equation are used to find the center of the circle, while the radius is obtained by taking the square root of
[tex](a^2 + b^2 - r^2).[/tex]
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Solve the equation:
3x - x + 4 = 4(2x +1)
Answer:
x = 0
Step-by-step explanation:
Step 1: Write equation
3x - x + 4 = 4(2x + 1)
Step 2: Solve for x
Distribute: 3x - x + 4 = 8x + 4Combine like terms: 2x + 4 = 8x + 4Subtract 2x on both sides: 4 = 6x + 4Subtract 4 on both sides: 0 = 6xDivide both sides by 6: x = 0Step 3: Check
Plug in x to verify it's a solution.
3(0) - 0 + 4 = 4(2(0) + 1)
4 = 4(1)
4 = 4
Answer:
x = 0Step-by-step explanation:
3x - x + 4 = 4(2x +1)
2x + 4 = 8x + 4
2x - 8x = 4 - 4
-6x = 0
x = 0
Please answer quickly
The average sneeze can travel three out of hundred miles in three seconds at this rate how far can you travel in one minute
Answer:
[tex]1min = 60 \: s \\ three \: seconds - - - - - 300 \: miles \\ 60 \: seconds = 3 \times 20 \: seconds \\ so \: we \: have \: 20 \: of \: three \: sconds \: \\ which \: means \: 20 \: three \: hundreds \: \\ 20 \times 300 = 6000 \: miles \: \\ and \: we \: are \: done.[/tex]
What is the hypothesis of the following statement?
If I study, then I pass the test.
If I study
I study
I pass the test
then I pass the test
BRAINLIEST IF RIGHT FOR SURE
the difference between a number is 12 is 30
show steps brainly if correct
Answer:
18
X + 12 = 30
-12. -12. Subtract 12
X = 18. Answer
Answer:
42
Step-by-step explanation:
solve the inequality 8 < 12 + c < 12
Separate the inequalities by part.
[tex]8<12+c\\12+c<12[/tex]
We'll do 8 < 12+c first then 12+c<12 next.
[tex]8-12<c\\-4<c\\c>-4[/tex]
Then 12+c<12
[tex]12+c<12\\c<12-12\\c<0[/tex]
Then mix c<0 and c>-4 as we'll get [tex]-4<c<0[/tex] #
An ash borer is an invasive pest whose larvae eat the pulp of ash trees as they mature. A park ranger has a tree that is infested with ash borers. She estimates they have eaten approximately 40% of the tree's pulp. If the ash tree's trunk has a radius of 2 feet and a height of 15 feet, what was the total volume of the tree trunk before the ash borers started eating it?
Answer:
[tex]188.6[/tex] cubic feet
Step-by-step explanation:
Let r, h denotes radius and height of the tree's trunk.
Radius of the tree's trunk = 2 feets
Height of the tree's trunk = 15 feets
The tree's trunk is in the shape of a cylinder.
Volume of cylinder (tree's trunk) [tex]=\pi r^2h[/tex]
Put [tex]r=2\,,\,h=15[/tex]
Volume of the tree's trunk [tex]=\pi (2)^2(15)=60\pi[/tex] cubic feet
Put [tex]\pi=\frac{22}{7}[/tex]
So,
Volume of the tree's trunk [tex]=60(\frac{22}{7})=\frac{1320}{7}=188.6[/tex] cubic feet
One hundred less than a half of a number is five
Answer:
x/2-100=5
Step-by-step explanation:
find two consecutive integers whose sum is 77
Answer:
38, 39Step-by-step explanation:
The difference between two consecutive integers is 1
So if
x - the smaller number
then
x+1 - the larger number
x + x+1 = 77
-1 -1
2x = 76
÷2 ÷2
x = 38
x+1 = 38+1 = 39
why does x^2 = 64 have two solutions but x^3 = 64 only has one?
Because if the exponent is an even number, x can also be -x. For example, -4^2=4^2 but -4^3 isn't the same as 4^3
What is the additive inverse of the polynomial?
Answer:
Option A is the correct answer
Step-by-step explanation:
Where there is + sign it changes to - and where there is - sign it change to + sign for the additive inverse
Answer:
Its the first one <3
Step-by-step explanation:
please help
What is the probability that either event will occur?
15
A
12
B
18
21
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Answer: 15
Step-by-step explanation:
The probability that either event A or event B will occur is approximately 0.9715.
To find the probability that either event A or event B will occur, we can use the formula P(A or B) = P(A) + P(B) - P(A and B). In this case, the probabilities of events A and B are given as 12/15 and 18/21, respectively. To find the probability of both A and B happening together, we can multiply their individual probabilities. Now we can plug these values into the formula to find the probability of A or B occurring.
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 12/15 + 18/21 - (12/15) * (18/21)
P(A or B) = 0.8 + 0.8571 - (0.8) * (0.8571)
P(A or B) = 0.8 + 0.8571 - 0.6856
P(A or B) = 0.9715
Therefore, the probability that either event A or event B will occur is approximately 0.9715.
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189. Which of the following integers has the
greatest number of factors ?
A 24
B 42
C 36
D 50
Answer:
i think its C but I'm still not sure.
The Sweet water High School Project Graduation committee is hosting a dinner-and-dance fundraiser at the Sweet water Community Center. The committee hopes to raise at least $7500 with this event. Tickets for the fundraiser are $75.00 per couple, and they have to pay a $375 fee for renting the community center. Write and solve an inequality to determine the minimum number of tickets they need to sell to reach their goal.
Answer:
At least 105 tickets must be sold for there to be a 7500 dollar profit
Step-by-step explanation:
Let c = number of couple tickets
ticket sales - costs = profits
We want profits greater than 7500
75c - 375 ≥ 7500
Add 375 from each side
75c-375+375 ≥ 7500 +375
75c ≥ 7875
Divide each side by 75
75c/75 ≥ 7875/75
c ≥ 105
At least 105 tickets must be sold for there to be a 7500 dollar profit
