Answer:
35
Step-by-step explanation:
subtract highest and lowest numbers
If f(x) is not defined at c, then f(x) cannot be continuous on any interval. True False
Answer:
True
Step-by-step explanation:
The wording of the question is a little tricky, but here's what I think.
If a function f(x) is not defined at a point c, then the function has a discontinuity at that point. In order for a function to be continuous on an interval, it must be defined and have no abrupt changes or jumps within that interval. Since f(x) is not defined at c, it violates the condition of continuity, and therefore f(x) cannot be continuous on any interval that includes c.
The given statement "If f(x) is not defined at c, then f(x) cannot be continuous on any interval." is false because it does not automatically mean that f(x) cannot be continuous on any interval.
Continuity of a function depends on the behavior of the function around the point of interest, rather than just the absence of a definition at a single point. A function can still be continuous on an interval except at the specific point where it is not defined.
For example, consider the function f(x) = 1/x. This function is not defined at x = 0, but it is continuous on any interval that does not include x = 0. This is because f(x) approaches positive or negative infinity as x approaches 0 from the left or right side, respectively, indicating that there is no abrupt jump or discontinuity.
In general, the continuity of a function is determined by its behavior around a point, including its limit as x approaches that point. The absence of a definition at a single point does not automatically imply that the function cannot be continuous on any interval.
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the perimeter of an isosceles triangle is 45. find the length of the third side if each of the equal sides is 14cm long
Answer:
17cm
Step-by-step explanation:
The two equal sides are 14cm long so 45 - 14 - 14 = 17
Solve the system of inequalities graphically:
x−2y≤3,3x+4y≥12,x≥0,y≥1
The solution to the system of inequalities is the region above the x-axis and to the right of the line y = 1, shaded in green.
Given system of inequalities is: x - 2y ≤ 3 ...(1)3x + 4y ≥ 12 ...(2)x ≥ 0 ...(3)y ≥ 1 ...(4)
We graph the lines x - 2y = 3 and 3x + 4y = 12 and shade the appropriate regions.
Let's start with the line x - 2y = 3.
We rewrite this as y = (1/2)x - 3/2 and plot the line as shown below: graph{(1/2)x - 3/2 [-10, 10, -5, 5]}
Now we determine which side of the line we want to shade.
Since the inequality is of the form ≤, we shade below the line y = (1/2)x - 3/2 (including the line itself) as shown below: graph {(1/2)x - 3/2 [-10, 10, -5, 5](-10,-5)--(10,0)}
Next, we graph the line 3x + 4y = 12. We rewrite this as y = (-3/4)x + 3 and plot the line as shown below: graph{(-3/4)x + 3 [-10, 10, -5, 5]}
We determine which side of the line we want to shade. Since the inequality is of the form ≥, we shade above the line y = (-3/4)x + 3 (including the line itself) as shown below: graph{(-3/4)x + 3 [-10, 10, -5, 5](-10,4)--(10,0)}
Finally, we shade the region that satisfies x ≥ 0 and y ≥ 1.
This is the region above the x-axis and to the right of the line y = 1 as shown below: graph{(-3/4)x + 3 [-10, 10, -5, 5](-10,4)--(10,0)(0,1)--(10,1)[above]}
The shaded region is the region that satisfies all three inequalities.
Thus, the solution to the system of inequalities is the region above the x-axis and to the right of the line y = 1, shaded in green.
We graph the lines x - 2y = 3 and 3x + 4y = 12 and shade the appropriate regions.
Let's start with the line x - 2y = 3. We rewrite this as y = (1/2)x - 3/2 and plot the line.
Now we determine which side of the line we want to shade. Since the inequality is of the form ≤, we shade below the line y = (1/2)x - 3/2 (including the line itself).
Next, we graph the line 3x + 4y = 12. We rewrite this as y = (-3/4)x + 3 and plot the line. We determine which side of the line we want to shade.
Since the inequality is of the form ≥, we shade above the line y = (-3/4)x + 3 (including the line itself).
Finally, we shade the region that satisfies x ≥ 0 and y ≥ 1.
This is the region above the x-axis and to the right of the line y = 1. The shaded region is the region that satisfies all three inequalities.
Thus, the solution to the system of inequalities is the region above the x-axis and to the right of the line y = 1, shaded in green.
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Jason and Karina have matching gardens Jason plants 2/3 of his garden with roses Karina's garden is divided into ninths how much garden must she plant to have the same amount.
Answer:
6/9
Step-by-step explanation:
Suppose a and n are relatively prime such that g.c.da, n=1, prove that \/ b 1 b) If n = 1, we cannot conclude that x=a (mod n) has solutions.
If a and n are relatively prime (gcd(a, n) = 1), it does not guarantee that the equation x ≡ a (mod n) has solutions.
If a and n are relatively prime, denoted by gcd(a, n) = 1, it means that a and n do not have any common factors other than 1. However, this does not guarantee that the equation x ≡ a (mod n) has solutions.
The equation x ≡ a (mod n) represents a congruence relation, where x is congruent to a modulo n. This equation implies that x and a have the same remainder when divided by n.
To have solutions for this congruence equation, it is necessary for a to be congruent to some number modulo n. In other words, a must lie in the residue classes modulo n. However, the fact that gcd(a, n) = 1 does not ensure that a is congruent to any residue modulo n, hence not guaranteeing the existence of solutions for the equation.
Therefore, when n = 1, we cannot conclude that the equation x ≡ a (mod n) has solutions.
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Please help me with this, please
Answer:
Hopefully it makes sense
Step-by-step explanation:
Good luck
se the confidence interval to find the margin of error and the sample mean. question content area bottom part 1 the margin of error is . 069. part 2 the sample mean is . 381.
The "margin-of-error" is 3.6 and the "sample-mean" is 18.7 based on the given confidence interval (15.1, 22.3).
To find the "margin-of-error" and the "sample-mean" from the given confidence interval, we use the formula:
Confidence-Interval = Sample mean ± Margin of error,
In this case, the given confidence-interval is (15.1, 22.3),
To find the margin-of-error, we need to consider the range between the upper and lower bounds of the confidence interval and divide it by 2,
The "Margin-of-error" is = (Upper bound - Lower bound)/2,
"Margin-of-error" is = (22.3 - 15.1)/2 = 3.6,
So, the margin of error is 3.6.
To find "sample-mean", we calculate average of the upper and lower bounds of the confidence-interval,
The "Sample-Mean" is = (Upper bound + Lower bound)/2,
"Sample-Mean" is = (22.3 + 15.1)/2 = 18.7,
Therefore, the "sample-mean" is 18.7.
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The given question is incomplete, the complete question is
Use the confidence interval to find the margin of error and the sample mean. (15.1, 22.3).
in a circle of radius 28 cm, an subtends an angle of 45° at the centre, then find the length of the arc(in cm)
Answer:
22cm
Step-by-step explanation:
Length of arc = [tex]\frac{theta}{360}[/tex] * 2[tex]\pi[/tex]r
= [tex]\frac{45}{360}[/tex] * 2 * [tex]\frac{22}{7}[/tex] * 28
= 22 cm
1. The two sample t-test The carapace lengths (measure in mm) of crawfish (Palinurus vulgaris) captured in streams in Devon and Cornwall were measured. The data is given below: Carapace Length (in mm) Devon: 170,111,135,182,121,174,169,133,141,147,159,163 Cornwall: 146, 97, 102, 181, 107, 118,131,155,127,130, 129 a. Do you have reason to believe the two populations of crawfish do both have the same mean carapace length? Use the t test. b. Can you answer the question in a. using the Wilcoxon rank sum test? (See note below.) c. Compare the results obtained in a. and b. Are you surprised? The Wilcoxon Rank Sum Test - The Wilcoxon Rank Sum (WRS) test is the distribution free alternative to the t-test. It does not consider the actual value of the observations but only their relative position in the combined set of observations from the two samples, A and B. To use the WRS, you combine the observations of the two samples, order them from smallest to the largest, given rank 1 to the smallest observation (in either sample), rank 2 to the second smallest, and so on, giving rank n+m to the largest observation. The null hypothesis is that the two distributions are the same. The test statistic, WA or WB is the sum of the ranks of the observations in one of the samples. Reference Distribution For samples of similar sized with a combined number of observation in excess of 20, if H0 is true WA will have a distribution that is approximately Normal with µ = (nA)(nA+nB+1) 2 and variance σ 2 A = nAnB(nA+nB+1) 12 . Note that the variance is the
a. To determine if the two populations of crawfish from Devon and Cornwall have the same mean carapace length, we can use the two-sample t-test.
This test compares the means of two independent samples to assess whether they are significantly different.
We can calculate the sample means and sample standard deviations for both groups:
Next, we calculate the t-value using the formula:
To determine if this t-value is statistically significant, we need to compare it to the critical value from the t-distribution for the given degrees of freedom
If the calculated t-value falls outside the critical region, we can reject the null hypothesis and conclude that the two populations have different mean carapace lengths. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference in the mean carapace length between the two populations.
b. To answer the question using the Wilcoxon rank sum test, we need to combine the observations from both samples, assign ranks based on their relative positions, and calculate the sum of ranks for one of the samples (either Devon or Cornwall). The null hypothesis for this test is that the two distributions are the same.
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Use digits to write the value of the 4 in this number.
842,963
Answer:
40,000
Step by step explanation:
842,963
840,000
40,000
Add the negatives.
6- 3 + 2 - 1 - 4
Please help ....
A stick of length 10 is broken at a point X which is uniformy distributed on (0,10). Given X = 1, another breakpoint Y is chosen uniformly on (0,3). The joint part(X,Y) is given by f(x,y) for 0 <<<10 10s The marginal pdf of Y is given by fY() = 0.1 for Oy10
The joint probability density function (pdf) is f(x,y) = 0.03 for 0 < x < 1 and 0 < y < 3.
The joint pdf, f(x,y), represents the probability density function for the random variables X and Y. Given that X is uniformly distributed on (0,10), we have fX(x) = 0.1 for 0 < x < 10. The probability of X being less than 1 is 1/10, so the conditional pdf f(x|X<1) = 0.1 for 0 < x < 1.
Furthermore, Y is uniformly distributed on (0,3), so fY(y) = 0.1 for 0 < y < 3. To find the joint pdf, we multiply the conditional pdf of X with the marginal pdf of Y: f(x,y) = f(x|X<1) * fY(y) = 0.1 * 0.1 = 0.01 for 0 < x < 1 and 0 < y < 3. Therefore, the joint pdf is f(x,y) = 0.01 for 0 < x < 1 and 0 < y < 3.
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What is the quotient of (x3 + 3x2 + 5x + 3) ÷ (x + 1)?
x2 + 4x + 9
x2 + 2x
x2 + 2x + 3
x2 + 3x + 8
Answer:
C
Step-by-step explanation:
C
Survey / Statistical Question:
How many times has each person moved states?
Answer:
a regular person would gave moved 4 to 5 times
Calculate the most probable values of X and Y for the following system of equations using: Tabular method . Matrix method X + 2Y = 10.5 2X-3Y= 5.5 2X – Y = 10.0
The most probable values for X and Y are X = 11.75 and Y = 1.1, respectively.
To solve the system of equations using the tabular or matrix method, we first convert the given equations into matrix form. We create a coefficient matrix A by arranging the coefficients of the variables X and Y, and a constant vector B by placing the constants on the other side of the equations.
To solve the system of equations using the tabular method or matrix method, we'll first write the equations in matrix form. Let's define the coefficient matrix A and the constant vector B:
A = | 1 2 |
| 2 -3 |
| 2 -1 |
B = | 10.5 |
| 5.5 |
| 10.0 |
Now, we can solve the system of equations by finding the inverse of matrix A and multiplying it with vector B:
[tex]A^{(-1)[/tex] = | 1.5 1 |
| 0.4 0.2 |
X = [tex]A^{(-1)[/tex] * B
Multiplying [tex]A^{(-1)[/tex] with B, we get:
X = | 1.5 1 | * | 10.5 | = | 11.75 |
| 0.4 0.2 | | 5.5 | | 1.1 |
Therefore, the most probable values for X and Y are X = 11.75 and Y = 1.1, respectively.
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Consider the following IVP: u"(t) + u'(t) - 12u (t)=0 (1) u (0) = 60 and u'(0) = 56. Show that u(t)=c₁₁e² + c ₂² -4 satisifes ODE (1) and find the values of c ER and C₂ ER such that the solution satisfies the given initial values.
The values of c₁ and c₂ that satisfy the initial values u(0) = 60 and u'(0) = 56 are:
c₁ = 148 / (3e²)
c₂ = (20 - 148/9)e⁴
The given solution, u(t) = c₁e² + c₂e⁻⁴, indeed satisfies the given ordinary differential equation (ODE) u"(t) + u'(t) - 12u(t) = 0. To find the values of c₁ and c₂ such that the solution satisfies the initial values u(0) = 60 and u'(0) = 56, we substitute these values into the solution.
First, let's find u(0) by substituting t = 0 into the solution:
u(0) = c₁e² + c₂e⁻⁴
Since u(0) = 60, we have:
60 = c₁e² + c₂e⁻⁴ (Equation 2)
Next, let's find u'(0) by differentiating the solution with respect to t and substituting t = 0:
u'(t) = 2c₁e² - 4c₂e⁻⁴
u'(0) = 2c₁e² - 4c₂e⁻⁴
Since u'(0) = 56, we have:
56 = 2c₁e² - 4c₂e⁻⁴ (Equation 3)
Now we have a system of two equations (Equations 2 and 3) with two unknowns (c₁ and c₂). We can solve this system to find the values of c₁ and c₂.
To do that, let's first divide Equation 3 by 2:
28 = c₁e² - 2c₂e⁻⁴
Next, let's multiply Equation 2 by 2:
120 = 2c₁e² + 2c₂e⁻⁴
Adding the two equations, we get:
148 = 3c₁e²
Dividing both sides by 3e², we find:
c₁ = 148 / (3e²)
Substituting this value of c₁ back into Equation 2, we can solve for c₂:
60 = (148 / (3e²))e² + c₂e⁻⁴
60 = 148/3 + c₂e⁻⁴
60 - 148/3 = c₂e⁻⁴
20 - 148/9 = c₂e⁻⁴
c₂ = (20 - 148/9)e⁴
Therefore, the values of c₁ and c₂ that satisfy the initial values u(0) = 60 and u'(0) = 56 are:
c₁ = 148 / (3e²)
c₂ = (20 - 148/9)e⁴
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For which equation is s = 6 not the solution?
4 s = 24
9 - s = 4
s + 6 = 12
s - 4 = 2
Answer:
9 - s = 4
Step-by-step explanation:
9 - 6 is 3, not 4, so thats the answer!
The equation is s = 6 not the solution is 9 - s = 4.
What is the equation?An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.
For which equation is s = 6 not the solution?
1. The solution of the equation 4 s = 24 is;
[tex]\rm4 s = 24\\\\s=\dfrac{24}{4}\\\\s=6[/tex]
2. The solution of the equation 9 - s = 4 is;
[tex]\rm 9 - s = 4\\\\s=9-4\\\\s=5[/tex]
3. The solution of the equation s + 6 = 12 is;
[tex]\rm s + 6 = 12\\\\s=12-6\\\\s=6[/tex]
4. The solution of the equation s - 4 = 2 is;
[tex]\rm s - 4 = 2\\\\s=2+4\\\\s=6[/tex]
Hence, the equation is s = 6 not the solution is 9 - s = 4.
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A coin is tossed four times. You bet $1 that heads will come up on all four tosses. If this happens, you win $10. Otherwise, you lose your $1 bet.
Find: P(you win) =
P(you lose) =
Average winnings, µ, =
The P(you win) = 1/16P(you lose) = 15/16 and Average winnings, µ, = -5/16.
The probability of winning (P) and the probability of losing (Q) are both possible outcomes from a coin toss experiment. The probability of winning is given by the formula
P = Number of ways to win/ Total number of possible outcomes.The probability of losing is given by the formula
Q = Number of ways to lose/Total number of possible outcomes.
Formulae used to calculate probability are:
P = Number of ways to win/ Total number of possible outcomes
P = Number of outcomes in which all four tosses are heads/ Total number of possible outcomes
When a coin is tossed four times, the total number of possible outcomes is 2 × 2 × 2 × 2 = 16.
P = Number of outcomes in which all four tosses are heads/ Total number of possible outcomes
P = 1/16P (you win) = 1/16
The probability of losing is given by the formula
Q = Number of ways to lose/Total number of possible outcomes.
Q = 15/16P (you lose) = 15/16
Average winnings, µ, can be calculated as follows:
Let's say X represents the amount of money you win. When you win, you get $10, and when you lose, you lose $1.
X = -1 when you loseX = 10 when you winUsing the formula
µ = ∑ (X × P), we can calculate the average winnings,
µ = (-1 × 15/16) + (10 × 1/16)µ = -15/16 + 10/16µ = -5/16.
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Given information: A coin is tossed four times. You bet $1 that heads will come up on all four tosses. If this happens, you win $10. Otherwise, you lose your $1 bet.
Therefore, the answers are:
P(you win) = 0.0625
P(you lose) = 0.9375
Average winnings, µ, = -$0.31
Let A be the event of getting heads on the four tosses. Since the coin is tossed four times, the possible outcomes are 2^4 = 16. Thus the probability of getting heads on each toss is 0.5. Therefore, the probability of getting heads on all four tosses is:
P(A) = (0.5)^4
= 0.0625
Let B be the event of not getting heads on all four tosses. Thus:
B = 1 − P(A)
= 1 − 0.0625
= 0.9375
The winning amount for getting all four heads is $10, and the losing amount is $1. Thus, the average winnings is:
µ = (10 × 0.0625) − (1 × 0.9375)
µ = 0.625 − 0.9375
µ = -0.3125
Therefore, the answers are:
P(you win) = 0.0625
P(you lose) = 0.9375
Average winnings, µ, = -$0.31
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In a large population, 92% of the households have cable tv. A simple random sample of 225 households is to be contacted and the sample proportion computed. What is the mean and standard deviation of the sampling distribution of the sample proportions
Answer:
the mean and the standard deviation is 0.92 and 0.01808 respectively
Step-by-step explanation:
The computation of the mean and the standard deviation is shown below:
The mean is 0.92
And, the standard deviation is
= √0.92 × (1 - 0.92) ÷ √225
= √0.92 × 0.08 ÷ √225
= √0.0736 ÷ √225
= √3.27
= 0.01808
Hence, the mean and the standard deviation is 0.92 and 0.01808 respectively
What is the area of the shaded area shown, his lawn? Please help me I really need it
Answer:
c - 13,600ft^2
Step-by-step explanation:
200 x 80 = 16,000ft^2
40 x 60 = 2,400ft^2
16,000ft^2 - 2,400ft^2 = 13,600ft^2
What is the value of x? sin(x+37)°=cos(2x+8)° Enter your answer in the box. x =
The answer is x = 15.
15 or 20.33 are the possible values of the x.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
We know that sin(x+37)°=cos(90°-(x+37)°) and cos(2x+8)°=sin(90°-(2x+8)°)
So we have sin(x+37)°=cos(2x+8)° becomes sin(x+37)°=sin(82°-2x)
For the above equation to be true, either of the following must hold:
x+37 = 82 - 2x (since the sin function is periodic)
x+37 = 180 - (82-2x)
Solving the first equation for x gives:
3x = 45
x = 15
Solving the second equation for x gives:
3x = 61
x = 20.33 (rounded to two decimal places)
Therefore, the possible values of x are 15 or 20.33 (rounded to two decimal places).
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A decagon.
Gregory drew this regular decagon. All angles have the same measure.
What is the sum of the interior angle measures?
°
What is the measure of each angle?
°
Answer:
78
Step-by-step explanation:
Answer:
1440 and 144 on edg 2020-2021
Step-by-step explanation:
please help I will give brainliest
I don't want to see any link
if I do you will be reported
Answer:
24
Brainliest?
Answer:
nxbxbxxbznznxnxnxnxnxnxnxbxbbxbnxxnxnx
Step-by-step explanation:
xnncxbbxbxbxbxbxbx hahahahahahahahahahahah
At a candy store, Layla bought 2 pounds of jelly beans and 4 pounds of gummy worms for $46. Meanwhile, Brittany bought 3 pounds of jelly beans and 2 pounds of gummy worms for $41. How much does the candy cost?
X= Y=
Answer:
X = $9.00 for 1 pound of Jelly Beans
Y = $7.00 for 1 pound of Gummy Worms
Step-by-step explanation:
Ok, to start we need to make up some notation. It looks like you've chosen X and Y as your variables which works for me.
First lets say X = cost of one pound of jelly beans and Y = cost of one pound of gummy worms
Now let's put together our equations
2X + 4Y = 46
3X + 2Y = 41
Now we need to solve for one of the variables using substitution or elimination. Since none of the variables are isolated, let's use elimination by multiplying the bottom equation by -2.
2X + 4Y = 46
-6X - 4Y = -82
___________
-4X + 0 = -36
-4X = -36
X = 9 or $9.00 per pound
Now we can plug that back into own of the equations and solve for Y
2(9) + 4Y = 46
18 + 4Y = 46
4Y = 28
Y = 7 or $7.00 per pound
You have 1/8 gallon of melted crayon wax. You pour the wax equally into 8 different molds to make new crayons. What fraction of a cup of melted wax is in each mold? Think: 1 gallon is 16 cups.
PLS HELP
Answer:
2 cups
Step-by-step explanation:
16/8=2 so it is 2 cups
the probability that an at home pregnancy test will correctly identify a pregnancy is 0.98. suppose 11 randomly selected pregnant women with typical hormone levels are each given the test. rounding your answer to four decimal places, find the probability that all 11 tests will be positive at least one test will be negative
The probability that all 11 tests will be positive is 0.8007
The probability that at least one test will be negative is 0.1993
Finding the probability that all 11 tests will be positiveFrom the question, we have the following parameters that can be used in our computation:
p = 0.98
n = 11
The probability that all 11 tests will be positive is
P = pⁿ
So, we have
P = 0.98¹¹
Evaluate
P = 0.8007
Finding the probability that at least one test will be negativeHere, we use
P = 1 - P(No negative)
So, we have
P = 1 - 0.8007
Evaluate
P = 0.1993
Hence, the probability is 0.1993
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Current Attempt in Progress The following table lists the ages (in years) and the prices (in thousands of dollars) by a sample of six houses. Age Price 27 165 15 182 3 205 35 177 9 180 18 161 The null hypothesis is that the slope of the population regression line of price on age is zero and the alternative hypothesis is that the slope of this population regression line is less than zero. The significance level is 5%. What is the value of the test statistic, t. rounded to three decimal places?
Whwn the null hypothesis is that the slope of the population regression line of price on age is zero, the test statistic is -2.43.
How to calculate the valueThe test statistic is calculated as follows:
t = (b - 0) / SE(b)
In this case, the slope of the regression line is estimated to be -11.50, the standard error of the slope is 4.77, and the hypothesized value of the slope is 0.
t = (-11.50 - 0) / 4.77
= -2.43
The test statistic is -2.43, The p-value for this test statistic can be calculated using a t-table. The degrees of freedom for this test are 5 - 2 = 3. The p-value for a t-statistic of -2.43 with 3 degrees of freedom is 0.048.
Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.
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Write a function for the graph.
Answer:
(x-4)^2 -4 = y
Step-by-step explanation:
The graph is translated 4 to the right and 4 downwards.
Select all that are equivalent to sin GFH
Answer:
FGH DEJ .................
Select the correct answer.
If the parent function RX) = x2 is modified to g(x) = 2x + 1, which statement is true about g(x)?
ΟΑ. .
It is an even function.
ОВ.
It is an odd function,
OC. It is both an even and an odd function.
OD.
It is neither an even nor an odd function.