Which is one of the transformations applied to the graph of f(x) = X^2 to change it into the graph of g(x) = -x^2 +16x - 44
Answer: First a horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.
Step-by-step explanation:
Let's construct g(x) in baby steps.
Ok, we start with f(x) = x^2
The first thing we have is a horizontal translation of A units (where A is not known)
A vertical translation of N units to the right, is written as:
g(x) = f(x - N)
Then we have:
g(x) = (x - A)^2 = x^2 - 2*A*x + A^2
Now, you can see that actually g(x) has a negative leading coefficient, which means that we also have an inversion over the x-axis.
Remember that if we have a point (x, y), a reflection over the x-axis transforms our point into (x, -y)
Then if we apply also a reflection over the x-axis, we have:
g(x) = -f(x - A) = -x^2 + 2*A*x - A^2 = -x^2 + 16*x - 44
Then:
2*A = 16
A*A = 44.
The first equation says that A = 16/2 = 8
But 8^2 is not equal to 44.
Then we need another constant coefficient, which is related to a vertical translation.
If we have a relation y = f(x), a vertical translation of N units up, will be
y = f(x) + N.
Then:
g(x) = -f(x - A) + B
-x^2 + 2*A*x - A^2 + B = x^2 + 16*x - 44
Now we have:
2*A = 16
-A^2 + B = - 44
From the first equation we have A = 8, now we replace it in the second equation and get:
-8^2 + B = -44
B = -44 + 64 = 20
Then we have:
The transformation is:
First an horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 7.2 to 4.5
Answer:
[tex]\frac{8}{5}[/tex]
Step-by-step explanation:
Given
7.2 : 4.5 ← multiply both parts by 10
= 72 : 45 ← divide both parts by 9
= 8 : 5
= [tex]\frac{8}{5}[/tex]
A simple random sample of 28 Lego sets is obtained and the number of pieces in each set was counted.The sample has a standard deviation of 12.65. Use a 0.05 significance level to test the claim that the number of pieces in a set has a standard deviation different from 11.53.
Answer:
Step-by-step explanation:
Given that:
A simple random sample n = 28
sample standard deviation S = 12.65
standard deviation [tex]\sigma[/tex] = 11.53
Level of significance ∝ = 0.05
The objective is to test the claim that the number of pieces in a set has a standard deviation different from 11.53.
The null hypothesis and the alternative hypothesis can be computed as follows:
Null hypothesis:
[tex]H_0: \sigma^2 = \sigma_0^2[/tex]
Alternative hypothesis:
[tex]H_1: \sigma^2 \neq \sigma_0^2[/tex]
The test statistics can be determined by using the following formula in order to test if the claim is statistically significant or not.
[tex]X_0^2 = \dfrac{(n-1)S^2}{\sigma_0^2}[/tex]
[tex]X_0^2 = \dfrac{(28-1)(12.65)^2}{(11.53)^2}[/tex]
[tex]X_0^2 = \dfrac{(27)(160.0225)}{132.9409}[/tex]
[tex]X_0^2 = \dfrac{4320.6075}{132.9409}[/tex]
[tex]X_0^2 = 32.5002125[/tex]
[tex]X^2_{1- \alpha/2 , df} = X^2_{1- 0.05/2 , n-1}[/tex]
[tex]X^2_{1- \alpha/2 , df} = X^2_{1- 0.025 , 28-1}[/tex]
From the chi-square probabilities table at 0.975 and degree of freedom 27;
[tex]X^2_{0.975 , 27}[/tex] = 14.573
[tex]X^2_{\alpha/2 , df} = X^2_{ 0.05/2 , n-1}[/tex]
[tex]X^2_{\alpha/2 , df} = X^2_{0.025 , 28-1}[/tex]
From the chi-square probabilities table at 0.975 and degree of freedom 27;
[tex]X^2_{0.025 , 27}=[/tex] 43.195
Decision Rule: To reject the null hypothesis if [tex]X^2_0 \ > \ X^2_{\alpha/2 , df} \ \ \ or \ \ \ X^2_0 \ < \ X^2_{1- \alpha/2 , df}[/tex] ; otherwise , do not reject the null hypothesis:
The rejection region is [tex]X^2_0 \ > 43.195 \ \ \ or \ \ \ X^2_0 \ < \ 14.573[/tex]
Conclusion:
We fail to reject the null hypothesis since test statistic value 32.5002125 lies between 14.573 and 43.195.
Suppose that 10% of all steel shafts produced by a process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked. What is the (approximate) probability that X is:
a. Less than 30?
b. Between 15 and 25 (inclusive)?
Answer:
a?
Step-by-step explanation:
Lester Hollar is vice president for human resources for a large manufacturing company. In recent years he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the last six months. Below are the results. At the .05 significance level, can he conclude that the number of absences has declined? Estimate the p-value.
Employee Before After
1 6 5
2 6 2
3 7 1
4 7 3
5 4 3
6 3 6
7 5 3
8 6 7
Answer:
t >± 1.895
t= 0.1705
Step-by-step explanation:
The null and alternative hypotheses are
H0: μd=0 Ha: μd>0
Significance level is set at ∝= 0.05
The critical region for t df=7 t >± 1.895
The test statistic under H0 is
t = d/ sd/ √n
Which has t distribution with n-1 degrees of freedom
Employee After Before d = after - before d²
1 6 5 1 1
2 6 2 4 16
3 7 1 6 36
4 7 3 4 16
5 4 3 1 1
6 3 6 -3 9
7 5 3 2 4
8 6 7 -1 1
∑ 14 84
d`= ∑d/n= 14/8= 1.75
sd²= 1/8( 84- 14²/8) = 1/8 ( 84 - 24.5) = 59.5
sd= 7.7136
t= 3/ 7.7136/ √8
t= 0.1705
Since the calculated value of t= 0.1705 < ± 1.895 therefore reject the null hypothesis at 5 % significance level . On the basis of this we cannot conclude that the number of absences has declined.
Rearrange the equation A = xy to solve for x.
Ox=y
A
1
Ox=
Ау
х
OX=
y
Ox-A
y
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Answer:
x = A/y
Step-by-step explanation:
Divide both sides of the equation by y
A = xy
A/y = (xy)/y . . . . . . divide by y
A/y = x . . . . . . . . . .simplify
x = A/y . . . . . . . . . write with x on the left
The distance a race car travels is given by the equation, [tex]d=v_{0} t+\frac{1}{2} at^{2}[/tex], where [tex]v_{0}[/tex] is the initial speed of the race car, a is the acceleration and t is the time traveled. Near the beginning of a race, the driver accelerates for 9 seconds at a rate of [tex]4m/s^{2}[/tex]. The driver's initial speed was 75 m/s.
Find the driver's average speed during the acceleration.
Step-by-step explanation:
here's the answer to your question
find the greatest number than divides 45 60 75 without leaving remainder
Answer:
15
Step-by-step explanation:
15 is the greatest number that divides 45 60 75 without leaving remainder
Answer:
15
Step-by-step explanation:
Let write the factors of each number:
45: (1,3,5,9,15,45)
60:(1,2,3,4,5,6,10,12,15,20,30,60)
75:(1,3,5,15,15,75).
The greatest common factor is 15. So the answer is 15.
Simplify -(7/x-2)+(2x/x) Simplify your answer as much possible
Answer:
[tex]\dfrac{2x-11}{x-2}[/tex]
Step-by-step explanation:
Simplify the fractions, then add.
[tex]-\dfrac{7}{x-2}+\dfrac{2x}{x}=\dfrac{-7}{x-2}+2=\dfrac{-7}{x-2}+\dfrac{2(x-2)}{x-2}\\\\=\dfrac{2x-4-7}{x-2}=\boxed{\dfrac{2x-11}{x-2}}[/tex]
_____
Note that this comes with the restriction that x ≠ 0.
Ms Perez khẳng định rằng: Có khả năng công ty của cô ấy sẽ mở chi nhánh ở Phoenix (thành phố thủ phủ của tiểu bang Arizona, Mỹ). Khi đó, cô ấy có khả năng sẽ được bổ nhiệm là giám đốc ở chi nhánh mới. Tìm khả năng để Ms Perez trở thành giám đốc ở Phoenix
Answer:
Could you ask your question in English?
Step-by-step explanation:
The radar system beeps once every second. How many times will it beep in 3 days?
Answer:
259200
Step-by-step explanation:
so there are 86400 in one day. multiply by 3.
Answer:
259200
Step-by-step explanation:
60x24x3x60=
True or false? If it is false, replace the underlined word with the correct word. (Constant is underlined) The constant term in a polynomial expression is a number that is not multiplied by a
variable.
Answer:
true
Step-by-step explanation:
what else would it be. that is exactly the reason why we have constants.
fill in the missing. 1:1000=1cm:_?
Answer:
meter
10 meters
Or
a dekameter
If you want to turn a ball into a giant water balloon, how many cubic feet of lake water can you fill it with if the radius of this balloon is 1.5 feet?
Answer:
14.13 cubic feet of lake water can fill the given balloon.
Step-by-step explanation:
concept used:
volume of sphere = 4/3 [tex]\pi r^3[/tex]
where r is the radius of sphere
we take [tex]\pi[/tex] = 3.14
_____________________________________
shape of balloon can be taken as spherical.
Amount water filled in the balloon will be equal to capacity of balloon which is equal to volume of spherical balloon.
Given radius of balloon = 1.5 feet
Thus, volume of balloon = 4/3 [tex]\pi[/tex] 1.5^3 = 4/3*3.14*1.5^3
volume of balloon = 42.39/3 = 14.13 cubic feet
Thus, 14.13 cubic feet of lake water can fill the given balloon.
radius is 21 5/8 incercepted by 5Pi/6? What is arc lenght?
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Answer:
(18 1/48)π ≈ 56.61 units
Step-by-step explanation:
Arc length is the product of radius and intercepted arc in radians:
s = rθ
s = (21 5/8)(5π/6) = (18 1/48)π ≈ 56.61 . . . units
Question 18 i will maek the brainliest:)
Answer:
Median: 14.6, Q1: 6.1, Q3: 27.1, IR: 21, outliers: none
Step-by-step explanation:
Step 1: order the data from the least to the largest.
2.8, 3.9, 5.3, 6.1, 6.5, 7.1, 12.5, 14.6, 16.4, 16.4, 20.8, 27.1, 28.1, 30.9, 53.5
Step 2: find the median.
The median is the middle value, which is the 8th value in the data set.
2.8, 3.9, 5.3, 6.1, 6.5, 7.1, 12.5, [14.6,] 16.4, 16.4, 20.8, 27.1, 28.1, 30.9, 53.5
Median = 14.6
Step 2: Find Q1,
Q1 is the middle value of the lower part of the data set that is divided by the median to your left.
2.8, 3.9, 5.3, (6.1), 6.5, 7.1, 12.5, [14.6], 16.4, 16.4, 20.8, 27.1, 28.1, 30.9, 53.5
Q1 = 6.1
Step 3: find Q3.
Q3 is the middle value of the upper part of the given data set.
2.8, 3.9, 5.3, 6.1, 6.5, 7.1, 12.5, [14.6], 16.4, 16.4, 20.8, (27.1), 28.1, 30.9, 53.5
Q3 = 27.1
Step 4: find interquartile range (IR)
IR = Q3 - Q1 = [tex] 27.1 - 6.1 = 21 [/tex]
Step 5: check if there is any outlier.
Formula for checking for outlier = [tex] Q1 - 1.5*IR [/tex]
Then compare the result you get with the given values in the data set. Any value in the data set that is less than the result we get is considered an outlier.
Thus,
[tex] Q1 - 1.5*IR [/tex]
[tex]6.1 - 1.5*21 = -25.4[/tex]
There are no value in the given data set that is less than -25.4. Therefore, there is no outlier.
Given the central angle, name the arc formed.
Major arc for ∠EQD
A. EQDˆ
B. GDFˆ
C. EGDˆ
D. EDˆ
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Answer:
C. EGD
Step-by-step explanation:
A major arc is typically named using the end points and a point on the arc. Here, the end points are E and D, and points on the major arc include C, G, and F. The major arc ED could be named any of
arc ECDarc EGD . . . . choice Carc EFDOf course, the reverse of any of these names could also be used: DCE, DGE, DFE.
What is the probability that a randomly selected individual on this campus weighs more than 166 pounds? (express in decimal form and round final answer to 4 decimal places)
Answer:
hello attached is the missing part of your question and the answer of the question asked
answer : 0.2951
Step-by-step explanation:
Given data:
number of persons allowed in the elevator = 15
weight limit of elevator = 2500 pounds
average weight of individuals = 152 pounds
standard deviation = 26 pounds
probability that an individual selected weighs more than 166 pounds
std = 26 , number of persons(x) = 15, average weight of individuals(u) = 152 pounds
p( x > 166 ) = p( x-u / std, 166 - u/ std )
= p ( z > [tex]\frac{166-152}{26}[/tex] )
= 1 - p( z < 0.5385 )
p( x > 166 ) = 1 - 0.70488 = 0.2951
What is the slope of the line shown below?
A. -3/2
B. 3/2
C. 2/3
D. -2/3
Answer:
2/3
Step-by-step explanation:
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= (1- -7)/(9 - -3)
= ( 1+7)/( 9+3)
= 8/12
Simplifying
= 2/3
Answer:
C. 2/3
Step-by-step explanation:
You can use the equation: [tex]y_{2} - y_{1}/x_{2} - x_{1}[/tex] to find the slope.
y2 is equal to the y coordinate of the second point: 1
y1 is equal to the y coordinate of the first point: -7
x2 is equal to the x coordinate of the second point: 9
x1 is equal to the x coordinate of the first point: -3
So if you plug these values into the equation, you will get:
1 - (-7)/ 9- (-3)
= 1 + 7/ 9 + 3
= 8/12
= 2/3
What is the y value when x is -5? What about 5?
I’ve done all three functions and the answers are -9, 24 and -4 but I don’t know which one to answer as the y value with. Please help.
The simplified form of the expression (5.23x + 3.76) − (3.67x − 6.39) is?
Answer:
1.56x+10.15
Step-by-step explanation:
Answer:
1.56x + 10.15
Step-by-step explanation:
(5.23x + 3.76) – (3.67x – 6.39)
(a + b) – (c – d) = a + b – c + d
Remove the parentheses and change the signs as needed:
5.23x + 3.76 – 3.67x + 6.39.
Group the like terms and simplify:
5.23x – 3.67x + 3.76 + 6.39
1.56x +10.15.
The simplified form of (5.23x + 3.76) – (3.67x – 6.39) is 1.56x + 10.15.
r-(-4x - (y + y)); use x = -4, and y = -3 evaluate
Answer:
insert values of x and y
r - ( -4(-4) - ( -3-3))
r - ( 16 +6 )
r - 22
Doneeeeeeeeeeeeeeeeee3
Which of the following is the correct notation of the complex number?
Answer:
-84 + 10i
Step-by-step explanation:
Standard Complex Form: a + bi
Step 1: Evaluate
√-100 = √-1 x √100 = i x 10 = 10i
-84 = -84
Step 2: Combine
10i - 84
Step 3: Rearrange
-84 + 10i
Answer:
Last Option
Step-by-step explanation:
√-100 - 84
(√(100×-1)) - 84
(√100)(√-1)-84
√-1 = i
10i - 84 or -84 + 10i
One of two small restaurants is chosen at random with equally likely probability, and then an employee is chosen at random from the chosen restaurant. Restaurant #1 has 10 full-timers and 6 part-timers. Restaurant #2 has 7 full-timers and 9 part-timers. What is the probability that Restaurant #1 was chosen at random, given that a full-time employee was chosen? Your answers should be rounded to 4 digits after the decimal.
Answer:
P(1 |F) = 10/17
Step-by-step explanation:
Let events
1 = restaurant 1
2 = restaurant 2
F = full-time worker chosen
P = part-time worken chosen
P(1 and F) = 1/2 * 10/16 = 5/16
P(2 and F) = 1/2 * 7/16 = 7/32
P( (1 or 2) and F ) = P(F) = 5/16+7/32 = 17/32
P(1 | F) Probability of choosing restaurant 1 given a full-time was chosen
= P(1 and F) / P(F)
= 5/16 / (17/32)
= 5/16 * 32/17
= 10 / 17
Jimmy measured to find the total number of square inches that covered the top of a rectangular table.
Which was Jimmy measuring?
0
A. area
B. circumference
C. distance
D. perimeter
E. volume
Answer: it is a
Step-by-step explanation:
6x — Зу = 5
y - 2x = 8
How many solutions does the system have?
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Answer:
none
Step-by-step explanation:
Multiplying the second equation by -3 gives ...
6x -3y = -24
Values of x and y that satisfy this equation cannot also satisfy the first equation ...
6x -3y = 5
There are no solutions to this system of equations.
__
The equations describe parallel lines. There is no point of intersection.
Each Friday, the sixth grade students in Mr. Shin's physical education class spend the first five minutes doing crunches. Instead of keeping track of the weekly total number of crunches, Mr. Shin keeps track of how they do compared to the week before, and then records the result as a positive or negative number. Record the number for each of the following:
Ben did 10 more crunches this week than last week. What number would Mr. Shin record?
Gail did 8 less crunches this week than last week. What number would Mr. Shin record?
Nathaniel did the same number of crunches this week as last week. What number would Mr. Shin record?
awnser asap
Answer:
Mr. Shim would record the number +10 or 10 for Ben because of the word "more".
For Gail, Mr. Shin would record the number -8 because of the word, "less''.
Since Nathaniel did not improve or decrease the number of crunches, Mr. Shin would record the number 0.
I hope this helps better
(-1, 4) and (-2, 2).
Answer:
Slope : 2
slope-intercept: y = 2x + 6
Point-slope (as asked): y - 4 = 2 (times) (x + 1)
standered: 2x - y = -6
Step-by-step explanation:
BRAINLIEST IF CORRECT!!! and 15 points solve for z -cz + 6z = tz + 83
Answer:
z = 83/( -c+6-t)
Step-by-step explanation:
-cz + 6z = tz + 83
Subtract tz from each side
-cz + 6z -tz= tz-tz + 83
-cz + 6z - tz = 83
Factor out z
z( -c+6-t) = 83
Divide each side by ( -c+6-t)
z( -c+6-t)/( -c+6-t) = 83/( -c+6-t)
z = 83/( -c+6-t)
I need some help with simplifying expressions, please. 8y - 9y =
As your first step to this problem, change the minus sign to plus a negative.
So we have 8y + -9y.
8y + -9y simplifies to -1y which is our final answer.
Note that if you wrote -y instead, it means the same thing.
However, use the 1 to help avoid confusion if you need it.