F(x) = x^2. What is g(x)
Answer:
g(x) = - x² - 4 ⇒ A
Step-by-step explanation:
Let us revise the reflection and translation of a function
If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h) If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h) If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – kf(x) = x² is the blue curve
g(x) is its image is the red curve
∵ g(x) is the image of f(x)
∵ f(x) is opened upward
∵ g(x) is opened downward
→ That means the sign of y-coordinates of all points on the blue
graph are opposite
∴ f(x) is reflected about the x-axis
∴ Its image is - f(x)
∵ The vertex of f(x) is (0, 0)
∵ The vertex of g(x) = (0, -4)
→ That means the function translated 4 units down
∴ - f(x) is translated 4 units down
∴ Its image is - f(x) - 4
∴ g(x) = - f(x) - 4
∵ f(x) = x²
∴ g(x) = - x² - 4
Write 64 as a product of primes.
Use index notation where appropriate.
Answer:
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Write 64 as a product of primes.
Use index notation where appropriate.
[tex]{\huge{\pink{\underline{\underline{Solution:}}}}}[/tex]
[tex]Prime\ no.\ is\ 2[/tex]
Factorisation of 64=2×2×2×2×2×2
[tex]{2}^{6} [/tex]
Which equation shows that (x^4)^3=x^12
Answer:
A
Step-by-step explanation:
based on exonent rule (#^x)^y=#^xy
Answer:
Its option B, because exponents add when the problem is based on multiplication.
PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA POINTS** !! DONT SKIP :((
Answer:
Fraction: 9/10
Decimal: 0.9
Percent: 90%
A plane flew at a constant speed and traveled 762762762 miles in 555 hours.
How many miles would the plane travel in 333 hours at the same speed?
Answer:
457657657.2
Step-by-step explanation:
(762762762/5)*3=457657657.2 miles
Jina bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $400 more than the desktop. She paid for the computers using two different financing plans. For the desktop the interest rate was 7% per year, and for the laptop it was 8% per year. The total finance charges for one year were $275. How much did each computer cost before finance charges?
Answer:
2100
Step-by-step explanation:
The laptop costs $300 less than the desktop, so...
let x = cost of laptop
then x+300 = cost of desktop
The total finance charge of $252 is from 7% of the cost of the laptop and 6% of the cost of the desktop:
252+=+.07%28x%29+%2B+.06%28x%2B300%29
252+=+.07x+%2B+.06x+%2B+18
234+=+.13x
1800+=+x
The cost of the laptop is x = $1800;
the cost of the desktop is x+300 = $2100
In a city with one hundred taxis,1 is blue, and 99 are green. A witness observes a hit-and-run by a taxi at night and recalls that the taxi was blue, so the police arrest the blue taxi driver who was on duty that night.The driver pro claims his in no cence and hires you to defend him in court. You hire a scientist to test the witness' ability to distinguish blue and green taxi's under conditions similar to the night of the accident.The data suggests that the witness sees blue cars as blue 99% of the time,and green cars as blue 2% of the time.
Required:
Use this information to perform an analysis where you show that there is reasonable doubt about your clients' guilt
Answer:
the probability the car was actually blue as claimed by the witness is 33.33%. This is a low percentage and thus, there is a reasonable doubt about the guilt of the client.
Step-by-step explanation:
We are given;
P(car is blue) = 1% = 0.01
P(car is green) = 99% = 0.99
P(witness said blue | car is blue) = 99% = 0.99
P(witness said blue | car is green) = 2% = 0.02
We will solve this by using Bayes’ formula for inverting conditional probabilities:
Thus;
P(car is blue | witness said blue) =
[P(witness said blue | car is blue) × P(car is blue)] / [(P(witness said blue | car is blue) × P(car is blue)) + (P(witness said blue | car is green) × P(car is green))]
Plugging in the relevant values gives;
(0.99 × 0.01)/((0.99 × 0.01) + (0.02 × 0.99)) = 0.3333
Thus, the probability the car was actually blue as claimed by the witness is 0.3333 or 33.33%
Help me out please
I need it done by Monday
Answer:
1 C
2 D
3 C
4 B
5 A
6 C
Step-by-step explanation:
Answer: 1 C
2 D
3 C
4 B
5 A
6 C
Step-by-step explanation:
Please HELPPPPPPPPPPPPPPPPPP
8x-6≥58
Answer:
x=8 but with the less than equal to sign
Step-by-step explanation:
you would add 6 to the -6 then add it to the 58. The 6 cancel so then add the 58 and the 6 when you do that you get 64 so now you are left with 8x with same sign and 64 now you would divide both side by 8 and you should get x less than or equal to 8
Answer: 8x -6 < 58
Step-by-step explanation:
8x -6 = -48 and -48 is less then 58 so it’s less than 58!
c/3 = 30/5 apply the order of operations and show work
Answer:
c = 18
Step-by-step explanation:
Given
[tex]\frac{c}{3}[/tex] = [tex]\frac{30}{5}[/tex] = 6
Multiply both sides by 3
c = 3 × 6 = 18
there’s the graph so yeah
Answer:
what
Step-by-step explanation:
8.
Fred's dog has been putting on weight and the veterinarian is concerned. At the dog's most recent veterinarian appointment in September the dog weighed 45 pounds. This was a 25% increase since the dog's last veterinarian appointment that was in March. How much did Fred's dog weigh at the veterinarian appointment in March?
Answer:
Fred's dog weighed 33.75 pounds at the appointment in March
Step-by-step explanation:
First you need to convert 25% to a decimal by moving the percent sign twice to the left and you will get 0.25.
Then you multiply 45 by 0.25 to find 25% of 45.
45 x 0.25= 11.25
After multiplying, you just have to subtract the product (11.25) by 45.
45 - 11.25 = 33.75
This is the same was doing 45-25%
Use rounding to estimate the product. Is your estimate an underestimate or an overestimate? 8 × 9.82
Answer:
Over
Step-by-step explanation:
Which inequality represents the values of x that ensure triangle ABC exists?
A.
0.5 < x < 7.5
B.
3.0 < x < 7.5
C.
-0.5 < x < 7.5
D.
-3.0 < x < 7.5
Answer:
A. 0.5 < x < 7.5
Step-by-step explanation:
The United States Coast Guard assumes the mean weight of passengers in commercial boats is 185 pounds. The previous value was lower, but was raised after a tragic boating accident. The standard deviation of passenger weights is 26.7 pounds. The weights of a random sample of 48 commercial boat passengers were recorded. The sample mean was determined to be 177.6 pounds. Find the probability that a random sample of passengers will have a weight that is as extreme or more extreme (either above or below the mean) than was observed in this sample. (Round your answer to 3 decimal places. Example: If the answer is 0.8976 then you would enter 0.898 in the answer box.) Note: As extreme or more extreme means that we are not only interested in values that are lower than the ones we observed, but also values that are as far away from the mean as ours in the positive direction.
Answer:
0.973
Step-by-step explanation:
Given the following :
Population mean (μ) = 185
Standard deviation (σ) = 26.7
Sample mean (m) = 177.6
Sample size (n) = 48
P(m > 177.6)
Z = (m - μ) / σ/√n
Z = (177.6 - 185) / (26.7/√48)
Z = −1.920176
P( z > - 1.920) = 1 - p(z < - 1.92)
Using the z table :
1 - p(z < - 1.920) = 1 - 0.0274 = 0.9726
= 0.973
Which of the following relations be a function? Select all that apply.
Evaluate the expression when y=2
y² – 5y—6
A statistician believes that women received more bachelor's degrees than men did last year. To test this claim, she selects colleges and universities randomly and compares the number of bachelor's degrees awarded to men and women. Suppose that data were collected for a random sample of 7 colleges and universities, where each difference is calculated by subtracting the number of degrees earned by men from the number of degrees earned by women. Assume that the number of degrees is normally distributed. The statistician uses the alternative hypothesis Ha:μd>0. Using a test statistic of t≈2.968, which has 6 degrees of freedom, determine the range that contains the p-value.
Answer:
0.0125
Step-by-step explanation:
The P-value can be calculated by using excel function T.DIST.RT(2.968,6).
Right tail is used in the function because our alternative hypothesis has greater than sign (>) whereas 2.968 represent test statistic value and 6 represents degree of freedom. The resultant p-value from excel function is 0.0125.
Or if we use t- distribution right tail area table, we see that 6 for degree of freedom the value in table is there are two value 2.44691 and 3.14627 which corresponds to p=0.025 and p=0.01. As 2.44691 is smaller than 2.968 so we take p=0.01 against 3.14627. Thus, in this scenario p-value would be 0.01.
Oliver is playing a game with his friends. Each player gets
7 pieces. In all, there are 70 pieces on the game board.
Which number sentence can be used to find the number
of people playing the game?
Help please
Answer: 70/7
Step-by-step explanation: If each player gets 7 pieces, and there are 70 pieces in total, you would divide the amount of pieces each player gets from the actual pieces.
Read the question tell me if it’s hard for a 5 grader
Answer:
No, all you are doing is ordering them from least to greatest value. Your answer would be C.
Step-by-step explanation:
Answer:
danggg them fifth graders are gonna break there head
Step-by-step explanation:
There are 285 seventh-graders at Greg's school.
If there are 19 more girls than boys, how many seventh-grade boys are there? How many girls are there?
Answer:
124 boys and 161 girls
Step-by-step explanation:
There are 285 students total. Divide 285 by 2, you get 142.5. Since you can't have half a student, lets round it up to 143. Now, there are 19 more girls than guys, so you would subtract 19 from 143. When you do that, (143-19) you get 124. Then you take 285 and subtract 124. You get 161.
Hope this is correct!
on a mountain the temperature decreases 18 degrees fahrenheit every 500 ft.what integer represents the change in temperature at 20,000 feet?
Step-by-step explanation:
first you double the temperature change and the hight of change being 18f and 500ft
this makes 36f and 1000ft
you then divide 20000 by 1000 witch is slightly easyer than 20000 divided by 500
this anwser is 20
then do 36-²⁰ witch you have to work out since i can do that in my head right now
Write 600 as the product of prime factors give your answer in index
Answer:
5²×2³×3
Step-by-step explanation:
600=5×5×2×3×2×2
In index form this would be 5²×2³×3
Confidence Interval Application Many people feel that the drying of pavement marking paint is much too slow. You spend several days looking for the fastest drying paint you can find; you plan to measure the time (in seconds) for this paint to dry. From information provided by the paint supplier, you believe the time to dry is normally distributed with a standard deviation of 4 seconds. How many paint samples would you need to test to be able to obtain an estimate of paint drying time that is within 1.5 seconds of the actual mean drying time with a probability of 97%
Answer:
The sample size is [tex]n =33[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is E = 1.5 seconds
The standard deviation is s = 4 seconds
Given that the confidence level is 97% then the level of significance is mathematically represented as
[tex]\alpha =( 100 -97)\%[/tex]
=> [tex]\alpha = 0.03[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.17[/tex]
Generally the sample size is mathematically represented as
[tex]n =[ \frac{Z_{\frac{\sigma }{2 } } * \sigma }{E} ]^2[/tex]
=> [tex]n =[ \frac{2.17 * 4 }{1.5} ]^2[/tex]
=> [tex]n =33[/tex]
Find p in terms of m if = r, r = p, p ≠0, and m > 0
Find the zeros of the function.
f(x) = 3x2 – 8x – 16
Answer:
amusing you mean 3x^2-8x-16 the answer is when x is equal to -4/3 and 4
Step-by-step explanation:
3x^2-8x-16 ------> (3x+4)(x-4)
3x+4=0 ----> 3x=-4 ----> x=-4/3
x-4=0 ----> x=4
WILL MARK BRAINLIEST Find the value of x in each case: c L, M ∈ KN
Answer:
x=27°
Step-by-step explanation:
2x+72° = x+<PLM
<PLM = x+72°
3x = x+<PML
<PML = 2x
(x)+(x+72)+(2x)=180°
4x = 108°
x = 27°
if 57.75 is after a 30% taken off then what was the original price
Answer: 40.425
Step-by-step explanation: multiply 57.75 by .3 to get 17.325 and then subtract that from the original amount
round 163,688 to the nearest hundred thousand
Answer:
200,000
Step-by-step explanation:
I hope this helped!
From my sis: Round each mixed number to the nearest whole number then estimate the difference.
8 9/11-8 3/8
A: 10
B: 9
C: 11
D: 8
Answer:
Step-by-step explanation: a