Answer:
(a) The probability of getting someone who was not sent to prison is 0.55.
(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is 0.63.
Step-by-step explanation:
We are given that in a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.
Let the probability that subjects studied were sent to prison = P(A) = 0.45
Let G = event that subject chose to plead guilty
So, the probability that the subjects chose to plead guilty given that they were sent to prison = P(G/A) = 0.40
and the probability that the subjects chose to plead guilty given that they were not sent to prison = P(G/A') = 0.55
(a) The probability of getting someone who was not sent to prison = 1 - Probability of getting someone who was sent to prison
P(A') = 1 - P(A)
= 1 - 0.45 = 0.55
(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is given by = P(A'/G)
We will use Bayes' Theorem here to calculate the above probability;
P(A'/G) = [tex]\frac{P(A') \times P(G/A')}{P(A') \times P(G/A') +P(A) \times P(G/A)}[/tex]
= [tex]\frac{0.55 \times 0.55}{0.55\times 0.55 +0.45 \times 0.40}[/tex]
= [tex]\frac{0.3025}{0.4825}[/tex]
= 0.63
A necklace was on sale for 20% discount off the original price of
$1250.00. What was the final sale price if 12.5% VAT has to be
paid?
Answer:
= $ [tex] \mathsf{1125}[/tex]Step-by-step explanation:
[tex] \mathrm{Given}[/tex],
[tex] \mathrm{Discount\% = 20\%}[/tex]
[tex] \mathrm{Marked \: price = 1250}[/tex]
[tex] \mathrm{Now \: let's \: find \: the \: discount \: amount}[/tex]
[tex] \mathrm{discount \: amount = dis\% \: of \: MP}[/tex]
[tex] \mathrm { = 20\% \: of \: 1250}[/tex]
[tex] \mathrm{ = 250}[/tex]
[tex] \mathrm{let's \: find \: the \: selling \: price}[/tex]
[tex] \mathrm{ = MP \: - \: discount \: amount}[/tex]
[tex] \mathrm{ = 1250 - 250}[/tex]
= $ [tex] \mathrm{1000}[/tex]
[tex] \mathrm{lets \: find \: the \: Vat \: amount}[/tex]
[tex] \mathrm{vat \: amount = vat\% \: of \: sp}[/tex]
[tex] \mathrm{ = 12.5\% \: of \: 1000}[/tex]
= $ [tex] \mathrm{ 125}[/tex]
[tex] \mathrm{Now \: finally \: let's \: find \: the \: selling \: price \: with \: vat}[/tex]
[tex] \mathrm{selling \: price \: + \: vat \: amount}[/tex]
[tex] \mathrm{ = 1000 + 125}[/tex]
= $ [tex] \mathrm{1125}[/tex]
Therefore, The final sale of the necklace is $ 1125
Hope I helped
Best regards!
01:
Which expression can be used to model the phrase the sum of three and a number?
Answer:
3+x
Step-by-step explanation:
sum= addition
a number= a number
Answer:
3+x
eplanation
f(x)=2x+1 and g(x)=3x2+4, find (f∘g)(−2) and (g∘f)(−2).
Answer:
Step-by-step explanation:
Fog=2(g)+1
2(3x+2+4)+1
2{3x+6)+1
6x+12+1
=6x+13
Fog(-2)=6(-2)+13
-12+13
=1
Gof=3(f)+2+4
=3(2x+1)+6
6x+3+6
=6x+9
Gof(-2)=6(-2)+9
-12+9
=-3
John needs to produce a scale diagram of a bedroom using a scale of 1:40. The length of the room is 3.4 metres. What is the length on the diagram? _____ cm
Answer:
8.5cm
Step-by-step explanation:
convert 3.4metres to cm that is by multiplying by 100
3.4×100=340cm
1rep 40
?rep 340
that is 340/40
=8.5cm
Answer:
8.5 cm
Step-by-step explanation:
Scale = 1:40
Length of the room = 3.4 meters
3.4 meters =3.4 X 100 =340 cm
Since 1 unit on the diagram represents 40 units
The length of the diagram
[tex]=\dfrac{340}{40}\\\\=8.5$ cm[/tex]
The length of the room on the diagram is 8.5 cm.
Arrange the cards below to show the solution to 40.091 x 10³
Answer:
40091.
Step-by-step explanation:
Multiply 40.091 by 10 three times to get the answer.
40.091 * 10 = 400.91
400.91 * 10 = 4009.1
4009.1 * 10 = 40091.
The expression 40.091 x 10³ can be represented as 40091.
What are exponents?The term xⁿ, read as x to the power n, shows an exponent n, which implies x is multiplied by itself n times.
How to solve the given question?In the question, we are asked to arrange the cards showing '.', '0', '0', '1', '4', and '9', to show the solution to the expression 40.091 x 10³.
Now, 10³ is 10 to the power 3, where 3 is the exponent, so 10 is multiplied by itself 3 times = 10*10*10 = 1000.
Now, the expression 40.091 x 10³ = 40.091 * 1000 = 40091.
∴ The expression 40.091 x 10³ can be represented as 40091.
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In a survey, 29 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $41 and standard deviation of $8. Construct a confidence interval at a 99% confidence level.
Give your answers to one decimal place.
Answer:
The 99% confidence interval is
[tex]37.167< \= x < 44.833[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 29[/tex]
The sample mean is [tex]\= x =[/tex]$41
The sample standard deviation is [tex]\sigma =[/tex]$8
The level of confidence is [tex]C =[/tex]99%
Given that the confidence level id 99% the level of confidence is evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1[/tex]%
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table which is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
The reason we are obtaining values for is because is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while is the area under the normal distribution curve for just one tail and we need the value for one tail in order to calculate the confidence interval
Next we evaluate the margin of error which is mathematically represented as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 2.58 * \frac{8 }{\sqrt{29} }[/tex]
[tex]MOE = 3.8328[/tex]
The 99% confidence level is constructed as follows
[tex]\= x - MOE < \= x < \= x + MOE[/tex]
substituting values
[tex]41 - 3.8328 < \= x < 41 + 3.8328[/tex]
[tex]37.167< \= x < 44.833[/tex]
easy math please help!
Answer:
[tex]\boxed{ \sf 41.81}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trigonometric functions.
[tex]\sf sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]\sf sin(?)=\frac{2}{3}[/tex]
[tex]\sf ?=sin^{-1}(\frac{2}{3})[/tex]
[tex]\sf ?= 41.81031489...[/tex]
Answer:
[tex]\boxed{41.81}[/tex]
Step-by-step explanation:
∠B is opposite of side AC, which has a length of 2 units. The hypotenuse of the triangle is equivalent to 3 units.
The trigonometric function that uses the opposite side and the hypotenuse is sine function. This is represented by [tex]sin = \frac{opposite}{hypotenuse}[/tex]. The side that is opposite to the angle being solved for is the opposite side (it does not border the angle and it is not the hypotenuse).
However, you are solving for an angle. So, you need to use the inverse sine function ([tex]sin^{-1}[/tex]) to solve this question properly.
Simply type into a calculator [tex]sin^{-1} (\frac{2}{3})[/tex] and it will evaluate the answer to approximately 41.81°.
determining the probability of events. please help :)
Answer:
C. 1/8
Step-by-step explanation:
Probability of shooting a goal on a throw is 2/4 = 1/2.
Probability of 3 in a row is (1/2)³ = 1/8.
help i will give you brailenst
Identify the percent, amount, and base in this problem What is 15% of 60?
Answer:
9
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
3.01)Which statement best describes the area of the triangle shown below?
9
It is one-half the area of a rectangle of length 4 units and width 2 units.
It is twice the area of a rectangle of length 4 units and width 2 units.
O It is one-half the area of a square of side length 4 units.
Ont is twice the area of a square of side length 4 units.
Answer:
C. It is one-half the area of a square of side length 4 units.
Step-by-step explanation:
Hey there!
Well if a square has side lengths of 4 units,
the area would be 16 because of l*w.
Now the formula for the area of a triangle is,
b*h/2
b = 4
h = 4
4*4=16
16 ÷ 2 = 8
So the area of a square is 16 units^2 whereas the area of a triangle with the same dimensions is 8 units^2,
meaning the area of a triangle is one-half the area of a square.
Hope this helps :)
What additional information do you need to prove △ABC ≅ △DEF by the SSS Postulate? A. BC = EF B. AB = DE C. AC = DF
Answer:
AC = DF
Step-by-step explanation:
The SSS Postulate occurs when all three corresponding pairs of sides are congruent, therefore, the only missing pair is AC = DF.
A Canadian longitudinal study1 examined whether giving antibiotics in infancy increases the likelihood that the child will be overweight later in life. The study included children and found that of the children had received antibiotics during the first year of life. Test to see if this provides evidence that more than of Canadian children receive antibiotics during the first year of life. Show all details of the hypothesis test, including hypotheses, the standardized test statistic, the -value, the generic conclusion using a significance level, and a conclusion in context.
1. Clearly state the null and alternative hypotheses.
2. Calculate the test statistic and p-value.
3. What is the conclusion?
4. Do we have evidence to conclude that more than 70% of Canadian infants receive antibiotics?
A. Yes
B. No
Answer:
1. [tex]H_{0}[/tex] : p = 0.70 , [tex]H_{a}[/tex] : p > 0.70
2. Test Statistic : 0.54 , P value : 0.2946
3. Fail to reject null Hypothesis
4. No.
Step-by-step explanation:
1. Null hypothesis is 70% of children receive antibiotics.
Alternative hypothesis is more than 70% of children receive antibiotics.
2. Test statistic is calculated as;
z = [tex]\frac{p (1 - p)}{\sqrt{\frac{p (1-p}{n} )} }[/tex]
z = [tex]\frac{0.01}{0.0185}[/tex]
z = 0.54
3. p value is calculated as;
1 - right tailed probability
1 - 0.7054 = 0.2946
ANZ Corporation manufactures a product available in two models: ABC, and PQR. Despite the growing popularity of the PQR model, company profits have been declining steadily, and management is beginning to think there might be a problem with their costing system. Material and Labour costs are given below:
ABC PQR
Sales demand 30000 15000
Direct material cost/unit $45 $60
Direct labour cost/unit $30 $40
Production overheads are $600,000 each month.
These are absorbed on a sales demand basis.
Calculate the full production costs for ABC and PQR, using traditional costing method
Answer:
The full production costs are:
ABC = $22,900,000
PQR = $1,700,000
Step-by-step explanation:
Traditional costing method is a costing method that allocates or applies overhead based on a particular metric determined by a company. It therefore add both direct cost of production and production overheads absorbed to obtain the full cost of production.
Since production overheads in this question is absorbed on demand sales basis, the full production costs for ABC and PQR can be computed as follows:
ANZ Corporation
Computation of Full Production Costs
Particulars ABC PQR
Sales demand 30,000 15,000
Cost $ $
Direct cost:
Direct materials cost (w.1) 1,350,000 900,000
Direct labor cost (w.2) 900,000 600,000
Total direct cost 22,500,000 1,500,000
Indirect cost:
Production overhead (w.3) 400,000 200,000
Full production cost 22,900,000 1,700,000
Workings:
w.1: Computation of direct material cost
Direct material cost = Direct material cost per unit * Sales demand
Therefore;
ABC Direct material cost = $45 * 30,000 = $1,350,000
PQR Direct material cost = $60 * 15,000 = $900,000
w.2: Computation of direct labor cost
Direct labor cost = Direct labor cost per unit * Sales demand
Therefore;
ABC Direct material cost = $30 * 30,000 = $900,000
PQR Direct material cost = $40 * 15,000 = $600,000
w.3: Allocation of production overhead
Production overheads allocated to a model = Production overheads * (Model's Sales Demand / Total Sales demand)
Total Sales demand = 30,000 + 15,000 = 45,000
Therefore, we have:
Production overhead allocated to ABC = $600,000 * (30,000 / 45,000) = $400,000
Production overhead allocated to PQR = $600,000 * (15,000 / 45,000) = $200,000
An appliance company determines that in order to sell x dishwashers, the price per dishwasher must be p = 420 - 0.3x. It also determines that the total cost of producing x dishwashers is given by C(x) = 5000 + 0.3x2. How many dishwashers must the company produce and sell in order to maximize profit? g
The company must produce and sell 350 dishwashers in order to maximize profit.
How to determine the number of dishwashersTo determine the number of dishwashers the company must produce and sell in order to maximize profit, we need to find the value of x that corresponds to the maximum point of the profit function.
The profit (P) is given by the equation:
P(x) = Revenue - Cost
The revenue is calculated by multiplying the price per dishwasher (p) by the number of dishwashers sold (x):
Revenue = p * x
The cost is given by the function C(x):
Cost = C(x)
Therefore, the profit function can be expressed as:
P(x) = p * x - C(x)
Substituting the given expressions for p and C(x):
P(x) = (420 - 0.3x) * x - (5000 + 0.3x²)
Expanding and simplifying the equation:
P(x) = 420x - 0.3x² - 5000 - 0.3x²
Combining like terms:
P(x) = -0.6x² + 420x - 5000
To find the value of x that maximizes profit, we need to find the vertex of the quadratic function. The x-coordinate of the vertex can be determined using the formula:
x = -b / (2a)
In our case, a = -0.6 and b = 420:
x = -420 / (2 * -0.6)
x = -420 / (-1.2)
x = 350
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350 dishwashers must the company produce and sell in order to maximize profit.
Maxima means a point at which the function attains the maximum value.
Given the following information:
Price per dishwasher, p = 420 - 0.3x
Total cost of producing x dishwashers, C(x) = 5000 + 0.3x2
Profit= Total Selling price- Total Cost Price
Total Selling price of x dishwasher, S.P= xp
S.P=x(420 - 0.3x)
S.P=420x - 0.3x²
Profit= 420x - 0.3x² - ( 5000 + 0.3x²)
Profit= 420x - 0.3x² - 5000 - 0.3x²
Profit= -0.6x²+420x-5000
So, profit, f(x)=-0.6x²+420x-5000
To determine the value of x so that maximum profit is possible:
1. Calculate the first derivative of profit function and calculate the value of x by equating it to zero.
2. Select that value of x for which the profit function attains the maximum value, to check the maxima calculate 2nd derivative, if it gives a negative value for the value of x. Then, x is the point of maxima for the given function.
[tex]f(x)=-0.6x^2+420x-5000\\f\prime(x)=-1.2x+420\\f\prime(x)=0\\-1.2x+420=0[/tex]
Calculating the value of x by transposing,
x=420/1.2
x=350
To check maxima, calculating second derivative.
[tex]f\prime(x)=-1.2x+420=0\\f\prime\prime(x)=-1.2[/tex]
2nd derivative is negative, it means that x=350 is the point of maxima.
Thus, a company must produce and sell 350 dishwashers in order to maximize profit.
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HEREEEEEEEEEEEEEElollll
Answer:
Hey there!
Your answer would be 4/50. The total times she drawed a purple tile was 4, and she drawed 50 times.
Hope this helps :)
The owner of a music store gathered data from several schools about the number of students in their concert and marching bands. The scatter plot shows the data she gathered and the line of best fit. The equation of the line of best fit is y = 0.677x + 1.77. Based on the line of best fit, approximately how many students are predicted to be in the marching band at a school with 35 students in the concert band?
Answer:
25 students
Step-by-step explanation:
Given the equation of the best line of fit, [tex] y = 0.677x + 1.77 [/tex] , the number of students predicted to be in the matching band, if we have 35 students in the concert band, can be approximated by plugging in 35 as "x" in the equation of the best line of fit, and solve for "y". y would give us the predicted number of students to expect in the marching band.
[tex] y = 0.677(35) + 1.77 [/tex]
[tex] y = 23.695 + 1.77 [/tex]
[tex] y = 25.465 [/tex]
The approximated number of to be in the marching band, with 35 students in the concert band is roughly 25 students.
Answer:25 students
Step-by-step explanation:
What rule (i.e. R1, R2, R3, R4, or R5) would you use for the hawk and for the grizzly bear? a. R2 and R5 b. R1 and R3 c. None of the above d. R1 and R4
Answer:
I NEED POINTS
Step-by-step explanation:
What scenario depicts two independent events
Step-by-step explanation:
A t
eacher is calling on students to present their reports. He calls on Mario first and then chooses the next presenter from the remaining students. The girls’ basketball team is playing against the boys’ basketball team. The coach chooses a captain for the girls’ team and then chooses a captain for the boys’ team. Yasmin is picking flowers from a garden to create a bouquet. She picks a flower, keeps it for the bouquet, and then she picks another. Felipe is making a dentist appointment. First he chooses the day for his appointment, and then he chooses the time from the available openings.
Answer:
A.The school play opens tonight and it is raining.
B.Neva is hungry and she buys a snack from the concession stand.
C. Ari chooses a partner for a group project and then Ezekial chooses a partner from the remaining classmates.
D.Luka paints during school and he stains his shirt.
Tabitha wants to hang a painting in a gallery. The painting and frame must have an area of 58 square feet. The painting is 7 feet wide by 8 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? (5 points)
Answer:
4x² + 30x - 2 = 0
Step-by-step explanation:
Given:
Area = 58 square feet
Width = 7 feet
Length = 8 feet
Since the area is 58, writing the equation, we have:
(8 + 2x)(7 + 2x) = 58
Now expand the equation:
56 + 16x + 14x + 4x² = 58
56 + 30x + 4x² = 58
Collect like terms:
30x + 4x² + 56 - 58 = 0
30x + 4x² - 2 = 0
Rearrange the equation to a proper quadratic equation:
4x² + 30x - 2 = 0
The quadratic equation that can be used to determine the thickness of the frame, x is 4x² + 30x - 2 = 0
Identify any outlier(s) in the data. {52, 61, 42, 46, 50, 51, 49, 44, 40, 66, 53, 67, 45, 64, 60, 69}
An outlier in statistics is a data point that deviates considerably from other observations. The given data set has no outlier.
What is an outlier?An outlier in statistics is a data point that deviates considerably from other observations. An outlier can be caused by measurement variability or by experimental mistake; the latter is sometimes eliminated from the data set.
To find the outlier for the given data set follow the given steps.
Step one: The first step is to find the quartiles for the data set.
For this data set, the quartiles are:
Q1 = 45.5
Q3 = 62.5
Step Two: Find the Interquartile Range
The interquartile range is the difference between the first and third quartiles.
IQR = Q3 - Q1
IQR = 45.5 - 62.5
IQR = 17
Step Three:
The next step is to set up a fence beyond the first and third quartiles using the interquartile range.
Lower Fence = Q1 - (1.5 × IQR)
Lower Fence = 45.5 - (1.5 × 17)
Lower Fence = 20
Upper Fence = Q3 + (1.5 × IQR)
Upper Fence = 62.5 + (1.5 × 17)
Upper Fence = 88
Step Four: Find the Outliers
Any numbers in the data that are above or below the fences are outliers.
Since there are no numbers outside the two fences. Hence, it can be concluded that the given data set does not have, any outlier.
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express 11011 in base two
Answer:
27
Step-by-step explanation:
Hello,
11011 in base 2 is
1 * 16 + 1 * 8 + 0 * 4 + 1 * 2 + 1 in base 10
which is 16 +8+2+1=27
Do not hesitate if you have any question
The line passing through points
(4,0) and (-2, 1) has a slope of?
A. -6
B. -1/6
C. 1/2
D. 2
E. 1/6
Answer:
b. -1/6
Step-by-step explanation:
slope = (difference in y)/(difference in x)
slope = (1 - 0)/(-2 - 4) = 1/(-6) = -1/6
Answer:
m = -1/6 = B
Step-by-step explanation:
[tex]m = \frac{y_2-y_1}{x_2-x_1} \\ x_1=4\\ y_1=0\\ x_2=-2\\y_2=1.\\m = \frac{1-0}{-2-4} \\m = \frac{1}{-6}[/tex]
At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 8 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 22 feet high
Answer:
(11π/9 )ft/s
Step by step Explanation
Let us denote the height as h ft
But we were told that The diameter of the base of the cone is approximately three times the altitude, then
Let us denote the diameter = 3h ft, and the radius is 3h/2
The volume of the cone is
V = (1/3)π r^2 h
Then if we substitute the values we have
= (1/3)π (9h^2/4)(h) = (3/4)π h^3
dV/dt = (9/4)π h^2 dh/dt
We were given as 22feet and rate of 8 cubic feet per minute
h = 22
dV/dt = 8
8= (9/4)π (22) dh/dt
= 11π/9ft/s
Therefore, the rate is the height of the pile changing when the pile is 22 feet is
11π/9ft/s
Lines $y=(3a+2)x-2$ and $2y=(a-4)x+2$ are parallel. What is the value of $a$?
Answer:
-8/5Step-by-step explanation:
Given two lines y=(3a+2)x-2 and 2y=(a-4)x+2, Since both lines are parallel to each other, this means that the slope of both lines are the same
Let's get the slope of both equation. For the first equation;
y=(3a+2)x-2
We can see that the equation is written in this form y = mx+c where m is the slope of the line. On comparison, the slope of the given line is 3a+2
Similarly for the second line;
2y=(a-4)x+2
Re-writing in the standard format we will have;
y = (a-4)x/2+2/2
y = (a-4)x/2 + 1
The slope of the second line is (a-4)/2
On equating the slope of both lines to get the value of 'a' we will have;
3a+2 = (a-4)/2
Cross multiplying
2(3a+2) = a-4
6a+4 = a-4
Collecting like terms;
6a-a = -4-4
5a = -8
a = -8/5
Hence the value of a is -8/5
Please answer this correctly without making mistakes Please simplify the correct answer
Answer:
1/5 are towboats
Step-by-step explanation:
In order to find the answer, we need to find the total number of flag vessels. We can find this by adding all the categories together
30k + 10k + 10k= 50k
In total there are 50,000 flag vessels
Of those 50,000, 10,000 of them are tow boats
10,000/50,000 can be simplified to 1/5
1/5 are towboats
Answer:
1/5
Step-by-step explanation:
Well to find the fraction we first need to know the total amount of Flag Vessels.
30,000 + 10,000 + 10,000 = 50,000
If there are 10,000 towboats we can make the following fraction.
10,000/50,000
Simplified
1/5
Thus,
the answer is 1/5.
Hope this helps :)
A casino offers a game wherein a player can roll one six sided die. If the player rolls a 1or 2, they
win. If the player rolls a 3, 4, 5, or 6, they lose. If a player bets $2.00 and wins, they will be paid out
an additional $3.00. If they lose, they lose their initial $2.00. Find the expected value of the $2.00
bet.
Enter your answer rounded to the nearest cent and don't forget, expected values can be negative!
Answer:
Expected Value of $2:
Expected Value of $2:
Win, 0.3333 x $3 = $1
Plus
Loss, 0.6667 x -$2 = -$1.33
Expected value = ($0.33)
Step-by-step explanation:
Probability of a win = 2/6 = 0.3333
Probability of a loss = 4/6 = 0.6667
Expected Value of $2:
Win, 0.3333 x $3 = $1
Plus
Loss, 0.6667 x -$2 = -$1.33
Expected value = ($0.33)
The casino game player's expected value is computed by multiplying each of the possible outcomes by the likelihood (probability) of each outcome and then adding up the values. The sum of the values is the expected value, which amounts to a loss of $0.33.
A simple random sample of 20 third-grade children from a certain school district is selected, and each is given a test to measure his/her reading ability. You are interested in calculating a 95% confidence interval for the population mean score. In the sample, the mean score is 64 points, and the standard deviation is 12 points. What is the margin of error associated with the confidence interval
Answer:
Margin of Error = ME =± 5.2592
Step-by-step explanation:
In the given question n= 20 < 30
Then according to the central limit theorem z test will be applied in which the standard error will be σ/√n.
Sample Mean = μ = 64
Standard Deviation= S= σ = 12
Confidence Interval = 95 %
α= 0.05
Critical Value for two tailed test for ∝= 0.05 = ±1.96
Margin of Error = ME = Standard Error *Critical Value
ME = 12/√20( ±1.96)=
ME = 2.6833*( ±1.96)= ± 5.2592
The standard error for this test is σ/√n
=12/√20
=2.6833
The height of a cylinder is 9.5 cm. The diameter is 1.5 cm longer than the height. Which is closest to the volume of the cylinder?
Answer:
853.8cm^3
Step-by-step explanation:
[tex]h = 9.5cm\\d = 1.5cm + 9.5 = 10.7\\r =d/2=10.7/2=5.35\\\\V = \pi r^2 h\\V = 3.14 \times (5.35)^2 \times 9.5\\\\V =853.8 cm^3[/tex]
Which equation represents a population of 250 animals that decreases at an annual rate of 21%
Answer:
y= 250( 1-0.21)^x
Step-by-step explanation:
This represents exponential decay
The equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.
What is an exponential function?The mathematical expression f(x)=[tex]e^t[/tex] denotes the exponential function. The term typically refers to the positive-valued function of a real variable, unless otherwise specified.
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
It is given that a population of 250 animals is decreasing at an annual rate of 21%.
p = a x b[tex].^t[/tex]
p = a x (1+r)[tex].^t[/tex]
p = 250 x (1+(-0.21))[tex].^t[/tex]
p = 250(0.79)[tex].^t[/tex]
Note that r = -0.21 is negative to indicate we have exponential decay.
Hence, the equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.
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