The probability of selecting a lemon-filled donut followed by a custard-filled donut is given as follows:
p = 15/92
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The probability of each event is given as follows:
First donut is lemon: 9/24.Second donut is custard: 10/23. -> 23 total outcomes as one has been eaten.Hence the probability is obtained as follows:
p = 9/24 x 10/23
p = 9/12 x 5/23
p = 3/4 x 5/23
p = 15/92
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what is the answer to this problem
Calculate the MAY raw materials purchases in dollars. (SEE IMAGE FOR DETAILS) financial accounting
Rensing Ltd estimates sales for the second quarter of 2020 will be as follows. April: 2,520 May: 2,440 June: 2,390
target ending inventory finished products. March 31: 2,010 April 30: 2,280 May 31: 2,170 June 30: 2,330
The May raw materials purchases for May in Rensing Ltd., in dollars terms, is $32,620.
How the raw materials purchases are determined:The cost of raw materials purchased in May is determined by computing the required production units and multiplying the result by 2 units and the unit raw material cost.
Purchase Budget:April May June
Sales 2,520 2,440 2,390
Ending inventory 2,280 2,170 2,330
Goods available for
sale 4,800 4,610 4,720
Beginning inventory 2,280 2,170
Production units 2,330
Raw materials purchases 4,660 (2,330 x 2)
Raw materials price per unit = $7
Total purchases of Raw Materials for May = $32,620 (4,660 x $7)
Thus, we can conclude that in May Rensing Ltd. purchased raw materials worth $32,620.
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A boat needs to travel North at 30km/h, a constant current of 4km/h is flowing in a north-west direction - What is the equivalent speed in still water for the boat to achieve actual speed of 30km/h ?
The equivalent speed in still water for the boat is 30.26 km/h.
What is the equivalent speed of the boat?
The equivalent speed of the boat in still water is calculated as follows;
The boat needs to travel North at 30 km/h,
The speed of the wave = 4 km/h
The equivalent speed of the boat in still water is calculated by applying Pythagoras theorem;
v² = (4 km/h)² + (30 km/h)²
v = √ [(4 km/h)² + (30 km/h)²]
v = 30.26 km/h
Thus, the equivalent speed of the boat is calculated by applying vector addition principle.
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using cramer rao lower bound method, with a random sample of size n, find a minimum variance unbiased estimator of the parameter,λ of a poisson population
The minimum variance unbiased estimator of the parameter,λ of a poisson population is λ = Σxi/n.
What is variance?Variance is a measure of how spread out a set of data is. In statistics, it is the average of the squared differences from the mean of a set of values. It is calculated by taking the sum of the squared deviations from the mean and dividing it by the number of data points.
According to given information:Let X1, X2, ..., Xn be a random sample from a Poisson distribution with mean λ. The likelihood function is given by:
[tex]L(\lambda | x) = \pi[e^{(-\lambda)} \lambda^{(xi)} / xi!][/tex]
Taking the natural logarithm and differentiating with respect to λ:
ln L(λ | x) = -nλ + ln(λ) Σxi - Σln(xi!)
d/dλ ln L(λ | x) = -n + Σxi/λ
Setting the derivative equal to zero and solving for λ, we get:
λ = Σxi/n
This is the sample mean of the Poisson distribution, which is an unbiased estimator of λ. Moreover, using the Cramer-Rao lower bound, we can show that it is also the minimum variance unbiased estimator of λ.
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Americans are stressed out!
A psychologist would like to estimate the proportion of Americans that say "the future of the nation is a
significant source of stress for me." To help form an estimate, the psychologist randomly selected 664
Americans and found that 69.6% of the sample agreed with the statement "the future of the nation is a
significant source of stress for me."
Using a 99% confidence level, determine the margin of error, E, and a confidence interval for the true
proportion of all Americans that say the "the future of the nation is a significant source of stress for me."
Report the confidence interval using interval notation. Round solutions to four decimal places, if necessary.
The margin of error is given by E:
A 99% confidence interval is given by:
To find the margin of error, we can use the formula: E = z√((p(1-p))/n)
How is margin of error determined?where z is the z-score for a 99% confidence level, p is the sample proportion, and n is the sample size.
From the table of standard normal distribution, the z-score for a 99% confidence level is 2.576.
Plugging in the values, we get:
E = 2.576√((0.696(1-0.696))/664) ≈ 0.0385
So the margin of error is 0.0385.
To find the confidence interval, we can use the formula:
p ± E
where p is the sample proportion and E is the margin of error.
Plugging in the values, we get:
0.696 ± 0.0385
So the 99% confidence interval for the true proportion of all Americans that say "the future of the nation is a significant source of stress for me" is (0.6575, 0.7345). In interval notation, this can be written as [0.6575, 0.7345].
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view the photo below. This is timed.
The other angle that is congruent to ∠DFA is: ∠BFC
How to identify Congruent angles?Congruent angles are defined as two or more angles that are said to be identical to each other. This means that the measure of these angles is equal to each other. These type of angles do not make any difference in the congruence of angles, which tells us that they can be acute, obtuse, exterior, or interior angles.
Now, we want to find the angle that is congruent to ∠DFA.
By inspection, we can see that ∠BFC is an opposite angle to ∠DFA.
We know that Opposite angles are the two angles opposite each other when two lines cross. They can also be called vertical angles due to sharing a vertex, which is the point where the two lines connect. Opposite angles always have the same measurement, making them congruent.
Thus, ∠BFC is congruent to ∠DFA.
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The box plot represents the scores on quizzes in a science class.
A box plot uses a number line from 74 to 86 with tick marks every one-half unit. The box extends from 77.5 to 81.5 on the number line. A line in the box is at 80. The lines outside the box end at 75 and 85. The graph is titled Science Quizzes, and the line is labeled Scores On Quizzes.
What value does 25% of the data lie above? Find the value.
Two different rectangles are joined together to make a compound shape. Shape A has a length of (x + 3) and a width of (x + 2). Shape B has a length of (x + 6) and a width of (x-2). All measurements are in centimetres. (x+3) Shape A Shape B (x+6) (x + 2) NOT TO SCALE (x-2) Find an expression for the area of the compound shape in cm². Give your answer in the form ax² + bx + c.
The expression for the area of the compound shape in cm² is 2x^2 + 11x - 6.
What is the expression for the area?To find the expression for the area of the compound shape, we need to first calculate the individual areas of Shape A and Shape B, and then add them together.
The area of Shape A is given by multiplying its length and width:
Area of Shape A = (x + 3) * (x + 2)
The area of Shape B is given by multiplying its length and width:
Area of Shape B = (x + 6) * (x - 2)
Now, we can add the two areas together to get the expression for the area of the compound shape:
Area of compound shape = Area of Shape A + Area of Shape B
= (x + 3) * (x + 2) + (x + 6) * (x - 2)
Expanding the above expression, we get:
= x^2 + 2x + 3x + 6 + x^2 + 6x - 12
= 2x^2 + 11x - 6
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What is the value of x in both these questions
Answer:
x + 5 + 7x - 5 + x = 180
9x = 180
x = 20
So the measure of angle M is x + 5 = 20 + 5 = 25°
Edward and Diana walked to the dock at 2 miles per hour, jumped into the boat, and motored to Dillion at 10 miles per hour. If the total distance was 12 miles and the trip took 5 hours in all, how far did they go by boat?
The distance for boat is,
= 43.2 miles
Given that;
Edward and Diana walked to the dock at 2 miles per hour, jumped into the boat, and motored to Dillion at 10 miles per hour
Now, For Walk DATA:
Rate = 2 mph ; time = x hrs.
Then, distance = 2x miles
For Boat DATA:
Rate = 10 mph ; time = 5 - x hrs
Then, distance = 10 (5 - x) miles
Hence, We can formulate;
distance + distance = 12 miles
2x + 10 (5 - x) = 20
2x + 50 - 10x = 20
30 = 8x
x = 3.6
Hence, Boat time ,
5 - x = 5 - 3.6 = 1.4 hr (boat time)
And, The value of Boat distance = 12x = 12 x 3.6 = 43.2 miles
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Sarah has a coupon for an oil change with synthetic oil for $49.95. She can buy 5 quarts of synthetic oil, which is what her car needs, for $37.54 and an oil filter for $9.47. How much can she save by doing the oil change herself?
Step-by-step explanation:
If Sarah buys the oil and oil filter separately, she would spend:
Cost of oil = $37.54
Cost of oil filter = $9.47
Total cost = $37.54 + $9.47 = $47.01
Therefore, Sarah can save:
Coupon price - Total cost = $49.95 - $47.01 = $2.94
So, Sarah can save $2.94 by doing the oil change herself instead of using the coupon.
HELPP Billie solved the equation below by completing the square, but she got the incorrect solution. In which step did Billie first make an error?
Step 1 : x 2 + 6 x = 16
Step 2 : x 2 + 6 x + 9 = 16
Step 3 : ( x + 3 ) 2 = 16
Step 4 : x + 3 = ± 4 Step 5 : x = 1 , x = − 7
Billie made the error in the second step of the equation
How to solve the equationBillie made an error in Step 2. She added 9 to one sides of the equation, but she should have added 9 to the left side only. The correct steps are as follows:
Step 1: x^2 + 6x = 16
Step 2: x^2 + 6x + 9 = 16 + 9
Step 3: (x + 3)^2 = 25
Step 4: x + 3 = ±√25
Step 5: x = -3 + 5, x = -3 - 5
Step 6: x = 2, x = -8
So, the correct solutions are x = 2 and x = -8.
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9999999999999999999999999999999999999999956596859873 -57854909049287634246299583729875472656475965593947699= ____________________________________________________________________98899876788877656687989/988998-*995895966++5966656566666666655555555555958545156548448489+4964898748/798784484878554659757564250216407694722=
Answer:
-4.7854909e+52
Step-by-step explanation:
how do i know
cuz i used a calculator
what evevn is your equation
A soccer goal is 8 yards wide. Suppose a goalie is standing on her line in
the center of her goal as a striker from the opposing team moves the ball
towards her. The near post angle, a, is formed by rays extending from the
ball to the near post and the goalie. Similarly, the far post angle, ß, is
formed by rays extending from the ball to the far post and the goalie. See
the figure.
a) Determine the near post angle and the far post angle when the striker is
24 yards from the near post and 28 yards from the far post.
b) How far is the goalie from the ball?
c) To cover the near post, the goalie moves toward the near post in order
to make the near post angle and the far post angle equal. How far
toward her near post does the goalie need to move?
Where the following triangle problem is given, note that:
A) α [tex]\approx[/tex] 11.0
β β [tex]\approx[/tex] 9.4
B) 25.59 yrds
C) 0.38 yrds
What is the explanation for the above?A) To determine the near post angle and the far post angle when the striker is 24 yards from the near post
1/2 (24²) + 1/2 (28²) - 1/4(10²) = 655 (central line length formula)
Cos α = (24² + 655 - 5²)/ (2 x 24 x √655)
= 0.98171498561
α = Cos ⁻¹ 0.98171498561
α = 10.973603643623608717848651724941
α [tex]\approx[/tex] 11.0° (Cosine Law)
For 28 yards from the far post.
Cos β = (28² + 655 - 5²)/ (2 x 28 x √655)
= 0.98659913977
β = Cos ⁻¹ 0.98659913977
β = 9.3905311636838307510867912796592
β [tex]\approx[/tex] 9.4°
B) Distance between the goalie from the ball is
√655 = 25.592967784139454896443137575823
Distance [tex]\approx[/tex] 25.59 yrds
C) 5-10 * ((24)/(24+28)) = 0.38 yrds (Angular Bisector Theorem)
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The polygon below is a regular polygon. Find the answer rounded to the nearest tenth.
HELP GIVING BRAINLIST HW DUE SOOON
Answer:
In a 30°-60°-90° right triangle, the length of the longer leg is √3 times the length of the shorter leg.
A = (1/2)Pa
= (1/2)(2)(8/√3)(6)(8)
= (384√3)/3 = 128√3 = 221.7 units^2
In circle O, chords AB and CD intersect at E, AE = 3 inches, BE = 8 inches, and CE is 2 inches longer than DE. What is the length of DE, expressed in inches?
Okay, let's break this down step-by-step:
* Circle O has chords AB and CD that intersect at E
* AE = 3 inches
* BE = 8 inches
* CE is 2 inches longer than DE
So we know:
AE = 3 inches
BE = 8 inches
CE = DE + 2 inches
To find DE, we can use the Pythagorean theorem for any right triangle:
a^2 + b^2 = c^2
In this case:
3^2 + 8^2 = c^2
9 + 64 = 73
c = 8 inches
So the hypotenuse AE forms a right triangle with leg BE of length 8 inches.
Now we have the length of one leg (BE = 8 inches) and the hypotenuse (AE = 8 inches).
We can use the relation between leg, hypotenuse and sine to calculate the other leg (DE):
sin(A) = DE / 8
DE = 8 * sin(A)
Without knowing the angle A, we can make an estimate:
sin(A) ≈ A (for small A)
So DE ≈ 8A inches
Now we know:
CE = DE + 2 inches
And DE ≈ 8A inches
So: 8A + 2 = DE
=> DE = 10A
And since A is small, we can say: DE ≈ 10 * A inches
To summary, if AE = 3 inches and BE = 8 inches,
then DE ≈ 10 * A inches
DE is approximately 10 times some small angle A.
Does this make sense? Let me know if you have any other questions!
Each marble bag sold by Eric’s Marble Company contains 3 red marbles for every 4 blue marbles. If a bag has 36 blue marbles, how many red marbles does it contain?
Which two values are located at the same point on a number line? 4/1 and 4 , 1/3 and 3 , 8/8 and 8 , 6/2 and 4
The two values which are located at the same point on a number line as required to be determined are; 4/1 and 4.
Which answer choice represents equivalent points on the number line?It follows from the task content that the answer choice which represents two values located at the same point on the number line be determined.
On this note, such two values must be equivalent.
Hence, by observation; the answer choice which represents two equivalent values is; 4/1 and 4 and they represent values located at the same point on the number line.
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the Ponde family's Powerjet pumps 420 gallons of water per hour. At this rate, how many gallons of water will it pump in 45 minutes?
the number of gallons of water it can pump inn 45 minutes is
How to determine the amount of water?The given parameters that will help us to determine the quantity are
Powejet pumps 420 gallons of water per hour
how many gallons of water will it pump in 45 minutes = ?
1 hour = 60 minutes
This means = 450/60 = 7 gallons
Therefore in 45 minutes it can pump 7*45 = 315 gollons
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NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #1
The end behavior of f(x) is described as follows:
As x -> -∞, f(x) -> ∞.As x -> ∞, f(x) -> 0.How to obtain the end behavior of a function?The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.
The function for this problem is given as follows:
f(x) = 4(5/7)^x.
It is an exponential function with base with absolute value less than 1, hence the end behavior is given as follows:
Increases to the left of the graph -> As x -> -∞, f(x) -> ∞.Approaches the horizontal asymptote y = 0 at the right of the graph -> As x -> ∞, f(x) -> 0.More can be learned about the end behavior of a function at brainly.com/question/1365136
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Find the range for the set numbers
Answer:
25
Step-by-step explanation:
range = largest number - smallest number
38-13=25
The mean weight of an adult is 70 kilograms with a standard deviation of 8 kilograms.
If 87 adults are randomly selected, what is the probability that the sample mean would be greater than 70.8 kilograms? Round your answer to four decimal places.
The probability that the sample mean would be greater than 70.8 kilograms is given as follows:
0.1762 = 17.62%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 70, \sigma = 8, n = 87, s = \frac{8}{\sqrt{87}} = 0.8577[/tex]
The probability is one subtracted by the p-value of Z when X = 70.8, hence:
Z = (70.8 - 70)/0.8577
Z = 0.93
Z = 0.93 has a p-value of 0.8238
1 - 0.8238 = 0.1762.
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Evaluate the function as indicated
[tex]g(x) = {5.9}^{x} [/tex]
(a) x = -1 G(-1) =
(b) G(-2) = x = -2
(c) x = √5 G(√5) =
what is the answer for a, b, and c?
Can somebody please help me find poetic elements in this poem fast!!!
Poem: citizenship by Javier Zamora
There’s also an image of the poem
Some poetic elements found in the poem are:
IronyRepetitionPersonificationMetaphorImageryWhat are poetic elements?Poetic elements are described as the devices used that characterize a piece of writing as a poem and are integral to categorise a piece of writing as poetry, such as poetic meter and rhyme scheme.
In the poem, the author uses Imagery which is described as use of sensory details to create vivid mental images in the reader's mind.
The author made use of metaphor as a comparison between two things that are not alike, in order to create an image or deepen understanding.
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a cuboid with length of 21 cm and height of 16 cm has a volume of 6384 cm3. find its breadth ik
Answer:18
Step-by-step explanation:18
Gary and Ann have a joint checking account their bounce at the beginning of October was 9145.87 during the month they made deposits totalling 2,783.71 wrote checks totaling 4,871.90 paid a maintenance fee of $12 earned 11.15 at interest on the account what was the balance at the end of the month?
The balance at the end of the month was $7046.93.
What is balance at the end of the month?To determine the balance at the end of the month, we need to:
add the initial balance to the deposits and interest earnedsubtract the checks written and fees paid.Data
Starting balance = $9145.87
Deposits = $2783.71
Interest earned = $11.15
Checks written = $4871.90
Maintenance fee = $12
Balance at the end of the month will be:
= Starting balance + Deposits + Interest earned - Checks written - Maintenance fee
= $9145.87 + $2783.71 + $11.15 - $4871.90 - $12
= $7046.93.
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help math will give brainlist
Answer:
arc PTR = 277°
Step-by-step explanation:
PS is the diameter of the circle , then arc PS = 180°
arc PTR = PS + SR = 180° + 97° = 277°
Answer:
arc PTR = 277°
Step-by-step explanation:
PS is the diameter of the circle , then arc PS = 180°
arc PTR = PS + SR = 180° + 97° = 277°
A surveyor whose eye level is 5 feet above the ground determines the angle of elevation to the top of an office building to be 41.7°. If the surveyor is standing 40 feet from the base of the building, what is the height of the building to the nearest foot?
A.) 32ft.
B)50 ft
C)36ft
D.)41ft
The height of the building when the surveyor is standing that far is D.)41ft
How to find the height of the building ?The tangent function would be best to use to find the height because we would be able to use the adjacent and and opposite.
Assuming that 5 feet is the height and the angle of elevation is 41. 7 degrees, and the distance of 40 feet, we have :
tan ( A ) = (h - x) / D
tan ( 41. 7° ) = ( h - 5 ) / 40
h - 5 = 40 x tan ( 41. 7 ° )
h - 5 = 40 x 0.8895
h = 35.58 + 5
= 40.58
= 41 feet
The height of the building is 41 feet.
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4. An opportunity cost that a business might face is
a. forgoing the interest that the owners could have earned on their savings if they had not
invested their savings in the business
Ob. forgoing rental income to be earned if the business rented out its building
forgoing the salaries the owners would have received at other jobs
OC.
c.
Od.
d. all of the above
5. The difference between macroeconomics and microeconomics is that
a. microeconomics studies inflation while macroeconomics studies taxes
Economics
b. macroeconomics looks at the economy as a whole while microeconomics looks at single
units in the economy
Oc. macroeconomics measures the price of a good and quantity demanded while
microeconomics looks
at things like unemployment or GDP
Od.
d. macroeconomics looks at single units in the economy while microeconomics looks at the
economy as a whole
Assume that when human resource managers are randomly selected, 49% say job applicants should follow up within two weeks. If 7 human resource managers are randomly selected, find the probability that exactly 2 of them say job applicants should follow up within two weeks.
The probability that exactly 2 of them say job applicants should follow up within two weeks is 33.02%.
How to find the probability ?We can use the binomial probability formula:
P(x) = C ( n, x ) × p ^ x × ( 1 - p ) ^ ( n - x )
Solving then gives:
P ( 2 ) = C ( 7, 2 ) x 0.49 ^ 2 x ( 1 - 0. 49 ) ^ ( 7 - 2)
P ( 2 ) = 21 x 0. 49 ^ 2 x ( 1 - 0. 49) ^5
= 21 x 0. 2401 x 0. 078109
= 0. 3302
In conclusion, the probability that 2 of the 7 human resource managers say job applicants should follow up within two weeks is approximately 0.3302 or 33.02%.
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