Answer:
-3/8
Step-by-step explanation:
Hey there!
Well to find the slope with 2 points “(0,-3) and (3,-11)”, we’ll use the following formula,
[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]
Plug in the given points.
[tex]\frac{-11 - - 3}{3-0}[/tex]
-11 + 3 = -8
3 - 0 = 3
Slope = -8/3
Hope this helps :)
Suppose that BC financial aid alots a textbook stipend by claiming that the average textbook at BC bookstore costs $ $ 93.29. You want to test this claim.Required:a. The null and alternative hypothesis in symbols would be: _______b. The null hypothesis in words would be: 1. The average price of textbooks in a sample is S 96.28 2. The proportion of all textbooks from the store that are less than 96.28 is equal to 50% 3. The average of price of all textbooks from the store is less than $96.28. 4. The average of price of all textbooks from the store is greater than $96.28. 'The average price of all textbooks from the store is S 96.28
Answer:
H₀: μ = 93.29 vs. Hₐ: μ ≠ 93.29.
Step-by-step explanation:
In this case we need to test whether the claim made by BC financial aid is true or not.
Claim: The average textbook at BC bookstore costs $93.29.
A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.
It is a hypothesis of no difference.
It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.
Whereas, the alternate hypothesis is the contradicting statement to the null hypothesis.
The alternate hypothesis describes direction of the hypothesis test, i.e. if the test is left tailed, right tailed or two tailed.
It is also known as the research hypothesis and is denoted by Hₐ.
The hypothesis to test this claim can be defined as follows:
H₀: The average textbook at BC bookstore costs $93.29, i.e. μ = 93.29.
Hₐ: The average textbook at BC bookstore costs different than $93.29, i.e. μ ≠ 93.29.
Find the intervals on which the function f(x) = ax2 + bx + c (where "a" doesn't = 0) is increasing and decreasing. Describe the reasoning behind your answer.
Answer:
Step-by-step explanation:
Given that:
[tex]\mathtt{f(x) = ax^2 + bx + c}[/tex]
The derivative of the function of x is [tex]\mathtt{f'(x) = 2ax + b}[/tex]
Thus; f(x) is increasing when f'(x) > 0
f(x) is decreasing when f'(x) < 0
i.e
f'(x) > 0 , when b > 0 and a < 0
∴
2ax + b < 0
2ax < - b
[tex]\mathtt{x < \dfrac{-b}{2a}}[/tex]
f'(x) < 0 , when b < 0 and a > 0
2ax + b > 0
2ax > - b
[tex]\mathtt{x > \dfrac{-b}{2a}}[/tex]
generate a continuous and differentiable function f(x) with the following properties: f(x) is decreasing at x=−5 f(x) has a local minimum at x=−3 f(x) has a local maximum at x=3
Answer:
see details in graph and below
Step-by-step explanation:
There are many ways to generate the function.
We'll generate a function whose first derivative f'(x) satisfies the required conditions, say, a quadratic.
1. f(x) has a local minimum at x = -3, and
2. a local maximum at x = 3
Therefore f'(x) has to cross the x-axis at x = -3 and x=+3.
Furthermore, f'(x) must be increasing at x=-3 and decreasing at x=+3.
f'(x) = -x^2+9
will satisfy the above conditions.
Finally f(x) must be decreasing at x= -5, which implies that f'(-5) must be negative.
Check: f'(-5) = -(-5)^2+9 = -25+9 = -16 < 0 so ok.
f(x) can then be obtained by integrating f'(x) :
f(x) = integral of -x^2+9 = -x^3/3 + 9x = 9x - x^3/3
A graph of f(x) is attached, and is found to satisfy all three conditions.
A function is differentiable at [tex]x = a[/tex], if the function is continuous at [tex]x = a[/tex]. The function that satisfy the given properties is [tex]f(x) = 9x - \frac{x^3}{3} + 3[/tex]
Given that:
The function decreases at [tex]x = -5[/tex] means that: [tex]f(-5) < 0[/tex]
The local minimum at [tex]x = -3[/tex] and local maximum at [tex]x = 3[/tex] means that:
[tex]x = -3[/tex] or [tex]x = 3[/tex]
Equate both equations to 0
[tex]x + 3 = 0[/tex] or [tex]3 - x = 0[/tex]
Multiply both equations to give y'
[tex]y' = (3 - x) \times (x + 3)[/tex]
Open bracket
[tex]y' = 3x + 9 - x^2 - 3x[/tex]
Collect like terms
[tex]y' = 3x - 3x+ 9 - x^2[/tex]
[tex]y' = 9 - x^2[/tex]
Integrate y'
[tex]y = \frac{9x^{0+1}}{0+1} - \frac{x^{2+1}}{2+1} + c[/tex]
[tex]y = \frac{9x^1}{1} - \frac{x^3}{3} + c[/tex]
[tex]y = 9x - \frac{x^3}{3} + c[/tex]
Express as a function
[tex]f(x) = 9x - \frac{x^3}{3} + c[/tex]
[tex]f(-5) < 0[/tex] implies that:
[tex]9\times -5 - \frac{(-5)^3}{3} + c < 0[/tex]
[tex]-45 - \frac{-125}{3} + c < 0[/tex]
[tex]-45 + \frac{125}{3} + c < 0[/tex]
Take LCM
[tex]\frac{-135 + 125}{3} + c < 0[/tex]
[tex]-\frac{10}{3} + c < 0[/tex]
Collect like terms
[tex]c < \frac{10}{3}[/tex]
[tex]c <3.33[/tex]
We can then assume the value of c to be
[tex]c=3[/tex] or any other value less than 3.33
Substitute [tex]c=3[/tex] in [tex]f(x) = 9x - \frac{x^3}{3} + c[/tex]
[tex]f(x) = 9x - \frac{x^3}{3} + 3[/tex]
See attachment for the function of f(x)
Read more about continuous and differentiable function at:
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10. (01.02)
Given the function f(x)
3x - 4
5
which of the below expressions is correct? (1 point)
5x+4
f-1(x) =
3
f-1(x)
5x - 4
3
O f-'(x)
-344
-3x – 4
5
4–3x
f-1(x) =
5
Answer:
5x+4f-1(x)=3 this is short answer
You make 85,000 per year and your company matches 50 cents for every dollar you deposit into your 401k plan, up to 8% of your salary.
Answer:
The question is incomplete, below is a possible match for the complete question:
You make $85,000 per year and your company matches 50 cents for every dollar you deposit into your 401k plan, up to 8% of your salary. Complete parts (a) through (c) below.
(a) If you contribute $200 every month to your 401k, what will your company contribute each month?
The company will contribute $ (Type an integer or a decimal rounded to two decimal places as needed.)
(b) If you contribute $830 every month to your 401k, what will your company contribute each month?
The company will contribute $ (Type an integer or a decimal rounded to two decimal places as needed.)
(c) What is the maximum amount of money the company will contribute to your 401k each year?
The maximum amount that the company will contribute each year is $
(Type an integer or a decimal rounded to two decimal places as needed.)
Answer:
a.) The company will contribute $100
b.) The company will contribute $415
c.) maximum amount the company will be willing to contribute = $6,800 per year
Step-by-step explanation:
First, let us calculate the maximum amount the company will be willing to pay into the 401k plan yearly:
Annual salary = $85,000
Monthly salary = $7083.3333
maximum amount = 8% = 8/100 = 0.08 of salary
maximum amount = 0.08 × 7083.3333 = $566.67
a.) If you contribute $200 every month.
Since $200 is less than the maximum amount that the company will be willing to contribute, let us calculate how much the company is willing to contribute:
Company matches 50 cents for every dollar you deposit
1 dollar deposited = 50 cents from company
but 1 cent = $0.01
∴ 50 cents = 0.01 × 50 = $0.5
$1 deposited = $0.5 from company
∴ $200 deposited = 0.5 × 200 = $100 contributed by company
Therefore, if you contribute $200 every month, your company will contribute $100 each month.
from this example, we can see that the company is willing to contribute half of every amount you deposit every month ($100 = half of $200), hence, subsequently, we will use this for calculations.
b.) If you contribute $830 every month, the company will be willing to contribute half this amount, which is:
half of $830 = 830 ÷ 2 = $415
Therefore, if you contribute $830 per month, your company will contribute $415 per month.
c.) The maximum amount the company will be willing to contribute each year = 8% of salary per year
= [tex]= \frac{8}{100}\times 85,000 \\ =0.08\ \times\ 85,000 = \$6,800[/tex]
Therefore, the company will be willing to contribute $6,800 per year.
What is the solution to the system of equations?
5x – 4y = 6
-5x + 4y = -10
O (4,4)
0 (-2,-5)
O infinitely many solutions
O no solution
Hey there! I'm happy to help!
We have a 5x is one equation and a -5x in another equation. We can combine the two equations to cancel out the x and then solve! This is called solving by elimination.
5x-4y=6
+
-5x+4y=-10
0= -4
Since we lost our x and y while solving, there cannot be any solution.
Therefore, the answer is no solution.
Have a wonderful day!
You sell tickets at school for fundraisers. You sold car wash tickets, silly string fight tickets and dance tickets – for a total of 380 tickets sold. The car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each. If you sold twice as many silly string tickets as car wash tickets, and you have $1460 total. Write the matrix in the box below. Write the solution set for this system and include any necessary work.
Answer:
Matrix :
[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]
Solution Set : { x = 123, y = 246, z = 11 }
Step-by-step explanation:
Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,
x + y + z = 380,
And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.
5x + 3y + 10z = 1460
The silly string tickets were sold for twice as much as the car wash tickets.
y = 2x
Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.
System of Equations :
[tex]\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}[/tex]
Matrix :
[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]
Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,
[tex]\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}[/tex] - Swap Matrix Rows
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}[/tex] - Cancel leading Co - efficient in second row
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}[/tex] - Cancel leading Co - efficient in third row
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}[/tex] - Swap second and third rows
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}[/tex] - Cancel leading co - efficient in row three
And we can continue, canceling the leading co - efficient in each row until this matrix remains,
[tex]\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}[/tex]
x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold
Mary states, "If the diagonals of a parallelogramare congruent, then the
parallelogram is a rectangle." Decide if her statement is wue or false.
A. True
B. False
Answer:
True
Step-by-step explanation:
A rectangle is a plane figure with congruent length of opposite sides. Considering a rectangle ABCD,
AD ≅ BC (opposite side property)
AB ≅ CD (opposite side property)
<ABC = <BCD = <CDA = <DAC = [tex]90^{0}[/tex] (right angle property)
Thus,
<ABC + <BCD + <CDA + <DAC = [tex]360^{0}[/tex]
AC ⊥ BD (diagonals are perpendicular to each other)
AC ≅ BD (congruent property of diagonals)
Therefore, the parallelogram is a rectangle.
Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
He expected to have 15 customers each day. To answer whether the number of customers follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha = 0.10)
What is the chi-squared test statistic? Answers are rounded to the nearest hundredth.
Answer:
The chi - square test can be [tex]\approx[/tex] 0.667
Step-by-step explanation:
From the given data :
The null hypothesis and the alternative hypothesis can be computed as:
Null hypothesis: The number of customers does follow a uniform distribution
Alternative hypothesis: The number of customers does not follow a uniform distribution
We learnt that: Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
The above given data was the observed value.
However, the question progress by stating that : He expected to have 15 customers each day.
Now; we can have an expected value for each customer as:
Observed Value Expected Value
Day Customers
Monday 17 15
Tuesday 13 15
Wednesday 14 15
Thursday 16 15
The Chi square corresponding to each data can be determined by using the formula:
[tex]Chi -square = \dfrac{(observed \ value - expected \ value )^2}{expected \ value}[/tex]
For Monday:
[tex]Chi -square = \dfrac{(17 - 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(2)^2}{15}[/tex]
[tex]Chi - square = \dfrac{4}{15}[/tex]
chi - square = 0.2666666667
For Tuesday :
[tex]Chi -square = \dfrac{(13- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(-2)^2}{15}[/tex]
[tex]Chi - square = \dfrac{4}{15}[/tex]
chi - square = 0.2666666667
For Wednesday :
[tex]Chi -square = \dfrac{(14- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(-1 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )}{15}[/tex]
chi - square = 0.06666666667
For Thursday:
[tex]Chi -square = \dfrac{(16- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )}{15}[/tex]
chi - square = 0.06666666667
Observed Value Expected Value chi - square
Day Customers
Monday 17 15 0.2666666667
Tuesday 13 15 0.2666666667
Wednesday 14 15 0.06666666667
Thursday 16 15 0.06666666667
Total : 0.6666666668
The chi - square test can be [tex]\approx[/tex] 0.667
At level of significance ∝ = 0.10
degree of freedom = n - 1
degree of freedom = 4 - 1
degree of freedom = 3
At ∝ = 0.10 and df = 3
The p - value for the chi - square test statistics is 0.880937
Decision rule: If the p - value is greater than the level of significance , we fail to reject the null hypothesis
Conclusion: Since the p - value is greater than the level of significance , we fail to reject the null hypothesis and conclude that there is insufficient evidence to show that the number of customers does not follows a uniform distribution.
Answer:.67
Step-by-step explanation:
ASAP HELP WILL MARK BRAINLIEST
Answer:
c(x)=(3/4)^x
(3/4)^-2= 16/9
(3/4)^-1 =4/3
(3/4)^0=1
(3/4)^1 = 3/4
(3/4)^2= 9/16
You work for a pharmacy and monthly sales of asthma inhalers in your pharmacy follows a normal distribution with a mean of 191 inhalers per month and a standard deviation of 21 due to a storm the next shipment of inhalers did not arrive. The pharmacy only has 163 inhalers currently in stock and available to sell for the current month. What is the z score corresponding to selling 163 inhalers?
Answer: -1.33 .
Step-by-step explanation:
Formula to find the Z-score :
[tex]Z=\dfrac{\text{Expected value - Mean}}{\text{Standard deviation}}[/tex]
Given: Mean = 191 and Standard deviation = 21
Then , the z-score corresponding to the expected value of 163 will be :
[tex]Z=\dfrac{163-191}{21}\\\\=\dfrac{-28}{21}\approx-1.33[/tex]
Hence, the z score corresponding to selling 163 inhalers is -1.33 .
You have 9kg of oats and cup scales that gears of 50g and 200g. How − in three weighings− can you measure 2kg of the oats?
Answer: You will need 8 cup scales
Step-by-step explanation:
kg=1000 grams
2000/250=8
In 8 cups it is possible to measure the 2kg or 2000 grams but in three weighs it is not possible to measure the 2kg or 2000 grams.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
You have 9kg of oats and cup scales that gears of 50g and 200g.
Total oats need to measure = 9kg
As we know in 1 kg there are 1000 grams.
1 kg = 1000 grams
9kg = 9000 grams
2kg = 2000 grams
Cup scales that gears: 50g and 200g
The number of cups if consider one cup is of 250 grams( = 200 + 50)
Number of cups = 2000/250
Number of cups = 8
In three weighs it is not possible to measure the 2kg or 2000 grams.
Thus, in 8 cups it is possible to measure the 2kg or 2000 grams but in three weighs it is not possible to measure the 2kg or 2000 grams.
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Find and interpret a 95% confidence interval to estimate the average number of bolts per box for all boxes in the population. Round to 3 decimal places.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The 95% confidence interval is [tex]49.85 < \mu < 54.15[/tex]
This means that there is 95% chance that the true population mean is within this interval
Step-by-step explanation:
From the question we are told that
The sample size is n = 30
The sample mean is [tex]\= x = 52[/tex]
The population standard deviation is [tex]\sigma = 6[/tex]
Given that the confidence level is 95% then the level of confidence is evaluate as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 * \frac{ 6 }{\sqrt{30} }[/tex]
[tex]E = 2.147[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]52 - 2.147 < \mu < 52 + 2.147[/tex]
[tex]49.85 < \mu < 54.15[/tex]
800,000+700 standard form
Answer:
800700
Step-by-step explanation:
800000 + 00000 + 0000 + 000 + 00 + 0
000000 + 00000 + 0000 + 700 + 00 + 0
------------------------------------------------------------
= 800700
Answer:
Hey there!
800000+700=800700
Hope this helps :)
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65. Can the company conclude that the correlation is positive
Complete Question
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65.At the 0.01 significance level Can the company conclude that the correlation is positive
Answer:
Yes the company conclude that the correlation is positive
Step-by-step explanation:
From the question we are told that
The sample size is n = 14
The correlation is r = 0.65
The null hypothesis is [tex]H_o : r < 0[/tex]
The alternative hypothesis is [tex]H_1 : r > 0[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]Sr = \sqrt{1- r}[/tex]
[tex]Sr = \sqrt{1- 0.65}[/tex]
[tex]Sr = 0.616[/tex]
The degree of freedom for the one-tail test is
[tex]df = n- 2[/tex]
[tex]df = 14- 2[/tex]
[tex]df = 12[/tex]
The standard error is evaluated as
[tex]SE = \frac{0.616}{ \sqrt{12} }[/tex]
[tex]SE =0.1779[/tex]
The test statistics is evaluated as
[tex]t = \frac{r }{SE}[/tex]
[tex]t = \frac{0.65 }{0.1779}[/tex]
[tex]t = 3.654[/tex]
The p-value of of t is obtained from the z table, the value is
[tex]p-value = P(t < 3.654) = 0.00012909[/tex]
Given that [tex]p-value < \alpha[/tex] then we reject the null hypothesis
Hence the company can conclude that the correlation is positive
a kicker starts a football game by "kicking off". The quadratic function y = -10x^2 + 25x models football's height after x seconds. How long, in seconds, is the football in the air?
Answer: 2.5 seconds
Step-by-step explanation:
x refers to time. Since we want to know how long it is in the air, we need to find the time (x) for the ball to land on the ground (y = 0)
0 = -10x² + 25x
0 = -5x(2x - 5)
0 = -5x 0 = 2x - 5
[tex]0 = x\qquad \dfrac{5}{2}=x[/tex]
x = 0 seconds is when the ball was kicked
x = 5/2 --> 2.5 seconds is when the ball landed on the ground
A researcher would like to test the claim that the mean lung capacity of middle-aged smokers is less than the mean lung capacity of senior citizen nonsmokers. Independent random samples of 34 middle-aged smokers and 34 senior citizen nonsmokers will be used in a hypothesis test of this claim, and it is believed that the standard deviations of the lung capacities in the populations of middle-aged smokers and senior citizen nonsmokers are the same. Which test statistic formula should be used for this test
Answer:
The respiratory system extends from the nose and upper airway to the alveolar surface of the lungs, where gas exchange occurs. Inhaled tobacco smoke moves from the mouth through the upper airway, ultimately reaching the alveoli. As the smoke moves more deeply into the respiratory tract, more soluble gases are adsorbed and particles are deposited in the airways and alveoli. The substantial doses of carcinogens and toxins delivered to these sites place smokers at risk for malignant and nonmalignant diseases involving all components of the respiratory tract including the mouth.
Is 55/22 a rational
Answer:
The fraction [tex]\displaystyle \frac{55}{22}[/tex] is indeed a rational number.
Step-by-step explanation:
A number [tex]x[/tex] is rational if and only if there exist two integers [tex]p[/tex] and [tex]q[/tex] (where [tex]q \ne 0[/tex]) such that [tex]x = \displaystyle \frac{p}{q}[/tex].
[tex]\displaystyle \frac{55}{22}[/tex], the number in question here is already written in the form of a fraction. The two integers [tex]p = 55[/tex] and [tex]q = 22[/tex] ([tex]q \ne 0[/tex]) meet the requirement that [tex]\displaystyle \frac{55}{22} = \frac{p}{q}[/tex]. Therefore, [tex]\displaystyle \frac{55}{22}\![/tex] is indeed a rational number.
Side note: the [tex]p[/tex] and [tex]q[/tex] here ([tex]q \ne 0[/tex]) don't have to be unique. For example:
because [tex]\displaystyle \frac{55}{22} = \frac{5 \times 11 }{2 \times 11} = \fraac{5}{2}[/tex], both of the following pairs could satisfy [tex]\displaystyle \frac{55}{22} = \frac{p}{q}[/tex]:
[tex]p = 55[/tex] and [tex]q = 22[/tex];[tex]p = 5[/tex] and [tex]q = 2[/tex].Starting with x1 = 2, find the third approximation x3 to the root of the equation x3 − 2x − 2 = 0.
Answer:
0.8989
Step-by-step explanation:
Using the Newton's Raphson approximation formula.
Xn+1 = Xn - f(Xn)/f'(Xn)
Given f(x) = x³-2x+2
f'(x) = 3x²-2
If the initial value X1 = 2
X2 = X1 - f(X1)/f'(X1)
X2 = 2 - f(2)/f'(2)
f(2) = 2³-2(2)+2
f(2) = 8-4+2
f(2) = 6
f'(2) = 3(2)²-2
f'(2) = 10
X2 = 2- 6/10
X2 = 14/10
X2 = 1.4
X3 = X2 - f(X2)/f'(X2)
X3 = 1.4 - f(1.4)/f'(1.4)
f(1.4) = 1.4³-2(1.4)+2
f(1.4) = 2.744-2.8+2
f(1.4) = 1.944
f'(1.4) = 3(1.4)²-2
f'(1.4) = 3.880
X3 = 1.4- 1.944/3.880
X3 = 1.4 - 0.5010
X3 = 0.8989
Hence the value of X3 is 0.8989
You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sample of business days, the mean closing price of a certain stock was $. Assume the population standard deviation is $. The 90% confidence interval is ( nothing, nothing). (Round to two decimal places as needed.) The 95% confidence interval is ( nothing, nothing). (Round to two decimal places as needed.) Which interval is wider? Choose the correct answer below
Complete Question
The complete question is shown on the first uploaded image
Answer:
The 90% confidence interval is [tex][108.165 ,112.895][/tex]
The 95% confidence interval is [tex][107.7123 ,113.3477][/tex]
The correct option is D
Step-by-step explanation:
From the question we are told that
The sample size is n = 48
The sample mean is [tex]\= x = \$ 110.53[/tex]
The standard deviation is [tex]\sigma = \$ 9.96[/tex]
Considering first question
Given that the confidence level is 90% then the level of significance is mathematically represented as
[tex]\alpha = (100 - 90)\%[/tex]
[tex]\alpha = 0.10[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = ZZ_{ \frac{x}{y} } * \frac{\sigma}{ \sqrt{n} }[/tex]
[tex]E = 1.645 * \frac{9.96}{ \sqrt{ 48} }[/tex]
[tex]E = 2.365[/tex]
The 90% confidence interval is
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]110.53 - 2.365 < \mu < 110.53 + 2.365[/tex]
=> [tex]108.165 < \mu < 112.895[/tex]
Considering second question
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100 - 95)\%[/tex]
[tex]\alpha = 0.05[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{ \frac{x}{y} } * \frac{\sigma}{ \sqrt{n} }[/tex]
[tex]E = 1.96 * \frac{9.96}{ \sqrt{ 48} }[/tex]
[tex]E = 2.8177[/tex]
The 95% confidence interval is
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]110.53 - 2.8177 < \mu < 110.53 + 2.8177[/tex]
=> [tex]107.7123 < \mu < 113.3477[/tex]
What is an equation of the line that passes through the points (-5, 8) and (5,0)?
Answer:
y= -0.8x + 4
Midpoint is 0,4
What is the value of n
Answer:
9 + 18 = 27
27 + n + 1
= n = 27 - 1 = 26.
n = 26
9 + 18 + 26 + n + 7 =
53 + n + 7
53 + 7 + n
60 + n = 360
n = 360 - 60 = 300
so, n 300
so = 9, 18, 300, 26
Q-The general solution of inequality cos 2 x≤- sin x is
Answer:
x∈[2nπ−5π/6, 2nπ−π/6]∪{(4n+1)π/2}, n ϵ I
Step-by-step explanation:
1−2sin2 x≤−sin x ⇒ (2sin x+1)(sin x−1)≥0
sin x≤−1/2 or sin x≥1
−5π/6+2nπ≤x≤−π/6+2nπ or , n ϵ I x=(4n+1)π/2, n ϵ I⇒ -5π6+2nπ≤x≤-π6+2nπ or , n ϵ I x=4n+1π2, n ϵ I (as sin x = 1 is valid only)
In general⇒ In general x∈[2nπ−5π/6, 2nπ−π/6]∪{(4n+1)π/2}, n ϵ I
3. Solve 6 + 5 √ 2 4 9 − 2 x = 7
Answer:
please mark my answer brainliest
Step-by-step explanation:
question is unclear to give u correct answer
a wolf population of 850 wolves is increasing by 7% each year. Find the wolf population after 7 years
Answer:
1,267 wolvesStep-by-step explanation:
Initial population of wolf = 850 wolves
If the wolves increases by 7% each year, yearly increment will be 7% of 850
= 7/100 * 850
= 7*8.5
= 59.5 wolves.
This shows that the wolves increases by 59.5 each year.
After 7 years, increment will be equivalent to 59.5 * 7 = 416.5
The wolf population after 7 years = Initial population + Increment after 7 years
= 850 + 416.5
= 1266.5
≈ 1267 wolves
Hence the population of the wolves after 7 years is approximately 1,267 wolves
A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles. HINT [See Example 7.] How many sets of seven marbles include at least one yellow one but no green ones
Answer: 8
Step-by-step explanation:
Given: A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marbles.
Total marbles other than green = 8
Total marbles other than green and yellow = 6
Then the number of sets of seven marbles include at least one yellow one but no green ones:-
[tex]^{2}C_1\times^{6}C_6+ ^2C_2\times^6C_5\\\\= 2\times 1+1\times6\\\\=2+6=8[/tex]
Number of sets of seven marbles include at least one yellow one but no green ones = 8
Evaluate S_5 for 600 + 300 + 150 + … and select the correct answer below. A. 1,162.5 B. 581.25 C. 37.5 D. 18,600
Answer:
A. 1,162.5
Step-by-step explanation:
Write the next two terms and add them up:
S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A
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Explanation:
{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5
Sn = a*(1-r^n)/(1-r)
S5 = 600*(1-0.5^5)/(1-0.5)
S5 = 1,162.5
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Check:
first five terms = {600, 300, 150, 75, 37.5}
S5 = sum of the first five terms
S5 = 600+300+150+75+37.5
S5 = 1,162.5
Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.
Nan lives 13 miles from the airport. Felipe lives 6 miles from the airport.
How many more miles does Nan live from the airport than Felipe?
Answer:
7
Step-by-step explanation:
it's simply 13 - 6
7 it the answer, that was easy
What is the x-intercept?
You have 9kg of oats and cup scales that gears of 50g and 200g. How − in three weighings− can you measure 2kg of the oats?
Answer: You will need 8 cup scales
Step-by-step explanation:
kg=1000 grams
2000/250=8
Answer:
8
Step-by-step explanation:
2000/250=8