Answer:
(a)[tex]9z+2=5[/tex]
(b)[tex]21z-11=-4[/tex]
(c)[tex]4z=2-2z[/tex]
Step-by-step explanation:
We are required to construct 3 linear equations starting with the given solution z = 1/3.
Equation 1
[tex]z=\frac{1}{3}[/tex]
Multiply both sides by 9
[tex]9z=\frac{1}{3}\times 9\\9z=3[/tex]
Rewrite 3 as 5-2
9z=5-2
Add 2 to both sides
Our first equation is: [tex]9z+2=5[/tex]
Equation 2
[tex]z=\frac{1}{3}[/tex]
Multiply both sides by 21
[tex]21z=\frac{1}{3}\times 21\\21z=7[/tex]
Rewrite 7 as 11-4
21z=11-4
Subtract 11 from both sides
Our second equation is: [tex]21z-11=-4[/tex]
Equation 3
[tex]z=\frac{1}{3}[/tex]
Multiply both sides by 6
[tex]6z=\frac{1}{3}\times 6\\6z=2[/tex]
Rewrite 6z as 4z+2z
4z+2z=2
Subtract 2z from both sides
Our third equation is: [tex]4z=2-2z[/tex]
help asapppp....thanks
Answer:
a) -8x^3 + x^2 + 6x
b)16x^2 -9
c) 24x^4 + 37x^3 +13x^2 -18x
Step-by-step explanation:
a) distribute -2x to x and 4x^2 then do the same for the other part and then add the ones w the same exponent.
b) do foil ( multiply first outside inside last) which will be 4x times 4x then 4x times 3 then -3 times 4x and 3 times -3. add like exponents
c) do the same as above
tina completes a 26 mile marathon in 150 minutes, what is her speed in mph
Answer:
0.17 mph
Step-by-step explanation:
speed=distance/ time
speed=26/150
speed=0.17...
speed=0.17 mph
Answer:
10.4 mph
Step-by-step explanation:
Speed = Distance/Time
Convert 150 minutes into hours.
150/60 = 2.5
Speed = 26/2.5
Speed = 10.4
Find F as a function of x and evaluate it at x = 2, x = 4 and x = 8. F(x) = x (t3 + 4t − 2) 2 dt?
Answer:
The function of x at x = 2, 4 and 8 are 0, 80 and 1256 respectivelyStep-by-step explanation:
Given [tex]f(x) =\int\limits^x_2 {(t^{3}+4t-2 }) \, dt[/tex], to express f as a function of x, we need to first integrate the function given with respect to t as shown;
[tex]f(x) =\int\limits^x_2 {(t^{3}+4t-2 }) \, dt\\\\f(x) = [\frac{t^{4} }{4} + \frac{4t^{2} }{2}-2t]\left \ {t =x} \atop {t=2}} \right.[/tex]
[tex]f(x) = [\frac{t^{4} }{4} + 2t^{2}-2t]\left \ {t =x} \atop {t=2}} \right.\\when\ t = x\\f(x) = \frac{x^{4} }{4} + 2x^{2}-2x\\\\[/tex]
[tex]when\ t = 2;\\f(2) = \frac{2^{4} }{4} + 8-4\\f(2) = 8\\[/tex]
[tex]f(x) - f(2) = \frac{x^{4} }{4} + 2x^{2}-2x -8\\\\at\ x =2; f(x) = \frac{2^{4} }{4} + 8-4 -8 =0\\\\at\ x =4; f(x) = \frac{4^{4} }{4} + 32-8 -8 =80\\\\at x = 8; f(x) = \frac{8^{4} }{4} + 4(8^{2})-16 -8 =1256[/tex]
The function of x at x = 2, 4 and 8 are 0, 80 and 1256 respectively
Check out the photo for the question
Answer:
50
Step-by-step explanation:
42/n³∑k²+12/n²∑k+30/n∑1
=42/n³[n(n+1)(2n+1)/6]+12/n²[n(n+1)/2]+30/n [n]
=7n(n+1)(2n+1)/n³+6n(n+1)/n²+30
=7(n+1)(2n+1)/n²+6(n+1)/n+30
=[7(2n²+3n+1)+6(n²+n)+30n²]/n²
=[14n²+21n+7+6n²+6n+30n²]/n²
=[50n²+27n+7]/n²
=[50+27/n+7/n²]
→50 as n→∞
because 1/n,1/n²→0 as n→∞
Answer:
B. 50
Step-by-step explanation:
[tex]\displaystyle S_n=\sum_{k=1}^n{\left(k^2\dfrac{42}{n^3}+k\dfrac{12}{n^2}+\dfrac{30}{n}\right)}\\\\=\dfrac{42}{n^3}\sum_{k=1}^n{k^2}+\dfrac{12}{n^2}\sum_{k=1}^n{k}+\dfrac{30}{n}\sum_{k=1}^n{1}\\\\=\dfrac{42n(n+1)(2n+1)}{6n^3}+\dfrac{12n(n+1)}{2n^2}+\dfrac{30n}{n}\\\\=14+\dfrac{21}{n}+\dfrac{7}{n^2}+6+\dfrac{6}{n}+30=50+\dfrac{27n+7}{n^2}[/tex]
As n gets large, the fraction disappears, so the limit is 50.
When graphing any equation what is a great fall back plan if you can't remember the learned procedure? (on all kinds of equations - some with x squared, x cubed etc)
Answer:
GOOGLE :)
equation:
y=mx+b
m= slope (how steep the line is(negative is \ positive is /))
b= y intercept (where it is on the vertical line(up and down line))
step by step
1. locate y intercept and plotthe point
2.from that point use slop to find second point and plot
Find the area of each circle, use 3.14 round to the hundredth place diameter 44.4
Answer:
A = 1547.52
Step-by-step explanation:
Area of Circle Formula: A = πr²
Simply find r and plug it in:
d = 44.4
r = d/2 = 44.4/2 = 22.2
A = π(22.2)²
A = 1547.52
I already completed part 1 as pictured, I need help solving part 2. Part 2: (c) How many new homes were completed in the 12-month period through January 2011, and how did that compare to the number of new homes started in 2010? If necessary, round your answer to the nearest whole number. In the 12 month period through January 2011, there were 423,831 new homes completed, which was _________ fewer OR more than the number of new homes in 2010.
Answer:
423,831104,840 fewerStep-by-step explanation:
Given:
281,000 homes sold through Jan 2011 was 66.3% of homes completed
378,000 homes was a 28.5% decrease from starts in 2010
Find:
(i) Homes completed in 12 months through Jan 2011
(ii) Comparison to homes started in 2010
Solution:
(i) Using the given relation, we can find homes completed through Jan 2011.
281,000 = 0.663×completed
completed = 281,000/0.663 = 423,831
__
(ii) Similarly, we can find the number of 2010 starts:
starts(1 -28.5%) = 378,000
starts = 378,000/0.715 = 528,671
The relation of completions in 2011 to starts in 2010 is ...
423,831 -528,671 = -104,840
__
Through Jan 2011, there were 423,831 homes completed, which was 104,840 fewer than the number of starts in 2010.
_____
Comment on your question
Your problem statement supplies the answer to the first question in 2(c). Part 1(b) tells you the relation between starts in 2011 and in 2010, so you can easily figure starts in 2010 from your answer to that question.
The sum of Joe's and Sheila's ages is 115. Fourteen years ago, Joe was twice as old as Sheila. How old is Sheila now?
Answer: Sheila today = [tex]46\dfrac{1}{3}[/tex] yrs old
Step-by-step explanation:
J + S = 115 v⇒ J = 115 - S
Current Ages Ages 14 years ago
Joe (J) = 115 - S J - 14 = 2(S - 14)
Sheila (S) = S
Substitute J = 115 - S into the "14 years ago" equation
J - 14 = 2(S - 14)
(115 - S) - 14 = 2(S - 14)
111 -S = 2S - 28
111 = 3S - 28
139 = 3S
46 [tex]\frac{1}{3}[/tex] = S
It is odd that the result was not an integer. I wonder if you meant to type "Joe was twice as old as Sheila is today. That would change the equation to:
J - 14 = 2S
111 - S = 2S
111 = 3S
37 = S
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = ln(x), [1, 5]
Answer:
Yes, the function satisfies the hypothesis of the Mean Value Theorem on the interval [1,5]
Step-by-step explanation:
We are given that a function
[tex]f(x)=ln(x)[/tex]
Interval [1,5]
The given function is defined on this interval.
Hypothesis of Mean Value Theorem:
(1) Function is continuous on interval [a,b]
(2)Function is defined on interval (a,b)
From the graph we can see that
The function is continuous on [1,5] and differentiable at(1,5).
Hence, the function satisfies the hypothesis of the Mean Value Theorem.
The CEO of Millennium Dairy Product, a small venture among 10 partners each having 100,000 shares, sought to raise an additional Rs.50 million in a private placement of equity in his early stage dairy product company. The CEO conservatively projected net income of Rs.50 million in year 5, and knew that the comparable companies traded at a price earnings ratio of 20X. She approached SBI caps, a venture capitalist with her proposal to seek funds. (10) a) What share of the company would SBI caps require today if their required rate of return was 50%? b) If the company had 1000,000 shares outstanding before the private placement, how many shares should SBI caps purchase? c)What price per share should she agree to pay if her required return was 50%? d)What are the pre money and post valuations? e) What are the Carried interests of the VC and the promoters?
Answer:
Millennium Dairy Product
a) Share of the company that SBI Caps should require today to get a required rate of return of 50%.
= 50%
b) If the company had 1,000,000 (100,000 x10) shares outstanding before the private placement, SBI Caps should purchase
1,000,000 shares = 50% of (1,000,000 + 1,000,000) shares
Assuming the founding promoters are not giving up their shares, instead, new equity shares are being issued.
c) The price per share SBI Caps should agree to pay, if her required return was 50% is
Rs.50 per share, which will provide the required additional equity financing of (Rs.50 million) since Rs.50 x 1,000,000 equals Rs.50 million.
d) Pre money and post money valuations:
These are based on the calculated Market Price of Rs.1,000 per share from the Price/Earnings Ratio.
Pre money valuation will be Rs.1,000 x 1,000,000 shares = Rs.1 billion
Post money valuation will be Rs.1,000 x 2,000,000 shares = Rs.2 billion
e) Carried interests of the VC and the promoters
VC's carried interest = share of profits = 50% xRs.50 million = Rs.25 million
Promoters' carried interest = Rs.25 million
Step-by-step explanation:
a) Calculation of share in the company:
SBI Cap's required rate of return is 50%
If she invests Rs.50 million today, her expected return will be equal to Rs.50 million x 50% = Rs.25 million
Since rate of return = Net Income/Initial Investment or (Current value of investment - Initial Investment)/Initial Investment.
This return will be equal to 50% of the total net income of Rs.50 million
b) Price/Earnings P/E ratio = Market price per share/Earnings per share (EPS)
Since P/E ratio of similar companies = 20 times,
The company's P/E = 20 times x EPS
With calculated EPS = Rs.50 million /1,000,000 = Rs.50
Therefore, price per share = 20 x Rs.50 = Rs.1,000
Pre money valuation = Rs.1,000 x 1 million shares = Rs.1 billion
Post money valuation = Rs.1,000 x 2 million shares = Rs.2 billion
c) The carried interest is the share of profits to which the promoters and the Venture Capitalists are entitled. Their respective shares are 50% of the net income = Rs.25 million each.
d) The pre money and post money valuations: The pre money valuation is the valuation of the company before the additional equity financing. The post money valuation is the valuation of the company after the additional equity financing. There are many ways to value a company. In this case, we have used the P/E ratio as a basis for the valuation. However, we did not dilute the earnings per share post money, for simplicity.
Will give brainliest answer
Answer:
A = 3.13841
Step-by-step explanation:
Circumference: C = 2πr
Area of a Circle: A = πr²
Step 1: Find r using circumference formula
6.28 = 2πr
r = 6.28/2π
r = 0.999493
Step 2: Plug in r in area formula
A = π(0.999493)²
A = 3.13841
Answer:
3.52
Step-by-step explanation:
6.68 = c
6.68/2 = 3.34
3.34/3.14 = 1.06
1.06^2 * 3.14 = 3.52
can someone help me with this please?!?
Answer:
The answer is 60cm^2.
hope it helps..
Suppose you invest $ 2,000 at 45% Interest
compounded daily. F(t) represents value of investments
in t years
A) Find equation For F(+)
B) use equation to find how much account will
be worth in 30 years round to nearest cent
C) How much you should invest now in
order to have 14.000 in 9 years round to the nearest cent
Answer:
You will have $29,000 in 30 years, and you need to start with about $2,772.28 to make $14,000 in 9 years
Step-by-step explanation:
To find the total investment use the equation [tex]A = P(1 + rt)[/tex]
Where A equals total investment, P is your start investment, r is your rate, and t is time.
[tex]A=2,000(1+(0.45 * 30))[/tex]
[tex]A=2,000(1+13.5)[/tex]
[tex]A=2,000*14.5[/tex]
[tex]A=29,000[/tex]
To find the start investment use the equation [tex]P = A / (1 + rt)[/tex]
[tex]P=14,000/(1+(0.45*9))[/tex]
[tex]P=14,000/(1+4.05)[/tex]
[tex]P=14,000/5.05[/tex]
[tex]P=2,772.28[/tex]
Two pumps connected in parallel fail independently of one another on any given day. The probability that only the older pump will fail is 0.15, and the probability that only the newer pump will fail is 0.10. What is the probability that the pumping system will fail on any given day (which happens if both pumps fail)
The probability of the pumping system failing on any given day is 0.015, or 1.5 percent.
Given data:
To find the probability that the pumping system will fail on any given day, consider the probabilities of different failure scenarios for the two pumps.
Let's denote the events as follows:
A = Only the older pump fails
B = Only the newer pump fails
P(A) = 0.15 (probability that only the older pump fails)
P(B) = 0.10 (probability that only the newer pump fails)
To find the probability that both pumps fail, which can be denoted as the event A ∩ B.
Since the two pumps fail independently of each other, use the multiplication rule for independent events to calculate the probability of both events occurring:
P(A ∩ B) = P(A) * P(B)
Substituting the given probabilities:
P(A ∩ B) = 0.15 * 0.10
= 0.015
Hence, the probability that the pumping system will fail on any given day (when both pumps fail) is 0.015 or 1.5%.
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Not sure of how I would solve this
At work, Brett must check and record the internal temperature of the freezer on an hourly basis. When working properly, the temperature should remain constant over time. What word describes the slope of a line showing the temperature of the freezer as a function of time in hours when the freezer is working properly?
a.positive
b.zero
b.negative
c.undefined
Answer:
B. zero
Step-by-step explanation:
If the temperature is supposed to remain constant over time (the same) when working properly, then this means that there is no increase or decrease over time.
If there were a line to represent this, then it would be a straight line with a slope of 0 because the temperature would remain the same.
Please help meeeeeeeee
Answer:
The lines will intersect infinitely many times, because they are identical.
Step-by-step explanation:
Let's change the equations of the lines into (y=mx+b) form.
6x-4y=2 Divide by 2.
3x-2y=1 Move x and divide by -2.
-2y=1-3x ---> y= -1/2+3/2x
The equation of the first line is y=3/2x- 1/2
-2y+3x=1
-2y=1-3x
y = 3/2x -1/2
The equation of the second line is y = 3/2x- 1/2.
The lines are identical- infinitely many intersections.
Step-by-step explanation:
I think the answer is third because it doesn't has a solution.
Question 1 of 16,
The area of a trapezoid is 189 cm . The height is 14 cm and the length of one of the parallel sides is 8 cm. Find the length of the second parallel side.
Answer:
19cm
Step-by-step explanation:
The area of a trapezoid [tex]=\dfrac12(a+b)h[/tex] (where a and b are the parallel sides).
Given:
Area = 189 Square cm
Height, h=14cm
a=8cm
We want to find the value of the other parallel side, b.
Substitution of the given values gives:
[tex]189=\dfrac12(8+b)14\\189=7(8+b)\\$Divide both sides by 7\\8+b=27\\Subtract 8 from both sides\\b+8-8=27-8\\b=19cm[/tex]
The length of the second parallel side is 19cm.
What is the value of x?
Enter your answer in the box.
X=
Answer:
3
Step-by-step explanation:
Triangle ABC is an isosceles triangle, so
[tex]x^2+x^2=(6\sqrt{2} )^2\\2x^2=6^2*2\\x^2=6^2\\x=6.[/tex]
Triangle BCD is a notable triangle and the sides are
BD=x, CD=[tex]x\sqrt{3}[/tex],BC=2x=6
2x=6
x=3
Given: y ll z
Prove: m25+ m2 2 + m26 = 180°
L
A
M
1
2
3
y
4
5
6
7
Z
С
B
Assemble the proof by dragging ties to
the Statements and Reasons columns.
Answer:
As per the properties of parallel lines and interior alternate angles postulate, we can prove that:
[tex]m\angle 5+m\angle 2+m\angle 6=180^\circ[/tex]
Step-by-step explanation:
Given:
Line y || z
i.e. y is parallel to z.
To Prove:
[tex]m\angle 5+m\angle 2+m\angle 6=180^\circ[/tex]
Solution:
It is given that the lines y and z are parallel to each other.
[tex]m\angle 5, m\angle 1[/tex] are interior alternate angles because lines y and z are parallel and one line AC cuts them.
So, [tex]m\angle 5= m\angle 1[/tex] ..... (1)
Similarly,
[tex]m\angle 6, m\angle 3[/tex] are interior alternate angles because lines y and z are parallel and one line AB cuts them.
So, [tex]m\angle 6= m\angle 3[/tex] ...... (2)
Now, we know that the line y is a straight line and A is one point on it.
Sum of all the angles on one side of a line on a point is always equal to [tex]180^\circ[/tex].
i.e.
[tex]m\angle 1+m\angle 2+m\angle 3=180^\circ[/tex]
Using equations (1) and (2):
We can see that:
[tex]m\angle 5+m\angle 2+m\angle 6=180^\circ[/tex]
Hence proved.
Answer: yes
Step-by-step explanation: yes
In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3. Triangle D E F is shown. Line G H is drawn parallel to side D E within the triangle to form triangle G F H. The length of D G is 12, the length of G F is 4, the length of E H is 9, and the length of H F is 3. To prove that △DFE ~ △GFH by the SAS similarity theorem, it can be stated that StartFraction D F Over G F EndFraction = StartFraction E F Over H F EndFraction and ∠DFE is 4 times greater than ∠GFH. ∠FHG is One-fourth the measure of ∠FED. ∠DFE is congruent to ∠GFH. ∠FHG is congruent to ∠EFD.
To prove that △DFE ~ △GFH by SAS similartiy theorem, then option C. ∠DFE is congruent to ∠GFH is appropriate. So that: [tex]\frac{DF}{GF}[/tex] = [tex]\frac{EF}{HF}[/tex] and ∠DFE is congruent to ∠GFH.
Given ΔDEF as shown in the diagram attached to this answer, the following can be observed:
By comparing ΔDEF and ΔGFH
DF = DG + GF
= 12 + 4
DF = 16
Also,
EF = EH + HF
= 9 + 3
EF = 12
Comparing the sides of ΔDEF and ΔGFH, we have;
[tex]\frac{DF}{GF}[/tex] = [tex]\frac{EF}{HF}[/tex]
[tex]\frac{16}{4}[/tex] = [tex]\frac{12}{3}[/tex]
4 = 4
Thus, the two triangles have similar sides.
Comparing the included angle <DFE and <GFH, then;
∠DFE is congruent to ∠GFH
So that the appropriate answer to the given question is option C. ∠DFE is congruent to ∠GFH
Therefore, to prove that △DFE ~ △GFH by the SAS similarity theorem;
[tex]\frac{DF}{GF}[/tex] = [tex]\frac{EF}{HF}[/tex] and ∠DFE is congruent to ∠GFH.
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Answer: C
Step-by-step explanation:
The voltage in a circuit is the product of two factors, the resistance and the current. If the voltage is 6ir + 15i + 8r+20, find the expressions for the current and resistance
Answer:
resistance: (2r +5)current: (3i +4)Step-by-step explanation:
The factors of the given expression are ...
6ir +15i +8r +20 = (3i +4)(2r +5)
Which factor is current and which is resistance is not clear. Usually, resistance is referred to using the variable r, so we suppose the expressions are supposed to be ...
resistance: (2r +5)
current: (3i +4)
2. Suppose the 90% confidence interval for the mean SAT scores of applicants at a business college is given by [1690, 1810]. This confidence interval uses the sample mean and sample standard deviation based on 25 observations. What are the sample mean and sample standard deviation used for this interval
Answer:
The sample mean used for this interval is 1750.
The sample standard deviation used for this interval was of 175.34
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
The margin of error is the subtraction of these two bounds divided by two.
In this question:
Lower bound: 1690
Upper bound: 1810
Sample mean
[tex]\frac{1690 + 1810}{2} = 1750[/tex]
The sample mean used for this interval is 1750.
Sample standard deviation:
The first step is finding the margin of error:
[tex]M = \frac{1810 - 1690}{2} = 60[/tex]
Now we have to develop the problem a bit.
We want the sample standard deviation, so we use the T-distribution.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 25 - 1 = 24
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.711
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
We have that: [tex]M = 60, T = 1.711, n = 25[/tex]
We have to find s
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
[tex]60 = 1.711\frac{s}{\sqrt{25}}[/tex]
[tex]1.711s = 60*5[/tex]
[tex]s = \frac{60*5}{1.711}[/tex]
[tex]s = 175.34[/tex]
The sample standard deviation used for this interval was of 175.34
helppppppppppppppp asap its cordinates
Answers from top to bottom:
(0,-6)
(-1,0)
(-1,-6)
(0,0)
Explanation:
The rule you use is [tex](x,y) \to (-x,-y)[/tex] when it comes to 180 degree rotations (either clockwise or anticlockwise/counterclockwise). So we flip the signs of the x and y coordinates. Any point on an axis will stay on the same axis. The origin is the intersection of the two axes, so this point does not move at all. We call this point fixed or stationary. The fixed point is one where every point rotates around it.
two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 100 miles per hour. The westbound train travels at 80 miles per hour. How long will it take for the two trains to be 252 miles apart? Do not do any rounding.
Answer:
1.4 hours
Step-by-step explanation:
you can write a system of equations to find the answer.
80t + 100t = 252
plug it into desmos to find the true value.
it is 1.4
the trains will be 252 miles apart after 1.4 hours.
if this helped, be sure to mark as brainliest :)
what is the value of -x+ the absolute value of -y
Answer:
[tex]-x+| \: y\: |[/tex]
Step-by-step explanation:
[tex]-x+|-y|[/tex]
[tex]\mathrm{Apply\:absolute\:rule}: \left|-y\right|\:=| \: y\: |[/tex]
[tex]-x+| \: y\: |[/tex]
two bags contains 10 balls each. Every round you choose with equal probability one of the two bags and pick out a ball. After a while, you choose an empty ball. What is the probability for the other bag to contain exactly 4 balls at that time？
Answer:
6.10%
Step-by-step explanation:
For every round since we are choosing with equal probability, then the probability of choosing from either of the bags is 1/2
Here, this scenario is only possible when a particular bag has been chosen 10 times and the other bag has been chosen 6 times ( meaning a particular bag has been emptied and for a particular bag to be emptied, all of its content would have been picked)
Now on the 17th trial, an empty bag is chosen
Therefore the required probability will be;
16C0 * (1/2)^10 * (1/2)^6 * 1/2 = 0.0610 = 6.1%
A die is rolled 7 times. Find the probability P(of exactly 5 occurrences of 5). a. 0.09% c. 0.08% b. 3.04% d. 0.19%
Answer:
I believe it might be d but I'm not sure, sorry hope I could help
The FDA regulates that a fish that is consumed is allowed to contain at most 1 mg/kg of mercury. In Florida, bass fish were collected in 53 different lakes to measure the amount of mercury in the fish from each of the 53 lakes. Do the data provide enough evidence to show that the fish in all Florida lakes have different mercury than the allowable amount?
Required:
State the random variable, population parameter, and hypotheses.
Answer:
Yes. At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.
The random variable is the sample mean amount of mercury in the bass fish from the lakes of Florida.
The population parameter is the mean amount of mercury in the bass fish of Florida lakes.
The alternative hypothesis (Ha) states that the amount of mercury significantly differs from 1 mg/kg.
The null hypothesis (H0) states that the amount of mercury is not significantly different from 1 mg/kg.
[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]
Step-by-step explanation:
The question is incomplete.
There is no data provided.
We will work with a sample mean of 0.95 mg/kg and sample standard deviation of 0.15 mg/kg to show the procedure.
This is a hypothesis test for the population mean.
The claim is that the fish in all Florida lakes have different mercury than the allowable amount (1 mg of mercury per kg of fish).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]
The significance level is assumed to be 0.05.
The sample has a size n=53.
The sample mean is M=0.95.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.15.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.15}{\sqrt{53}}=0.0206[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.95-1}{0.0206}=\dfrac{-0.05}{0.0206}=-2.427[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=53-1=52[/tex]
This test is a two-tailed test, with 52 degrees of freedom and t=-2.427, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t<-2.427)=0.019[/tex]
As the P-value (0.019) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.
simplity 1-5(3 + 2-3)?
Answer:
-9
Step-by-step explanation:
1 - 5 (3 + 2 - 3)
1 − 5 ( 5 − 3 )
1 - 5 x 3
1 - 10
-9