Using translation concepts, the vertex of k(x) is 6 units below the vertex of f(x) = x² for:
D. f(x) = x² and k(x) = x² - 6.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
We want to shift the vertex 6 units down, hence the transformation is y -> y - 6, so the correct pair is:
D. f(x) = x² and k(x) = x² - 6.
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If a person high jumps 6 feet 2 inches, how many inches is the jump?
Answer:
74 inches
Step-by-step explanation:
1 foot is 12 inches, so 6 x 12 = 72, and just add the other 2 inches to get 74 inches.
Answer:
74 inches.
Step-by-step explanation:
Each foot has 12 inches, so multiply 6 by 12 to get 72 inches. Then add the remaining two inches to get a total of 74 inches.
According to a Gallup poll, 60% of American adults prefer saving over spending. In a random sample of 10 American adults, what is the probability that more than 3 adults in the sample prefer saving over spending
Answer:
0.9452 = 94.52% probability that more than 3 adults in the sample prefer saving over spending
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they prefer saving over spending, or they do not. The answers for each adult are independent, which 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.
According to a Gallup poll, 60% of American adults prefer saving over spending.
This means that [tex]p = 0.6[/tex]
Sample of 10 American adults
This means that [tex]n = 10[/tex]
What is the probability that more than 3 adults in the sample prefer saving over spending?
This is:
[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]
In which
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.6)^{0}.(0.4)^{10} = 0.0001[/tex]
[tex]P(X = 1) = C_{10,1}.(0.6)^{1}.(0.4)^{9} = 0.0016[/tex]
[tex]P(X = 2) = C_{10,2}.(0.6)^{2}.(0.4)^{8} = 0.0106[/tex]
[tex]P(X = 3) = C_{10,3}.(0.6)^{3}.(0.4)^{7} = 0.0425[/tex]
Then
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0001 + 0.0016 + 0.0106 + 0.0425 = 0.0548[/tex]
[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.0548 = 0.9452[/tex]
0.9452 = 94.52% probability that more than 3 adults in the sample prefer saving over spending
what is the approximate value of x in the diagram below?
Answer:
Where is the diagram though..
Step-by-step explanation:
To add radical expressions, the expressions must have the same index and radicand,
True
False
In a shipment of toys from a manufacturer, the probability that a toy is defective is
1
50
. If Marie selects 2 toys from a shipment, what is the probability that both toys are defective?
Answer:
The probability is 1/2500. (1/50)*(1/50)
Step-by-step explanation:
According to Okun's law, if the unemployment rate goes from 5% to 3%, what will be the effect on the GDP?
A. It will increase by 7%.
B. It will decrease by 7%.
C. It will decrease by 1%.
D. It will increase by 1%.
Answer:
D. It will increase by 1%.
Step-by-step explanation:
Given
[tex]u_1 = 5\%[/tex] --- initial rate
[tex]u_2 = 3\%[/tex] --- final rate
Required
The effect on the GDP
To calculate this, we make use of:
[tex]\frac{\triangle Y}{Y} = u_1 - 2\triangle u[/tex]
This gives:
[tex]\frac{\triangle Y}{Y} = 5\% - 2(5\% - 3\%)[/tex]
[tex]\frac{\triangle Y}{Y} = 5\% - 2(2\%)[/tex]
[tex]\frac{\triangle Y}{Y} = 5\% - 4\%[/tex]
[tex]\frac{\triangle Y}{Y} = 1\%[/tex]
This implies that the GDP will increase by 1%
Answer: A. It will increase by 7%.
Step-by-step explanation: I took this course!
Assume 10% of Berkeley students are left-handed. If you are in a class of 50 people, what is the probability that exactly 4 of them are left-handed? Round your answer to the nearest hundredth, and omit the leading zero. Enter your answer here.
Answer:
The answer is "0.18"
Step-by-step explanation:
[tex]10\% \ of \ 50= 5 \text{are left handed}\\\\45\ \text{are right handed}\\\\[/tex]
If the probability exactly 4 were heft handed
[tex]=^{50}_{C_4}\times (\frac{5}{50})^4 \times (\frac{45}{50})^{4b}\\\\=^{50}_{C_4} \times (0.1)^4 \times (0.9)^{4b}\\\\=230300 \times (0.1)^4 \times (0.9)^{4b}\\\\=0.181 \approx 0.18[/tex]
Leroy borrowed $1500 at an annual simple interest rate of 12%. He paid $270 in interest. For what time period did Leroy borrow the money?
Answer:
i hope you understand easily
mark me brainlist
Step-by-step explanation:
Find the indicated confidence interval. Assume the standard error comes from a bootstrap distribution that is approximately normally distributed. A 90% confidence interval for a mean μ if the sample has n-80 with X-22.1 and s = 5.6, and the standard error is SE = 0.63.
The 90% confidence interval is to :_________
Answer:
(21.064 ; 23.136)
Step-by-step explanation:
Given :
Sample, n = 80
Mean, xbar = 22.1
Standard deviation, s = 5.6
Standard Error, S. E = 0.63
Confidence interval :
Xbar ± Zcritical * S.E
22.1 ± (1.645 * 0.63)
22.1 ± 1.036
Lower boundary = 22.1 - 1.036 = 21.064
Upper boundary = 22.1 + 1.048 = 23.136
(21.064 ; 23.136)
Which of the following is not true regarding the flow of information from the adjusted trial balance on the end-of-period spreadsheet?
The correct statement about the flow of information from the adjusted trial balance on the end-of-period spreadsheet is A. The revenue and expense account balances flow into the income statement.
What is an Adjusted Trial Balance?This refers to the general ledger balance after some changes have been done an account balance such as accrued expenses, depreciation, etc.
Therefore, we can see that from the complete information, the statement that is false about the adjusted trial balance on the end-of-period spreadsheet is option A because the revenue and expense account balances does not flow into the income statement.
The other options from the complete text are:
a. The revenue and expense account balances flow into the income statement.b. The asset and liability account balances flow into the retained earnings statement.c. The revenue and expense account balances flow into the retained earnings statement.d. The retained earnings and dividends account balances flow into the balance sheet.
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please help me solve this math
Answer:
d
Step-by-step explanation:
Hw help ASAP PLZZZZZZ
Answer:
Your answer is C. X = 29/8c
Step-by-step explanation:
2/3(cx + 1/2) - 1/4 = 5/2
2cx/3+1/3-1/4=5/2
2cx3+1/12=5/2
2cx/3=5/2-1/12
2cx/3=29/12
(3)2cx/3=29/12(3)
2cx= 31/4
(2c)2cx=29/4(2c)
X=29/8c
Your answer is C. X = 29/8c
what is the sum of the complex numbers -9-i, and -5-i?
Answer:
-14-2i
Step-by-step explanation:
-9-i+(-5-i)
collect like terms(real-real, imaginary-imaginary)
=(-9-5)+(-i-i)
=-14-2i
All I need is number one
Answer:
a. 7 ÷ 4 yes
b. 4 ÷ 7 no
c. [tex]\frac{7}{4}[/tex] yes
d. [tex]\frac{4}{7}[/tex] no
e. 7 × [tex]\frac{1}{4}[/tex] yes
f. [tex]1\frac{3}{4}[/tex] yes
Step-by-step explanation:
hope this helps ^^
Please hlep x^2+6x+1=0
Answer:
Substitute into the quadratic formula
-6 ± √32 / 2
= -3 ± √16
= 1 and -1 are the answer
Answer:
x = - 3 ± 2[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Given
x² + 6x + 1 = 0 ( subtract 1 from both sides )
x² + 6x = - 1
Using the method of completing the square
add/ subtract ( half the coefficient of the x- term)² to both sides
x² + 2(3)x + 9 = - 1 + 9
(x + 3)² = 8 ( take the square root of both sides )
x + 3 = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex] ( subtract 3 from both sides )
x = - 3 ± 2[tex]\sqrt{2}[/tex]
Then
x = - 3 - 2[tex]\sqrt{2}[/tex] , x = - 3 + 2[tex]\sqrt{2}[/tex]
HELP PLEASE! I tried everything from adding to dividing, subtracting, multiplying but still no correct answer. Can someone help me out here please? I am not sure where to start. Thank you for your time.
Answer:
6.09 is the answer rounded to nearest hundredths.
Step-by-step explanation:
It gives you n=150, p=0.55, and q=1-p.
If p=0.55 and q=1-p, then by substitution property we have q=1-0.55=0.45.
It ask you to evaluate the expression sqrt(npq).
So npq means find the product of 150 and 0.55 and 0.45. So that is 150(0.55)(0.45)=37.125.
The sqrt(npq) means we need to find the square root of that product. So sqrt(37.125)=6.093 approximately .
If the nth term of a sequence is
28-3n what is the 7th term?
Answer:
7
Step-by-step explanation:
28-3(7)
The 7th term of the given sequence 28 - 3n is 7.
What is sequence?A sequence is an ordered list of elements with a specific pattern.
According to the given question.
We have a sequence 28 - 3n.
So, for finding the value 7th term of the sequence substitute n = 7 in
28 - 3n.
Therefore, the 7th term of the given sequence
= 28 - 3(7)
= 28 - 21
= 7
Hence, the 7th term of the given sequence 28 - 3n is 7.
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At an intersection, the red light times are normally distributed with a mean time of 3 minutes and a standard deviation of 0.25 minutes. Approximately what percent of red lights last between 2.5 and 3.5 minutes? (2 points)
Answer:
95.4%
Step-by-step explanation:
Z(low)=-2 0.022750132
Z(upper)=2 0.977249868
what can you infer about angles w and z based on the information in the other triangles?
Answer:
They are supplementary and their sum is 180°
w = 45 + 60 or w = 105
z = 180 - 105 or z = 75
I need help :)What’s m
Answer:
[tex] \large{ \tt{❃ \: S \: O \: L \: U \: T \: I \: O \: N : }}[/tex]
[tex] \large{ \tt{⇢m \: \angle \: GHI= m \: \angle \: GHQ + m \: \angle \: QHI}}[/tex]
[tex] \large{ \tt{➝14x + 6 = 3x - 3 + 130 \degree}}[/tex]
[tex] \large{ \tt{➝14x + 6 = 3x + 127}}[/tex]
[tex] \large{ \tt{➝ \: 14x - 3x = 127 - 6}}[/tex]
[tex] \large{ \tt{➝ \: 11x = 121}}[/tex]
[tex] \large{ \tt{➝ \: x = \frac{121}{11} }}[/tex]
[tex] \large{ \tt{➝ \: x = 11}}[/tex]
[tex] \large{ \tt{✣ \: REPLACING \: VALUE}} : [/tex]
[tex] \large{ \tt{✺ \: m \: \angle \: GHI = 14x + 6 = 14 \times 11 + 6 = \boxed{ \tt{160 \degree}}}}[/tex]
Our final answer : 160° . Hope I helped! Let me know if you have any questions regarding my answer! :)▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
NFL Pre-Season Teams in the National Football League (NFL) in the US play four pre-season games each year before the regular season starts. Do teams that do well in the pre-season tend to also do well in the regular season? We are interested in whether there is a positive linear association between the number of wins in the pre-season and the number of wins in the regular season for teams in the NFL.
Required:
a. What are the null and alternative hypotheses for this test?
b. The correlation between these two variables for the 32 NFL teams over the 10 year period from 2005 to 2014 was 0.067. Use this sample (with n=320) to calculate the appropriate test statistic and determine the p-value for the test.
c. State the conclusion in context, using a 5% significance level.
Answer:
H0 : ρ = 0
H1 : ρ ≠ 0
Test statistic = 1.197
Pvalue = 0.2335
There is no correlation between the two variables
Step-by-step explanation:
The null and alternative hypothesis :
H0 : No correlation exist,
H1 : Correlation exist
H0 : ρ = 0
H1 : ρ ≠ 0
Test statistic, T = r / √(1 - r²) / (n - 2)
T = 0.067 / √(1 - 0.067²) / (320 - 2)
T = 0.067 / √(0.995511 / 318)
T = 0.067 / 0.0559512
T = 1.197
The Pvalue obtained from the Rscore, at df = 320 - 2 = 318 is 0.2335
α = 5% = 0.05
The Pvalue > α ; we fail to reject the null and conclude that, there is no correlation between the two variables.
some pleaseeeeee help!!
f(x) = 3x + 4 + 2
g(x) = 4
Find (f +g)(x).
Answer:
3x^2 + 10x
Step-by-step explanation:
If u wrote it correctly it would be ((x+4+2)+4)(x)
If you apply for a job with Globo Corp, there is a 75% chance that you will get an interview.
If you get an interview, there is a 48% chance that you will get the job.
If you apply for a job with Globo Corp, what is the probability that you will get the job?
Express your answer as a decimal, rounded to the nearest hundredth.
Answer:
The probability that you will get the job If you apply for a job with Globo Corp=0.36
Step-by-step explanation:
We are given that
If you apply for a job with Globo Corp, then the probability of getting interview P(A)=75%=0.75
If you get an interview, then the probability of getting job=P(B)=48%=0.48
We have to find the probability that you will get the job If you apply for a job with Globo Corp.
If you apply for a job with Globo Corp, the probability of getting job=[tex]P(A)\times P(B)[/tex]
If you apply for a job with Globo Corp, the probability of getting job=[tex]0.75\times 0.48[/tex]
If you apply for a job with Globo Corp, the probability of getting job=0.36
Hence, the probability that you will get the job If you apply for a job with Globo Corp=0.36
HELPPP
3p-4-8p<-19
i need the steps as well
9514 1404 393
Answer:
p > 3
Step-by-step explanation:
3p -4 -8p < -19 . . . . . . given
-5p -4 < - 19 . . . . . . . . collect terms
-5p < -15 . . . . . . . . . . . add 4
p > 3 . . . . . . . . . . . . . . divide by -5 (reverses the inequality symbol)
Subtract and show work.
Answer:
[tex]31y^{3} -28y^{2}[/tex]+35y
Step-by-step explanation:
At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those customers using regular gas, only 10% fill their tanks (event B). Of those customers using plus, 20% fill their tanks, whereas of those using premium, 30% fill their tanks.
Required:
a. What is the probability that the next customer will request plus gas and fill their tank ?
b. What is the probability that the next customer fills the tank ?
c. If the next customer fills the tank, what is the probability that the regular gas is requested?
Answer:
Remember that for an event with a percentage probability X, the probability is given by:
P = X/100%
a) What is the probability that the next customer will request plus gas and fill their tank ?
We know that 35% of the customers use plus gas, and of these using plus, 20% fill their tank.
So the probability that the next customer uses plus gas is:
p = 35%/100% = 0.35
And the probability that the customer fills the tank (given that the customer uses plus gas) is:
q = 20%/100% = 0.2
The joint probability is just the product between the individual probabilities:
Then the probability that the next customer uses plus gas and fills their tank is:
P = 0.35*0.2 = 0.07
b) What is the probability that the next customer fills the tank?
We know that 20% of the ones that use plus gas (with a probability of 0.35) fill their tank, 10% of these that use regular gas (with a probability of 0.4) and 30% of these that use premium (with a probability of 0.25) fill their tank,
Then the probability is computed in a similar way than above, here the probability is:
P = 0.2*0.35 + 0.1*0.4 + 0.3*0.25 = 0.185
The probability that the next customer fills the tank is 0.185
c) If the next customer fills the tank, what is the probability that the regular gas is requested?
Ok, now we already know that the customer fills the tank.
The probability that a customer uses regular and fills the tank, is
p = 0.1*0.4
The probability that a customer fills the tank is computed above, this is:
P = 0.185
The probability, given that the customer fills the tank, the customer uses regular gas, is equal to the quotient between the probability that the customer fills the tank with regular and the probability that the customer fills the tank, this is:
Probability = p/P = (0.1*0.4)/(0.185) = 0.216
Does it pay to ask for a raise? A national survey of heads of households showed the percentage of those who asked for a raise and the percentage who got one. According to the survey, of the men interviewed, 21% had asked for a raise and 60% of the men who had asked for a raise received the raise. If a man is selected at random from the survey population of men, find the following probabilities. (Enter your answers to three decimal places.)
Answer:
a) P(man asked for a raise) = 0.21.
b) P(man received raise, given he asked for one) = 0.6.
c) P(man asked for raise and received raise) = 0.126.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Question a:
21% asked for a raise, so:
P(man asked for a raise) = 0.21.
Question b:
Event A: Asked for a raise.
Event B: Received a raise:
21% had asked for a raise and 60% of the men who had asked for a raise received the raise:
This means that [tex]P(A) = 0.21, P(A \cap B) = 0.21*0.6[/tex], thus:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.21*0.6}{0.6} = 0.6[/tex]
P(man received raise, given he asked for one) = 0.6.
Question c:
[tex]P(A \cap B) = 0.21*0.6 = 0.126[/tex]
P(man asked for raise and received raise) = 0.126.
slove the following systems of equations using any method. y= 3x + 7 , y= x- 9 , 3x- y= 1 , 7x + 2y = 37.
y=3× + 7 , y=×- 9 , 3×- 9 , 3×- y= 1 , 7× + 2y = 37.
The pre-image, ΔSTU, has undergone a type of transformation called a rigid transformation to produce the image, ΔVWX. Compare the measures of the triangles by dragging the image to the pre-image.
Which measures are equal? Check all that apply.
ST = VW
SU = VX
TU = WX
m∠SUT = m∠VXW
m∠TSU = m∠WVX
m∠UTS = m∠XWV
Answer:
its all of them
Step-by-step explanation:
since its the same shape as the old one all the measurements are the same.
Answer:
its all of them
Step-by-step explanation:
The triangles are similar. If QR = 9, QP = 6, and TU = 19, find TS. Round to the nearest tenth.
A) 16
B) 12.7
C) 2.8
D) 28.5
Answer:
TS = 12.7
Step-by-step explanation:
From the question given above, the following data were obtained:
QR = 9
QP = 6
TU = 19
TS =?
Since the triangles are SIMILAR, then,
QR / TU = QP / TS
With the above equation, we can obtain the value of TS as follow:
QR = 9
QP = 6
TU = 19
TS =?
QR / TU = QP / TS
9 / 19 = 6 / TS
Cross multiply
9 × TS = 19 × 6
9 × TS = 114
Divide both side by 9
TS = 114 / 9
TS = 12.7
