Answer:
C. With a p-value less than 0.0001, there is sufficient evidence to reject the null hypothesis and accept the alternative as true.
Step-by-step explanation:
She performed an hypothesis test with the sample of size n=15 that she takes. The t-statistic has a value of 6.661.
The degrees of freedom for this sample size are:
[tex]df=n-1=15-1=14[/tex]
The P-value for a statistic t=6.661 and 14 degrees of freedom is:
[tex]\text{P-value}=P(t>6.661)=0.00001[/tex]
With these P-value we know that the effect is significant and the null hypothesis is rejected. There is enough evidence to support the claim that the mean height of Mountain Ash trees is greater than the coastal Douglas Firs.
Trey is out shopping and sees that striped shirts are on sale for $25.00 each, and plaid pants are on sale for $22.50 each. He buys 2 shirts and 4 pairs of pants. What is the total of his
purchase?
The total was $______
Answer:
$140
Step-by-step explanation:
You can add up the prices to find the total. Most of us find it easier to multiply the price by the number of items.
cost of 2 shirts = (2)($25.00) = $50
cost of 4 pants = (4)(22.50) = $90
The total was $50 +90 = $140.
Aunit cube is shown.
Select the true statements
A unit cube can have a length of 1 inch, a width of 1 inch, and a height of 2 inches
A unit cube has one cubic unit of volume.
Another unit cube with the same length, width and height as the unit cube shown would have
the same volume
Aunit cube can be used to measure the weight of a rectangular prism.
A unit cube can be used to measure the volume of a rectangular prism.
Aunit cube can have a length of 4 feet, a width of 4 feet, and a height of 4 feet.
A unit cube can be used to determine the angle measures of a rectangular prism,
4 of 10 Answered
Session Timer: 11:03
Session Score: 259
Answer:
A unit cube has one cubic unit of volume.
Another unit cube with the same length, width and height as the unit cube shown would have the same volume
Step-by-step explanation:
A cube is a shape formed from the combination of a square.
A cube has equal sides.
But a unit cube has equal sides and equal volume to be equal to one, i.e unity.
In the expression what is the numerical coefficient in this question ?
Answer:
-7
Step-by-step explanation:
The numerical coefficient of [tex] - 7yz^2 [/tex] is - 7.
The coefficient of -7yz² is -7
In the given equation,
5x⁶÷3xy-7yz²+2y÷z
the coefficient is -7 , because the coefficient is the constant term of an expression.
A numerical coefficient is a constant multiplier of the variable in a term. And here, -7 is preceded by -7yz²
Hence it is the numerical coefficient.
learn more about numerical coefficients:
brainly.com/question/25420238
A company sells eggs whose individual weights are normally distributed with a mean of 70\,\text{g}70g70, start text, g, end text and a standard deviation of 2\,\text{g}2g2, start text, g, end text. Suppose that these eggs are sold in packages that each contain 444 eggs that represent an SRS from the population. What is the probability that the mean weight of 444 eggs in a package \bar x x ˉ x, with, \bar, on top is less than 68.5\,\text{g}68.5g68, point, 5, start text, g, end text?
Answer:
6.68% probability that the mean weight is below 68.5g.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 70, \sigma = 2, n = 4, s = \frac{2}{\sqrt{4}} = 1[/tex]
Probability that the mean weight is below 68.5g:
This is 1 subtracted by the pvalue of Z when X = 68.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{68.5 - 70}{1}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
6.68% probability that the mean weight is below 68.5g.
Answer:
P(x ∠ 68.5) = 0.07
Step-by-step explanation:
Got it right on khan.
The price of a ring was increased by 9% to £1800. What was the price before the increase? Give your answer to the nearest penny.
Answer:
1651
Step-by-step explanation:
let s say that the price before the increase is x
to apply an increase of 9% it does x + x*0.09 = x*(1+0.09)=x*1.09
and we know that this value is 1800
so
x*1.09=1800
<=>
x = 1800/1.09=1651.376147
to the nearest penny it gives 1651
Answer:
Hello!
Answer: 1651
I hope that was correct. Please let me know, thank you!
Step-by-step explanation:
PLEASE HELP the inverse of the function graphed below is a function
True or false
Functions
Function NotationVertical Line Test
ApplicationStep 1: DefineLet's see what we are given.
We are given a graph of an inverse of a function.
Step 2: IdentifyWe need to figure out whether the graphed inverse function is a function or not.
By the definition of a function, we know that every x input must correlate with one y output. In layman's terms, each respective x input has its own specific y output.
This definition builds the foundation of the Vertical Line Test. We can use this simple "tool" to verify whether or not a given graph is a function or not.
By placing a vertical line "on" the graph, we can move it to determine whether an x input has only one y output.If a graph passes the Vertical Line Test, it is said to be a function.If a graph fails the Vertical Line Test, it is said to not be a function, but rather a relation, etc.Step 3: TestWhen we apply the Vertical Line Test to the graphed inverse function, we can see that every x input has only one specific y output.
∴ we can conclude that the graphed inverse function is indeed a function.
AnswerThe answer to the question would be A. True.
___
Learn more about functions: https://brainly.com/question/30017262
Learn more about Algebra I: https://brainly.com/question/17011730
___
Topic: Algebra I
Unit: Functions
the ratio of the ages of Kissi and Esinam is 3:5 and that of Esinam and Lariba is 3:5 and
the sum of the ages of all 3 is 147 years, what is the age difference between oldest the youngest
Answer:
The age difference between oldest the youngest is of 48 years.
Step-by-step explanation:
We can solve this question using a system of equations.
I am going to say that:
Kissi's age is x.
Esinam's age is y.
Lariba's age is z.
The ratio of the ages of Kissi and Esinam is 3:5
This means that [tex]\frac{x}{y} = \frac{3}{5}[/tex], so [tex]5x = 3y[/tex]
That of Esinam and Lariba is 3:5
This means that [tex]\frac{y}{z} = \frac{3}{5}[/tex], so[tex]5y = 3z[/tex]
The sum of the ages of all 3 is 147 years
This means that [tex]x + y + z = 147[/tex]
What is the age difference between oldest the youngest
z is the oldest
x is the youngest.
First i will find y.
We have that, from the equations above: [tex]x = \frac{3y}{5}[/tex] and [tex]z = \frac{5y}{3}[/tex]
So
[tex]x + y + z = 147[/tex]
[tex]\frac{3y}{5} + y + \frac{5y}{3} = 147[/tex]
The lesser common multiple between 5 and 3 is 15. So
[tex]\frac{3*3y + 15*y + 5*5y}{15} = 147[/tex]
[tex]49y = 147*15[/tex]
[tex]y = \frac{147*15}{49}[/tex]
[tex]y = 45[/tex]
Youngest:
[tex]x = \frac{3y}{5} = \frac{3*45}{5} = 27[/tex]
Oldest:
[tex]z = \frac{5y}{3} = \frac{5*45}{3} = 75[/tex]
Difference:
75 - 27 = 48
The age difference between oldest the youngest is of 48 years.
Some college professors make bound lecture notes available to their classes in an effort to improve teaching effectiveness. A study of business student's opinions of lecture notes. Two groups of students were surveyed - 86 students enrolled in a promotional strategy class that required the purchase of lecture notes, and 35 students enrolled in a sales/retailing elective that did not offer lecture notes. At the end of the semester :"Having a copy of the lecture notes was helpful in understanding the material." Responses were measured on a nine-point semantic difference scale, where 1="strongly disagree" and 9=" strongly agree." A summary of the results is reported in the follow:
Classes Buying Lecture Notes Classes Not Buying Lecture Notes
n1=86 n2=35
X1=8.48 X2=7.80
S21=.94 S22=2.99
a. Describe the two populations involved in the comparison.
b. Do the samples provides sufficient evidence to conclude that there is a difference in the mean responses of the two groups of the students? Test using α=.01
c. Construct a 99% confidence interval for (μ1-μ2). Interpret the result.
d. Would a 95% confidence interval for (μ1-μ2) be narrow or wider than the one you found in part c? Why?
Answer:
Step-by-step explanation:
a) The number of students sampled in both populations are large. We can assume that the populations are normally distributed. The populations are also independent.
b) This is a test of 2 independent groups. Let μ1 be the mean responses of students buying lecture notes and μ2 be the mean responses of students not buying lecture notes.
The random variable is μ1 - μ2 = difference in the mean responses of students buying lecture notes and the mean responses of students not buying lecture notes.
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0
This is a two tailed test.
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
From the information given,
x1 = 8.48
x2 = 7.8
s1 = 0.94
s2 = 2.99
n1 = 86
n2 = 35
t = (8.48 - 7.8)/√(0.94²/86 + 2.99²/35)
t = 1.32
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [0.94²/86 + 2.99²/35]²/[(1/86 - 1)(0.94²/86)² + (1/35 - 1)(2.99²/35)²] = 0.0706/0.00192021883
df = 37
We would determine the probability value from the t test calculator. It becomes
p value = 0.195
c) Since alpha, 0.01 < than the p value, 0.195, then we would fail to reject the null hypothesis. Therefore, at 5% significance level, the samples do not provide sufficient evidence to conclude that there is a difference in the mean responses of the two groups of the students.
d) The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
For a 99% confidence interval, the z score is 1.2.58. This is determined from the normal distribution table.
x1 - x2 = 8.48 - 7.8 = 0.68
z√(s1²/n1 + s2²/n2) = 2.58√(0.94²/86 + 2.99²/35) = 1.33
The confidence interval is
0.68 ± 1.33
The upper boundary for the confidence interval is
0.68 + 1.01 = 2.01
The lower boundary for the confidence interval is
0.68 - 1.33 = - 0.65
We are confident that the difference in population means responses between the students buying lecture notes and the students not buying lecture notes is between - 0.65 and 2.01
d) For a 95% confidence interval, the z score is 1.96.
z√(s1²/n1 + s2²/n2) = 1.96√(0.94²/86 + 2.99²/35) = 1.01
The confidence interval is
0.68 ± 1.01
The upper boundary for the confidence interval is
0.68 + 1.01 = 1.69
The lower boundary for the confidence interval is
0.68 - 1.01 = - 0.33
Therefore, a 95% confidence interval for (μ1-μ2) would be narrower. This is seen in the values in both scenarios.
Please help! Correct answer only, please! Consider the matrix shown below: Find the determinant of the matrix Q. A. -67 B. -65 C. 65 D. 67
Answer: d) 67
Step-by-step explanation:
[tex]determinant\ \left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&j\end{array}\right] = a\cdot det\left[\begin{array}{cc}e&f\\h&j\end{array}\right] -\ b\cdot det\left[\begin{array}{cc}d&f\\g&j\end{array}\right] +\ c\cdot det\left[\begin{array}{cc}d&e\\g&h\end{array}\right][/tex]
[tex]determinant\ \left[\begin{array}{ccc}2&3&4\\-3&2&1\\5&-1&6\end{array}\right] \\\\\\= 2\cdot det\left[\begin{array}{cc}2&1\\-1&6\end{array}\right] -\ 3\cdot det\left[\begin{array}{cc}-3&1\\5&6\end{array}\right] +\ 4\cdot det\left[\begin{array}{cc}-3&2\\5&-1\end{array}\right]\\\\\\=2[2(6)-1(-1)]-3[-3(6)-1(5)]+4[3(-1)-2(5)]\\\\\\=2(13)-3(-23)+4(-7)\\\\\\=26+69-28\\\\\\=\large\boxed{67}[/tex]
Alguien me puede ayudar con en esto por favor !!!
Answer:
y=cosx
Step-by-step explanation:
cosx has a domain of all real numbers
I need help! Someone help me please
Answer:
4. 27
Step-by-step explanation:
11-10=1 which is <=16
15-10=5 which is <=16
26-10=16 which is <=16
27-10=17 which isn't <=16
Therefore 27 doesn't satisfy the inequality
Answer:
4. 27
Step-by-step explanation:
w - 10 ≤ 16
w≤16 + 10
w ≤ 26
11 ≤ 26
15≤26
26≤26
26≤ 27 False
someone pls pls pls help me
Answer:
A, C, D, E
Step-by-step explanation:
According to the rational root theorem, any rational roots will be of the form ...
±(divisor of the constant)/(divisor of the leading coefficient)
The constant is 8, and its divisors are 1, 2, 4, 8.
The leading coefficient is 6, and its divisors are 1, 2, 3, 6.
So, no rational root will have 3 in the numerator, eliminating choices B and F. The remaining choices are possible rational roots:
A, 2/3C, -8D, 4E, -1/6Help me pleaseeee and thanks
Work Shown:
v - w = ( v ) - ( w )
v - w = ( -3i ) - ( 2-4i)
v - w = ( 0-3i ) - ( 2-4i)
v - w = 0-3i -2+4i
v - w = (0-2) + (-3i+4i)
v - w = -2 + i
A group of 8 friends (5 girls and 3 boys) plans to watch a movie, but they have only 5 tickets. If they randomly decide who
what is the probability that there are at least 3 girls in the group that watch the movle?
Answer:
53.57%
Step-by-step explanation:
We have to calculate first the specific number of events that interest us, if at least 3 are girls, they mean that 2 are boys, therefore we must find the combinations of 3 girls of 5 and 2 boys of 3, and multiply that, so :
# of ways to succeed = 5C3 * 3C2 = 5! / (3! * (5-3)!) * 3! / (2! * (3-2)!)
= 10 * 3 = 30
That is, there are 30 favorable cases, now we must calculate the total number of options, which would be the combination of 5 people from the group of 8.
# of random groups of 5 = 8C5 = 8! / (5! * (8-5)!) = 56
That is to say, in total there are 56 ways, the probability would be the quotient of these two numbers like this:
P (3 girls and 2 boys) = 30/56 = 0.5357
Which means that the probability is 53.57%
Answer:
Actually, the correct answer for plato users is option D
Step-by-step explanation:
D. 0.821
Find the area of a circle with radius, r = 5.7m.
Give your answer rounded to 2 DP.
The diagram is not drawn to scale.
(I attached the diagram below!)
Answer:
the area of the circle is 102.11 square metres
Please answer this correctly
Answer:
the base is 5 meters long.
Step-by-step explanation:
To find the a missing side when given the area you have to multiply the area by 2 which in this case would be 50 so 50/10 would be 5m which is your answer.
So the right answer is 5m
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment..
For what value of the variable will the value of 7y−2 be ten more than the value of 2y?
Answer:
y=2.4
Step-by-step explanation:
7y-2=2y+10
7y-2y=10+2
5y=12
y=12/5=2.4
Solve for the unknown value
X=______Degrees
Answer:
Step-by-step explanation:
_______________________________
Hey!!
Solution,
X+61+42=180[ sum of angle in triangle]
or,X+103=180
or,X=180-103
X=77°
So the value of X is 77°
Hope it helps..
Good luck on your assignment
____________________________
The probability of event A is 0.48, the probability of event A and B is 0.21, and the probability of events A or B is 0.89. What is the probability of event B? THE ANSWER IS 0.62
Answer:
P(B) = 0.62
Step-by-step explanation:
P(A or B) = P(A) + P(B) - P(A and B)
So, Putting the givens
0.89 = 0.48 + P(B) - 0.21
0.89 = 0.27 + P(B)
P(B) = 0.89 - 0.27
P(B) = 0.62
Please help me :( with this
Answer:
21
Step-by-step explanation:
Similar triangles. MNL is just ABC but 3/4 the size.
x = 8*3/4 = 6
perimeter woudl be 6+6+9 = 21
Find the volume of the cone below.
Answer:
[tex] V =\frac{1}{3} \pi r^2 h[/tex]
For this case we know that the radius is r=7cm and the height is h =11cm. And replacing we got:
[tex] V=\frac{1}{3} \pi (7cm)^2 (11cm)= \frac{1}{3} \pi (49cm^2) (11 cm)=\frac{539}{3} \pi cm^3[/tex]
And the best option would be:
[tex] V = \frac{539}{3} \pi cm^3 [/tex]
Step-by-step explanation:
For this case we know that the volume of the cone is given by:
[tex] V =\frac{1}{3} \pi r^2 h[/tex]
For this case we know that the radius is r=7cm and the height is h =11cm. And replacing we got:
[tex] V=\frac{1}{3} \pi (7cm)^2 (11cm)= \frac{1}{3} \pi (49cm^2) (11 cm)=\frac{539}{3} \pi cm^3[/tex]
And the best option would be:
[tex] V = \frac{539}{3} \pi cm^3 [/tex]
hord
12 cm
5 cm
Resu
5 cm
A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. A pyramid with the same base and half the
height of the prism is placed inside the prism, as shown in the figure.
SUME
The volume of the space outside the pyramid but inside the prism is
cubic centimeters,
Answer:
The volume of the space outside the pyramid but inside the prism is 225 cubic centimeters.
Step-by-step explanation:
To find this, you subtract the volume of the pyramid from the volume of the rectangular prism.
The prism and pyramid's bases is 25 cm²
The pyramid's height is 12÷2 or 6 cm
The volume formula for a prism is l×w×h
The volume formula for a pyramid is [tex]\frac{1}{3}[/tex] ×b×h
The area of the prism is 5×5×12 or 300 cm³
The area of the pyramid is [tex]\frac{1}{3} *25*6[/tex] or 75 cm³
300 cm³-75 cm³=225 cm³
The volume outside the pyramid but inside the prism is 225 cm³.
Find the m∠YAX in the figure below
Answer:
76
Step-by-step explanation:
The two angles are vertical angles so they are equal
3x+7 = 4x-16
Subtract 3x from each side
3x-3x+7 = 4x-3x-16
7 = x-16
Add 16 to each side
7+16 = x-16+16
23 =x
We want YAX
YAX = 3x+7
3*23+7
69+7
76
Lola bought x pencils that cost $0.25 each and y erasers that cost $0.50. She spent less than $3. Which graph represents Lola’s purchase?
Answer:
Graph C is the answer.
Step-by-step explanation:
Lola bought X pencils that cost $0.25 and Y erasers that cost $0.50.
Total expenditure is less than $3.
If we represent expense in the equation form then it will be
Expense on pencils + expense on erasers = Total expense which is < 3
0.25X + 0.50Y < 3
Now we divide the inequality by 0.25
X + 2Y < 12
This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.
Slope of this line is = (-1/2) {from the standard equation of line y = mx + c)
Now we come to the graphs. Here dotted line graphs are A or C.
We will calculate the slopes of the lines from the graphs A and C to get tha answer.
For Graph A
The end points are (12, 0) and (0, 3)
So slope = (y-y')/(x-x') = (3-0)/(0-12) = -3/12 = -1/4
For Graph C.
End points the line are (0, 6) and (12, 0)
Slope of the line = (0-6)/(12-0) = -6/12 = -1/2
Therefore Graph C is the answer.
Answer:
Graph C is the answer.
Step-by-step explanation:
Lola bought X pencils that cost $0.25 and Y erasers that cost $0.50.
Total expenditure is less than $3.
If we represent expense in the equation form then it will be
Expense on pencils + expense on erasers = Total expense which is < 3
0.25X + 0.50Y < 3
Now we divide the inequality by 0.25
X + 2Y < 12
This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.
Slope of this line is = (-1/2) {from the standard equation of line y = mx + c)
Now we come to the graphs. Here dotted line graphs are A or C.
We will calculate the slopes of the lines from the graphs A and C to get tha answer.
For Graph A
The end points are (12, 0) and (0, 3)
So slope = (y-y')/(x-x') = (3-0)/(0-12) = -3/12 = -1/4
For Graph C.
End points the line are (0, 6) and (12, 0)
Slope of the line = (0-6)/(12-0) = -6/12 = -1/2
Therefore Graph C is the answer.
Step-by-step explanation:
make brainiest please
an=(−3n+4)n(−4n−8)n In this problem you must attempt to use the Root Test to decide whether the series converges. Compute L=limn→[infinity]|an|−−−√n Enter the numerical value of the limit L if it converges, INF if it diverges to infinity, MINF if it diverges to negative infinity, or DIV if it diverges but not to infinity or negative infinity. L= Which of the following statements is true? A. The Root Test says that the series converges absolutely. B. The Root Test says that the series diverges. C. The Root Test says that the series converges conditionally. D. The Root Test is inconclusive, but the series converges absolutely by another test or tests. E. The Root Test is inconclusive, but the series diverges by another test or tests. F. The Root Test is inconclusive, but the series converges conditionally by another test or tests. Enter the letter for your choice here:
Answer:
L = 3/4
Option A. The Root Test says that the series converges absolutely.
Step-by-step explanation:
By using the root test equation given in the question. L = 3/4
Since L < 1, the series converges absolutely.
For clarity of expression, the detailed calculation is contained in the attached file. Check the file attached for the complete calculation to this question.
The amount of energy associated with a production of bottled water is approximately Normal with a mean of 8.7 million Joules and a standard deviation 0.5 million Joules. How much energy should be required for the bottom 80% of bottled water?
Answer:
At most 9.12 joules should be required for the bottom 80% of bottled water
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 8.7, \sigma = 0.5[/tex]
How much energy should be required for the bottom 80% of bottled water?
At most the 80th percentile.
The 80th percentile is X when Z has a pvalue of 0.8. So it is X when Z = 0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.84 = \frac{X - 8.7}{0.5}[/tex]
[tex]X - 8.7 = 0.84*0.5[/tex]
[tex]X = 9.12[/tex]
At most 9.12 joules should be required for the bottom 80% of bottled water
In a preschool, there are 5 students per teacher. There are 10 teachers in the school. How many students are in the school?
2
5
15
50
Answer: 50 student in the school
Step-by-step explanation: 5x10=50 so that’s the answer.
PLEASE HELP
In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = (x-2)2 -3. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
Answer:
Ok, for f(x) = x^2 we have only one x-intercept (actually, two equal x-intercepts) at x = 0.
Now, for g(x) = (x - 2)^2 - 3
First, let's analyze the transformations.
When we have g(x) = f(x - a) this means that we moved "a" units to the right (if a is positive)
When we have g(x) = f(x) + a, this means that (if a > 0) we move the graph "a" units up.
In this case we have both those transformations:
g(x) = f(x - 2) - 3
this means that we move 2 units to the right, and 3 units down (because the number is negative)
now we can find the roots of g(x) as:
g(x) = (x - 2)^2 - 3 = x^2 - 4x + 4 - 3 = x^2 - 4x + 1 = 0
using the Bhaskara's equation:
[tex]x = \frac{4 +-\sqrt{4^2 - 4*1*1} }{2*1} = \frac{4 +- 3.5}{2}[/tex]
then the roots are:
x = (4 + 3.5)/2 = 3.75
x = (4 - 3.5)/2 = 0.25
Here we have two different x-intercepts
what is 3z square rooted by 2 - 2xy
x=3 y=7 z=2
Answer:
So if you multiply you get 3*2 square rooted of 2-2*3*7 =
6 square rooted of -40
That is the most simplified I hope
A street performer earns 40% of all his daily earnings at the barclays center subway station.He earns about $60 at that station. Assuming he works everyday and earns the same amount, how much does he earn in two weeks?
Answer:
He earns $2,100 in two weeks.
Step-by-step explanation:
We know that this street performers earn $60 per day at the Barclays center subway station, and that this earning represents 40% (or a proportion of 0.4) of his daily earnings. We can calculate his daily earnings as:
[tex]0.4D=\$\,60\\\\D=\dfrac{\$\,60}{0.4}=\$\,150[/tex]
If the daily earnings are $150, the earnings in 2 weeks (14 days) will be:
[tex]W=14\cdot\$\,150=\$\,2100[/tex]