The number of rats in the sample are less than 30, therefore, according
to the central limit theorem, cannot approximate the population.
Response:
a) Should not be used because the Large Counts Condition is violated
Which condition are necessary for the hypothesis test?The proportion of the rats given M that succeeded, [tex]\hat p_1[/tex] = 7 ÷ 10 = 0.7
The proportion of the control rats that succeeded, [tex]\hat p_2[/tex] = 2 ÷ 10 = 0.2
H₀: [tex]\hat p_1[/tex] = [tex]\hat p_2[/tex]
Hₐ: [tex]\hat p_1[/tex] > [tex]\hat p_2[/tex]
The z-test formula for the difference between two proportion is given as follows;
[tex]Z= \mathbf{\dfrac{\hat{p}_1-\hat{p}_2}{\sqrt{\hat{p} \cdot (1-\hat{p})\left (\dfrac{1}{n_{1}}+\dfrac{1}{n_{2}} \right )}}}[/tex]
Where;
[tex]\hat p = \dfrac{7 + 2}{10 + 10} = 0.45[/tex]
[tex]Z=\dfrac{0.7-0.2}{\sqrt{0.45\times (1-0.45) \times \left (\dfrac{1}{10}+\dfrac{1}{10} \right )}} \approx \mathbf{ 2.25}[/tex]
p = 1 - p(z < 2.25) = 1 - 0.9878 = 0.0122
However, the number of rats in the sample, n are less than 30
Therefore;
The sample is not large enough for the test compared to the population,
and for a normal approximation which gives;
a) Should not be used because the Large Counts Condition is violated
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The ratio of males to females at a gym is 4:5. There are 20 females at the gym. How many males are in the gym?
Answer:
Step-by-step explanation:
The ratio of males to females at a gym is 4:5. There are 20 females at the gym. How many males are in the gym?
4 : 5 = x : 20
x = 4 * 20 : 5
x = 16
---------------------
check
4 : 5 = 16 : 20
4 : 5 = 4 : 5
the answer is good
Help me out please!!!!!! I’d appreciate it so much (:
Answer:
x = 11/7 y = -1/7
Step-by-step explanation:
2x + y = 3
2x + y - 2y = 3 - 2y
y = 3 - 2x
x - 3(3 - 2x) = 2
x - 9 + 6x = 2
x - 9 + 6x + 9 = 2 + 9
x + 6x = 11
7x = 11
7x / 7 = 11/7
x = 11/7
2(11/7) + y = 3
22/7 + y = 3
22/7 + y - 22/7 = 3 - 22/7
y = -1/7
Answer:
(¹¹⁄₇, -⅐)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}2x+y=3&\\x-3y=2\end{cases}[/tex]
What is the elimination method?
The elimination method is when you rewrite the two equations so that when added together, one of the two variables (x or y) is eliminated.
Step 1: Multiply the first equation by [tex]3[/tex].
[tex]\implies (3)2x+(3)y=(3)3[/tex]
[tex]\implies 6x+3y=9[/tex]
Step 2: Add the above equation to the second equation to eliminate 3y.
[tex]\begin{array}{r l}6x+3y & = 9\\+\ x-3y&=2\\\cline{1-2}7x&=11 \end{array}[/tex]
Step 3: Solve for x (by dividing both sides by 7).
[tex]\implies \dfrac{7x}{7}=\dfrac{11}{7}[/tex]
[tex]\implies \boxed{x=\dfrac{11}{7}}[/tex]
Step 4: Substitute ¹¹⁄₇ as the value of [tex]x[/tex] in any of the given equations and solve for [tex]y[/tex].
[tex]\implies 2\left(\dfrac{11}{7}\right)+y=3[/tex]
[tex]\implies \dfrac{22}{7}+y=3[/tex]
Step 5: Convert [tex]3[/tex] into a fraction and subtract ²²⁄₇ from both sides of the equation.
[tex]\implies \dfrac{22}{7}-\dfrac{22}{7}+y=\dfrac{21}{7}-\dfrac{22}{7}[/tex]
[tex]\implies \boxed{y=-\dfrac{1}{7}}[/tex]
The solution to the given system of equations is (¹¹⁄₇, -⅐).
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Mrs. Thomas is planning a business trip. she lives in Austin and will be driving through San Antonio to Laredo, the distance between Austin and San Antonio is 79 miles. the distance from Austin to Laredo is 6 miles less than 3 times the distance from Austin to San Antonio.
a. Write an equation that can solve be sloved to find the distance from Austin to Laredo.
Answer:
231 miles.
Step-by-step explanation:
79*3 = 237
237-6 = 231.
13.12:3 and 4: 6 are equal.
(A) True
(B) False
(C) Cannot be determined
Answer:
13. (B). False
Explanation
in the image
Please help me:() show work thanks!!
Step-by-step explanation:
area of ∆ = .5*pq*qr* sin q
= 23.63
Izzy's Ice Cream shop sells a variety of flavors
each day. Izzy serves 15 scoops in 10 minutes.
Which figure represents the rate if it stays constant
Answer:
Figure D
Step-by-step explanation:
15/10 can be simplified to 3/2. Figure D represents a consistent rate of 3/2
3 + (2 + 8)2 ÷ 4 × 1 over 2 to the power of 4
Answer:
[tex]\frac{13}{32}[/tex]
Step-by-step explanation:
Based on the table below,
Locate 6 in the x row. Directly below this is 96
This means f(6) = 96
------------------------------------------------------
Now locate 3 in the f(x) row. Directly above this is 7
You are correct in stating that f(7) = 3
Hi please help!! i will mark as brainliest if i can
Anya’s team won 5 out of every 7 games this season.
If the team played 28 games this season, how many games did they win?
Enter your answer in the box.
Answer:
20 out of 28 games.
Step-by-step explanation:
28 divided by 7 is 4.
5 times 4 is 20.
20 out of 28 games.
(This is simple math honestly.)
18.14 divided by 0.06 ASAP TEST TOMMOROW
Answer:
302.33
Step-by-step explanation:
Answer:
302.333... Its a repeating number.
Step-by-step explanation:
Flaws in a certain type of drapery material appear on the average of one in 150 square feet. If we assume a Poisson distribution, find the probability of at least one flaw appearing in 300 square feet.
Using the Poisson distribution, it is found that there is a 0.8647 = 86.47% probability of at least one flaw appearing in 300 square feet.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.Flaws in a certain type of drapery material appear on the average of one in 150 square feet, hence, considering 300 square feet, the mean is of:
[tex]\mu = \frac{300}{150} \times 1 = 2[/tex]
The probability of at least one flaw appearing in 300 square feet is given by:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}2^{0}}{(0)!} = 0.1353[/tex]
Then:
[tex]P(X \geq 1) = 1 - 0.1353 = 0.8647[/tex]
0.8647 = 86.47% probability of at least one flaw appearing in 300 square feet.
More can be learned about the Poisson distribution at https://brainly.com/question/13971530
Andres is offered a job as manager of a health club. The job will pay $3,100 per month, paid
semimonthly. Along with the base salary, the company offers to pay half the cost of medical
insurance and will match Andres' contribution to a retirement plan up to a total of $3,500. If
the full cost of the medical insurance is $450 per month and Andres plans to contribute the
full $3,500 every year to a retirement plan, what is the actual annual value of this job to
Andres?
A)$83,300
B)$43,400
C)$42,600
D)$37,200
E)$46,100
what is the measure of n? 5 15 m
Answer:
[tex]n= 5 \sqrt{3} [/tex]
Step-by-step explanation:
[tex]n = \sqrt{15 \times 5} = \sqrt{75} \\ \\ \huge n=\boxed{ 5 }\sqrt{\boxed{3}} [/tex]
Elliot’s dad bought a new car for $31,000 in 2012. Elliot read that a new car loses about 13% of its value each year. What is the multiplier for this situation?
PLEASE SHOW ALL WORK!
The multiplier that would be used to calculate the depreciation of the car is 0.83^y.
What does depreciation mean?Depreciation is when the value of an asset declines due to wear and tear.
The equation that can be used to represent depreciation is:
Value of the asset x (1 - rate of depreciation)^years
$31,000 x 0.83^y.
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7.40- 2.75 ... show your work
Robert has a balance of $ 3,000 in his first state bank checking account. he deposits $ 345.97 paycheck, a $ 567.28 dividend check, and a personal check for $ 150 into his account. her wants to receive $ 200 in cash. how much will he have in his account after the transaction
Answer:
$3863.17
Step-by-step explanation:
This is simple adding and subtracting.
3000.00
345.97
567.20
+ 150.00
4063.17
-200.00
$3863.17
What key features do the functions f(x) = 3x and g of x equals the square root of the x minus 3 end root have in common?
1-Both f(x) and g(x) include domain values of [3, ∞) and range values of (0, ∞), and both functions are positive for the entire domain.
2- Both f(x) and g(x) include domain values of [–3, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common.
3- Both f(x) and g(x) include domain values of [3, ∞) and range values of (0, ∞), and both functions have a y-intercept in common.
4- Both f(x) and g(x) include domain values of [–3, ∞) and range values of (–∞, ∞), and both functions increase over the interval (–3, 0).
Functions can be represented using equations and graphs
The key features are (1) both f(x) and g(x) include domain values of [3, ∞) and range values of (0, ∞), and both functions are positive for the entire domain.
How to determine the key featuresThe functions are given as:
[tex]f(x) = 3^x[/tex]
[tex]g(x) = \sqrt{ x - 3}[/tex]
Using a graphing calculator:
The domain of g(x) is [tex][3,\infty)[/tex]The range of g(x) is [tex][0,\infty)[/tex]The domain of f(x) is [tex](-\infty,\infty)[/tex]The range of f(x) is [tex](0,\infty)[/tex]Both functions have positive values for their domainsBy comparing the above highlights, the true statement between functions g(x) and f(x) is option (1)
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What the rate of change for f(t)=70(5/2)^t
help
Answer:
No t-intercept/zero
Step-by-step explanation:
1- Substitute f (t) = 0
Rewrite
2- Calculate
3- The statement is false for any of t
4- there is no t-intercept/zero
ANSWER PLEASE HELP!!!
Answer:
It should be <AFB
Step-by-step explanation:
The reason is that supplementary angels add up to 180 degrees which is a flat line and <AFB and <CFA do that
QUICK ITS TIMED
Solve for h.
A= 1/2bh
Answer:
Clear the fraction first which means multiply both side by the reciprocal (2)
2a = bh
Divide both sides by b since you are solving for h
Your answer is 2a/b = h
Shelley is searching online for airline tickets. Two weeks ago, the cost to fly from Orlando to Hartford was $200. Now the cost is $280. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
What is the percent increase from $200 to $280?
[tex]\frac{280}{200} *100 -100[/tex] → [tex]140 -100[/tex] → 40%There was 40% increase from $200 to $280
What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
increase with baggage fee:new ticket cost + baggage free280 + 50 $330 [tex]\frac{330}{200} *100 - 100[/tex] → 165% - 100% → 65%There was 65% increase with the baggage fee.
#1
Old price=200$New price=280$Increase=280-200=80$Rate of increase (Percent increase)
[tex]\\ \tt\hookrightarrow \dfrac{80}{200}\times 100[/tex]
[tex]\\ \tt\hookrightarrow 40\%[/tex]
#2
New price=280+50=330$Increase=330-200=130$Percent increase:-
[tex]\\ \tt\hookrightarrow \dfrac{130}{200}(100)[/tex]
[tex]\\ \tt\hookrightarrow 65\%[/tex]
у 0 1 1 1.5 ON 2.25 3 3.38
what do you mean by that?
4. John, Jim, Jay, and Jack have formed a band consisting of 4 instruments. If each of the boys can play all 4 instruments, how many different arrangements are possible? What if John and Jim can play all 4 instruments, but Jay and Jack can each play only piano and drums?
Answer:
The first part is correct! → There are 4 distinct instruments to distribute to 4 distinct people. And there are 4!=24 distinct ways of doing this.
For the second part. → Jay and Jack can only play 2 instruments, therefore we have 2 instruments for 2 people, and the distribution for these guys can be made in 2!=2 distinct ways.
Then, note that all that is left are 2 distinct instruments for 2 people. So there is an additional 2 distinct ways of doing this distribution for these other guys.
By the product rule, in total, we can do 4 distinct distribution in this condition.
Step-by-step explanation:
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ben fills a glass with orange jiuce and lemonade in the ratio of 1:4 by volume . he mixes the liquid in the glass . Ben then drinks 1/4 of this liquid
Solve the formula for T. L=4 πzt+5 πz^3
Answer:
[tex]{ \tt{L = 4\pi zt + 5\pi {z}^{2} }} \\ \\ { \tt{L = \pi z(4t + 5z)}} \\ \\ { \tt{ \frac{L}{\pi z} = 4t + 5z}} \\ \\ { \tt{4t = \frac{L}{\pi z} - 5z}} \\ \\ { \tt{t = \frac{L}{4\pi z} - \frac{5z}{4} }} \\ \\ { \boxed{ \tt{t = \frac{L - 5\pi {z}^{2} }{4\pi z} }}}[/tex]
I need a definition and example of the multiplication property of equality
Answer:
➢ The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal. Example 1 : Lisa and Linda have got the same amount of money. ... Multiply both sides by 4.
Step-by-step explanation:
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[tex]kai6417[/tex]
#carry on learning
Write the slope-intercept form of the equation of each line.
Step-by-step explanation:
9.
the first we see when going from left to right : the line goes down, so it has a negative slope (factor of x).
then we look at the y-intercept (the point where the line crosses the y-axis) : negative y and around -5.
with all that we have eliminated B and D.
and not only does the line go down, it goes sharply down. so, the absolute value of the slope must be bigger.
therefore, C is the right answer.
and a quick check confirms, as the slope -10/3 means that for a change of x by +3 units causes y to change by -10, and that is what we are seeing on the chart.
at x = -3 it looks like y is about +5.
and at x = 0 (change by +3) it looks like y is about -5 (change by -10).
10.
the y-intercept does not give us a clue here, it is 1 for all 4 options, and the graph confirms it.
but this line goes up, so the slope is positive.
it is rather "flat" and by far not even diagonally, so the absolute value of the slope must be a small value (much smaller than 1, as a slope of 1 means "diagonally").
therefore, D is the right answer.
a quick check confirms, as the slope 1/5 means that for a change in x by +5 would lead to a change in y by +1.
and that is what we are seeking on the chart.
at x = -5 it looks like y is about 0.
at x = 0 (change by +5) it looks like y is about +1 (change by +1) - the y-intercept.
a car travels for 300 km at an average speed of 65 km/h.How long does the car take to travel the distance
What is the value of the expression “-5(3+5)”
-5 (3 + 5)
-5 (8)
-5 × 8
= -40
Good luck :)
Answer:
-40
Step-by-step explanation:
First you distribute
-5 · 3 = -15
-5 · 5 = -25
Then you add
-15 + (-25) = -40