Use the formula below:
[tex] \large \boxed{h = - \frac{b}{2a} }[/tex]
From the given equation:
[tex] \large{y = 2 {x}^{2} - 6x + 2}[/tex]
Substitute a = 2 and b = -6 in the formula.
[tex] \large{h = - \frac{ - 6}{2(2)} } \\ \large{h = - \frac{ - 6}{4} } \\ \large{h = - \frac{ - 3}{2} \longrightarrow \boxed{h = \frac{3}{2} }}[/tex]
Since h is from (h,k). From an ordered pair, h = x and k = y. When answering the axis of symmetry, you should answer in term of x.
Answer
The axis of symmetry is x = 3/2NO LINKS!!!
Change the standard form equation to vertex form and compare the function to the parent function y = x^2.
1. y = x^2 - 2x - 2
Completing the square gives
[tex]x^2-2x-2=(x-1)^2-3[/tex]
and comparing to [tex]y=x^2[/tex], the graph of [tex]y=x^2-2x-2[/tex] would be a horizontal shift to the right by 1 unit, and a vertical shift down by 3 units.
Hope this help!!!
Have a nice day!!!
A positive real number is 1 more than another. When -2 times the smaller is added to the square of the larger, the result is 33. Find the numbers.
Answer:
The smaller number is 4√2 and the larger number is (4√2 + 1).
Step-by-step explanation:
Let the two numbers be x and y, where y is the larger of the two numbers.
Since y is the larger number, it is one more than the smaller number. So:
[tex]y=x+1[/tex]
When negative two times the smaller is added to the square of the larger, the result is 33. In other words:
[tex]-2x+y^2=33[/tex]
Substitute:
[tex]-2x+(x+1)^2=33[/tex]
Solve for x. Square:
[tex]-2x+(x^2+2x+1)=33[/tex]
Simplify:
[tex]x^2+1=33[/tex]
Subtract one from both sides:
[tex]x^2=32[/tex]
And take the square root of both sides:
[tex]x=\pm\sqrt{32}=\pm 4\sqrt{2}[/tex]
Since y is positive, we can ignore the negative case. So, the smaller number is:
[tex]x=4\sqrt{2}\approx5.66[/tex]
And the larger number is:
[tex]y = 4\sqrt{2} + 1 \approx6.66[/tex]
At the beginning of the year, the odometer on an SUV read 37,532 miles. At the end
of the year, it read 52,412 miles. If the car averaged 24 miles per gallon, how many
gallons of gasoline did it use during the year?
He used 620 gallons of gas
I have a test please someone help me I need this asp
Answer:
Step-by-step explanation:
the tilt has no impact...
if not tilted then h=14 r=3 vol = pi 3^3 h = 14*9 π
=126π
What is the area of the triangle
Answer:
60m^2 is the answer im pretty sure
Step-by-step explanation:
yeah man thats it
Which is a stretch of an exponential decay function?
f(x)=4/5(5/4)x
f(x)=4/5(4/5)x
f(x)=5/4(4/5)x
f(x)=5/4(5/4)x
Evan invested $800 in an account that pays 3.25% interest compounded annually.
Assuming no deposits or withdrawals are made, find how much money Evan would
have in the account 12 years after his initial investment. Round to the nearest tenth
(if necessary).
Answer:
Evans would have $852.8
Step-by-step explanation:
Given
[tex]PV = \$800[/tex]
[tex]r = 3.25\%[/tex]
[tex]t = 2[/tex]
[tex]n = 1[/tex] --- annually'
Required
The future value
This is calculated using:
[tex]FV = PV*(1 + \frac{r}{n})^{nt[/tex]
So, we have:
[tex]FV = 800 * (1 + 3.25\%/1)^{2*1}[/tex]
[tex]FV = 800 * (1 + 3.25\%)^{2}[/tex]
[tex]FV = 800 * (1 + 0.0325)^{2}[/tex]
[tex]FV = 800 * (1 .0325)^2[/tex]
[tex]FV = 852.845[/tex]
[tex]FV = 852.8[/tex]
FV =
Suppose that your boss must choose four employees in your office to attend a conference in Jamaica. Because all 15 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Kyle, Carol, and Adam are chosen? Enter a fraction or round your answer to 4 decimal places, if necessary.
Answer:
1 / 1365
Step-by-step explanation:
Given that :
Number of employees to choose from = 15
Number of employees to be chosen = 4
Probability of choosing You, Kyle, Carol and Adam
Recall ;
P(A) = number of required outcome / Total possible outcomes
Number of required outcome = 4C4
Total possible outcomes = 15C4
nCr = n! ÷ (n-r)!r!
Using calculator to save computation time :
15C4 = 1365
4C4 = 1
P(choosing you, Kyle, Carol and Adam) :
1 / 1365
Which of the following correctly names a side of the triangle below?
A. ZC
B. B
С. АВ
D. AABC
Answer:
C. [tex]\frac{}{AB}[/tex]
Step-by-step explanation:
You can solve this in two ways, firstly by eliminating all the wrong answers, and secondly by just knowing that the horizontal line in [tex]_[/tex][tex]\frac{}{AB}[/tex] means that we are talking about a line.
This is how we solve this question by using the eliminating process.
(A. ∠C) is not the right answer because the ∠ sign lets us know that this answer represents an angle, not a line
(B. B) is not the right answer because it represent a point, not a line (in math we use a singular capital letter to represent points)
(D. ΔABC) is not the right answer because the Δ sign lets us know that the answer represents a triangle, not a line.
Therefore, the only option left is C. [tex]\frac{}{AB}[/tex]
please help me this is due today!! it’s number 6
what is the length of AB
Donte simplified the expression below.
4(1+3i)-(8-5i)
4+3i-8+5i
-4+8i
What mistake did he make?
Answer:
A. He did not apply the distributive property correctly for 4(1+3i)
Step-by-step explanation:
Solve x^2 -6x=-5 by completing the square. Show all work for the steps below. (a) For x^2 -6x+c+-5+c, what value of c is used to complete the square? (b) Substitute the value for c in Part 2(a). Then complete the square to rewrite the equation as the square of a binomial. (c) Solve for x
How much of a radioactive kind of rhodium will be left after 120 seconds if the half-life is 30 seconds and you start with 480 grams?
9514 1404 393
Answer:
30 grams
Step-by-step explanation:
The time 120 seconds is 4 times the half-life of 30 seconds. That means (1/2)^4 = 1/16 of the original amount will remain. That is (480 g)(1/16) = 30 g.
30 g of the radioactive rhodium will be left
Zahara frosted eleven cupcakes today. Dania frosted seven times as many. How many cupcakes did Dania frost?
The table shows the results of an experiment in which the spinner shown above was spun 50 times. Find the experimental probability of each outcome.
not shaded
Answer:
[tex]P(x < 4) = \frac{9}{50}[/tex]
Step-by-step explanation:
Given
[tex]n(S) = 50[/tex]
See attachment for distribution
Required
[tex]P(x < 4)[/tex]
This is calculated as:
[tex]P(x < 4) = \frac{n(1) + n(2) + n(3)}{n(S)}[/tex]
Using the data on the frequency distribution table, we have:
[tex]P(x < 4) = \frac{4 + 2 + 3}{50}[/tex]
[tex]P(x < 4) = \frac{9}{50}[/tex]
A line intersects the point (3,4) and has a slope of -2. Substitute the values into point-slope form.
9514 1404 393
Answer:
y -4 = -2(x -3)
Step-by-step explanation:
The point-slope form of an equation for a line through point (h, k) with slope m is ...
y -k = m(x -h)
You have (h, k) = (3, 4) and m = -2, so your equation is ...
y -4 = -2(x -3)
10. (10.04 MC)
What are the period and phase shift for f(x) = -4 tan(x − n)? (1 point)
T
Period: n; phase shift: x =
2
Period: n; phase shift: x = n
TT
Period: 2n; phase shift: x =
2
Period: 2n; phase shift: x = 0
Answer:
Period: [tex]\pi[/tex]
Phase shift: n
Step-by-step explanation:
Tangent function:
Has the following format:
[tex]f(x) = \tan{ax - n}[/tex]
In which the period is [tex]\frac{\pi}{x}[/tex] and the phase shift is n.
In this question:
[tex]f(x) = -4\tan{(x-n)}[/tex]
[tex]a = 1[/tex], and thus, the period is [tex]\pi[/tex], with a phase shift of n.
Select the true statement about the relationship between sample size and the standard deviation of distribution of sample means, also known as the standard error.
a. As sample size increases, standard error increases.
b. Sample size does not have an impact on standard error.
c. As sample size increases, standard error decreases.
d. As sample size decreases, standard error decreases.
Answer:
c. As sample size increases, standard error decreases.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
Thus:
The standard error is inversely proportional to the square root of the sample size, that is, as the sample size increases, the standard error decreases, and the correct answer is given by option c.
ou want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 99% confident that you esimate is within 0.1% of the true population proportion. How large of a sample size is required
Answer: the required sample size =1658944
Step-by-step explanation:
When the prior population proportion for the study is unknown , then the formula for sample size is [tex]Sample \ size = 0.25(\dfrac{z^*}{Margin\ of \ error})^2[/tex]
z-value for 99% confidence = 2.576
[tex]Sample \ size = 0.25(\dfrac{2.576}{0.001})^2\\\\=0.25(2576)^2\\\\=1658944[/tex]
Hence, the required sample size =1658944
plz help i dont know what to do
ANSWER QUICK
Answer:
the last one is correct.............
The time it takes to build a house (T), varies directly with the floor area (A), and inversely with the number of workers (W). What is the equation that models this situation?
Answer:
T = k * (A/W)
Step-by-step explanation:
where is EF to the nearest tenth??
Answer:
37.7
Step-by-step explanation:
EF and ED define the Tangent of D
Tan(37) = side opposite D / side adjacent to D
Opposite means a line (FE) that is not connected to the angle. It is never the longest line (hypotenuse) in a Right Triangle
Adjacent means the leg that is connected to the angle, but is not the hypotenuse.
Tan(D) = opposite over adjacent
Opposite = x
Adjacent = 50
Tan(37) = 0.7536 rounded to 4 places, but I've kept the exact value in my calculator.
0.7536 = x / 50 Multiply both sides by 50
0.7536*50 = x
x = 37.6777
The nearest 1/10 is 37.7
The volume of the prism is 900 cubic centimeters. The
height of the prism is 15 centimeters and the height of
the triangular base is 10 centimeters. What is the
length of edge FC?
Answer:
?
Step-by-step explanation:
i dont now how to arrange
Answer:
12
Step-by-step explanation:
trust me bro
A person takes a multiple-choice exam in which each question has five possible answers. Suppose that the person has no idea about the answers to three of the questions and simply chooses randomly for each one.
Required:
a. What is the probability that the person will answer all three questions correctly?
b. What is the probability that the person will answer exactly two questions correctly?
c. What is the probability that the person will answer exactly one question correctly?
d. What is the probability that the person will answer no questions correctly?
e. Suppose that the person gets one point of credit for each correct answer and that 1/3 point is deducted for each incorrect answer. What is the expected value of the person’s score for the three questions?
Answer:
a. 0.008 = 0.8% probability that the person will answer all three questions correctly.
b. 0.096 = 9.6% probability that the person will answer exactly two questions correctly.
c. 0.384 = 38.4% probability that the person will answer exactly one question correctly.
d. 0.512 = 51.2% probability that the person will answer no questions correctly.
e. The expected value of the person’s score for the three questions is -0.2.
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the person answers it correctly, or they do not. The probability of a person answering a question correctly is independent of any other question. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Each question has five possible answers.
Person has no idea which option is correct, so the probability of answering correctly is:
[tex]p = \frac{1}{5} = 0.2[/tex]
Three questions:
This means that [tex]n = 3[/tex]
a. What is the probability that the person will answer all three questions correctly?
This is [tex]P(X = 3)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.2)^{3}.(0.8)^{0} = 0.008[/tex]
0.008 = 0.8% probability that the person will answer all three questions correctly.
b. What is the probability that the person will answer exactly two questions correctly?
This is [tex]P(X = 2)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{3,2}.(0.2)^{2}.(0.8)^{1} = 0.096[/tex]
0.096 = 9.6% probability that the person will answer exactly two questions correctly.
c. What is the probability that the person will answer exactly one question correctly?
This is [tex]P(X = 1)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{3,1}.(0.2)^{1}.(0.8)^{2} = 0.384[/tex]
0.384 = 38.4% probability that the person will answer exactly one question correctly.
d. What is the probability that the person will answer no questions correctly?
This is [tex]P(X = 0)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.2)^{0}.(0.8)^{3} = 0.512[/tex]
0.512 = 51.2% probability that the person will answer no questions correctly.
e. Suppose that the person gets one point of credit for each correct answer and that 1/3 point is deducted for each incorrect answer. What is the expected value of the person’s score for the three questions?
The expected number of correct answer is:
[tex]E(X) = np = 3*0.2 = 0.6[/tex]
And the expected number of wrong answers is 3 - 0.6 = 2.4. So, the expected score is:
[tex]S(x) = 0.6 - \frac{2.4}{3} = 0.6 - 0.8 = -0.2[/tex]
The expected value of the person’s score for the three questions is -0.2.
NEED HELP ON THIS ASAP PLZ!!
Answer:
cos0 = 6.8556546i/23 or sqrt-47/23
Step-by-step explanation:
hypotenuse is 23, opposite is 24
we have to find the adjacent using the pythagorean theorem
24^2 + b^2 = 23^2
576+b^2=529
subtract
b^2=-47
b=sqrt-47
sqrt of -47 is 6.8556546i, there is an i since it is the square root of a negative
cos = adjacent/hypotenuse
All of the following solid figures except a _____ have two bases.
Answer:
All of the following solid figures except a square pyramid have two bases.
Determine the value of x.
1) 14.75
2)15.25
3)11.92
4)18.56
What is the total cost of a bag chips that cost $0.99 with 7% sales tax?
Linear function please help it’s due in 30 mins
how can i solve the following
2(x + 3) = x - 4
Answer:
x=-10
Step-by-step explanation:
2(x+3)=x-4
2*x+2*3=x-4
2x+6=x-4
2x-x=-4-6
x=-10
Answer:
[tex]x = - 10[/tex]
Step-by-step explanation:
Let's solve:
[tex]2(x+3)=x−4[/tex]
Step 1: Simplify both sides of the equation.
[tex]2(x+3)=x−4 \\ (2)(x)+(2)(3)=x+−4(Distribute) \\ 2x+6=x+−4 \\ 2x+6=x−4[/tex]
Step 2: Subtract x from both sides.
[tex]2x+6−x=x−4−x \\ x+6=−4[/tex]
Step 3: Subtract 6 from both sides.
[tex]x+6−6=−4−6 \\ x=−10[/tex]
