The polynomial function f(x) = 5x³ + 5x² - 60x has two factors: (x + 3) and (x - 4).
To determine if a given polynomial function has a factor, we can use the factor theorem. According to the factor theorem, if a polynomial function f(x) has a factor (x - a), then f(a) will be equal to zero.
Let's apply the factor theorem to the polynomial function f(x) = 5x³ + 5x² - 60x.
We need to find a value, let's call it "a," for which f(a) equals zero.
f(a) = 5a³ + 5a² - 60a
To find the factor, we set f(a) equal to zero and solve for "a":
5a³ + 5a² - 60a = 0
Now, we can factor out an "a" from the equation:
a(5a² + 5a - 60) = 0
The quadratic factor 5a²+ 5a - 60 cannot be factored further. Therefore, we need to solve it using the quadratic formula or factoring techniques:
5a² + 5a - 60 = 0
We can factor the quadratic equation as follows:
(5a + 15)(a - 4) = 0
This equation will be true when either (5a + 15) = 0 or (a - 4) = 0.
Solving for "a" in each case:
5a + 15 = 0
5a = -15
a = -3
a - 4 = 0
a = 4
Therefore, the polynomial function f(x) = 5x³ + 5x² - 60x has two factors: (x + 3) and (x - 4).
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Roads connecting the towns of Oceanside, River City, and Lake View form a triangle. The distance from Oceanside to River City is 38 kilometers. The distance from River City to Lake View is 26 kilometers. What is the smallest possible whole number of kilometers between Lake View and Oceanside?
Answer:
13 km
Step-by-step explanation:
By Triangle Inequality Theorem: The sum of two smallest sides is greater than the third side.
Small Values of X:
X + 26 > 38
X > 38 - 26
X > 12
If we know that 38 km is the longest side, then the sum of other two sides must be greater than 38 km. Therefore the minimum value of X is 13 km.
Test whether there is a difference in the pattern of freshman class ranks (an ordinal scale variable) of the newly-inducted sophomore members across five sororities at Mega University.
The required answer is by conducting the Kruskal-Wallis test, we can determine if there are statistically significant differences in the pattern of freshman class ranks among the sophomore members across the five sororities at Mega University.
To test whether there is a difference in the pattern of freshman class ranks among the sophomore members across five sororities at Mega University, we can use a statistical test called the Kruskal-Wallis test. The Kruskal-Wallis test is a non-parametric test used to compare the distributions of three or more independent groups.
In this case, the five sororities represent the independent groups, and the freshman class ranks of the sophomore members within each sorority are the ordinal scale variable of interest. The Kruskal-Wallis test will assess whether there are statistically significant differences in the distribution of freshman class ranks across the five sororities.
Here is a step-by-step explanation of how to conduct the Kruskal-Wallis test:
Step 1: Formulate the null and alternative hypotheses.
Null hypothesis (H₀): There is no difference in the pattern of freshman class ranks across the five sororities.
Alternative hypothesis (H₁): There is a difference in the pattern of freshman class ranks across the five sororities.
Step 2: Collect the data.
Gather the freshman class ranks of the sophomore members for each sorority. Ensure that the data is properly coded and organized.
Step 3: Perform the Kruskal-Wallis test.
Apply the Kruskal-Wallis test to the data. The test will compare the distributions of the ordinal data across the five sororities and determine if there are significant differences.
Step 4: Interpret the results.
Analyze the output of the Kruskal-Wallis test, which typically provides a test statistic and a p-value. If the p-value is below a predetermined significance level (e.g., 0.05), we reject the null hypothesis and conclude that there is evidence of a difference in the pattern of freshman class ranks across the five sororities.
Step 5: Post-hoc analysis (if necessary).
If the Kruskal-Wallis test indicates significant differences, further analyses, such as pairwise comparisons or Dunn's test, can be conducted to identify which specific sororities differ from each other.
By conducting the Kruskal-Wallis test, we can determine if there are statistically significant differences in the pattern of freshman class ranks among the sophomore members across the five sororities at Mega University.
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2. (1 point each) Let f(x) = √x and g(x) = 1/x. In the space
provided, compute each of the following, if possible:
(a) f(36)
(b) (g+f)(4)
(c) (f · g)(0)
(a) f(36) is equal to 6.
(b) (g+f)(4) = g(4) + f(4) = 9/4
(c) we cannot compute (f · g)(0).
(a) To find f(36), we substitute x = 36 into the function f(x) = √x:
f(36) = √36 = 6
Therefore, f(36) is equal to 6.
(b) To find (g+f)(4), we need to evaluate g(4) and f(4), and then add the results:
g(4) = 1/4
f(4) = √4 = 2
(g+f)(4) = g(4) + f(4) = 1/4 + 2 = 1/4 + 8/4 = 9/4
Therefore, (g+f)(4) is equal to 9/4 or 2.25.
(c) To find (f · g)(0), we need to evaluate f(0) and g(0), and then multiply the results:
f(0) = √0 = 0
g(0) = 1/0
However, g(0) is undefined because division by zero is not defined in mathematics.
Therefore, we cannot compute (f · g)(0) in this case.
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Find the distance between (5, -1) and (1,-5).
4 units I assume. that it is a very basic answer tho and I am not sure if a specific formula or lesson was supposed to be applied to that andwer
Let V be the set of all ordered triples of real numbers with addition and scalar multiplication defined as follows: (x, y, z) + (x'. y' z') = (x + x'.0,2 + z!) and k(x,y,z) (kx,ky, kz) for all real numbers k. Prove that V is not a vector space.
The set V, defined as the set of all ordered triples of real numbers with the given addition and scalar multiplication operations, is not a vector space. Therefore, we can conclude that V is not a vector space, as it does not fulfill the required vector space axioms.
To prove that V is not a vector space, we need to demonstrate that it fails to satisfy at least one of the vector space axioms.
Let's consider the closure under scalar multiplication axiom. According to the given scalar multiplication operation, k(x, y, z) = (kx, ky, kz) for all real numbers k. However, in a vector space, scalar multiplication should be distributive over both addition of vectors and scalar addition.
Let's choose a specific example to illustrate the issue. Consider the vector (x, y, z) = (1, 1, 1) in V and the scalar k = 2. According to the defined scalar multiplication operation, 2(x, y, z) = 2(1, 1, 1) = (2, 2, 2).
Now, let's compute (1 + 1)(x, y, z) = 2(x, y, z) = 2(1, 1, 1) = (2, 2, 2).
However, in a vector space, the distributive property should hold, meaning that (1 + 1)(x, y, z) should equal (1, 1, 1) + (1, 1, 1) = (2, 2, 2).
Since (1 + 1)(x, y, z) ≠ (1, 1, 1) + (1, 1, 1), V fails to satisfy the closure under scalar multiplication axiom.
Therefore, we can conclude that V is not a vector space, as it does not fulfill the required vector space axioms.
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can some please help me with this problem?
Answer:
b
Step-by-step explanation:
its a negative slope, so you can eliminate c and d. even though the scale is 2, the slope always pertains to $1 increase and not $2 increase.
Can someone help me out please.
Answer:
area = (10 x 19) - (0.5 x 19 x 5) = 142.5 in²
Step-by-step explanation:
Answer:
142.5 in^2
Step-by-step explanation:
Area of trapezoid= a + b / 2 · h (a and b are bases of the trapezoid)
A= 5 + 10 / 2 · 19
A= 15 / 2 · 19
A= 7.5 · 19
A= 142.5 in^2
This is just one way to do it. There are many more ways.
Find the distance between the points (–10,3) and (–2,3).
Answer:
8
Step-by-step explanation:
10 - 2
On Saturday, a local hamburger shop sold a combined total of 261 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Answer:
134 hamburgers
Step-by-step explanation:
Let H = # of hamburgers
# of cheeseburgers = 2H
H + 2H = 402
3H = 402
H = 402/3
H = 134
A "pay-what-you-pull" raffle is an alternative to a standard raffle where a person blindly draws a raffle ticket, say out of bag, and agrees to pay the amount written on the raffle ticket (as opposed to having one fixed price for each raffle ticket). The raffle ticket is then entered into a draw for a prize. Suppose you draw 2 raffle tickets without replacement from a bag with 4 tickets which have prices $1, $2, $3 and $4. How much can you expected to pay for your 2 raffle tickets?
To find the expected amount you would pay for your two raffle tickets, we need to calculate the expected value of the sum of the prices on the tickets.
Let's denote the prices on the tickets as follows:
Ticket 1: $1
Ticket 2: $2
Ticket 3: $3
Ticket 4: $4
Since you are drawing two tickets without replacement, there are a total of 4C2 = 6 possible combinations of two tickets.
The expected value (E) can be calculated by summing up the products of each combination and its corresponding probability. The probability of each combination is 1/6 since all combinations are equally likely.
The expected amount you would pay for your two raffle tickets is given by:
[tex]\[E = \frac{1}{6}(\$1 + \$2) + \frac{1}{6}(\$1 + \$3) + \frac{1}{6}(\$1 + \$4) + \frac{1}{6}(\$2 + \$3) + \frac{1}{6}(\$2 + \$4) + \frac{1}{6}(\$3 + \$4)\][/tex]
Simplifying the expression, we find:
[tex]\[E = \frac{\$3 + \$4 + \$5 + \$5 + \$6 + \$7}{6} = \$5\][/tex]
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20 POINTS‼️‼️Which of the following does NOT represent the number of months in a year?
A and b are in the attached photo.
C. y= 12x, where x represents the number of years and y represents the number of months
D. There are 96 months in 8 years.
‼️PLEASE DO YOUR BEST TO SHOW WORK FOR BRAINLIEST‼️
Answer:
B because when you multiply the first number by twelve the first two are correct but the second ones are not
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
12 times 6 = 72, not 60
Rewrite as an addition equation and determine the answer: -3 - - 8 =
Answer:
-3 + 8 = 5
Step-by-step explanation:
When we have a "minus a negative", it's a positive. So the - -8 is the same as + 8.
LMK if you have questions.
-3 + -8 = -11
is that a nice one or something
need help plz im struggling
Answer:
12057.6
Step-by-step explanation:
V = πr²h
3.14 x 16² x 15
3.14 x 16² = 803.843.14 x 803.84 = 12057.6Find the sum of the interior angle measures of the polygon.
Answer:
360
Step-by-step explanation:
All the angles of a polygon add up to 360, thats kinda just how it is haha
Find the Errors: A student multiplied the two polynomials below.
(a) Clearly state the two errors that the student made in their multiplication table. (4 points)
(b) State what the correct answer should be. (2 points)
PLEASE ANSWERS FAST
how do you find the perimeter of the base?
A. Multiply the side lengths
B. Divide the side lengths
C. Add all sides of the base shape
D. Take the square root after multiplying the side lengths
Answer:
C. Add all sides of the base shape
Step-by-step explanation:
perimeter = sum of length of sides of a polygon
Answer: C. Add all sides of the base shape
please help with right answers xoxo
Refer to Exhibit 6-6. What percentage of tires will have a life of 34,000 to 46,000 miles? a. 38.49% b. 76.98% c. 50% d. None of the alternative answers is correct
The percentage of tires will have a life of 34,000 to 46,000 miles is the correct answer is d. None of the alternative answers is correct.
The provided percentages do not offer a precise estimate of the proportion of tires with a life of 34,000 to 46,000 miles.
Determining the percentage of tires falling within a specific mileage range requires access to accurate statistical data from tire manufacturers or comprehensive studies. Several factors affect tire lifespan, such as driving habits, road conditions, maintenance, and the type of tire itself.
These variables make it difficult to provide an exact percentage without specific information about the tire population in question. To obtain a more accurate estimate, it would be necessary to analyze relevant data, such as tire industry reports or studies on tire longevity.
Tire manufacturers often provide estimated mileage ratings for their products, but these figures are averages and can vary depending on the factors mentioned above.
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help║...................
help i need the answer
Answer:
NO
Step-by-step explanation:
If the diameter of the circle is doubled the area will be increased 4 times
Complete the table below for the equation y=1+2x
helllllllllllllp me please i just wanna finish this worksheet
Answer:
what
Step-by-step explanation:
Which solution for z makes the equation true?? 10+10+z=40=10 (pls explain why. Thanks)
Answer:
z=30
Step-by-step explanation:
40-10=30
10+10+?=30
30-10-10=10
I'm sorry cuz I don't know how to explain it
Answer:
z = 10
Step-by-step explanation:
10 + 10 + z = 40 - 10
10 + 10 + z = 30
10 + 10 + 10 = 30
since 40 - 10 = 30, then Z has to equal 10 because 10 + 10 + z needs to be 30
To estimate the average service time at a hamburger fast-food restaurant, a management
consultant noted the times that it took for 35 counter persons, a random sample, to complete a
standard order. It took, on average, 72.2 seconds with a standard deviation of 12.8 seconds to
complete the orders.
a)
What can the consultant assert with 95% confidence about the maximum error, if he uses
X bar = 72.2 seconds as an estimate of the true average time to complete a standard order?
b)
Construct a 95 percent confidence interval for the true average time that it takes a counter
person to complete the standard order/
The consultant can assert with 95% confidence that the true average time to complete a standard order is within 4.23 seconds of the sample average time of 72.2 seconds.
With 95% confidence, the true average time it takes for a counter person to complete the standard order is between 68.0 and 76.4 seconds.
How to solve the problemsThe standard error of the mean is given by the formula:
SE = s / sqrt(n)
where s is the sample standard deviation and n is the sample size.
In this case, the standard error is:
SE = 12.8 / sqrt(35) = 2.16 seconds (approximately)
The Z-value that corresponds to a 95% confidence level is approximately 1.96 (this value can be looked up in a standard Z-table).
Therefore, the maximum error E can be calculated as:
E = Z * SE = 1.96 * 2.16 = 4.23 seconds (approximately)
This means that the consultant can assert with 95% confidence that the true average time to complete a standard order is within 4.23 seconds of the sample average time of 72.2 seconds.
b) To construct a 95% confidence interval for the true average time, the consultant can use the formula:
CI = x ± E
where x is the sample mean and E is the maximum error.
Substituting the given values:
CI = 72.2 ± 4.23 = (68.0, 76.4)
So, with 95% confidence, the true average time it takes for a counter person to complete the standard order is between 68.0 and 76.4 seconds.
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If vector v = ( 9 ) find -v and 3v
-6
(z^6/z)^2 QUICK ILL GIVE BRANLIEST
Answer, z10
Step-by-step explanation:
Find the area of the figure.
Answer:
353.93 ft²
Step-by-step explanation:
Step 1:
Find the area of the Trapezoid.
(a + b) ÷ 2 × height
20 + 17 = 37
37 ÷ 2 = 18.5
18.5 × 13 = 240.5 ft²
Step 2:
Find the Area of the Semicircle:
1/2 × πr²
1/2 × 3.14 = 1.57
1.57 × 8.5² = 113.43 ft²
Step 3:
Add the two areas together:
240.5 + 113.43 = 353.93 ft²
Please Help, GodBless
Answer:
-3/2
Step-by-step explanation:
The rate of change is the same as slope
Thomas has finished 50% of an art project that has taken him a total of 9 hours so far. If he continues to work at the same rate, how many hours will it take for him to complete the entire project?
Answer:
18 hours
Step-by-step explanation:
9/0.50 = 18 hours
Which of the following is the correct alternative hypothesis constructed in the binomial test? A. H, :P Previous question
The correct alternative hypothesis constructed in a binomial test is (a) H₁ :P < Q
How to determine the correct alternative hypothesis constructed in a binomial test?From the question, we have the following parameters that can be used in our computation:
A. H₁ :P < Q
B. H₁: P - Q
C. H₁ : P = Q
D. H₁ : P ≤ Q
As a general rule of test of hypothesis, alternate hypothesis are represented using inequalities
This means that we make use of <, > or ≠
Hence, the correct alternative hypothesis is (a) H₁ :P < Q
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Question
Which of the following is the correct alternative hypothesis constructed in the binomial test?
A. H₁ :P < Q
B. H₁: P - Q
C. H₁ : P = Q
D. H₁ : P ≤ Q