Using the Central Limit Theorem, it is found that Jackson has 8 guinea pigs.
What does the Central Limit Theorem state?It states that the sampling distribution of sample means of size n has standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], in which [tex]\sigma[/tex] is the standard deviation of the population.
In this problem, we have that [tex]s = 0.2227, \sigma = 0.63[/tex], hence we solve for n to find the number of guinea pigs that he has.
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.2227 = \frac{0.63}{\sqrt{n}}[/tex]
[tex]0.2227\sqrt{n} = 0.63[/tex]
[tex]\sqrt{n} = \frac{0.63}{0.2227}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{0.63}{0.2227}\right)^2[/tex]
[tex]n = 8[/tex]
Jackson has 8 guinea pigs.
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
Kelsey wants to buy a new video game.
he has a $50 gift card and wants to spend less than $20 on his own money.
which of the following amounts would kelsey be willing to spend on the video game?
a. $75
b. $70
c. $65
Answer: c: $65
Step-by-step explanation:
Find m\angle Am∠Am, angle, A. Note that m\angle Am∠Am, angle, A is acute. Round to the nearest degree. \Large{^\circ} ∘ degrees
Answer:
The answer is that the measure of ∠α is ≈ 20° when rounded to the nearest °
Step-by-step explanation:
To find the measure of ∠α you need to use the reciprocal of the formula for the law of sine which says that a/Sinα = b/Sinβ = c/Sin C. The reciprocal of this gives the new equation that states Sinα/a = Sinβ/b = Sin C/c, and this will help you to find the measure of the missing angle in °'s.
In the triangle line segment BC = 5units is opposite to point A & ∠α. Line segment AC = 7units is opposite of point and ∠β which is = 28°. And finally, the hypotenuse length and the values of point C & ∠C are unknown, so they aren't important to solving the problem. Knowing all this you can plug in all the known values into the new formula, and start working on figuring things out.
To find the measure ∠α, you first write down everything, putting things into their proper places, so since you're solving for sinα you want the equation to look like this:
sinα/5 = sin28°/7
Then for the second step, you want to isolate the sinα. (To get it by itself × both left and righthand sides by 5 to begin simplifying).
This leaves you with :
sinα = sin28°÷7 · (5) [And allows you to now solve for the right side of the equation, bringing us to our third step which is to once again simplify. So what you want to do is whip out your calculator and set it to degree mode, so you can find the of sin28° which is = 0.46947156278. Then ÷ that by 7, which will get you a number = 0.06706736611. Finally, take 0.06706736611 × 5, and you will get the value = 0.33533683056, as your final answer in the third step]
Your equation should now look something like this :
sinα = 0.06706736611 × 5 or 0.33533683056
Moving onto the fourth step, you need to use the inverse of the trig function of sin to get your absolute value. (remember the inverse of sine or acrsin = sin^-1) Here you will need to multiply sin^-1 by 0.33533683056.
And also by now, you'll want to stop writing the equation as sinα = sin^-1 ×
0.33533683056, otherwise you won't get an answer, instead, you'll need to write:
α = sin^-1 × 0.33533683056
So once you do that for the fifth and final step, you'll need to simplify the equation on the righthand side one last time, and you should get the answer of α = 19.5930217327°. Which when rounded to the nearest ° is ≈ 20°.
880,005 rounded to the nearest hundred thousand is
Answer:
900,000
Step-by-step explanation:
2/7(x+4)=−6 solve for x
Answer:
x = -25
Step-by-step explanation:
solve for x by simplifying both sides of the equation, then isolating the variable.
1/ (12b + 5) for b = 5/6
Answer:
1/15
Step-by-step explanation: Just equate the values like my last ans
Answer:
Step-by-step explanation:
Step 1:
Put value of b = 5/6
1/(12(5/6)+5
1/60/6 +5
1/10+5
Answer:
1/15 or 0.06666
3(4.x – 5) - 4x +1= -6
please help I don’t really understand
Answer:
Your answer is that X=1
Answer:
The answer is 1.
Step-by-step explanation:
12x-15-4x+1 = -6
8x = 8
Therefore x = 1
What is the image point of (1,0)(1,0) after a translation right 1 unit and up 4 units?
Answer:
0,4
Step-by-step explanation:
Simplify 3x*3y^2/9xy^5 and explain please
so, my teacher barley taught us this yesterday and i'm still having trouble with some questions, could anyone please help? ( this is 7th grade math )
5.) x>20
11.)x≤−15
13.)x≥−21
2.)x≤−7
6.)x≤−45
10.)x≤10
12.)x≥−12
16.)x≤−4
Answer:
2. x ≤ -7
5. x > 36
6. x ≤ -40
10. x ≤ 10
11. x ≤ -15
12. x ≥ -12
13. x ≥ -21
16. x ≤ -4
Step-by-step explanation:
2. x ≤ -7 (You want to add 8 to both sides like any equation, but don't forget it is an inequality, not an equation!)
5. x > 36 (You need to multiply by 2, to get rid of the division. So multiply both sides by 2, that gets rid of the 2 on the one side, and you get 36 on the other side when you multiply 18 by 2).
6. x ≤ -40 (You need to multiply by -5. REMEMBER: When you multiply or divide by a negative, you switch the sign. So if it is a < then it would be a > and same with if you had ≤ then it would be ≥ instead).
10. x ≤ 10 (You need to divide by -2. And once again you switch the signs).
11. x ≤ -15 (Add 8, like you did in number 2).
12. x ≥ -12 (Multiply by 6. REMEMBER: Do NOT switch the signs if you the number you are dividing by is in the numerator, or if you multiply and the negative number is first, UNLESS you have 2 negatives.
13. x ≥ -21 (Multiply by 7).
16. x ≤ -4 (Divide by 10).
Write each equation in slope-intercept form.
19. y - 4 = 3(x - 2)
20. y + 2 = -(x + 4)
21. y - 6 = -2(x + 2)
22. y + 1 = -5(x - 3)
23. y - 3 = 6(x - 1)
24. y - 8 = 3(x + 5)
Answer:
Lol, here is the answer again. Good luck
Tyler's mom purchased a savings bond for Tyler. The value of the savings bond increases by 4% each year. One year after it was purchased, the value of the savings bond was $156. Find the value of the bond when Tyler's mom purchased it. Explain your reasoning
Answer:
I think it is 6.24
Step-by-step explanation:
not really sure
Answer:
150
Step-by-step explanation:
The graph shows a function that models the value V (in millions of dollars) of a stock portfolio as a function of time t (in months) over a 18-month period.
Answer:
Option (A)
Step-by-step explanation:
Graph attached shows a function that models the value V of a stock portfolio as a function of time.
y-values on the graph shows the value of V and x-values represent the time.
Lowest point of the curve shows the minimum value of V and highest point of the curve shows the maximum value.
Maximum value of the function → 6.93 at t = 4
Minimum value of the function → 1.05 at t = 15
Therefore, Option (A) will be the answer.
Tickets to a basketball game can be ordered online for a set price per ticket plus a $5 service fee. The total cost in dollars for ordering 5 tickets is $110.00. Which linear function represents c, the total cost, when x tickets are ordered?
c(x) = 5 + 21x
c(x) = 5x + 21
c(x) = 5 + 25x
c(x) = 5x + 21x
Answer:
A, c(x)=5+21x
Step-by-step explanation:
`
Evaluate the expression for j = -5.
6 -
Answer:
1
Step-by-step explanation:
The bars around the j mean absolute value, meaning any number inside those brackets, you make it positive. So, 6-5=1
The jewelry store had a watch sale for Father’s Day. The watch I want is priced $75 but is on sale for 40% off what, is the sale price of the watch?
Answer:
$45
Step-by-step explanation:
The watch was sold on sale of 40%. This means that the price of the watch on sale is 60% of the original price. (100%-40%=60%)
So, you find the 60% of the original price, $75.
75*0.6=45
Hope that helps!!!
Which equation is an identity? O 3(x - 1) = x + 2(x + 1) + 1 O x-4(x + 1) = -3(x + 1) +1 O 2x + 3 = 1 = 1 (4x + 2) + 2 01 1 (6x – 3) = 3(x + 1) - x-2
HURRY!!!!
Answer:
Step-by-step explanation: C. 2x+3=1/2(4x+2)+2 hopes this helps:)
The equations that are identities are option B x – 4(x + 1) = –3(x + 1) + 1 and option C 2x + 3 = 1/2(4x + 2) + 2.
To check which equation is an identity, we need to simplify each equation and see if it is true for all values of x.
A. 3(x – 1) = x + 2(x + 1) + 1
Expanding the right side:
3(x – 1) = x + 2x + 2 + 1
3x – 3 = 3x + 3-3 = 3
This is a contradiction and cannot be true for any value of x. Therefore, option A is not an identity.
B. x – 4(x + 1) = –3(x + 1) + 1
Expanding both sides:
x – 4x – 4 = –3x – 3 + 1
-3x – 3 = -3x – 3
This equation simplifies to -3x - 3 = -3x - 3, which is true for all values of x. Therefore, option B is an identity.
Similarly,
Option C is an identity.
Option D is not an identity.
Learn more about equations here:
brainly.com/question/10413253
#SPJ7
B=10, 20 30, 40, 50, , in set builder notation
Answer:
40
Step-by-step explanation:
bexause u are a kid so dont ask this question again
(1) alex has a collection of coins, consisting of nickels and dimes that total to $3.90. if the number of dimes is 4 more then 3 times the number of nickels. find the number
of each of coin. "please show the work"
(2)a satellite television company charges a one time installation fee and a monthly service charge.(A)use your equation from above to find out how many months(m)of television were used if the charges totaled $650.(B)write an equation for the total charges.(C)if they charge $75.per month(m) and a one time installation fee is $50.
The answer is 8months "i need help showing the work so please show the work."
Answer:
1. 10 nickels and 34 dimes
Step-by-step explanation:
Please help ASAP!!
If KL NM and KN ≈ KM, find NM and mMKN.
A. NM = 6; mK=70°
B. NM = 9; mK=35°
C. NM = 12; mK=55
D. NM = 12; mK=70
Answer:
D. NM=12; mK=70°
Step-by-step explanation:
KN≈KM so they have the same 55° and then
180°-55°-55°=70° and
6*2=12
T(X,Y)_____
Name a line segment parallel to RS
Answer:
PQ
Step-by-step explanation:
Parallel lines are a pair of lines in a plane that do not meet/intersect
Question Progress
"HOT PIZZA” is offering a 20% discount on all its pizzas.
Tim orders a pizza for the reduced price of £7.20
What was the original price of the pizza?
Answer:
the answer is £1.44
Step-by-step explanation:
hope this helps
Let R be a relation on a collection of sets defined as follows,
R={(A,B)|A⊆B}
Then pick out the correct statement(s).
1) R is reflexive and transitive
2) R is symmetric
3) R is antisymmetric.
4) R is reflexive but not transitive
Answer:
Options 1) and 3) are correct.
Step-by-step explanation:
R={(A,B)|A⊆B}
Reflexive:
As A⊆A, [tex](A,A)[/tex]∈ R.
So, R is reflexive
Symmetric:
Let [tex](A,B)[/tex]∈ R. So, A⊆B
Take [tex]A=\{1,2\}\,,\,B=\{1,2,3,4\}[/tex]
Here, A⊆B but B⊄A
So, [tex](B,A)[/tex]∉ R
R is not symmetric
Transitive:
Let [tex](A,B)[/tex]∈ R and [tex](B,C)[/tex]∈ R
So, A⊆B and B⊆C.
Therefore, A⊆C
So,
[tex](A,C)[/tex]∈ R
Hence, R is transitive.
Option 1) is correct.
Antisymmetric:
Let (A,B)∈R and (B,A)∈R
So, A⊆B and B⊆A
Hence, A = B
So, R is antisymmetric
Option 3) is also correct.
If a standard die is rolled twice, what is the probability that it lands on a
number greater than 4 both times?
Bone-shaped treats are 5 for $3.50 at Shelley’s store and Sarah wants to buy 12. She set up and solved this proportion to find how much they would cost. Describe her error and find the correct solution.
5
3.5
=
12
x
3.5x = 60
x = $17.14
Answer:
Sarah multiplied the denominator by the denominator and the numerator by the numerator instead of finding the cross products. The equation should be 5x = 42, so the cost should be $8.40.
Step-by-step explanation:
Can I get brainliest?
Each time a machine is repaired, it remains up for an exponentially distributed time with mean 5 hours. When it fails, its failure will be a type 1 failure with probability 0.7 and a type 2 failure with probability 0.3. Type 1 failures take an exponential amount of time with mean 1 hour to repair. Type 2 failures take an exponential amount of time with mean 1.25 hours. The status of the machine can be monitored as a continuous-time Markov chain with states 0 (= working), 1 (= repairing a type 1 failure), 2 (= repairing a type 2 failure). The parameters for the continuous-time Markov chain are:______
How do you these two questions?
Answer:
a) A = 3π/16
b) A = ∑₂°° (π/n⁴) = π⁵/90 − π
Step-by-step explanation:
(a) The area between the curve and the x-axis is:
A = ∫ₐᵇ y (dx/dt) dt
x = ½ (1 − cos t) cos t
dx/dt = ½ (1 − cos t) (-sin t) + ½ sin t cos t
dx/dt = -½ sin t + ½ cos t sin t + ½ sin t cos t
dx/dt = -½ sin t + sin t cos t
dx/dt = -½ sin t (1 − 2 cos t)
y dx/dt = -½ sin t (1 − 2 cos t) × ½ (1 − cos t) sin t
y dx/dt = -¼ sin²t (1 − 3 cos t + 2 cos²t)
y dx/dt = -¼ sin²t + ¾ sin²t cos t − ½ sin²t cos²t
y dx/dt = ⅛ (-2 sin²t) + ¾ sin²t cos t − ½ (sin t cos t)²
y dx/dt = ⅛ (-1 + 1 − 2 sin²t) + ¾ sin²t cos t − ½ (½ sin(2t))²
y dx/dt = ⅛ (-1 + cos(2t)) + ¾ sin²t cos t − ⅛ sin²(2t)
y dx/dt = -⅛ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ (-2 sin²(2t))
y dx/dt = -⅛ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ (-1 + 1 − 2 sin²(2t))
y dx/dt = -⅛ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ (-1 + cos(4t))
y dx/dt = -⅛ + ⅛ cos(2t) + ¾ sin²t cos t − ¹/₁₆ + ¹/₁₆ cos(4t)
y dx/dt = -³/₁₆ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ cos(4t)
A = ∫₀ᵖⁱ [-³/₁₆ + ⅛ cos(2t) + ¾ sin²t cos t + ¹/₁₆ cos(4t)] dt
A = -³/₁₆ t + ¹/₁₆ sin(2t) + ¼ sin³t + ¹/₆₄ sin(4t) |₀ᵖⁱ
A = [-³/₁₆ π + ¹/₁₆ sin(2π) + ¼ sin³π + ¹/₆₄ sin(4π)] − [0 + ¹/₁₆ sin(0) + ¼ sin³0 + ¹/₆₄ sin(0)]
A = -³/₁₆ π
We got a negative answer because the graph traces to the left (x decreases as t increases). So the area is simply ³/₁₆ π.
b) Each circle has radius 1/n², so the area is π (1/n)² = π/n⁴.
The sum of the areas from n=2 to n=∞ is:
A = ∑₂°° (π/n⁴)
A = ∑₁°° (π/n⁴) − π
A = π ∑₁°° (1/n⁴) − π
A = π (π⁴/90) − π
A = π⁵/90 − π
Do someone know how much is 3/4 of 12?
3/4 of 12 is 9
I hope it helps!
Answer:
9 is 3/4 0f 12
Step-by-step explanation:
Multiply by the numerator of the fraction and divide by the denominator.
You can do this in either order.
12 × 3 = 36 then 36 ÷ 4 = 9 OR
12 ÷ 4 = 3 then 3 × 4 = 9
A researcher wants to test to see if husbands are significantly older than their wives. To do this, he collects the ages of husbands and pairs them with the ages of their respective wives for a random set of married couples. Suppose that data were collected for a random sample of 12 couples, where each difference is calculated by subtracting the age of the wife from the age of the husband. Assume that the ages are normally distributed. The test statistic is t≈1.434, α=0.05, the corresponding rejection region is t>1.796, the null hypothesis is H0:μd=0, and the alternative hypothesis is Ha:μd>0. Which of the following statements are accurate for this hypothesis test in order to evaluate the claim that the true mean difference between the age of the husband and the age of the wife is greater than zero?
Complete Question
The complete is shown on the first uploaded image
Answer:
The correct option are option 2 and option 4
Step-by-step explanation:
From the question we are told that
The sample size is n = 12
The test statistics is [tex]t \approx 1.434[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The rejection region is t>1.796
The null hypothesis [tex]H_o: \mu_d=0[/tex]
The alternative hypothesis is [tex]H_a : \mu_d >0[/tex]
From the given values we see that t < 1.796(i.e 1.434 < 1.796 ) which implies that t is not within the rejection region
Hence we fail to reject the null hypothesis
The conclusion is that there is insufficient evidence to suggest that that the husbands are significantly older than the wife.
Which of the following sequence of transformations takes point J(9, 1) to J’(-3, 7)?
reflected across x-axis and translated (x, y) → (x - 2, y - 2)
translated (x, y) → (x - 2, y + 2) and rotated 270° counterclockwise about the origin
rotated 90° counterclockwise about the origin and reflected across x-axis
translated (x, y) → (x - 2, y + 2) and rotated 90° counterclockwise about the origin
Answer:
translated (x, y) → (x - 2, y + 2) and rotated 90° counterclockwise about the origin
Step-by-step explanation:
The image point is in the 3rd quadrant, and the pre-image point is in the first quadrant. This means there has been any of ...
reflection across the y-axistranslationrotation 90° CCWThe only answer choice involving the appropriate rotation is ...
translated (x, y) → (x - 2, y + 2) and rotated 90° counterclockwise about the origin
__
Checking this, we have
(x, y) ⇒ (x -2, y +2) . . . . translation left 2, up 2
(x -2, y +2) ⇒ (-y -2, x -2) . . . . followed by 90° CCW rotation
J(9, 1) ⇒ J'(-3, 7) . . . . . consistent with the given image point
Four times the sum of a number and 20 is at most -17
Answer:
4(20+b)≤-17
Step-by-step explanation:
I hope this helps!