Answers
Answer:
2MN=RA+TP
13×2=x+18
26=x+18
26-18=x
8=x
Related Questions
Describe how the graph of each function can be obtained from the graph of y = f(x). Make sure you use full sentences to explain the transformation of the new function.
a) y=3f(x)–2
(b) y=f(x-1)–4
(c) y=f(1⁄2x)+5
Answers
Using translation concepts, the changes are described as follows:
a) The function is vertically stretched by a factor of 3, and shifted down 2 units.
b) The function is shifted 1 unit right and 4 units down.
c) The function is horizontally compressed by a factor of 2 and shifted up 5 units.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Item a:
The changes are as follows:
y -> 3y, hence the function is vertically stretched by a factor of 3.y -> y - 2, hence the function is shifted down 2 units.Item b:
The changes are as follows:
x -> x - 1, hence the function is shifted right 1 unit.y -> y - 4, hence the function is shifted down 4 units.Item c:
The changes are as follows:
x -> 0.5x, hence the function is horizontally compressed by a factor of 2.y -> y + 5, hence the function is shifted up 4 units.More can be learned about translation concepts at https://brainly.com/question/4521517
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Solve 7x2(x + 1) = 6x + 14
Ox=-12
Ox = 12
Ox= -16
Ox = 16
Answers
[tex]\large\displaystyle\text{$\begin{gathered}\sf 7x-2(x+1)=6x+4 \end{gathered}$}[/tex]
Use the distributive property to multiply −2 by x+1.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 7x-2x-2=6x+14 \end{gathered}$}[/tex]Combine 7x and −2x to get 5x.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5x-2=6x+14 \end{gathered}$}[/tex]Subtract 6x on both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5x-2-6x=14 \end{gathered}$}[/tex]Combine 5x and −6x to get −x.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -x-2=14 \end{gathered}$}[/tex]Add 2 to both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -x=14+2 \end{gathered}$}[/tex]Add 14 and 2 to get 16.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -x=16 \end{gathered}$}[/tex]Multiply both sides by −1.
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=-16 \ \ \to \ \ \ Answer \end{gathered}$}[/tex]{ Pisces04 }[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{7x - 2(x + 1) = 6x + 14}[/tex]
[tex]\huge\textbf{DISTRIBUTE 2 WITHIN the}\\\\\huge\textbf{PARENTHESES:}[/tex]
[tex]\mathsf{7x - 2(x) + 2(1) = 6x + 14}[/tex]
[tex]\mathsf{7x - 2x - 2 = 6x + 14}[/tex]
[tex]\huge\textbf{COMBINE the LIKE TERMS (if you}\\\\\huge\textbf{have any):}[/tex]
[tex]\mathsf{(7x - 2x) - 2 = 6x + 14}[/tex]
[tex]\mathsf{5x - 2 = 6x + 14}[/tex]
[tex]\huge\textbf{ADD 2 to BOTH SIDES:}[/tex]
[tex]\mathsf{5x - 2 + 2 = 6x + 14 + 2}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathsf{5x = 6x + 16}[/tex]
[tex]\huge\textbf{SUBTRACT 6x to BOTH SIDES}[/tex]
[tex]\mathsf{5x - 6x = 6x + 16 - 6x}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathsf{-x = 16}[/tex]
[tex]\mathsf{-1x = 16}[/tex]
[tex]\huge\textbf{DIVIDE -1 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{-1x}{-1} = \dfrac{16}{-1}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathsf{x = \dfrac{16}{-1}}[/tex]
[tex]\mathsf{x = -16}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = -16}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
■.Given angle TUV and ray UW, if m/TUV = 89,
m/TUW = 22 +7x, and m/WUV = 41+ 6x, find m/WUV.
Assume that point W is on the interior of TUV
Giving brainliest
Answers
The measure of m<WUV is 53 degrees
Lines and angles
Given the following parameters
m<TUW = 22 +7x,
m<WUV = 41+ 6x
m<TUV. = 89
The related expression is given as:
m<TUV + m<WUV = m<TUV.
Substitute
22+7x+41+6x = 89
63 + 13x = 89
13x = 89 - 63
13x = 26
x = 2
Determine the measure of m<WUV
m<WUV = 41 + 6(2)
m<WUV = 41 + 12
m<WUV =53 degrees
Hence the measure of m<WUV is 53 degrees
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The mean annual cost of an automotive insurance policy is normally distributed with a mean of $1140 and standard deviation of $310.
a. What is the probability that a random sample of 16 policyholders will have a mean insurance policy cost between $1000 and $1250?
Round your z value(s) to two decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places.
Probability =
b. What is the probability that a random sample of 16 policyholders will have a mean insurance policy cost which exceeds $1250?
Round your z value(s) to two decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places.
Probability =
c. What is the probability that a random sample of 16 policyholders will have a mean insurance policy cost below $1220?
Round your z value(s) to two decimal places. Do not round any other intermediate calculations. Round your answer to four decimal places.
Probability =
Answers
Using the normal distribution, it is found that the probabilities are given as follows:
a) 0.8871 = 88.71%.
b) 0.0778 = 7.78%.
c) 0.8485 = 84.85%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters in this problem are given as follows:
[tex]\mu = 1140, \sigma = 310, n = 16, s = \frac{310}{\sqrt{16}} = 77.5[/tex]
Item a:
The probability is the p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1000, hence:
X = 1250:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1250 - 1140}{77.5}[/tex]
Z = 1.42
Z = 1.42 has a p-value of 0.9222.
X = 1000:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1000 - 1140}{77.5}[/tex]
Z = -1.81
Z = -1.81 has a p-value of 0.0351.
0.9222 - 0.0351 = 0.8871 = 88.71% probability.
Item b:
The probability is one subtracted by the p-value of Z when X = 1250, hence:
1 - 0.9222 = 0.0778 = 7.78%.
Item c:
The probability is the p-value of Z when X = 1220, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1220 - 1140}{77.5}[/tex]
Z = 1.03
Z = 1.03 has a p-value of 0.8485.
0.8485 = 84.85% probability.
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someone help me understand this
Answers
Answer:
Step-by-step explanation:
for reflection around x-axis.
(x,y)→(x,-y)
so P' is (-7,4)
Which graph corresponds to the table? Giving brainliest to accurate answer.
Answers
Answer:
Last graph that slopes upwards from left to right and that has an y-intercept of -1
Step-by-step explanation:
let us pick some points!(you can chose any two)
when x =3 , y = 14 : helps us get points (3,14)
when x =1 , y = 4 : helps us get points (1,4)
so we find the gradient using the two points:
[tex]gradient \ =\frac{14-4}{3-1} =\frac{10}{2} \\[/tex]
we now use gradient 10/2 and point (1,4) to find the equation of the line:
[tex]\frac{10}{2} =\frac{y-4}{x-1} \\2(y-4)=10(x-1)\\2y-8=10x-10\\2y=10x-10+8\\2y=10x-2\\y=5x-1[/tex]
from the equation of the line found we are able to find the y- intercept of the line is -1 and that the line has a positive gradient thus should slope upwards from left to right.
From the pictures you posted, we pick the last graph as it seem to slope upwards from left to right and has the line cutting y axis at around -1
Find the value of x. Round to the nearest tenth. X 12 32° Not drawn to scale Find the value of x . Round to the nearest tenth . X 12 32 ° Not drawn to scale
Answers
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!!What types of Functions will left endpoint lead to an under approximation and right endpoints lead to and over approximation?
What types of Functions will left endpoint lead to an over approximation and right endpoints lead to and under approximation?
Answers
The functions that the left endpoint lead to an under approximation and right endpoints lead to and over approximation is the positive and increasing function.
How to illustrate the function?It should be noted that function simply means the illustration that shows the relationship between the variables.
In this case, the functions that the left endpoint lead to an under approximation and right endpoints lead to and over approximation is the positive and increasing function.
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The set of natural numbers x that satisfy x+8=3
Answers
Answer:
-5
Step-by-step explanation:
x+8=3
x=3-8
we can easily say +3-8=-5
Write the nth term of the arithmetic sequence 2,6,18,54 find the 10th term of the sequence
Answers
Answer:
Step-by-step explanation:
Givens
t1 = 2
r = 3
n = 10
Formula
tn = a*r^(n -1) Substitute the givens into the this formula
Solution
t10 = 2 * 3^(10 - 1)
t10 = 2 * 3^9
t10 = 2 * 19683
t10 = 39366
Answer: 39366
pls solve...I will mark as BRAINLIST
Answers
Answer:
Here you go with your answer
Mark me as brainlist may your parents live long life
Part II: Describe the pattern of the following sequence. (2 points)
Answers
1 subract 6
2 add 8
3 add 11
4 subract 5
5 add 10
Please help! Fred mixes a solution using two types of solutions: 0.60 liters containing 10% alcohol and 0.40 liters containing 35% alcohol.
What is the alcohol concentration of the mixed solution?
Answers
Answer:
20%
Step-by-step explanation:
Total Litres in mixture=(0.60+0.4)=1 Litre
alcohol in first portion:=0.10(0.60)=0.06 Litres
alcohol in second portion:=0.35(0.40)=0.14 Litres
Total alcohol in mixture = 0.06 +0.14 = 0.20
% of alcohol in mixture:
[tex]\frac{0.2}{1} (100) = 20%[/tex]%
Answer: 20%. Based on the given conditions, formulate:: 35% * 0.4 + 0.6 * 10% / 0.4 + 0.6Calculate the product
The value of y varies inversely with x. What is the value of k when y=12.7 and x=8
Answers
Answer: 101.6
Step-by-step explanation:
y∝(1/x)
this implies that
y=k/x eq(*)
when y=12.7 and x=8
12.7=k/8
(12.7)(8)=k
101.6 =k
a group of 4 numbers have an average of 15, three of the numbers are 18,11 and 25. what is the other number??
Answers
Answer:
6
Step-by-step explanation:
The average of a set of numbers is their sum divided by their number. This fact lets us write an equation to find the missing number.
SetupLet x represent the missing number. The average of the 4 numbers is ...
(x +18 +11 +25)/4 = 15
SolutionMultiplying by 4 gives ...
x +54 = 60
Subtracting 54, we find the missing number:
x = 6
The other number is 6.
Sasha made a model of a clipper ship. If her model has a length of 18 inches, and the original ship has a length of 160 feet and a width of 32 feet, what should be the width of her model?
Answers
The width of the model is 3.6 inches.
What are Similar Figures?The figures with the same shape are said similar when the sides of both the figures are in proportion.
Sara has a model of length = 18inches.
The original ship has a length is 160 ft
The width of the original ship is 32 ft
The model is a scaled-down version of the original figure and so the length and width of the model will be in the same proportion as the original dimensions.
Let x represents the width of the model then,
160/18 = 32/x
x = 32 * 18 / 160
x= 3.6 inches.
Therefore, the width of the model is 3.6 inches.
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What is 1/4+1/6=
Please help me I’ll make the first person Brainiest
Answers
Answer:
[tex]\dfrac{5}{12}[/tex]
Explanation:
[tex]\dfrac{1}{4} + \dfrac{1}{6}[/tex]
The least common multiple of 4 and 6 is 12
So, make the denominator's same
[tex]\dfrac{3(1)}{12} + \dfrac{2(1)}{12}[/tex]
multiply numbers
[tex]\dfrac{3}{12} + \dfrac{2}{12}[/tex]
Join both fractions
[tex]\dfrac{3+ 2}{12}[/tex]
simplify following
[tex]\dfrac{5}{12}[/tex]
You plan to borrow $36,500 at a 7.7% annual interest rate. The terms require you to amortize the loan with 7 equal end-of-year payments. How much interest would you be paying in Year 2?
Answers
The amount of interest you would be paying in Year 2 is: $2,492.62.
InterestFirst step is to calculate the Equal Monthly Payment
Equal Monthly Payment=P×r×(1+r)^t/(1+r)^t-1
Where:
P=Principal=$36,500
r=Rate=7.7%
t=Time=7 years
Equal Monthly Payment=36,500×0.077×(1+0.077)^7÷(1+0.077)^7-1
Equal Monthly Payment=36,500×0.077×(1.077)^7÷(1.077)^7-1
Equal Monthly Payment=36,500×0.077×1.6807763÷1.6807763-1
Equal Monthly Payment=4,723.82/0.6807763
Equal Monthly Payment=$6,938.875
Second step is to calculate Year 1 Closing balance
Year 1 Closing balance = Beginning balance + Interest - EMI Payment
Year 1 Closing balance= $36,500 +($36,500×7.7%) - $6,938.875
Year 1 Closing balance= $36,500 + $2,810.5 -$6,938.875
Year 1 Closing balance = $32,371.625
Third step is to calculate year 2 interest
Year 2 Interest= $32,371.625×7.7%
Year 2 Interest=$2,492.62
Therefore the amount of interest you would be paying in Year 2 is: $2,492.62.
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Evaluate 2b2+b+y2 when b=5
Answers
Answer:
[tex]y^2 + 55[/tex]
Step-by-step explanation:
Solution
Step 1: Plug in value of b as 5.
[tex]2(5)^2 + (5) + y^2[/tex]Step 2: Simplify
[tex]50 + 5 +y^2[/tex] [tex](50+5) + (y^2)[/tex] [tex]y^2 + 55[/tex]Therefore, the answer is y^2 + 55.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{2b^2 + b + y^2}[/tex]
[tex]\huge\textbf{Conversion:}[/tex]
[tex]\mathbf{2(5)^2 + 5 + y^2}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathbf{2(5)^2 + 5 + y^2}[/tex]
[tex]\mathbf{= 2(5\times5) + 5 + y^2}[/tex]
[tex]\mathbf{= 2(25) + 5 + y^2}[/tex]
[tex]\mathbf{= 50 + 5 + y^2}[/tex]
[tex]\mathbf{= 55 + y^2}[/tex]
[tex]\mathbf{= y^2 + 55}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\textsf y\frak{^2 + 55}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Which shows the rational expression written using the least common denominator x 1/4x2 x 1/x2
Answers
The rational expression written using the least common denominator [tex]\frac{x+1}{4x^{2} }+\frac{x+1}{x^{2} }\\[/tex] is [tex]\frac{x+1}{4x^{2} }+\frac{4(x+1)}{4x^{2} }[/tex].
What is a rational expression?The ratio of two polynomials is displayed in rational expressions. It indicates that the denominator and numerator are polynomials. It is an algebraic expression that has a ratio and an unknown variable, just like a fraction. Although we can simplify this kind of equation with the aid of a calculator.
Because one is divided by the other, just like a ratio, it is a "rational expression."
The polynomial that we divide by cannot be zero, as a reminder.
The least common denominator for [tex]4x^{2}[/tex] and [tex]x^{2}[/tex] is calculated to be [tex]4x^{2}[/tex].
Thus, the required rational expression is [tex]\frac{x+1}{4x^{2} }+\frac{4(x+1)}{4x^{2} }[/tex].
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The ratio of the numerator to the denominator of a certain fraction is one to four. If three is added to the numerator and
subtracted from the denominator, the new fraction reduces to one-third. What is the original fraction?
A 12/45
B 15/45
C 12/48
Answers
Answer:
C 12/48
Step-by-step explanation:
Original fraction:
x/y
The ratio of the numerator to the denominator is 1:4, so
x/y = 1/4
Cross multiply:
y = 4x
If three is added to the numerator and subtracted from the denominator, the new fraction reduces to one-third.
(x + 3)/(y - 3) = 1/3
Cross multiply:
3(x + 3) = 1(y - 3)
3x + 9 = y - 3
Above, we have y = 4x, so substitute 4x for y in the equation just above and solve for x.
3x + 9 = 4x - 3
12 = x
x = 12
y = 4(12) = 48
The original fraction is x/y = 12/48
Solve quadratic equation 10x^2+x-2=0
Answers
Answer:
[tex]\{-\frac{1}{2} \} \cup \{\frac{2}{5}\}[/tex]
Step-by-step explanation:
[tex]10x^2 + x - 2 = 0; \\ a = 10, b = 1, c = -2; \\ D = b^2 - 4ac = 1^2 - 4 * 10 * (-2) = 1 + 80 = 81 = 9^2, > 0; \\ x_{1, 2} = \frac{-b \pm \sqrt{D}}{2a} = \frac{-1 \pm \sqrt{9^2}}{2 * 10} = \frac{-1 \pm 9}{20} = \left \ [ {{\frac{-1 - 9}{20} = -\frac{10}{20} = -\frac{1}{2} } \atop {\frac{-1 + 9}{20} = \frac{8}{20} = \frac{2}{5}}} \right.[/tex]
ali picks three numbers out of a hat the lowest number was 11 the range was 13 and the median was 17 what was the three numbers
Answers
Answer:
11 , 17 , 24
Step-by-step explanation:
• Since the Lowest number is 11 and the range is 13 then
The greatest number is 11 + 13 = 24
• Therefore the three numbers are 11 , 17 and 24
because the median of the set 11 , 17 , 24 is 17
Identify the factors of x² - 4x - 12.
(x+4)(x-3)
(x-4)(x+3)
(x-2)(x + 6)
(x + 2)(x-6)
Answers
Answer:
Step-by-step explanation:
Please answer all parts as I know the answers but need the work to go with them. Thus, I believe the below answers are correct. Thank you!
Answers
The problem proves that the distributor's claim is true and he has a right to complain.
But when the confidence interval is changed from 95% to 90% the distributor's claim proves to be false.
The Confidence Interval for 95% is 0.9687;0.98532
For a sample size of n>30 the central limit theorem allows us to assume that the sampling distribution of x~ is approximately normal.
The critical region is Z ≥ 1.28 therefore the 1.877 lies in the rejection region that the distributor's claim is not true.
The Confidence Interval for 90% is 0.97156;0.982431
Here
μ = 0.977
s= σ= 0.03
95 % confidence interval is given by
x~± z∝/2 (s/√n)
Putting the values
0.977 ± 1.96 (0.03/√50)
=0.977 ± 0.008315
0.9687;0.98532
Part B:
x~+ 0.95= 0.977+0.95= 1.927
The critical region is Z ≥ 1.96 therefore the 1.927 lies in the acceptance region that the distributor's claim is true.
Part C:
For a sample size of n>30 the central limit theorem allows us to assume that the sampling distribution of x~ is approximately normal.
Part D:
μ = 0.977
s= σ= 0.03
90 % confidence interval is given by
x~± z∝/2 (s/√n)
Putting the values
0.977 ± 1.28 (0.03/√50)
=0.977 ± 0.005431
0.97156;0.982431
Part D:
x~+ 0.90= 0.977+0.90= 1.877
The critical region is Z ≥ 1.28 therefore the 1.877 lies in the rejection region that the distributor's claim is not true.
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given m∠J = 40° and HJ = 10, what is the length of GH
Answers
The required length of GH is 7.7.
Given, HJ = 10
m∠J = 40°
These are the equation which contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.
Let assume that there is right angle triangle GHJ.
Where HJ is base and GH is perpendicular.
Now,
cos40 = GH/HJ
GH = cos40 HJ
GH = 10 cos40
GH = 7.7
Thus, the required length of GH is 7.7.
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The simple interest on a certain sum of money for 2 years at 5% per annum is Rs 320. What will be the compound interest on the same sum for the same time at the same rate, the interest being calculated yearly? D 1800 cimple interest in 10 years. Find the The simple interest on a certain sum of money for 2 years at 5 % per annum is Rs 320. What will be the compound interest on the same sum for the same time at the same rate , the interest being calculated yearly ? D 1800 cimple interest in 10 years . Find the
Answers
Answer:
Rs 328
Step-by-step explanation:
Find the principal amount invested.
Simple Interest Formula
I = Prt
where:
I = interest earnedP = principalr = interest rate (in decimal form)t = time (in years)Given:
I = Rs 320r = 5% = 0.05t = 2 yearsSubstitute the given values into the formula and solve for P:
⇒ 320 = P(0.05)(2)
⇒ 320 = P(0.1)
⇒ P = 3200
Compound Interest Formula
[tex]\large \text{$ \sf I=P\left(1+\frac{r}{n}\right)^{nt} -P$}[/tex]
where:
I = interest earnedP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = 3200r = 5% = 0.05n = 1 (annually)t = 2 yearsSubstitute the given values into the formula and solve for I:
[tex]\implies \sf I=3200\left(1+\frac{0.05}{1}\right)^{2} -3200[/tex]
[tex]\implies \sf I=3200\left(1.05\right)^{2} -3200[/tex]
[tex]\implies \sf I=3200\left(1.1025\right) -3200[/tex]
[tex]\implies \sf I=3528-3200[/tex]
[tex]\implies \sf I=328[/tex]
Therefore, the compound interest on the same sum for the same time at the same rate is Rs 328.
A baker buys 10 apples from a farmer for $.25/each. the baker uses the 10 apples to make an apple pie that they sell in their bakery for $7.99. what is the total contribution to gdp?
Answers
The total contribution to the GDP is $5.49.
How to find the total contribution to GDP?GDP, the gross domestic product is the sum of all final goods and services produced in an economy within a given period.
When calculating GDP, only the value added of final goods and services are included. Intermediate goods are not added.
Therefore,
Total contribution to GDP = 7.99 - (10 X 0.25) = $5.49.
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Problem
(a) Expand and simplify [tex](x^2+2)^2[/tex].
(b) Hence fully factorise [tex]x^4 +4x+3[/tex].
Answers
a. [tex]x^4 + 4x^2 + 4[/tex]
b. x = ∛-1 and -3
How to expand the expressiona. Given
(x² + 2)²
First, we open up the bracket
[tex](x^2 + 2) (x^2 + 2)[/tex]
Multiply through
[tex]x^4 + 2x^2 + 2x^2 + 4[/tex]
Collect like terms
[tex]x^4 + 4x^2 + 4[/tex]
b. Let's factorize
[tex]x^4 + 4x + 3[/tex]
Find the factors of 3 that are products of 4, they are 3 and 1
Use it to replace 4x as 3x and x
[tex]x^4 + 3x + x + 3[/tex]
Let's make the expression two
[tex](x^4 + 3x) (x+ 3)[/tex]
Find the common factor
[tex]x^3(x + 3)+ 1(x+ 3)[/tex]
So,
[tex]x^3 + 1 = 0[/tex] and [tex]x + 3 = 0[/tex]
[tex]x = 3\sqrt{-1}[/tex] and x = -3
Thus, x = ∛-1 and -3
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A real estate agent is working for a developer who claims that the average commute time to downtown is 20 minutes with a standard deviation of 7 minutes. Stephon is an independent real estate agent and wants to check the times for his client. He took a random sample of 15 commute times and found an average of 26 minutes. He did hypothesis testing using a significance level of 5%. Which conclusion could he make?
The z-statistic is 0.22, so the null hypothesis should not be rejected.
The z-statistic is 1.69, so the null hypothesis should not be rejected.
The z-statistic is 3.32, so the null hypothesis should be rejected.
The z-statistic is 3.67, so the null hypothesis should be rejected.Tyesha found that the z-statistic was 2.1 and that the critical z-values were -1.96 and 1.96. Which of the following is a valid conclusion based on these results?
One can reject the null hypothesis.
One can reject the alternate hypothesis.
One can accept the null hypothesis.
One cannot accept or reject the null hypothesis.
Answers
The correct option is C which is The z-statistic is 3.32, so the null hypothesis should be rejected. One can reject the null hypothesis.
What is the null hypothesis?When there are two possibilities then we calculate the null hypothesis if the hypothesis is true hypothesis is accepted if it is
To conduct a hypothesis test for the above situation. We define the null hypothesis and the alternative hypothesis.
The null hypothesis is the claim that the average commute time to downtown is 20 minutes while the alternative hypothesis is a contradiction of the null hypothesis which is that the average commute time to downtown is not 20 minutes.
i.e. H0: μ = 20 and H1: μ ≠ 20.
The z-statistics is given by (sample mean - hypothesized mean) divided by (standard deviation divided by the square root of the sample size).
i.e.
[tex]z= \dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
x = 26, [tex]\mu[/tex] = 20, [tex]\sigma[/tex] = 7 and n = 15 putting the values in the question we will get the z-score value.
[tex]z = \dfrac{26-20}{\dfrac{7}{\sqrt15}}[/tex]
z = 6 / 1.807
z = 3.32
Therefore, the z-statistic is 3.32, so the null hypothesis should be rejected. Because the calculated value of z (3.32) is greater than the table value of z (1.96).
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