Answers
let's bear in mind that complex roots never come alone, their conjugate sister is always with her, so if we have the complex root of "i" or namely "0 + i", her conjugate is also coming along, or "0 - i", so we really have four roots, so
[tex]\begin{cases} x = 0+i &\implies x -i=0\\ x = 0-i &\implies x +i=0\\ x = \sqrt{2} &\implies x -\sqrt{2}=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{we are assuming that}}{a=1} \\\\\\ 1( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y\implies ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{ \textit{difference of squares} }{( x -i )( x +i )}\implies x^2 - i^2\implies x^2-(-1)\implies x^2+1 \\\\[-0.35em] ~\dotfill\\\\ (x^2+1)( x -\sqrt{2} )( x -3 )\implies (x^2+1)(x^2-3x-x\sqrt{2}+3\sqrt{2}) \\\\\\ (x^2+1)[x^2-x(3+\sqrt{2})+3\sqrt{2}] \\\\\\ x^4-x^3(3+\sqrt{2})+3x^2\sqrt{2}+x^2-x(3+\sqrt{2})+3\sqrt{2} \\\\\\ \boxed{x^4-x^3(3+\sqrt{2})+x^2(3\sqrt{2}+1)-x(3+\sqrt{2})+3\sqrt{2}~~ = ~~y}[/tex]
Related Questions
11). Evaluate the definite integral.
Answers
The value of the definite integral is determined as -1/28.
What is a definite integral?A definite integral is a mathematical concept that represents the area under a curve between two specific points, called the limits of integration. The definite integral is denoted by the symbol ∫, and the limits of integration are written as a and b, where a is the lower limit and b is the upper limit.
To evaluate the definite integral, we will use the following method:
[tex]\int\limits^2_0 {- \frac{6x}{(3x + 2)^2} } \, dx ; u = 3x^2 + 2[/tex]
We can start by substituting [tex]$u=3x^2+2$[/tex], which gives us [tex]$du/dx=6x$[/tex], or [tex]$x,dx=du/6$[/tex].
Using this substitution, we can rewrite the integral as:
[tex]\int\limits^2_0 - \frac{6x}{(3x^2 + 2)^2} , dx &\\\\\\\=\ \int\limits^{u(2)}{u(0)} -\frac{1}{u^2},du/6\\\\\\&= \left[ \frac{1}{6u} \right]^{u(2)}{u(0)} \\\\\\&= \frac{1}{6}\left(\frac{1}{u(2)} - \frac{1}{u(0)}\right)\\\\\\\&= \frac{1}{6}\left(\frac{1}{3(2)^2 + 2} - \frac{1}{3(0)^2 + 2}\right) \\\\\\\&= \frac{1}{6}\left(\frac{1}{14} - \frac{1}{2}\right)\\\\\\\ &= \frac{1}{6}\left(-\frac{6}{28}\right) \\\\\\\\&= \boxed{-\frac{1}{28}}\end{align*}[/tex]
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Number 5 Please look at image
Answers
The solutions to the quadratic equations are as follows
4a. The rocket was launched from an initial height of 10 meters.
b. The maximum height of the rocket was 55 meters.
c. The rocket reaches its maximum height at 3 seconds
d. the rocket is in the air for t = 6.316 seconds
5. when the horizontal distance is 1 foot, the height of the balloon is 8.875 feet
b. when the horizontal distance is 33 feet, the height of the balloon is 0.875 feet.
How do we solve the quadratic equation?The function is a quadratic equation, and here is how we solve each problem;
a. The initial height of the rocket is the value of h when t=0. So we substitute t=0 into the equation to find:
h = -5(0)² + 30(0) + 10 = 10 meters
b. & c. The maximum height of a projectile launched upward occurs at the vertex of the parabola represented by the quadratic function. For a quadratic function in the form y = ax² + bx + c, the time at which the maximum (or minimum) occurs is -b/2a. In this case, a = -5 and b = 30. So:
t = -b/2a = -30 / (2×-5) = 3 seconds
So, the rocket reaches its maximum height at t=3 seconds. We can find this maximum height by substituting t=3 into the equation:
h = -5(3)² + 30(3) + 10 = -5×9 + 90 + 10 = 45 meters
The rocket is in the air from the time it was launched until it hits the ground. The time when it hits the ground is when h = 0. So we can set the equation to 0 and solve for t:
0 = -5t² + 30t + 10
This is a quadratic equation and can be solved using the quadratic formula: t = [-b ± √(b² - 4ac)] / (2a)
Let's calculate the roots:
t = [-30 ± √((30)² - 4×-5×10)] / (2×-5)
= [-30 ± √(900 + 200)] / -10
= [-30 ± √(1100)] / -10
= 6.316 or -0.32
5. a. To find the height of the balloon when d=1, we substitute d=1 into the equation:
h = -1/8(1)²+ 4(1) + 5 = -1/8 + 4 + 5 = 8.875 feet
b. To determine whether the balloon hits your enemy, we need to see if the balloon's height (h) is above ground level (h > 0) when d=33. So, we substitute d=33 into the equation:
h = -1/8(33)² + 4(33) + 5
h = -1/8×1089 + 132 + 5
h = -136.125 + 132 + 5
h = 0.875 feet
when the horizontal distance is 33 feet, the height of the balloon is 0.875 feet. This means the balloon is above ground level and therefore would indeed hit your nemesis standing 33 feet away.
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A researcher is studying life Expectancy in different parts of the world. Using birth and death records, she randomly select a sample of 20 people from town A and a sample of 20 people from town B and record their lifespan in years.
The researcher wants to test the claim that there is a significant difference in life span for people in the two towns. What are the Noel and alternative hypotheses that should be used to test this claim?
Please see photo below for the options of answer , thank you!
Answers
Answer:
Null Hypothesis (H0): There is no significant difference in life span for people in the two towns.
Alternative Hypothesis (H1): There is a significant difference in life span for people in the two towns.
Answer:
The null and alternative hypotheses that should be used to test this claim are:
Null hypothesis: There is no significant difference in lifespan for people in the two towns. Symbolically, this can be represented as H0: μ1 = μ2, where μ1 and μ2 are the population mean lifespans of Town A and Town B, respectively.
Alternative hypothesis: There is a significant difference in lifespan for people in the two towns. Symbolically, this can be represented as Ha: μ1 ≠ μ2.
To test this claim, the researcher can conduct a two-sample t-test using the data collected from the two towns. The test statistic can be calculated as:
t = (x1 - x2) / (s1^2/n1 + s2^2/n2)^0.5
where x1 and x2 are the sample mean lifespans of Town A and Town B, respectively, s1 and s2 are the sample standard deviations of Town A and Town B, respectively, and n1 and n2 are the sample sizes of Town A and Town B, respectively.
Using the given data, the test statistic can be calculated as:
t = (78.5 - 74.4) / (11.2^2/20 + 12.3^2/20)^0.5 = 1.02
At a significance level of 0.05 with 38 degrees of freedom (df = n1 + n2 - 2), the critical value for a two-tailed test is ±2.024. Since the calculated t-value (1.02) falls within the acceptance region (-2.024 < t < 2.024), the null hypothesis cannot be rejected. Therefore, we do not have enough evidence to conclude that there is a significant difference in lifespan for people in the two towns.
Step-by-step explanation:
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The measure of an angle is twice less than that of its supplement angle.
Answers
The supplementary angle will be 60°.
What are supplementary angles?
Supplementary angles are angles (only two) whose sum is equal to 180 degrees. In other words, if we add two angles together and the result is 180 degrees, those angles are considered supplementary.
For example, if we have angle A that measures 60 degrees, its supplement angle B will measure 120 degrees (180 - 60 = 120). Angles A and B are supplementary angles.
Supplementary angles can be adjacent, meaning they share a common vertex and side, or they can be non-adjacent. In either case, their sum will always be 180 degrees.
Supplementary angles are commonly used in geometry and trigonometry to solve problems related to angles and triangles.
Now,
Let x = measure of the angle.
Then, the supplement angle is 180 - x.
According to the problem, x is twice less than the supplement angle. In other words, the supplement angle is twice greater than x. We can write this as:
180 - x = 2x
Solving for x, we get:
180 = 3x
x = 60
Therefore, the angle measures 60 degrees.
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Right Question:- The measure of an angle is twice less than that of its supplement angle. find that angle?
I need to find f(g) f(x) please
Answers
The answers f(g(x)) = x and g(f(x)) = x tell us that the two functions f(x) and g(x) are inverses of each other.
What is inverse?The inverse of a function is a second function that "undoes" the effect of the first function. More specifically, if f is a function that maps elements from a set A to a set B, then its inverse function, denoted as f^(-1), maps elements from B back to A.
According to question:(a) To find f(g(x)), we need to substitute the expression for g(x) into f(x):
f(g(x)) = g(x) / (6 + g(x))
Substituting the expression for g(x) yields:
f(g(x)) = (6x / (1 - x)) / (6 + (6x / (1 - x)))
This equation can be made simpler by first locating a common denominator:
f(g(x)) = (6x / (1 - x)) / ((6(1 - x) / (1 - x)) + (6x / (1 - x)))
f(g(x)) = (6x / (1 - x)) / ((6 - 6x + 6x) / (1 - x))
f(g(x)) = (6x / (1 - x)) / (6 / (1 - x))
f(g(x)) = 6x / 6
f(g(x)) = x
To find g(f(x)), we need to substitute the expression for f(x) into g(x):
g(f(x)) = 6f(x) / (1 - f(x))
Substituting the expression for f(x) yields:
g(f(x)) = 6(x / (6 + x)) / (1 - (x / (6 + x)))
To simplify this expression, we can first find a common denominator:
g(f(x)) = 6(x / (6 + x)) / (((6 + x) / (6 + x)) - (x / (6 + x)))
g(f(x)) = 6(x / (6 + x)) / ((6 + x - x) / (6 + x))
g(f(x)) = 6(x / (6 + x)) / (6 / (6 + x))
g(f(x)) = x
(b) The answers f(g(x)) = x and g(f(x)) = x tell us that the two functions f(x) and g(x) are inverses of each other. This means that when we apply one function and then the other, we get back to the original input value. Specifically, if we apply f(x) to x and then apply g(x) to the result, we get x back, and if we apply g(x) to x and then apply f(x) to the result, we also get x back. This is a useful property when analyzing functions and their relationships.
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Use the distributive property to solve 4 2/5 x 10. Where 4 2/5 is a fraction. Please show work so I can explain. Thank you.
Answers
Answer:
Step-by-step explanation:it will be 44/1 = 44
Since 4 2/5 x 10
We will use 10 as 10/1
and 4 2/5 as 22/5 so
22/5 x 10/1 we cross out the 5 and 10 since there a factor of each other
then it will be 22/1 x 2/1 it will be much easier
Then 22 x 2 = 44
1x1 = 1
=44/1 = 44
To amend a country’s constitution, 7/9 of the 84 states in that country must approve the amendment. If 66 states approve the amendment, will the constitution be amended?
Answers
Answer:
Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.
Step-by-step explanation:
To determine whether the constitution will be amended, we need to compare the number of states that have approved the amendment to the required number of states needed for approval.
The requirement is that 7/9 of the 84 states must approve the amendment. So, we need to calculate 7/9 of 84 to find out how many states need to approve the amendment:
(7/9) x 84 = 66.67
Rounding up, we see that 66.67 is equivalent to 67 states. This means that in order for the amendment to be approved, at least 67 states must approve it.
Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.
Researchers comparing the effectiveness of two pain medications randomly selected a group of patients who had been complaining of a certain kind of joint pain. They randomly divided these people into two groups, then administered the pain killers. Of the 112 people in the group who received medication A, 84 said this pain reliever was effective. Of the 108 people in the other group, 66 reported that pain reliever B was effective.
(a)Find a 95% confidence interval for the difference in the proportions of people who may find these medications effective. Interpret your interval.
(b) Does this interval contain zero? What does that mean for the hypothesis test of the difference in proportions?
Answers
(a) The 95% confidence interval for the difference in proportions of people who may find these medications effective is 0.029 to 0.231, which suggests that medication A is more effective than medication B in relieving joint pain.
(b) No, the interval does not contain zero, which means that the difference in proportions is statistically significant and supports the hypothesis that medication A is more effective than medication B.
Ice cream is packaged in cylindrical gallon tubs. A tub of ice cream has a total surface area of 183.69 square inches.
If the diameter of the tub is 6 inches, what is its height? Use π = 3.14.
A 2.25 inches
B 4.5 inches
C 6.75 inches
D 12.75 inches
Answers
Answer:
6.75 inches.
Step-by-step explanation:
[tex]183.69 = 2*3.14*3^2 + 2*3.14*3*h[/tex]
[tex]= 56.52 + 18.84h[/tex]
[tex]183.69 - 56.52 = 18.84h[/tex]
[tex]127.17 = 18.84h[/tex]
[tex]=\frac{127.17}{18.84}[/tex]
[tex]=6.75[/tex]
If 9x+10=20
, what is the value of 18x+1
?
Answers
Answer:
21
Step-by-step explanation:
9x + 10 = 20
9x = 10
x = 10/9
What is the value of 18x + 1?
18(10/9) + 1
= 20 + 1
= 21
So, the value of 18x + 1 is 21
I will mark you brainiest!
If AB = 35,BC = 15, and EF = 60, then the value of DE IS
A) 140
B) 180
C) 200
D) 210
Answers
AB/BC = DE/EF
35/15 = DE/60
DE = 35*60 / 15
DE = 140
answer
A 140
88.128 x 0.5 Multiplication question
Answers
Answer:
44.064x
Step-by-step explanation:
Answer: when you time 88.128 by 0.5, it gives you an answer of 44.064
Hope this helps :)
What is 6% times 39%
Answers
Answer:
0.0234
Step-by-step explanation:
please give brainliest
for each situation, determine taxable income, assuming pretax accounting income is $100 million
Answers
Answer:
Temporary Differences Reported First on: The Income Statement The Tax Return Revenue Expense Revenue Expense1) $272) $273) $274) $275) $22 $276) $27 $227) $22 $27 $178) $22 $27 $12 $17Taxable Income assuming pretax accounting income is $100 million1) Pretax Income - Revenue = $100m - $27m = $73m2) Pretax Income + Expense = $100m + $27m = $127m3) Pretax Income + Revenue Return = $100m + $27m = $127m4) Pretax Income - Expense Return = $100m - $27m = $73m5) Pretax Income - Revenue + Expense = $100m - $22m + $27m = $105m6) Pretax Income + Expense + Revenue Return = $100m + $27m + $22m = $149m7) Pretax Income - Revenue + Expense - Expense Return = $100m - $22m + $27m - $17m = $88m8) Pretax Income - Revenue + Expense + Revenue Return - Expense Return = $100m - $22m + $27m + $12m- $17m = $100m
Step-by-step explanation:
First, return is added to differentiate revenue and expense from the tax return from that of the income statement.Temporary difference is defined as the difference between the tax and financial reporting bases of assets and liabilities. These differences can result in taxable or deductible amounts in future years (deferred tax assets or liabilities).For each scenario, temporal difference of revenue reported first in the income statement is deducted from the pretax accounting income while expenses are added back to the pretax accounting income.For temporal differences from the tax return, the revenue is added to the pretax accounting income while expenses are deducted.
(-8)-(-2) porfa lo necesito
Answers
Answer:
-6
Step-by-step explanation:
All I need to know is the answer to this problem so I can compare mine.
Answers
Answer:
we will do TanA = perpendicular / Base
A = 35°
Tan 35° = 217 / W
value of Tan 35° is approx = 0.7
0.7 = 217/ W
W = 217 / 0.7
W = 310
A person travels 30 miles in 40 minutes
Answers
The distance that the person will be able to cover in an hour would be = 45 miles
How to calculate the distance travelled?The distance that the individual covers in in 40 mins = 30 miles.
Therefore in an hour(60 mins) the distance would be = X mile
That is ;
40 mins = 30 miles
60 mins = X
make X the subject of formula;
X = 60×30/40
X = 1800/40
x = 45 miles.
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The height of an object launched into the air can be modeled by the graph shown.
When does the object return to the ground?
Answers
Answer:
9 seconds
Step-by-step explanation:
right side of the graph touches the x axis at 9
Suppose you have two six-sided dice where each side is equally likely to land face up when rolled.
What is the probability that you will roll doubles?
(Give your answer as a number between 0 and 1. Round to 2 decimal places.)
What is the probability that you will roll a sum of twelve?
(Give your answer as a number between 0 and 1. Round to 2 decimal places.)
Answers
Answer:
12/12 and 1/12
Step-by-step explanation:
Gianna is going to throw a ball from the top floor of her middle school. When she throws the ball from 48feet above the ground, the function h(t)=-16t^2+32t +48 models the height,h, of the ball above the ground as a function of time, t. Find the zero of this function that tells us when the ball will hit the ground.
Answers
Substitute h(t) = 0 in the given equation:
-16t^2 + 32t + 48 = 0
Dividing both sides by -16:
t^2 - 2t - 3 = 0
Factorizing the equation:
(t - 3)(t + 1) = 0
So, the solutions are t = 3 or t = -1.
Since time can't be negative, the only solution that makes sense in this context is t = 3.
Therefore, the ball will hit the ground after 3 seconds.
Factor by substitution: (3y−2)2−(3y−2)−2.
Answers
The simplification of the polynomial using factor by substitution is: ((3y - 2)⁴ - 1)/(3y - 2)²
How to factor Polynomial by substitution?Factoring polynomials simply means separating a polynomial into its component polynomials.
Sometimes, in the event that polynomials are particularly complicated, it is usually easiest to substitute a simple term and factor down.
We have the equation:
(3y - 2)² - (3y - 2)⁻²
Let 3y - 2 be denoted by S and as such we have:
S² - S⁻²
= S² - 1/S²
Using the denominator as factor, we have:
= (S⁴ - 1)/S²
Plugging 3y - 2 for S gives us:
((3y - 2)⁴ - 1)/(3y - 2)²
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A quadratic function passes through the points (-2,5) and (-8,5) and has a graph in the xy-plane that opens downward. Which of these could be the coordinates of the highest point of the graph?
O (5, 1)
O (5, 8)
O (5, 1)
O (5, 8)
Answers
The highest point of the quadratic equation that opens down can be (-5, 8)
Which of these could be the coordinates of the highest point of the graph?We have a quadratic equation whose graph opens downwards, and we know that it also passes through the points (-2,5) and (-8, 5).
The highest point will be of the form (x, y).
Such that y is larger than 5, and the value of x is right between the two values above:
x = (-2 - 8)/2
x = -5
So the point is of the form (-5, y) where again y > 5.
From the given options the only of this form is (-5, 8)
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a rocket is launched from the top of a 30 foot cliff with an initial velocity of 170 feet per second. the height, h, of the rocket after t seconds is given by the equation h=-16t^2+170t+30. How long after the rocket is launched will it be 20 feet from the ground?
Answers
However, we need to choose the positive value for t, since time cannot equation be negative in this case. Therefore, the rocket will be 20 feet from the ground approximately 1.411 seconds after it is launched.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
So we have:
[tex]-16t^2 + 170t + 30 = 20\\-16t^2 + 170t + 10 = 0\\8t^2 - 85t - 5 = 0\\t = (-b + \sqrt(b^2 - 4ac)) / 2a\\t = (-(-85) + \sqrt((-85)^2 - 4(8)(-5))) / 2(8)\\t = (85 + \sqrt(7225 + 160)) / 16\\t = (85 + \sqrt(7385)) / 16[/tex]
However, we need to choose the positive value for t, since time cannot be negative in this case. Therefore, the rocket will be 20 feet from the ground approximately 1.411 seconds after it is launched.
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A primary credit card holder has a current APR of 14.75%. What is the monthly periodic interest rate, rounded to the nearest hundredth of a percent? 12.29% 14.75% 0.01% 1.23%
Answers
Answer:
12.29 I thin
Step-by-step explanation:
The monthly periodic interest rate is 0.01%.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
We are given that;
APR=14.75%
Now,
The monthly periodic interest rate is the annual interest rate divided by 12 months. According to 1, the formula is:
r = (1 + i/m)^(m/n) - 1
Where:
r = periodic interest rate
i = nominal annual rate
m = number of compounding periods per year
n = number of payments per year
In this case, i = 14.75%, m = 12 and n = 12. Plugging these values into the formula, we get:
r = (1 + 0.1475/12)^(12/12) - 1
r = (1 + 0.012292) - 1
r = 0.012292 or 1.23%
Therefore, by the given APR the interest rate will be 0.01%, rounded to the nearest hundredth of a percent.
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Of the 40 learners in the class, 12 walks to school, twice the number who walk, come by car or taxi and the remainder cycle to school. What fraction does not cycle to school? Answer must be simplest form.
Answers
The fraction of learners who do not cycle to school is equal to 9/10.
How to evaluate for the fraction of learners.Given that the total number of learners is 40, 12 of which walk to school and twice of the number of learners who walk, come to school by car or taxi, then the remainder of learners who cycle to school is calculated as;
40 - [12 +2(12)] = 4
The number of learners who do not cycle to school is;
12 + 2(12) = 36
fraction of learners who do not cycle to school = 36/40
by simplification;
fraction of learners who do not cycle to school = 9/10.
Therefore, the fraction of learners who do not cycle to school is equal to 9/10.
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ABCD is a trapezium. P is a point along AC such that AP=4PC. DC=1/4AB.
a) express PB in terms of a and b in its simplest form
b) express DP in terms of a and b in its simplest form
c) does DPB form a straight line?
Answers
Answer:
a) We can use similar triangles to find PB in terms of a and b. Let x be the length of AD. Then, using the fact that AP = 4PC, we have:
PC = CP = x - b
AP = 4(x - b)
Also, using the fact that DC = (1/4)AB, we have:
AD = x
AB = 4DC = x/4
BC = AB - AD = x/4 - x = -3x/4
Now, consider the similar triangles PBC and ABD:
PB/AB = BC/AD
PB/(x/4) = (-3x/4)/x
PB = -3/4(x/4) = -3x/16
Finally, substituting x = a + b, we have:
PB = -3(a + b)/16
b) Using the same similar triangles as in part (a), we have:
DP/DC = PB/BC
DP/(1/4)AB = PB/(-3x/4)
DP = -3/4(PB)(DC/BC)AB
DP = -3/4(PB)(1/4)/(AB - AD)AB
Substituting the expressions for PB, AB, and AD from part (a), we get:
DP = -3(a + b)/16 * 1/4 / (-3(a + b)/4) * (a + b)/4
DP = -3/16 * 1/4 * 4/(3(a + b)) * (a + b)
DP = -3/16
So, DP = -3/16(a + b)
c) To check if DPB forms a straight line, we need to verify if the slopes of DP and PB are equal. Using the expressions we found in parts (a) and (b), we have:
Slope of PB = Δy/Δx = (-3/16(a+b) - 0)/(0 - (-3(a+b)/16)) = 3/16
Slope of DP = Δy/Δx = (-3(a+b)/16 - (-3/16(a+b)))/(1/4 - 0) = -3(a+b)/4
Since the slopes are not equal, DPB does not form a straight line.
3/10=
19/50=
5/10=
1/5=
14/25=
3/25=
Answers
Answer:
3/10 = 0.3
19/50 = 0.38
5/10 = 0.5
1/5 = 0.2
14/25 = 0.56
3/25 = 0.12
The gasoline gauge on a van initially read
1/4 full. When 12 gallons were added to the tank, the gauge read 3/4 full. How many more gallons are needed to fill the tank?
Answers
Initially, 1/4 of the tank was filled.
After adding 12 gallons, it was 3/4 full.
Increase in fuel filled portion =
[tex]\dfrac{3}{4} -\dfrac{1}{4} =\dfrac{3-1}{4} =\dfrac{2}{4}[/tex]
So 2/4 of the tank = 12 gallons
1/4 of tank [tex]= 12 \div 2 = 6[/tex] gallons
4/4 of tank [tex]= 6\times4 = 24[/tex] gallons
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Portion remaining to be filled =
[tex]1-\dfrac{3}{4} =\dfrac{4-3}{4} =\dfrac{1}{4}[/tex]
Fuel needed [tex]= \dfrac{1}{4} \times 24 = 6[/tex] gallons
So you need 6 more gallons to fill the tank
A business analyst wants to determine if the prices of goods at a supermarket have changed significantly since the new owner of the company took over. She looks at the prices of ten items before the new owner took over compared to after the new owner started.
(Chart in photo below)
Based on the data in the table and using a significance level of 0.05, what is the correct P-value and conclusion?
A. With a t statistic of 1.4789 and a P-value of 0.173292, reject the no hypothesis that prices have not changed
B. With a T statistic of 1.4789 and a P value of 0.173292, fail to reject the null hypothesis. The prices have not changed.
C. With a T statistic of 0.7394 and a P value of 0.478505, reject the no hypothesis that prices have not changed.
D. With a T statistic of 0.7394 anda P value of 0.478505, fail to reject the no hypothesis that prices have not changed.
Please answer quickly, 100 points thank you !
Answers
Answer: Option A
Step-by-step explanation:
The t-statistic and P-value can be calculated using statistical software or a t-test calculator. Using a two-tailed t-test with a significance level of 0.05 and 8 degrees of freedom (n1 + n2 - 2), we obtain:
t = -1.4789
P-value = 0.173292
Therefore, the correct answer is A. With a t statistic of -1.4789 and a P-value of 0.173292, we fail to reject the null hypothesis that the prices have not changed significantly since the new owner took over. We cannot conclude that the prices have changed significantly.
With a T statistic of 0.7394 and a P value of 0.478505, fail to reject the no hypothesis that prices have not changed. The correct option is D.
What is null hypothesis?A null hypothesis is a type of statistical hypothesis that asserts that there is no statistical significance in a given set of observations.
Using sample data, hypothesis testing is used to assess the credibility of a hypothesis.
To determine if the prices of goods at a supermarket have significantly changed since the new owner took over, we can perform a two-sample t-test with the null hypothesis being that the mean difference in prices before and after the new owner took over is zero.
Using a significance level of 0.05, the critical t-value for a two-tailed test with 9 degrees of freedom is approximately 2.306.
To calculate the t-statistic, we first need to calculate the mean and standard deviation of the differences in prices:
Mean difference = (0.30 - 0.07) / 10 = 0.023
Standard deviation = 2.967
t-statistic = (0.023 - 0) / (2.967 / sqrt(10)) = 0.7394
The calculated t-value of 0.7394 is less than the critical t-value of 2.306, and the corresponding p-value is 0.4785. This means we fail to reject the null hypothesis that the mean difference in prices is zero.
Therefore, based on the given data and using a significance level of 0.05, the correct P-value and conclusion are:
Thus, the correct option is D.
For more details regarding null hypothesis, visit:
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What are the steps to solving the following problem,
5x+4=19
List at least 4 steps
Answers
Answer:
5x+4=19
5x=19-4
5x=15
5x÷5=15÷5
x=3
5x=19-4
5x=15 /:5
X=3