Answer:
It would be located in the second quadrant
Step-by-step explanation:
The reason for this is because the x is a negative and the y is positive.
Describe who is responsible for the cost and efficiency variances for direct materials, direct labor, and manufacturing overhead
Answer:
The materials price variance is usually the responsibility of the purchasing manager. The materials quantity and labor efficiency variances are usually the responsibility of production managers and supervisors.
In a study of 806 randomly selected medical malpracticeâ lawsuits, it was found that 513 of them were dropped or dismissed. Use a 0.01 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed. What is the hypothesis test to beâ conducted?
Solution :
[tex]$H_0: p = 0.5$[/tex]
[tex]$H_a: p > 0.5$[/tex]
Alpha, α = 0.01
The sample proportion is :
[tex]$p'=\frac{x}{n}$[/tex]
[tex]$=\frac{513}{806}$[/tex]
= 0.636
Test statistics, [tex]$z=\frac{p'-p}{\sqrt{\frac{pq}{n}}}$[/tex]
[tex]$z=\frac{0.636-0.5}{\sqrt{\frac{0.5\times 0.5}{806}}}$[/tex]
[tex]$z=\frac{0.136}{0.0176}$[/tex]
z = 7.727
The p value = 0.00001
Here we observe that p value is less than α, and so we reject the hypothesis [tex]H_0[/tex].
Therefore, there is sufficient evidence,
Hey, babes! Here is a question for today-
How do you write an equation to show the relationship between the Independent and Dependent Variables?
Answer:
The equation has the form: y = a + b * x where a and b are constant numbers. The variable x is the independent variable, and y is the dependent variable. Typically, you choose a value to substitute for the independent variable and then solve for the dependent variable.
Student A, lives in Phoenix, Arizona and submits an assignment for math class. The teacher notices the student IP address is 75.167.171.149. Has this student committed one of the forms of plagiarism? Check all that apply.
Group of answer choices
Yes, this student is using an academic broker.
Yes, this student copied directly from an online site.
No, this students IP address matched her location.
No, the teacher does not have proof plagiarism.
Answer:
Yes, this student copied directly from an online site.
Step-by-step explanation:
According to whatismyip.live, this IP address is from Chandler, Arizona not Phoenix.
Which of the following best describes the line that divides a design so that
every point on one side of the line coincides with a point on the other side of
the line?
A. Line of Symmetry
B. Point of Translation
C. Angle of Symmetry
D. Point of congruency
Answer:
Line of Symmetry i think
Line of symmetry best describes the line that divides a design so that every point on one side of the line coincides with a point on the other side of the line.
What is Coordinate Geometry?Coordinate Geometry (or the analytic geometry) describes the link between geometry and algebra through graphs involving curves and lines.
A line of symmetry is a line that divides a figure into two congruent parts such that if one part is folded over the line of symmetry, it will coincide with the other part.
In other words, each point on one side of the line of symmetry is equidistant from the line as the corresponding point on the other side of the line.
The line that divides a design so that every point on one side of the line coincides with a point on the other side of the line is called the Line of Symmetry.
Hence, line of symmetry best describes the line that divides a design so that every point on one side of the line coincides with a point on the other side of the line.
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(-2x) (x-3) answer please
Answer:
−2x^2+6x
Explanation:
You just have to distribute meaning you have to multiply -2x to the equation.
Four friends bought books at a bookstore. The person who got the best deal has the lowest ratio of cost to number of books purchased. Book Purchases Name Total Cost Number of Books Jo $9 4 Kei $12 8 Kate $30 16 Bryn $8 4
Answer:
Kei got the best deal.
Explanation:
The ratio of cost to number of books purchased for all of four friends will be.....
Jo ⇒ [tex]\frac{9}{4}[/tex], Kei ⇒ [tex]\frac{12}{8}[/tex] , Kate ⇒ [tex]\frac{30}{16}[/tex], Bryn ⇒ [tex]\frac{8}{4}[/tex]
From here you have to find the common denominator in this case is 16.
[tex]\frac{9}{4} =\frac{9*4}{4*4} =\frac{36}{16}[/tex]
[tex]\frac{12}{8} =\frac{12*2}{8*2} =\frac{24}{16}[/tex]
[tex]\frac{30}{16} =\frac{30*1}{16*1} =\frac{30}{16}[/tex]
[tex]\frac{8}{4} =\frac{8*4}{4*4} =\frac{32}{16}[/tex]
As you could tell the lowest is [tex]\frac{24}{16}[/tex] so the lowest is Kei.
What is a segment parallel to ba in a cube
Answer:
Two planes that do not intersect are said to be parallel. Parallel planes are found in shapes like cubes, which actually has three sets of parallel planes. The two planes on opposite sides of a cube are parallel to one another. ... So those will be 2 that are in the same plane that will never intersect.
Find the shortest distance from
A to B in the diagram below.
Shortest distance = Displacement
And please provide the diagram
Must click thanks and mark brainliest
The table shows how surveyed drivers obtained their current vehicle and how they plan to get their next vehicle.
A 2-way table. A 4-column with 4 rows titled Plan for Next Vehicle. Column 1 has entries Current vehicle, bought new, bought used, leased total. Column 2 is labeled Buy new with entries 39, 19, 5, 63. Column 3 is labeled Buy used with entries 6, 146, 2, 154. Column 4 is labeled Lease with entries 6, 9, 18, 33. Column 5 is labeled Total with entries 51, 174, 25, 250.
What percent of drivers surveyed bought their current vehicle new and will buy a new vehicle again next time? Round your answer to the nearest whole number; you do not need to enter the percent symbol.
I think it's 16. Can someone help check it?
Answer:
The answer is 16!
EDGE2021
Answer:
16%
Step-by-step explanation:
edge 2023
Find the time it takes for $6,400 to double when invested at an annual interest rate of 19%, compounded
continuously.
years
Find the time it takes for $640,000 to double when invested at an annual interest rate of 19%, compounded
continuously.
years
Give your answers accurate to 4 decimal places.
Question Holn Video M Message instructor
9514 1404 393
Answer:
3.6481 years
Step-by-step explanation:
The doubling time is not a function of the amount invested. It can be found by considering the account balance multiplier:
2 = e^(rt) = e^(0.19t)
Taking logs, we can solve for t:
ln(2) = 0.19t
t = ln(2)/0.19 ≈ 3.6481431
Rounded to 4 decimal places, the doubling time is 3.6481 years, for either balance.
5 people cleared a plot of land in 15 days.How many people would i need to hire to clear three times that plot in 5 days
Answer:
45 people
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
ln 15 days 5ppl work
ln 15 days if three times of that ppl work=5×3
=15ppl
So in 1 day=15×15\5 ppl
=45ppl
lt takes 45ppl to clear three times the plot in 5 days.
Find y' for the following.
Answer:
[tex]\displaystyle y' = \frac{5x - 2xy^2}{2y(x^2 - 3y)}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle 5x^2 - 2x^2y^2 + 4y^3 - 7 = 0[/tex]
Step 2: Differentiate
Implicit Differentiation: [tex]\displaystyle \frac{dy}{dx}[5x^2 - 2x^2y^2 + 4y^3 - 7] = \frac{dy}{dx}[0][/tex]Rewrite [Derivative Property - Addition/Subtraction]: [tex]\displaystyle \frac{dy}{dx}[5x^2] - \frac{dy}{dx}[2x^2y^2] + \frac{dy}{dx}[4y^3] - \frac{dy}{dx}[7] = \frac{dy}{dx}[0][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle 5\frac{dy}{dx}[x^2] - 2\frac{dy}{dx}[x^2y^2] + 4\frac{dy}{dx}[y^3] - \frac{dy}{dx}[7] = \frac{dy}{dx}[0][/tex]Basic Power Rule [Product Rule, Chain Rule]: [tex]\displaystyle 10x - 2 \Big( \frac{d}{dx}[x^2]y^2 + x^2\frac{d}{dx}[y^2] \Big) + 12y^2y' - 0 = 0[/tex]Basic Power Rule [Chain Rule]: [tex]\displaystyle 10x - 2 \Big( 2xy^2 + x^22yy' \Big) + 12y^2y' - 0 = 0[/tex]Simplify: [tex]\displaystyle 10x - 4xy^2 - 4x^2yy' + 12y^2y' = 0[/tex]Isolate y' terms: [tex]\displaystyle -4x^2yy' + 12y^2y' = 4xy^2 - 10x[/tex]Factor: [tex]\displaystyle y'(-4x^2y + 12y^2) = 4xy^2 - 10x[/tex]Isolate y': [tex]\displaystyle y' = \frac{4xy^2 - 10x}{-4x^2y + 12y^2}[/tex]Simplify: [tex]\displaystyle y' = \frac{5x - 2xy^2}{2y(x^2 - 3y)}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
Use the ratio of a 45-45-90triangle to solve for the variables. Make sure to simplify radicals. Leave your answers as radicals in simplest form.
Answer:
Step-by-step explanation:
in this specific case the two legs are congruent:
b = 18
For the Pythagorean theorem
a = √ 2 * 18^2 = 18√2
What type of line is PQ?
A. altitude
B. angle bisector
C. side bisector
D. median
The line PQ of the triangle is an altitude. The correct option is A.
What is the altitude of the triangle?
A line segment passing through a triangle's vertex and running perpendicular to the line containing the base is the triangle's height in geometry.
The extended base of the altitude is the name given to this line that contains the opposing side. The foot of the altitude is the point at where, the extended base and the height converge.
In the given triangle the line segment PQ is passing through a triangle's vertex and running perpendicular to the line containing the base is the triangle's height in geometry.
Therefore, the line PQ of the triangle is an altitude. The correct option is A.
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Use: Ck = k! (n-k)!
n!
n k
to solve the combination.
How many ways can you
choose steak, fish, or chicken if you
can only choose two meats?
Answer:
3 ways.
Step-by-step explanation:
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
2 meats from a set of 3(steak, fish or chicken). So
[tex]C_{3,2} = \frac{3!}{2!1!} = 3[/tex]
3 ways.
15. On Sports Day, Mike runs 100 metres in 13.89 seconds and Neal runs the same distance in 13.01 seconds. Who is the FASTER runner?
Answer:
Neal
Step-by-step explanation:
13.01 < 13.89
I do not understand this and could use help it needs the work shown
Answer:
a = 9
Step-by-step explanation:
The given trinomial is :
[tex]x^2-6x+\_\_\__[/tex]
let the blank is a.
So, we need to find the value of a so that it results in a perfect square trinomial.
We know that, [tex](m-n)^2=m^2-2mn+n^2[/tex]
So,
[tex]x^2-6x+a=x^2-2(1)(3)+3^2\\=(x-3)^2[/tex]
So, the value of a is 9. If a is 9, then only it would be a perfect square trinomial.
What is the GCF of the expression 7xyz - 21xyz + 49yz + 14yz2?
Answer:
7yz
Step-by-step explanation:
You can take 7yz common from all the terms in the given expression
Answered by GAUTHMATH
Explain how to multiply
the following
binomials
(2x - y)(2x + y).
Step-by-step explanation:
you can just use the punnet square method to multiply it
Use FOIL; first, outer, inner, last. Multiply the first terms in each binomial, the outer terms of each binomial, the inner terms of each binomial, and the last terms of each binomial. In this case, you multiply 2x*2x, 2x*y, -y*2x, and -y*y.
To almirahs are purchased for 7,800.
200 was spent on the transportation. One of them is sold at a profit of 40% and the other one at a loss of 40% If the selling price was same in both the cases, and the cost price of each almirah
Answer:
The Cost Price of the Almirah Is 4000
Is segment AB tangent to circle O shown in the diagram, for AB = 8, OB = 3.75, and AO = 10.25. Explain your reasoning and show all work in your own words. (The figure is not drawn to scale.)
9514 1404 393
Answer:
not tangent
Step-by-step explanation:
AB will be tangent to circle O if AB ⊥ BO. That can be tested by checking to see if AB, BO, and AO satisfy the Pythagorean theorem.
According to the Pythagorean theorem, the length of the hypotenuse of a right triangle with legs 3.75 and 8 will be ...
hypotenuse = √(3.75² +8²) = √78.0625 ≈ 8.835
The length of AO is somewhat greater than that, so AB cannot be a tangent to the circle.
__
The angle ABO is obtuse.
In an annual report to investors, an investment firm claims that the share price of one of their bond funds had very little variability. The report shows the average price as $15.00 with a variance of 0.19. One of the investors wants to investigate this claim. He takes a random sample of the share prices for 22 days throughout the last year and finds that the standard deviation of the share price is 0.2517. Can the investor conclude that the variance of the share price of the bond fund is different than claimed at α = 0.05. Assume the population is normally distributed.
Required:
State the null and alternative hypotheses. Round to four decimal places when necessary
In this question, the variance of the population is tested. From the data given in the exercise, we build the hypothesis, then we find the value of test statistic and it's respective p-value, to conclude the test. From this, it is found that the conclusion is:
The p-value of the test is 0.0038 < 0.05, which means that the investor can conclude that the variance of the share price of the bond fund is different than claimed at α = 0.05.
----------------
Claimed variance of 0.19:
This means that at the null hypothesis, it is tested if the variance is of 0.19, that is:
[tex]H_0: \sigma^2 = 0.19[/tex]
----------------
Test if the variance of the share price of the bond fund is different than claimed at α = 0.05.
At the alternative hypothesis, it is tested if the variance is different of the claimed value of 0.19, that is:
[tex]H_1: \sigma^2 \neq 0.19[/tex]
The test statistic for the population standard deviation/variance is:[tex]\chi^2 = \frac{n-1}{\sigma_0^2}s^2[/tex]
In which n is the sample size, is the value tested for the variance and s is the sample standard deviation.
----------------
0.19 is tested at the null hypothesis, as the variance:
This means that [tex]\sigma_0^2 = 0.19[/tex]
----------------
He takes a random sample of the share prices for 22 days throughout the last year and finds that the standard deviation of the share price is 0.2517.
This means that [tex]n = 22, s^2 = (0.2517)^2 = 0.0634[/tex]
----------------
Value of the test statistic:
[tex]\chi^2 = \frac{n-1}{\sigma_0^2}s^2[/tex]
[tex]\chi^2 = \frac{21*0.0634}{0.19}[/tex]
[tex]\chi^2 = 7[/tex]
----------------
P-value of the test and decision:
The p-value of the test is found using a chi-square for the variance calculator, considering a test statistic of [tex]\chi^2 = 7[/tex] and 22 - 1 = 21 degrees of freedom, and a two-tailed test(test if the mean is different of a value).
Using the calculator, the p-value of the test is 0.0038.
The p-value of the test is 0.0038 < 0.05, which means that the investor can conclude that the variance of the share price of the bond fund is different than claimed at α = 0.05.
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A shop sells a particular of video recorder. Assuming that the weekly demand for the video recorder is a Poisson variable with the mean 3, find the probability that the shop sells. . (a) At least 3 in a week. (b) At most 7 in a week. (c) More than 20 in a month (4 weeks).
Answer:
a) 0.5768 = 57.68% probability that the shop sells at least 3 in a week.
b) 0.988 = 98.8% probability that the shop sells at most 7 in a week.
c) 0.0104 = 1.04% probability that the shop sells more than 20 in a month.
Step-by-step explanation:
For questions a and b, the Poisson distribution is used, while for question c, the normal approximation is used.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
In which
x is the number of successes
e = 2.71828 is the Euler number
[tex]\lambda[/tex] is the mean in the given interval.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The Poisson distribution can be approximated to the normal with [tex]\mu = \lambda, \sigma = \sqrt{\lambda}[/tex], if [tex]\lambda>10[/tex].
Poisson variable with the mean 3
This means that [tex]\lambda= 3[/tex].
(a) At least 3 in a week.
This is [tex]P(X \geq 3)[/tex]. So
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which:
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
Then
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]
So
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0498 + 0.1494 + 0.2240 = 0.4232[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 1 - 0.4232 = 0.5768[/tex]
0.5768 = 57.68% probability that the shop sells at least 3 in a week.
(b) At most 7 in a week.
This is:
[tex]P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]
[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]
[tex]P(X = 4) = \frac{e^{-3}*3^{4}}{(4)!} = 0.1680[/tex]
[tex]P(X = 5) = \frac{e^{-3}*3^{5}}{(5)!} = 0.1008[/tex]
[tex]P(X = 6) = \frac{e^{-3}*3^{6}}{(6)!} = 0.0504[/tex]
[tex]P(X = 7) = \frac{e^{-3}*3^{7}}{(7)!} = 0.0216[/tex]
Then
[tex]P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680 + 0.1008 + 0.0504 + 0.0216 = 0.988[/tex]
0.988 = 98.8% probability that the shop sells at most 7 in a week.
(c) More than 20 in a month (4 weeks).
4 weeks, so:
[tex]\mu = \lambda = 4(3) = 12[/tex]
[tex]\sigma = \sqrt{\lambda} = \sqrt{12}[/tex]
The probability, using continuity correction, is P(X > 20 + 0.5) = P(X > 20.5), which is 1 subtracted by the p-value of Z when X = 20.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20 - 12}{\sqrt{12}}[/tex]
[tex]Z = 2.31[/tex]
[tex]Z = 2.31[/tex] has a p-value of 0.9896.
1 - 0.9896 = 0.0104
0.0104 = 1.04% probability that the shop sells more than 20 in a month.
The probability of the selling the video recorders for considered cases are:
P(At least 3 in a week) = 0.5768 approximately.P(At most 7 in a week) = 0.9881 approximately.P( more than 20 in a month) = 0.0839 approximately.What are some of the properties of Poisson distribution?Let X ~ Pois(λ)
Then we have:
E(X) = λ = Var(X)
Since standard deviation is square root (positive) of variance,
Thus,
Standard deviation of X = [tex]\sqrt{\lambda}[/tex]
Its probability function is given by
f(k; λ) = Pr(X = k) = [tex]\dfrac{\lambda^{k}e^{-\lambda}}{k!}[/tex]
For this case, let we have:
X = the number of weekly demand of video recorder for the considered shop.
Then, by the given data, we have:
X ~ Pois(λ=3)
Evaluating each event's probability:
Case 1: At least 3 in a week.
[tex]P(X > 3) = 1- P(X \leq 2) = \sum_{i=0}^{2}P(X=i) = \sum_{i=0}^{2} \dfrac{3^ie^{-3}}{i!}\\\\P(X > 3) = 1 - e^{-3} \times \left( 1 + 3 + 9/2\right) \approx 1 - 0.4232 = 0.5768[/tex]
Case 2: At most 7 in a week.
[tex]P(X \leq 7) = \sum_{i=0}^{7}P(X=i) = \sum_{i=0}^{7} \dfrac{3^ie^{-3}}{i!}\\\\P(X \leq 7) = e^{-3} \times \left( 1 + 3 + 9/2 + 27/6 + 81/24 + 243/120 + 729/720 + 2187/5040\right)\\\\P(X \leq 7) \approx 0.9881[/tex]
Case 3: More than 20 in a month(4 weeks)
That means more than 5 in a week on average.
[tex]P(X > 5) = 1- P(X \leq 5) =\sum_{i=0}^{5}P(X=i) = \sum_{i=0}^{5} \dfrac{3^ie^{-3}}{i!}\\\\P(X > 5) = 1- e^{-3}( 1 + 3 + 9/2 + 27/6 + 81/24 + 243/120)\\\\P(X > 5) \approx 1 - 0.9161 \\ P(X > 5) \approx 0.0839[/tex]
Thus, the probability of the selling the video recorders for considered cases are:
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1. (02.01)
Solve -4(x + 10) - 6 = -3(x - 2). (1 point)
-40
-46
-52
52
Answer:
-52
Step-by-step explanation:
-4(x + 10) - 6 = -3(x - 2)
Distribute the left side to get:
(-4x + -40) - 6
Now distribute the right side to get:
-3x + 6
Arrange the equation as the following:
-4x - 40 - 6 = -3x + 6
Add the like terms on each side:
-4x - 46 = -3x + 6
Do the inverse operation of each term:
-x = 52
Now we need to get x to become a positive, so we just divide -x by -1 to get x.
And 52/-1 to get our final answer of -52.
Answer: -52
Step-by-step explanation:
-4(x + 10) - 6 = -3(x - 2)
Distribute the left side to get:
(-4x + -40) - 6
Now distribute the right side to get:
-3x + 6
Arrange the equation as the following:
-4x - 40 - 6 = -3x + 6
Add the like terms on each side:
-4x - 46 = -3x + 6
Do the inverse operation of each term:
-x = 52
Now we need to get x to become a positive, so we just divide -x by -1 to get x.
And 52/-1 to get our final answer of -52.
2cos2+cos2(2)−2cos2cos2=1
g(x) = -8x + 2, find
a. g(x+4)
b. g(x) + g(-2)
Answer:
g(x+4)= -8(x+4)+2
=-8x-32+2=-8x-30
g(x)+g(-2)=-8x+2+(-8(-2)+2)
=-8x+2+(16+2)
=-8x+20
a.=-8x-30
b.=-8x+20
If you deposit $500 dollars “Each Month!” Into an account paying 3% interest, compounded monthly, how much would be in said account after 4 years.
Please show proper work and give a good explanation in regards as to how you got your answer
Answer:
26029.26
Step-by-step explanation:
Assuming we are investing the 500 at the end of the period and starting with 500 in the account
[ P(1+r/n)^(nt) ]+PMT × {[(1 + r/n)^(nt) - 1] / (r/n)}
PMT = the monthly payment
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the time in years
[ 500(1 + .03/12)^(4*12) ]+500 × {[(1 + .03/12)^(4*12) - 1] / .03/12)}
[ 500(1 + .0025)^(48) ]+500 × {[(1 + .0025)^(48) - 1] / .0025)}
563.66 +25465.60
A simple random sample of 27 filtered 100-mm cigarettes is obtained from a normally distributed population, and the tar content of each cigarette is measured. The sample has a standard deviation of 0.20 mg. Use a 0.05 significance level to test the claim that the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.30 mg, which is the standard deviation for unfiltered king-size cigarettes. Complete parts (a) through (d) below. a. What are the null and alternative hypotheses?
Answer:
The null hypothesis is [tex]H_0: \sigma = 0.3[/tex]
The alternative hypothesis is [tex]H_1: \sigma \neq 0.3[/tex]
Step-by-step explanation:
Test if the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.30 mg.
At the null hypothesis, we test if the standard deviation is of 0.3, that is:
[tex]H_0: \sigma = 0.3[/tex]
At the alternative hypothesis, we test if the standard deviation is different of 0.3, that is:
[tex]H_1: \sigma \neq 0.3[/tex]
You decide to determine, once and for all, which chocolate brownies are best-- yours or your sister-in-law's Yolanda-- by devising a test of hypothesis. She is a superb baker and she mocks your baking as inferior. Undaunted, you decide to randomly select 100 names from the NYC phone book. You contact each selected individual and they agree to participate in your study. Then, you send your brownies with instructions for rating the taste and one week later you send Yolanda's brownies with the same instructions. Each group rates the brownies on a 10 point ordinal scale--10 implies exquisite and 1 implies inedible. True or False: This test is performed on paired or matched samples.
Answer:
Ture
Step-by-step explanation:
The rates of the same participatant are paired.