To set up a partial fraction decomposition for a rational expression, we want to express it as a sum of simpler fractions, with each denominator being a linear factor (i.e. a factor of the form ax + b, where a and b are constants). The general form of a partial fraction decomposition is:
f(x) = A/(ax + b) + B/(cx + d) + ...
where A, B, etc. are constants that we'll need to solve for.
Note that we're not trying to find specific values for A, B, etc. in this question - we're just setting up the decomposition.
So, for each rational expression, we'll need to factor the denominator into linear factors (if it's not already in that form). Then we'll set up the partial fraction decomposition using the formula above. Here are a few examples:
Example 1: (x^2 + 5x + 6)/(x^2 + 4x + 3)
First, let's factor the denominator: x^2 + 4x + 3 = (x + 1)(x + 3). So we can write:
(x^2 + 5x + 6)/(x^2 + 4x + 3) = A/(x + 1) + B/(x + 3)
Note that we have two linear factors in the denominator, so we need two terms in the partial fraction decomposition. We don't know what A and B are yet - we'll need to solve for them.
Example 2: (2x + 5)/(x^2 - 4)
The denominator here is not yet in factored form, so we'll need to factor it first: x^2 - 4 = (x + 2)(x - 2). Then we can write:
(2x + 5)/(x^2 - 4) = A/(x + 2) + B/(x - 2)
Again, we have two linear factors in the denominator, so we need two terms in the partial fraction decomposition.
Example 3: (4x^2 - 2x + 1)/(x^3 + x)
The denominator here is not in factored form, so we'll need to factor it: x^3 + x = x(x^2 + 1). Then we can write:
(4x^2 - 2x + 1)/(x^3 + x) = A/x + B/(x^2 + 1)
In this case, we have one linear factor (x) and one quadratic factor (x^2 + 1), so we need two terms in the partial fraction decomposition.
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List the sample space for rolling a fair seven-sided die.
S = {1, 2, 3, 4, 5, 6, 7}
S = {1, 2, 3, 4, 5, 6, 7, 8}
S = {1}
S = {7}
The sample space for rolling a fair seven-sided die is S = {1, 2, 3, 4, 5, 6, 7}.
Given that,
A fair seven sided die is rolled.
We have to find the sample space of the rolling.
A sample space is a set of all the possible outcomes in a random experiment. It is usually denoted by the letter, S.
The subset of the sample space are events.
The die has the numbers marked from 1 to 7.
So when we roll the die,
The possible numbers are 1, 2, 3, 4, 5, 6, 7
Sample space = {1, 2, 3, 4, 5, 6, 7}
Hence the sample space is {1, 2, 3, 4, 5, 6, 7}.
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Mrs. Pellegrin has weighed 5 packages of cheese and recorded the weights as 10.2 oz, 10.5 oz, 9.3 oz, 9.8 oz, and 10.0 oz. She calculated the standard deviation to be 0.45 oz. The cheese factory lists the package weight at 10 oz.
The t-statistic for a two-sided test would be
O +0.20
O -0.40
O -0.20
O +0.40
Our calculated t-value of -0.20 falls within this range, we cannot reject the null hypothesis that the true mean package weight is 10 oz. The t-statistic for a two-sided test would be -0.20.
To calculate the t-statistic, we use the formula:
t = (x - μ) / (s / √n)
Where:
x = mean of the sample = (10.2 + 10.5 + 9.3 + 9.8 + 10.0) / 5 = 10.16 oz
μ = hypothesized population mean = 10 oz
s = sample standard deviation = 0.45 oz
n = sample size = 5
Plugging in the values, we get:
t = (10.16 - 10) / (0.45 / √5) ≈ -0.20
Since this is a two-sided test, we look for the t-value that corresponds to a two-tailed 95% confidence interval with 4 degrees of freedom (n-1 = 4). Using a t-table or calculator, we find that the critical t-value is ±2.776.
Since our calculated t-value of -0.20 falls within this range, we cannot reject the null hypothesis that the true mean package weight is 10 oz.
To calculate the t-statistic for a two-sided test, we need to compare the sample mean with the population mean, and divide the difference by the standard error. First, let's calculate the sample mean and standard error:
Sample mean = (10.2 + 10.5 + 9.3 + 9.8 + 10.0) / 5 = 49.8 / 5 = 9.96 oz.
Standard error = standard deviation / √(sample size) = 0.45 / sqrt(5) ≈ 0.20
Now, let's find the t-statistic:
t-statistic = (sample mean - population mean) / standard error = (9.96 - 10) / 0.20 = -0.04 / 0.20 = -0.20
The t-statistic for a two-sided test would be -0.20. So, the correct answer is:
O -0.20
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what is the area of a equilateral triangle with radius 8√ 3
Answer:
Answer and Explanation: The side length of the equilateral triangle is 8√3 . Therefore, the area of the equilateral triangle is 48√3 square units 48 3 square units .
Step-by-step explanation:
Mark brainliest, pls
Please help! 40 points! Convert the following function from vertex form to standard form. Show your work.
f(x) = 3(x — 8)^2 — 160
The standard form is y= 3x² - 16x + 132.
We have Equation,
f(x) = 3(x-8)² - 160
We know the standard form is
y= ax² + bx + c
Now, converting vertex form to standard form
y = 3(x-8)² - 160
y = 3 (x² + 64 - 16x )-60
y= 3x² + 192 - 16x -60
y= 3x² - 16x + 132
Thus, the standard form is y= 3x² - 16x + 132.
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a math teacher gives two different tests to measure students' aptitude for math. scores on the first test are normally distributed with a mean of 23 and a standard deviation of 5.1. scores on the second test are normally distributed with a mean of 68 and a standard deviation of 10.4. assume that the two tests use different scales to measure the same aptitude. if a student scores 30 on the first test, what would be his equivalent score on the second test? (that is, find the score that would put him in the same percentile.)
The student's equivalent score on the second test would be approximately 82.2, placing them in the same percentile as their score on the first test.
To find the equivalent score on the second test, we need to first find the student's percentile rank on the first test.
Using a z-table, we can find that a score of 30 on the first test has a z-score of (30-23)/5.1 = 1.37. This means that the student scored higher than approximately 91% of the other students who took the first test.
Next, we need to find the score on the second test that corresponds to the same percentile rank. To do this, we can use the formula:
z = (x - μ) / σ
where z is the z-score corresponding to the desired percentile rank, x is the corresponding score on the second test, μ is the mean of the second test (68), and σ is the standard deviation of the second test (10.4).
Substituting the z-score we found earlier (1.37) and solving for x, we get:
1.37 = (x - 68) / 10.4
Multiplying both sides by 10.4 and adding 68, we get:
x = 83.29
Therefore, if a student scores 30 on the first test, their equivalent score on the second test would be approximately 83.29. This means that if they scored 83.29 or higher on the second test, they would be in the same percentile as they were on the first test (in this case, approximately the 91st percentile).
To find the equivalent score on the second test, follow these steps:
1. Determine the student's z-score on the first test:
z-score = (student's score - mean) / standard deviation
z-score = (30 - 23) / 5.1 ≈ 1.37
2. The z-score of 1.37 represents the student's percentile ranking on the first test. Now we need to find the equivalent score on the second test that corresponds to the same percentile.
3. Convert the z-score back to a raw score using the second test's mean and standard deviation:
Equivalent score = (z-score * standard deviation) + mean
Equivalent score = (1.37 * 10.4) + 68 ≈ 14.2 + 68 = 82.2
So, the student's equivalent score on the second test would be approximately 82.2, placing them in the same percentile as their score on the first test.
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12. Lucy earned $400 and
$550 in interest the last 2
years. How much interest
must she earn this year so
that her average earnings
over the three year period
is more than $600?
Inequality:
Answer:
Answer:
Check Screenshot for answer and explanation
Step-by-step explanation:
Select True or False for each statement.
1. (1/64)^–⅚ = 32 True
2. √12 - 2/5 × √75 = 4√3 = False
3. √9a + √98b -a+√2b = 2a+10√b = 0 =True
4. 1/(√5-√6)² = 11-2√30/241 = False
How did we arrive at these assertions?1. (1/64)^–⅚ = 32
write in exponential form
2⁵ = 2⁵, hence, true
2. √12 - 2/5 × √75 = 4√3
Simplify the expressions
2√3-2√3 = 4√3
Eliminate the opposites
0 = 4√3
The statement is false
3. √9a + √98b -a+√2b = 2a+10√b = False
Evaluate
3a + √98b-a + √2b = 2a+10√b
Collect like terms
2a + √98b+ √2b = 2a+10√b
Cancel equal terms
98b+ √2b = 10√b Simplify the equation
98b+28b+2b = 100b
Collect like terms
128b = 100b
Move the variable to the left
128b 100b = 0
28b = 0
Divide both sides
b = 0
4. 1/(√5-√6)² = 11-2√30/241 = False
The approximate value of 1 / (√5-√6)² is 21.95445 and the approximate value of 11-2√30/ 241 is 0.000188999, meaning 1/(√5-√6)² ≠ 11-2√30/241
1/(√5-√6)² = 11-2√30/241, so equality is false
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Marissa is selecting a sports ball she selects one at random replaces it and then selects another ball what is the probability that Marissa selects a football both times
The probability that Marissa selects a football both times is 4/81.
We have,
Number of American Football = 4
Number of Football = 2
Number of Basketball = 1
Number of Baseball = 2
So, the probability that Marissa selects a football both times
= 2/ 9 x 2/9
= 4/ 81
Thus, the required probability is 4/81.
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Find the area of the shaded region.
80⁰
5 cm
A≈ [?] cm²
Enter a decimal rounded to the nearest tenth.
The area of the shaded region for the circle is derived to be equal to 73.4 square centimeters.
How to evaluate for the area of shaded regionThe shaded region is the segment area in the circle, so it is derived by subtracting the area of the segment from the area of the circle as follows:
area of the circle = 22/7 × 5 cm × 5 cm
area of the circle = 78.57 cm²
area of sector = 80/360 × 22/7 × 5 cm × 5 cm
area of sector = 17.46 cm²
area of triangle = 5 cm × sin40° × 5 cm × cos40°
area of triangle = 12.31 cm²
area of the segment = 17.46 cm² - 12.31 cm²
area of the segment = 5.15 cm²
area of the shaded region = 78.57 cm² - 5.15 cm²
area of the shaded region = 73.42 cm²
Therefore, the area of the shaded region for the circle is derived to be equal to 73.4 square centimeters.
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for a fundraiser, there is a raffle with 800 tickets, each costing $15. 1 ticket will win a $400 prize, 4 tickets will win a $200 prize, 12 tickets will win a $125 prize, 30 tickets will win a $60 prize, and the remaining tickets will win nothing. if you buy a ticket, what is the expected winnings per ticket? question options:
The expected winning and the value of that prize, which gives an expected winning is c. $3.13 per ticket.
The expected winnings per ticket in the raffle can be calculated by adding the products of the probability of the expected value of winning each prize. The predicted wins per ticket may be computed as the total of each prize's value multiplied by its probability of winning, i.e.
Expected winnings per ticket
= (1/800) × $400 + (4/800) × $200 + (12/800) × $125 + (30/800) × $60 + (753/800) × $0
If we condense the equation, we obtain:
Calculating the total wins anticipated per ticket
= $0.50 + $1.00 + $1.88 + $0.75 + $0
Expected winnings per ticket = $3.13
Therefore, if you buy a ticket, the expected winnings per ticket are $3.13.
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Complete question:
For a fundraiser, there is a raffle with 800 tickets, each costing $15. 1 ticket will win a $400 prize, 4 tickets will win a $200 prize, 12 tickets will win a $125 prize, 30 tickets will win a $60 prize, and the remaining tickets will win nothing. if you buy a ticket, what are the expected winnings per ticket? question options:
a) $5.36
b) $5.63
c) $5.33
d) $5.66
The gym coach needs to know the volume of one of the practice balls so he can buy the right size bag to hold them. What is the volume of one ball if the diameter is 18 inches?
The volume of one ball is approximately 4,058.67 cubic inches.
We have,
The volume of a sphere is given by the formula:
V = (4/3)πr³
where r is the radius of the sphere.
Since the diameter of the ball is given as 18 inches, the radius is half of the diameter, which is 9 inches.
Substituting this value into the formula for the volume of a sphere, we get:
V = (4/3)π(9³) = 4,058.67 cubic inches (rounded to two decimal places)
Therefore,
The volume of one ball is approximately 4,058.67 cubic inches.
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Answer these questions?
The dimensions of this rectangle are 6 units by 7 units.
The coordinates of the new point is (3, -3).
The length of the line segment with end points A and B is 7 units.
The length of the line segment with end points C and D is 11 units.
How to determine the dimensions of this rectangle?In order to determine the dimensions of this rectangle, we would use the distance formula. In Mathematics, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance AB = √[(5 + 1)² + (4 - 4)²]
Distance AB = √[36 + 0]
Distance AB = 6 units
For the width, we have:
Distance AC = √[(-1 + 1)² + (4 + 3)²]
Distance AC = √[0 + 49]
Distance AC = 7 units.
In Mathematics and Geometry, a reflection over the x-axis is modeled by this transformation rule;
(x, y) → (-x, y)
New point = (-3, -3) → (3, -3).
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Complete Question:
The coordinates of the vertices of a rectangle are (-1, 4), (5, 4), (5, -3), and (-1, -3). What are the dimensions of this rectangle?
Paula 64 grams of ground coffee beans to make 32 fluid ounces of coffee. Yesterday she made 480 fluid ounces of coffee. how many grams of ground coffee beans did paula use to make coffee
Answer:
960 grams
Step-by-step explanation:
We know from the problem that grams is proportional to fluid ounces. Therefore, if we allow g to represent the number of grams of ground coffee Paula used, we can find it using a proportion:
[tex]\frac{64}{32}=\frac{g}{480}\\\\ 32g=30720\\\\ g=960[/tex]
H. :P - 0.65 and H.: p > 0.65 where p = the proportion of students who were quarantined at some point during the Fall Semester of 2020. Identify the correct explanation for a Type II error. Conclude the percent was higher than 65%, but it was not higher. Conclude the percent was higher than 65% and it was higher. Did not conclude the percent was higher than 65%, but it was higher. Did not conclude the percent was higher than 65% and it was not higher.
A Type II error occurs when we fail to reject a null hypothesis that is actually false. In this case, the null hypothesis is that the proportion of students who were quarantined at some point during the Fall Semester of 2020 is equal to or less than 0.65.
The alternative hypothesis is that the proportion is greater than 0.65. If we make a Type II error, we fail to reject the null hypothesis when it is actually false, meaning we do not conclude that the proportion is higher than 0.65 even though it actually is higher.
Therefore, the correct explanation for a Type II error, in this case, we would be: "Did not conclude the percent was higher than 65%, but it was higher."
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Eli cut out a 12-inch square. Then he cut off 2-inch squares from each corner of his large square. Which expression can be used to find the remaining area of the larger square?
The expression which can be used to find the remaining area of the larger square is calculated to be A = (12 in)² - 4(2 in)²
If Eli cuts off a 2-inch square from each corner of his 12-inch square, the new dimensions of the square will be 12 - 2 - 2 = 8 inches. Therefore, the remaining area of the larger square is:
(8 in) x (8 in) = 64 square inches
We can also express this mathematically as:
(12 in)A = (12 in)² - 4(2 in)² - 4(2 in)^2 = 144 sq in - 16 sq in = 128 sq in
So the expression that can be used to find the remaining area of the larger square is:
A = (12 in)² - 4(2 in)²
where A is the remaining area of the larger square.
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pls hlp thx your the best
The total cost for 13 rides is 46 $.
Amount to be paid as entry fee = 20 $
Amount to be paid in each ride = 2 $
Therefore, total cost for 13 rides, P = 20 + (2 x 13)
P = 46 $
Total cost for r rides, P' = (20 + 2r) $
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(Chapter 13) If |r(t)| = 1 for all t, then r'(t) is orthogonal to r(t) for all t.
The statement is true. This means that r'(t) is orthogonal (perpendicular) to r(t) for all t.
If |r(t)| = 1 for all t, then r(t) is a unit vector for all t. Differentiating both sides of this equation with respect to t, we get:
|r(t)|' = 0
Using the chain rule and the fact that the magnitude of a vector is the square root of the dot product of the vector with itself, we have:
|r(t)|' = (r(t) · √r(t))
= (2r(t) · r'(t)) / (2|r(t)|)
= r(t) · r'(t) / |r(t)|
= r(t) · r'(t)
Since |r(t)|' = 0, we have:
r(t) · r'(t) = 0
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What is the mapping formula expressed by the vector that translates JKLM to J’K’L’M’.
(x,y) → (x - 2, y - 3)
(x,y) → (x +1, y - 4)
(x,y) → (x +1, y + 4)
(x,y) → (x - 2, y +3)
Answer:
The answer to your problem is, D. (x,y) → (x - 2, y +3)
Step-by-step explanation:
We can see that the vector that translates JKLM to J'K'L'M' is given by the difference between the coordinates of J and J', and the difference between the coordinates of K and K'.
The differences can be called, "a" and "b", respectively. Then we can write:
a = J' - J = (-1) - 0 = -1
b = K' - K = 3 - (-1) = 4
Which can conclude to the mapping formula expressed by the vector that translates JKLM to J'K'L'M' is:
(X,Y) → (X - 1, Y + 4)
Thus the answer to your problem is, D. (x,y) → (x - 2, y +3)
size N becomes large, sample mean of IID random sample from a population is getting very small. 2) If IID random samples of size N are from a normal distribution, the random variable T = mean(c) propean({ X) is oft-distribution with N degree of freedom. widerr a) Only the first b) Only the second c) Both of them d) None of them
a) Only the first statement is true. As the sample size N becomes large, the sample mean of IID random samples from a population becomes more precise and approaches the true population mean.
However, there is no direct relationship between the sample size and the distribution of the sample mean.
The second statement is only true if the population is normally distributed. If the population is not normal, the distribution of the sample mean may not be normal, and the central limit theorem may not apply. Therefore, option c) is not the correct answer. Option d) is also not correct as the first statement is true.
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A ball is thrown downward from the top of a 200 -foot building with an initial velocity of 12 feet per second. The height of the ball h in feet after t seconds is given by the equation h=-16t^2+220 How long after the ball is thrown will it strike the ground?
The ball will strike the ground approximately 3.71 seconds after it is thrown.
To determine when the ball will strike the ground, we need to find the value of t when h = 0.
So we need to solve the equation:
h = -16t² + 220
0 = -16t² + 220
16t² = 220
t² = 220/16
t² = 13.75
Taking the square root of both sides, we get:
t = ± √13.75
Since time cannot be negative, we take the positive root:
t = √13.75
t ≈ 3.71 seconds (rounded to two decimal places)
Therefore, the ball will strike the ground approximately 3.71 seconds after it is thrown.
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Please help me with this homework only the answer
Answer:
[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
[tex]\frac{-8-(-3)}{-12-(-4)}[/tex] = [tex]\frac{-8+3}{-12+4}[/tex] = [tex]\frac{-5}{-8}[/tex] = [tex]\frac{5}{8}[/tex]
Helping in the name of Jesus.
Find the value of each variable in the
circle to the right. The dot represents
the center of the circle.
131°
a =
(Simplify your answer. Do not include the degree symbol in
your answer.)
The value of each variable in the given circle are:
a = 65.5° b = 90° c = 49°
How to Find the Value of each Variable in the Circle?In order to find the value of each variable in the given circle, recall the following:
The measure of an inscribed angle of half a circle is equal to 90 degrees.The measure of an inscribed angle is half the measure of any arc it intercepts.These facts are true based on the inscribed angle theorem.Find a:
a = 1/2(131)
a = 65.5°
Find b:
b is an inscribed angel of half of the circle, therefore:
b = 90°
Find c:
c = 180 - 131
c = 49°
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Use the image to determine the direction and angle of rotation
Answer:
180
Step-by-step explanation:
rotate it 90 degrees 2 times
What is area and perimeter?
Answer:
Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.
Step-by-step explanation:
Your welcome ;)
In one week, a bakery made 1,244 trays of 26 chocolate chip cookies. The bakery also baked 694 trays of 19 sugar cookies. How many cookies did the bakery bake during the week?
The total number of cookies baked during the week if a bakery baked 1,244 trays of 26 chocolate chip cookies and also 694 trays of 19 sugar cookies are 336530.
To calculate the total number of cookies we have to find the number of chocolate chip and sugar cookies.
The total number of chocolate cookies is given by the product of the number of cookies in a tray and the number of trays.
Trays of chocolate chip cookies = 1244
Number of chocolate chip cookies per tray = 26
Total number of chocolate chip cookies = 1244 * 26
= 32344
Similarly, the total number of sugar cookies is given by the product of the number of cookies in a tray and the number of trays.
Trays of sugar cookies = 694
Number of sugar cookies per tray = 19
Total number of chocolate chip cookies = 694 * 19
= 13186
Total number of cookies = total number of chocolate chip cookies + sugar cookies
= 32344 + 13186
=336530
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a publisher reports that 43% of their readers own a particular make of car. a marketing executive wants to test the claim that the percentage is actually different from the reported percentage. a random sample of 200 found that 38% of the readers owned a particular make of car. is there sufficient evidence at the 0.10 level to support the executive's claim?
Therefore, we do not have sufficient evidence to support the executive's claim that the true proportion of readers who own the particular make of car is different from the reported proportion of 43% at the 0.10 level of significance.
To determine whether there is sufficient evidence to support the executive's claim that the percentage of readers who own a particular make of car is different from the reported percentage of 43%, we need to conduct a hypothesis test.
The null hypothesis H0 is that there is no difference between the true proportion of readers who own the particular make of car and the reported proportion of 43%:
H0: p = p0
The alternative hypothesis Ha is that the true proportion of readers who own the particular make of car is different from the reported proportion:
Ha: p ≠ p0
We can use a z-test for proportions to test this hypothesis, since the sample size is sufficiently large and the sampling distribution of the sample proportion can be approximated by a normal distribution.
test statistic is calculated as:
z = (x/n - p0) / √(p0*(1-p0)/n)
Substituting the values from the problem statement, we get:
z = (0.38 - 0.43) / √(0.43*(1-0.43)/200)
= -1.51
At the 0.10 level of significance, the critical values for a two-tailed test are ±1.64. Since our calculated z-value of -1.51 is not in the rejection region, we fail to reject the null hypothesis.
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Write an equation to match the graph.
The equation which matches the absolute value function graph given as required is; y = -1 |x + 1| + 1.
What is the equation which matches the graph?As evident from the task content, the equation which matches the given graph is to be determined.
On this note, recall that the absolute value function takes the form;
f (x) = a |x - h| + k where the vertex is; (h, k).
Therefore, since the vertex is; (-1, 1); we have;
f (x) = a |x + 1| + 1
To find a; use point (0, 0)
0 = a |0 + 1| + 1
a = -1.
Ultimately, the equation which matches the graph is; y = -1 |x + 1| + 1.
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Factor out the greatest common factor from the following polynomial.
10b³ +5b² +4
I
OA. 10b³ +5b²+4=
3
(Factor completely.)
OB. The polynomial has no common factor other than 1.
The polynomial 10b³ + 5b² + 4 has no common factor other than 1.
Factoring out the greatest common factor from the polynomial.From the question, we have the following parameters that can be used in our computation:
10b³ + 5b² + 4
The terms of the above expressions are
10b³, 5b² and 4
The terms of the above polynomial have no common factor other than 1.
Hence, the polynomial cannot be factored
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The solid below is made from cubes.
Find its volume.
1 yd
The Volume of the solid which is made of small-cubes is 15 yd³.
The "Volume" of a cube is the measure of the amount of space that the cube occupies in three-dimensional space. It is calculated by multiplying the cube's three side lengths.
In the figure, we can see that, the solid consists of 5×3 = 15 cubes,
The side-length of each small cube is = 1 yd,
So, the volume of each small-cube is = (side)×(side)×(side),
⇒ Volume = 1 yd³.
To find the volume of the entire solid, we multiply the volume of single-cube, by the "total-number" of cubes,
So, Volume of Solid is = 15×1 = 15 yd³.
Therefore, the volume of the solid is 15 yd³.
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2) The same liquor store owner wants to do a similar comparison but for high end wines to see if there is a difference. The owner samples 16 white wines finding an average of $45.13 (s=5.10) and samples 16 red wines and finds an average of $48.69 (s=5.23). Use alpha=0.05.
2a) What is the standard error?
2b) What is the test statistic?
2c) What is the p-value?
2d) What can you conclude about cost of high end wines?
Answer:
2a) The standard error is given by:
SE = sqrt[(s1^2/n1) + (s2^2/n2)]
= sqrt[(5.10^2/16) + (5.23^2/16)]
= 2.32
2b) The test statistic is given by:
t = (x1 - x2) / SE
= (45.13 - 48.69) / 2.32
= -1.53
2c) The p-value for a two-tailed test with alpha = 0.05 and degrees of freedom = 30 (n1 + n2 - 2) is 0.1384.
2d) Since the p-value (0.1384) is greater than the level of significance (0.05), we fail to reject the null hypothesis that there is no difference in the cost of high end red and white wines. Therefore, we cannot conclude that there is a significant difference in the cost of high end wines.
