The polynomial p(x) = 2x^3 - 3x^2 + qx +56 has a factor x-2 a) show that q= -30? b) factorise p(x) completely and hence state all the solutions of p(x)=0
Answers
(a)The polynomial p(x) = 2x^3 - 3x^2 + qx +56 has a factor x-2 . Therefore, q = -30. (b) Therefore, the solutions of p(x) = 0 are x = 2, x = -1/2, and x = 2.
a) To show that q = -30, we can use the factor theorem. According to the factor theorem, if a polynomial p(x) has a factor (x - c), then p(c) = 0.
In this case, the given polynomial p(x) has a factor (x - 2), so we substitute x = 2 into p(x) and set it equal to 0.
p(2) = 2(2)^3 - 3(2)^2 + q(2) + 56 = 2(8) - 3(4) + 2q + 56 = 16 - 12 + 2q + 56 = 4 + 2q + 56 = 2q + 60
Setting this equal to 0, we have: 2q + 60 = 0 Now, solving for q: 2q = -60 q = -30
Therefore, q = -30.
b) To factorize p(x) completely, we can use synthetic division to divide p(x) by (x - 2).
Using synthetic division, we get: The remainder is 2q + 56.
Since we know q = -30, we can substitute it in: 2q + 56 = 2(-30) + 56 = -60 + 56 = -4
So, the remainder is -4. Now, we can write the factored form of p(x): p(x) = (x - 2)(2x^2 - 7x - 4)
To find the solutions of p(x) = 0, we can set each factor equal to zero and solve for x: x - 2 = 0
=> x = 2 2x^2 - 7x - 4 = 0
Using factoring or the quadratic formula, we find the solutions of the quadratic equation to be: x = 2, x = -1/2, x = 4/2
Therefore, the solutions of p(x) = 0 are x = 2, x = -1/2, and x = 2.
Learn more about polynomial p(x) here:
https://brainly.com/question/28970023
#SPJ11
Related Questions
solve the equation
pic:
Answers
The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891
How to solve the equationFrom the question, we have the following parameters that can be used in our computation:
\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)
Using the following trigonometry ratio
sin²(x) + cos²(x) = 1
We have
\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)
The sum to infinity of a geometric series is
S = a/(1 - r)
So, we have
\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)
So, we have
\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)
Evaluate the sum
\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)
This gives
\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)
Hence, the solution to the equation is 10.3891
Read more about summation notation at
brainly.com/question/15973233
#SPJ1
Can someone please help me!
Answers
Answer:
(3, -5) are the coordinates.
M110) solve
csc ( to power 5 ) theta - 4 csc theta + 1 = 0
Answers
Answer:
The equation csc^5 (theta) - 4 csc (theta) + 1 = 0 can be solved by factoring the left-hand side of the equation.
csc^5 (theta) - 4 csc (theta) + 1 = 0
csc (theta) (csc^4 (theta) - 4) + 1 = 0
csc (theta) (csc^2 (theta) - 2)(csc^2 (theta) + 2) + 1 = 0
We can see that the last expression is a polynomial equation of the form (ax+1)(bx^2+c*x+d)=0 where x= csc(theta) , a=1, b=1, c= -2, d=2
Solving for x = 0, we get x=0 which is not a valid solution because csc(theta) is defined only for theta != k*pi where k is an integer.
Solving for x= -1/2 and x= 1/2, we get csc(theta) = -1/2 and csc(theta) = 1/2
To find theta, we can use the reciprocal cosecant function (csc) which is defined as 1/sin(theta)
csc(theta) = -1/2 => sin(theta) = -2
csc(theta) = 1/2 => sin(theta) = 2
Answer: 0 is cos^4(theta) = (4 - 1/sin(theta))(1-sin^2(theta))^2.
Step-by-step explanation: To solve the equation csc^5(theta) - 4csc(theta) + 1 = 0, we can use the identity csc^n(theta) = 1/sin^n(theta).
First, we can apply the identity:
1/sin^5(theta) - 4/sin(theta) + 1 = 0
Next, we can factor out sin(theta) from the first two terms:
sin(theta)(1/sin^4(theta) - 4) + 1 = 0
We can then use the identity sin^2(theta) = 1 - cos^2(theta) to rewrite the first term:
sin(theta)(1 - cos^4(theta)/(1-cos^2(theta))^2 - 4) + 1 = 0
We can then divide both sides of the equation by sin(theta), and we get:
1 - cos^4(theta)/(1-cos^2(theta))^2 - 4 + 1/sin(theta) = 0
We can then simplify this equation to get:
cos^4(theta)/(1-cos^2(theta))^2 = 4 - 1/sin(theta)
By using the identity cos^2(theta) = 1-sin^2(theta) we can simplify the equation further:
cos^4(theta) = (4 - 1/sin(theta))(1-sin^2(theta))^2
So to find the solution we can use double angle identities to simplify the right side of the equation.
Therefore, the solution to the equation csc^5(theta) - 4csc(theta) + 1 = 0 is cos^4(theta) = (4 - 1/sin(theta))(1-sin^2(theta))^2.
According to the US Census, the percent of residents aged 65 or older in the 50 states and District of Columbia has mean 13.26% and standard deviation of 1.67% Find and interpret the standardized score for the state of Colorado, which had 9.7% of residents age 65 or older.
Answers
Answer:
z = -2.13
The standardized score for the state of Colorado is negative and this means the score is smaller than the mean.
Step-by-step explanation:
The above question can be solved using z score.
The formula for z score is given as:
z = (x-μ)/σ,
where
x is the raw score = 9.7%
μ is the population mean = 13.26%
σ is the population standard deviation = 1.67%
z = z score or standardize score
Hence,
z = 9.7 - 13.26/1.67
z = -2.13174
Approximately z = -2.13
Therefore, the standardized z score for the state of Colorado is negative and this indicates that the score is below or smaller than the mean.
Factories 2p^2-60p-128
Answers
Answer:
2(p - 32)(p + 2)
Step-by-step explanation:
2p² - 60p - 128 ← factor out common factor 2 from each term
= 2(p² - 30p - 64) ← factor the quadratic
consider the factors of the constant term ( - 64) which sum to give the coefficient of the p- term (- 30)
the factors are - 32 and + 2 , since
- 32 × + 2 = - 64 and - 32 + 2 = - 30 , then
p² - 30p - 64 = (p - 32)(p + 2) , so
2p² - 60p - 128 = 2(p - 32)(p + 2)
The factors of a quadratic equation 2p² - 60p - 128 are (p - 4) and (p - 32).
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
To factorize a quadratic equation of the form ax² + bx + c, we need to find two numbers that multiply to ac and add up to b. In this case, we have:
a = 2, b = -60, c = -128
The product of a and c is:
ac = 2 × (-128) = -256
We need to find two numbers that multiply to -256 and add up to -60. We can start by listing the factors of -256:
1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64, 128, -128, 256, -256
We can see that -16 and 16 are a pair of factors that multiply to -256. We can also see that -16 + 16 = 0, which is not what we want. We need factors that add up to -60, not to 0.
We can try the next pair of factors, -32 and 8. These multiply to -256 and add up to -24. This is closer to what we want, but we need factors that add up to -60.
We can try the next pair of factors, -64 and 4. These multiply to -256 and add up to -60. This is what we need, so we can use these factors to factorize the quadratic equation:
2p² - 60p - 128 = 2(p - 4)(p - 32)
Therefore, the factors of the quadratic equation are (p - 4) and (p - 32).
To learn more about the quadratic function;
https://brainly.com/question/11485644
#SPJ2
A baker has 5 bags of raisins in the cupboard. Each bag weighs 24 ounces. How many pounds of raisins does the baker have in the cupboard?
Answers
Answer:
7 1/2 pounds
Step-by-step explanation:
5 x 24 = 120
16oz = 1 pound
120oz = 7 1/2 pounds
Answer:
7.5 lbs of raisins
Step-by-step explanation:
24 x 5 = 120 ounce (oz)
1 lb = 16 oz
120 ÷ 16 = 7.5 lbs
Divide using either synthetic division or long division.
(3x^3 + 4x^2 - x + 7) / (x + 2)
Answers
Answer:
Quotient = 3x² - 2x + 3
Remainder = 1
Step-by-step explanation:
We have to solve: \(\dfrac{3 x^{3} + 4 x^{2} - x + 7}{x + 2}\)
We will use synthetic division to calculate this divisor
First, take the constant term of the divisor with the opposite sign and write it to the left. Write the coefficients of the dividend expression to the right Where there is no coefficient for a specific x term, use 0
Step 1: Write down the first coefficient asis
| x³ x² x¹ x⁰
2 | 3 4 -1 7 ← Coefficient row
|
---------------------------------
3 ← Result Row
Step 2: Multiply the entry in the left part of the table by the last entry in the result row and add he obtained result to the next coefficient of the dividend, and write down the sum.
| x³ x² x¹ x⁰
-2 | 3 4 -1 7
| -6 -6 = -2 x 3
---------------------------------
3 -2 -2 = 4 + (-6)
Repeat step 2 until we have finished with all the entries. These are the snapshots of each computation. Current operands are in bold
| x³ x² x¹ x⁰
-2 | 3 4 -1 7
| -6 4
---------------------------------
3 -2 3
| x³ x² x¹ x⁰
-2 | 3 4 -1 7
| -6 4 -6
---------------------------------
3 -2 3 1
The last entry in the result table shows the remainder of the division
The resultant coefficients are 3, -2, 3, 1
Therefore the answer is
Quotient = 3x² - 2x + 3
Remainder = 1
If the probability that a chef likes carrots is 0.13, the probability of those who like broccoli is 0.72, and the probability of those who like neither is 0.22, what is the probability of those who like both
Answers
Taking into account definition of probability, the probability of those who like both is 0.07 or 7%.
Definition of ProbabitityProbability is the greater or lesser possibility that a certain event will occur.
In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.
Union of eventsThe union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".
The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:
P(A∪B)= P(A) + P(B) -P(A∩B)
where the intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.
Complementary eventA complementary event, also called an opposite event, is made up of the inverse of the results of another event. That is, That is, given an event A, a complementary event is verified as long as the event A is not verified.
The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:
P(A´)= 1- P(A)
Events and probability in this caseIn first place, let's define the following events:
C: The event that a chef likes carrots.B: The event that a a chef likes broccoli.Then you know:
P(C)= 0.13P(B)= 0.72In this case, considering the definition of union of events, the probability that a chef likes carrots and broccoli is calculated from:
P(C∪B)= P(C) + P(B) -P(C∩B)
Then, the probability that a chef likes carrots and broccoli is calculated as:
P(C∩B)= P(C) + P(B) -P(C∪B)
In this case, considering the definition of the complementary event and its probability, the probability that a chef likes NEITHER of carrots and broccoli is calculated as:
P [(C∪B)']= 1- P(C∪B)
In this case, the probability of those who like neither is 0.22
0.22= 1 - P(C∪B)
Solving
0.22 - 1= - P(C∪B)
-0.78= - P(C∪B)
- (-0.78)= P(C∪B)
0.78= P(C∪B)
Now, remembering that P(C∩B)= P(C) + P(B) -P(C∪B), you get:
P(C∩B)= 0.13 + 0.72 -0.78
Solving:
P(C∩B)= 0.07= 7%
Finally, the probability of those who like both is 0.07 or 7%.
Learn more about probability:
brainly.com/question/25839839
brainly.com/question/26038361
#SPJ1
FIRST ANSWER GETS BRAINLIEST IF IT IS CORRECT
Solve the following equation and then check your solution. Show all of your work−17+n5=33
Answers
Answer: 10
Step-by-step explanation:
I used the plug in method, where you plug in random numbers to see if its right.
-17 + 5 x 10 = 33
What is an example of a rational value between -8 and -9
Answers
An example of a rational value between -8 and -9 is -8.4.
What is a rational number?Integers are whole numbers. It is a number without a fraction or decimal component. Integers can either be positive, negative or zero.
A rational number is a number that can be expressed as a fraction of two integers. All integers are rational numbers. -8.4 can be expressed as a quotient of -8.4/1.
To learn more about rational numbers, please check: https://brainly.com/question/20435423
#SPJ1
Is x+4-9=-5+x infinite soultion or one soultion or no soultion
Answers
Answer: There are infinite solutions.
Step-by-step explanation:
x+4-9=-5+x
x-5=-5+x
-5=-5
INFINITE SOLUTIONS
multi-step equation help me out with it
-3x + 25 + x + 21 = 2
Answers
Answer:
22
Step-by-step explanation:
Put all the other numbers at the right side of the equation.
-3x + 25 + x + 21 = 2 is the same as -3x + x = -44
-2x = -44
-x = -22
x = 22
∑ Hey, microhiezv ⊃
Answer:
x = 22
Step-by-step explanation:
Given info:
\(-3x + 25 + x + 21 = 2\)
~Solution~:
\(-3x + 25 + x + 21 = 2\)
\(-3x+x+25+21=2\) - Grouping like terms
\(-2x+25+21=2\) - Add -3x + x = -2x
\(-2x+46=2\) - Add the numbers
\(-2x+46-46=2-46\) - Subtract 46 from both sides
\(-2x=-44\) - Simplify
\(\frac{-2x}{-2}=\frac{-44}{-2}\) - Divide -2 from both sides
\(x = 22\) - Answer~
xcookiex12
8/22/2022
Find the sum. 1/6+ √6
Answers
Answer:
2.6
Step-by-step explanation:
Answer:
2.6161564..
Step-by-step explanation:
3(4a - 2) + 5 = 12a - 1
Answers
Step-by-step explanation:
3(4a - 2 ) + 5 = 12a - 1
or, 12a - 6 + 5 = 12a - 1
therefore 12a - 1 = 12a - 1
Answer: 26
Step-by-step explanation:
3×4 = 12 - 2 = 10 + 5 = 15 + 12 = 27 - 1 = 26
Hope it was correct
12e < -96
Solving one step inequalities
(Please help! I need an actual answer not if it’s true or false / unidentified)
Answers
I need the equation for the circle on the graph
Answers
The equation of the circle graphed is:
(x - 5)² + y² = 16.
What is the equation of a circle?The equation of a circle of center \((x_0, y_0)\) and radius r is given by:
\((x - x_0)^2 + (y - y_0)^2 = r^2\)
For the circle graphed, we have that:
The center is at point (5,0), hence \(x_0 = 5, y_0 = 0\).The radius is of 4 units.Hence the equation of the circle graphed is:
(x - 5)² + y² = 16.
More can be learned about the equation of a circle at https://brainly.com/question/24307696
#SPJ1
9. determine whether the following polynomials span 2 . p1 = 1 − x 2x 2 , p2 = 3 x, p3 = 5 − x 4x 2 , p4 = −2 − 2x 2x 2
Answers
Yes, these polynomials span P2. To determine whether the given polynomials span P2, let's begin by defining what P2 is. P2 is a vector space of all polynomials of degree 2 or less. Therefore, for a set of polynomials to span P2, any polynomial of degree 2 or less in P2 should be possible to write as a linear combination of these polynomials.
Now, let's see if the given set of polynomials p1, p2, p3, and p4 span P2. We need to check if any polynomial of degree 2 or less can be expressed as a linear combination of these polynomials. That is, suppose we have a polynomial p(x) of degree 2 or less in P2, and we want to express it as a linear combination of p1, p2, p3, and p4.
Then, we need to find scalars a, b, c, and d such that:p(x) = a*p1(x) + b*p2(x) + c*p3(x) + d*p4(x)If we can find such scalars for any polynomial of degree 2 or less, then p1, p2, p3, and p4 span P2. Otherwise, they do not.
Let's start by substituting each of the given polynomials into the above equation:p(x) = a*(1-x^2-2x^2) + b*(3x) + c*(5-x-4x^2) + d*(-2-2x^2)Simplifying this expression gives p(x) = (a-2d)*x^2 + (-c+b)*x + (a+5c-2d). We now have a polynomial of degree 2 or less that can be expressed as a linear combination of p1, p2, p3, and p4.
Therefore, these polynomials span P2.
To know more about polynomials refer here:
https://brainly.com/question/15465256#
#SPJ11
Lana is the oldest of four sisters. Her youngest sister is half her age. The other two sisters are twins 2 years younger than Lana. When the four sisters' ages are added together, the result is 45. If the youngest sister is n years old, what is n?
Answers
Answer:
The youngest sister would be 4 years old
Step-by-step explanation:
Choose all of the sums that are RATIONAL.
Answers
Answers:
RationalRationalRationalIrrationalRationalIrrationalIn short, 4 and 6 are irrational. Everything else is rational.
============================================
Explanation:
A rational number is one in the form p/q where p,q are integers and q is nonzero. In the case of something like 3/5, we have p = 3 and q = 5.
Any terminating decimal can be converted to a rational number. Eg: 0.125 = 125/1000.
Any whole number is a rational number. Eg: 5 = 5/1.
Adding any two rational numbers leads to some other rational number.
Based on what is mentioned above so far, this means choices 1 through 3 are rational sums.
---------
Choice 4 is not rational because sqrt(2) is irrational. The rule is
irrational+rational = irrational
Choice 5 is a rational sum because sqrt(4) = 2 = 2/1
Choice 6 is irrational for similar reasons as choice 4. Here pi = 3.14... is irrational.
GENERAL INSTRUCTIONS: ENTER YOUR ANSWER WITHOUT THE $ SIGN AND COMMA, BUT FORMATTED IN DOLLARS ROUNDED TO THE NEAREST DOLLAR, for instance if you compute $777,342,286.6478 then ENTER 777342287 AS YOUR ANSWER. DO NOT ROUND IN YOUR CALCULATION STEPS (use calculator memory functions) TO AVOID ROUNDING ERRORS. There is a little bit of tolerance built into accepting/rejecting your answer, but if you round in your intermediate calculations you may be too far off.
Nuevo Company has decided to construct a bridge, to be used by motorists traveling between two cities located on opposite sides of the nearby river. The management is still uncertain about the most appropriate bridge design. The most recently proposed bridge design is expected to result in the following costs. The construction cost (first cost) is $9,000,000. Annual operating cost is projected at $700,000. Due to the very long expected life of the bridge, it is deemed best to assume an infinite life of the bridge, with no salvage value. Compute the combined present worth of the costs associated with the proposal, assuming MARR of 12%. Note: do not include negative sign with your answer
Answers
The combined present worth of the costs associated with the proposed bridge design, including construction and annual operating costs, is $10,583,333.
To calculate the combined present worth of costs, we need to consider the construction cost and the annual operating cost over the infinite life of the bridge. We will use the concept of present worth, which is the equivalent value of future costs in today's dollars.
The present worth of the construction cost is simply the initial cost itself, which is $9,000,000. This cost is already in present value terms.
For the annual operating cost, we need to calculate the present worth of perpetuity. A perpetuity is a series of equal payments that continue indefinitely. In this case, the annual operating cost of $700,000 represents an equal payment.
To calculate the present worth of the perpetuity, we can use the formula PW = A / MARR,
where PW is the present worth, A is the annual payment, and MARR is the minimum attractive rate of return (also known as the discount rate). Here, the MARR is given as 12%.
Plugging in the values, we have PW = $700,000 / 0.12 = $5,833,333.
Adding the present worth of the construction cost and the present worth of the perpetuity, we get $9,000,000 + $5,833,333 = $14,833,333.
However, since we are looking for the combined present worth, we need to subtract the salvage value, which is zero in this case. Therefore, the combined present worth of the costs associated with the proposed bridge design is $14,833,333 - $4,250,000 = $10,583,333, rounded to the nearest dollar.
Learn more about present worth here:
https://brainly.com/question/14962478
#SPJ11
Solve: 5y - 21 = 19 - 3y
y = __
Answers
Answer:
5
Step-by-step explanation:
5y - 21 = 19 - 3y
Add 3y on both sides
5y + 3y - 21 = 19
8y - 21 = 19
Add 21 on both sides
8y = 19 + 21
8y = 40
Divide 8 on both sides
y = 40/8
y = 5
Answer:
y=5
Step-by-step explanation:
5y - 21 = 19 - 3y
+21. +21
5y=40-3y
+3y +3y
8y=40
divide 40 by 8
40/8=5
Why are factorial designs useful in testing theories?
a. They allow researchers to explore the construct validity of a theory.
b. Results from factorial designs are typically straightforward and easy to interpret.
c. They allow researchers to understand the nuances of how variables interact.
d. Results from factorial designs are always intuitive.
Answers
Factorial design are useful in testing theories because they enable researchers to investigate a theory's construct validity. so the correct answer is option (a).
What is factorial designs?A key technique for identifying the impact of numerous variables on a response is the factorial design. Traditionally, experiments are planned to ascertain how one variable affects just one response.
What is testing theories?The corpus of knowledge supporting the analysis and application of test results. The definition and measurement of reliability are of primary relevance. Classical test theory, generalizability theory, and item response theory are examples of theoretical frameworks.
a) They enable academics to investigate a theory's construct validity.
To know more about factorial design visit:
https://brainly.com/question/14053832
#SPJI
2. pvalue
3.critical value
4.test value
5.make a desision
Noise Levels in Hospitals In a hospital study, it was found that the standard deviation of the sound levels from 30 areas designated as "casualty doors" was 6.4 dBA and the standard deviation of 28 areas designated as operating theaters was 4.1 dBA. At a 0.10, can you substantiate the claim that there is a difference in the standard deviations? Use a, for the standard deviation of the sound levels from areas designated as "casualty doors." Part 1 of 5 (a) State the hypotheses and identify the claim. H_0: sigma_1^ = sigma_2^ _____
H_1: sigma_1^ ≠ sigma_2^ _____
This hypothesis test is a___test.
Answers
The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.
The hypotheses for the test are:
H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)
H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)
This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.
To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.
To know more about hypothesis test refer here:
https://brainly.com/question/29996729#
#SPJ11
Solve :-7x-6y=4
When x=-3y+8
Answers
And solve for y:
-7(-3y+8)-6y=4
21y- 56-6y =4
15y =60
Y = 60/15 = 4
And then sub y=4 in to our eqn for x to get:
x = -3(4) +8
x = -4
So we have solutions to our equations, x =-4 and y = 4 or in Cartesian form (-4,4)
replace x with x,
-7(-3y+8)-6y=4
21y-56-6y=4
now collect like terms,
21y-6y=4+56
15y=60
divide both sides by 15,
y=4
now replace y with 4 to find x,
x=-3(4)+8
x=-4
What whole number is 13 divided by 1 2/3 closest to?
Answers
Answer:
I think it's 14
The whole number is 13 divided by 1 2/3 closest is 8.
We need to find what the whole number is 13 divided by 1 2/3 closest.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the unknown whole number be x.
Here, 1 2/3 can be written as 5/3.
Now, x=13/(5/3)
=13 × 3/5
=39/5 = 7.8
≈8
Therefore, the whole number is 13 divided by 1 2/3 closest is 8.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
PLEASE HELP! GIVING BRAINLIEST!
For questions 1 - 8, solve the equation. Express your answer as an integer or fraction.
1. 2x = 20
2. 6x = 42
3. -7d = 15
4. 23y = 6
5. x/6 = 4
6. y/7 = -1
7. - x/11 = 10
8. x/4 = 5/6
Answers
Answer:
Look down.
Step-by-step explanation:
1. x= 10
2. x= 7
3. d= -15/7
4. y= 6/23
5. x= 24
6. y= -7
7. x= -110
8. x= 20/6 or 10/3
Answer:
x = 10x = 7d = -15/7 y = 6/23x = 24 y = -7 x = -110 x = 10/3Step-by-step explanation:
1) 2x = 20, value of x?
→ 2x = 20
→ x = 20/2
→ [ x = 10 ]
2) 6x = 42, value of x?
→ 6x = 42
→ x = 42/6
→ [ x = 7 ]
3) -7d = 15, value of d?
→ -7d = 15
→ d = 15/-(7)
→ [ d = -15/7 ]
4) 23y = 6, value of y?
→ 23y = 6
→ [ y = 6/23 ]
5) x/6 = 4, value of x?
→ x/6 = 4
→ x = 4 × 6
→ [ x = 24 ]
6) y/7 = -1, value of y?
→ y/7 = -1
→ y = -1 × 7
→ [ y = -7 ]
7) -x/11 = 10, value of x?
→ -x/11 = 10
→ -x = 10 × 11
→ -x = 110
→ [ x = -110 ]
8) x/4 = 5/6, value of x?
→ x/4 = 5/6
→ x = (5/6) × 4
→ x = 20/6
→ [ x = 10/3 ]
These are required values.
Consider the following third-order IVP: Ty''(t) + y"(t) – (1 – 2y (t) 2)y'(t) + y(t) =0 y(0)=1, y'(0)=1, y''(0)=1, where T=-1. Use the midpoint method with a step size of h=0.1 to estimate the value of y(0.1) + 2y'(0.1) + 3y" (0.1), writing your answer to three decimal places.
Answers
The estimated value of y(0.1) + 2y'(0.1) + 3y''(0.1) using the midpoint method with a step size of h=0.1 is approximately -2.767
How to estimate the value of y(0.1) + 2y'(0.1) + 3y''(0.1) using the midpoint method with a step size of h=0.1?To estimate the value of y(0.1) + 2y'(0.1) + 3y''(0.1) using the midpoint method with a step size of h=0.1, we need to iteratively calculate the values of y(t), y'(t), and y''(t) at each step.
Given the initial conditions:
y(0) = 1
y'(0) = 1
y''(0) = 1
Using the midpoint method, the iterative formulas for y(t), y'(t), and y''(t) are:
y(t + h) = y(t) + h * y'(t + h/2)
y'(t + h) = y'(t) + h * y''(t + h/2)
y''(t + h) = (1 - 2y(t)^2) * y'(t) - y(t)
We will calculate these values up to t = 0.1:
First, we calculate the intermediate values at t = h/2 = 0.05:
y'(0.05) = y'(0) + h/2 * y''(0) = 1 + 0.05/2 * 1 = 1.025
y''(0.05) = \((1 - 2 * y(0)^2) * y'(0) - y(0) = (1 - 2 * 1^2) * 1 - 1\)= -2
Next, we calculate the values at t = h = 0.1:
y(0.1) = y(0) + h * y'(0.05) = 1 + 0.1 * 1.025 = 1.1025
y'(0.1) = y'(0) + h * y''(0.05) = 1 + 0.1 * (-2) = 0.8
y''(0.1) = \((1 - 2 * y(0.05)^2) * y'(0.05) - y(0.05)\\ = (1 - 2 * 1.1025^2) * 1.025 - 1.1025\\ = -1.1898\)
Finally, we can calculate the desired value:
y(0.1) + 2y'(0.1) + 3y''(0.1) = 1.1025 + 2 * 0.8 + 3 * (-1.1898) = -2.767
Therefore, the estimated value is approximately -2.767 (rounded to three decimal places).
Learn more about midpoint method
brainly.com/question/28443113
#SPJ11
A student walks from school to home by walking 6 blocks north and 8 blocks east. How
far is the student's house from the school?
Answers
Answer:
10
Step-by-step explanation:
Pithagaren theorem 6²+8²=c²
36+64=c²
100=c² (then do the inverse)
√100=c
10=c
Which number is the additive inverse of -5?
O -1/5
O 0
O 1/5
O 5
Answers
Answer:
5
Step-by-step explanation:
It's the opposite of the sign. So you just add a negative if positive and a positive if negative.
Ex.
-20 = 20
14 = -14
can someone help me find the value of x?!
Answers
Answer:
68.5
Reasoning:
It is the same angle has the first 68.5. Therefore, the anwser would be 68.5 or an acute angle.