Show Sample Answer
Part B
In general, how do the measures of the angles in the image compare with the measures of the angles in the preimage?
What affect does the scale factor of the dilation have on the angles, if any?
Answers
After a dilation, the angle measures remain constant, meaning that they are not affected by the scale factor of the dilation.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The side lengths are changed, but the original figure and the dilated figure are similar, meaning that the angle measures remain constant, no matter the scale factor.
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Related Questions
Warning MEGA HARD question
What’s 9999999999999999x99999999999999
Answers
Answer:
1E+30
Step-by-step explanation:
If one zero of the polynomial (3
2 + 8 + ) is the reciprocal of the
other, then find the value of k
Answers
If one zero of the polynomial 3x^2 + 8x + k is the reciprocal of the
other, then k = 3 by applying product of roots formula.
The quadratic polynomial is 3x^2 + 8x + k.
Let the roots of 3x^2 + 8x + k be m and n where m and n are reciprocal of each other. Therefore, n = 1/m
Thus, the product of roots is = m*n = m*(1/m) = 1 ____(1)
The general equation of a quadratic equation can be written as,
ax^2 + bx + c = 0
where a and b are coefficients of x^2 and x respectively and c is a constant term.
From product of roots formula we know that,
Product of roots =constant term/ coefficient of x^2 = c/a
Therefore, for polynomial is 3x^2 + 8x + k we get,
Product of roots = k/3 ____(2)
From equating equation (1) and (2) we get,
k/3 = 1
⇒ k = 3
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The given question is incomplete, the complete question is
"If one zero of the polynomial 3x^2+8x+k is the reciprocal of the other, then find the value of k."
At a small high school, there are 80 girls in the senior class. Some of them play basketball, some play soccer, some play both, and some play neither. The table shows the joint and marginal frequencies for the senior girls.
If you know that a girl plays soccer, what is the probability that she also plays basketball? Express your answer as a decimal. If necessary, round your answer to the nearest hundredth
Answers
If you know that a girl plays soccer, then the probability that she also plays basketball = 0.23
The correct answer is an option (c)
Let's assume that event S: a girl plays soccer
event B: a girl plays basketball
Here, the probability that the girl plays soccer would be,
P(S) = P(SB) + P(SB')
where B' means a girl does not play basketball
here, P(SB) = 0.075 and P(SB') = 0.250
So, P(S) = 0.075 + 0.250
P(S) = 0.325
We need to find the probability that a girl plays basketball knowing that she plays a soccer.
i.e., the conditional probability P(B|S)
Using formula for the conditional probability,
P(B|S) = P(BS) / P(S)
= 0.075 / 0.325
= 0.23
Therefore, the correct answer is an option (c)
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Find the complete question below.
study of ancient pottery. refer to the chance (fall 2000) study of ancient pottery found at the greek settlement of phylakopi, presented in exercise 2.14 (p. 36). of the 837 pottery pieces uncovered at the excavation site, 183 were painted. these painted pieces included 14 painted in a curvilinear decoration, 165 painted in a geometric decoration, and 4 painted in a naturalistic decoration. suppose 1 of the 837 pottery pieces is selected and examined. a. what is the probability that the pottery piece is painted? b. given that the pottery piece is painted, what is the probability that it is painted in a curvilinear decoration?
Answers
To discover the probability that the ceramics piece is painted, we basically separate the number of painted pieces by the whole number of pieces: P(painted) = 183/837 ≈ 0.2185
b. To discover the likelihood that the painted ceramics piece is painted in a curvilinear enhancement, we utilize Bayes' hypothesis:
P(curvilinear | painted) = P(painted | curvilinear) * P(curvilinear) / P(painted)
We are given that there are 183 painted pieces, of which 14 are painted in a curvilinear enrichment. In this manner,
P(painted | curvilinear) = 14/183 ≈ 0.0765
We are moreover given that there are 837 pieces in add up, of which 183 are painted.
P(painted) = 183/837 ≈ 0.2185, we ought to discover the likelihood that a painted piece is painted in a curvilinear enrichment, which is given as 14 out of 183 painted pieces. P(curvilinear) = 14/183 ≈ 0.0765
P(curvilinear | painted) = (0.0765) * (0.0765) / (0.2185) ≈ 0.0266
thus, given that the pottery piece is painted, the likelihood that it is painted in a curvilinear enhancement is roughly 0.0266, or 2.66%.
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Mrs. Brown records the rainfall in Seattle, Washington during each month of 2021. (8.75, 4.68, 2.61, 1.03, 1.12, 1.91, 0.00, 0.11, 3.02, 5.76, 10.62, 4.38} Mrs. Brown wants to use a graphical representation that will allow her students to see the overall shape of the data and provide enough information to determine the 5-number summary Which representations should Mrs. Brown consider? Select all that apply.
Answers
Mrs. Brown should consider the box and whisker plot as well as the stem and leaf plot to represent the data and determine the 5-number summary.
Mrs. Brown should consider using a box plot (also called a box and whisker plot) and/or a modified box plot.
A box plot is a useful graphical representation because it shows the overall shape of the data and displays the 5-number summary, which includes the minimum value, first quartile (Q1), median (second quartile, Q2), third quartile (Q3), and the maximum value. A modified box plot also provides this information and additionally identifies any potential outliers in the data.
Therefore, Mrs. Brown should consider the box and whisker plot as well as the stem and leaf plot to represent the data and determine the 5-number summary.
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Correct question is "Mrs. Brown records the rainfall in Seattle, Washington during each month of 2021. (8.75, 4.68, 2.61, 1.03, 1.12, 1.91, 0.00, 0.11, 3.02, 5.76, 10.62, 4.38} Mrs. Brown wants to use a graphical representation that will allow her students to see the overall shape of the data and provide enough information to determine the 5-number summary then find which representations should Mrs. Brown consider? "
1. a national organization sets out to investigate the change in prevalence of hiv since the last census in 2010. a total of 4,706 participants were interviewed and a total of 468 responses were confirmed to be hiv positive. assume that the data from the census indicated that the prevalence of hiv in the particular population was 7.5%. a) is the sample size large enough to justify the use of the z formula? show your calculation to support your answer. (3 points)
Answers
Yes, the sample size of 4,706 is large enough to justify the use of the z formula.
To determine whether the sample size is large enough to justify the use of the z formula, we need to check whether the sample size is sufficiently large to meet the central limit theorem (CLT) conditions. The CLT states that the distribution of the sample mean of a sufficiently large sample size from any population, regardless of the distribution of the population, will be approximately normal.
One of the conditions for the CLT is that the sample size is large enough. There is no hard and fast rule for determining what is considered a "large" sample size, but a commonly used rule of thumb is that the sample size should be at least 30.
In this case, the sample size is 4,706, which is much larger than 30. Therefore, we can conclude that the sample size is large enough to justify the use of the z formula.
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Chris uses a pump to fill a giant beach ball that has a radius of 4 feet. What volume of air will it take to fill the ball?
Answers
It will take approximately 268.08 cubic feet of air to fill the giant beach ball.
Define sphereA sphere is a three-dimensional geometric shape that is perfectly round in shape, with every point on its surface equidistant from its center. It is a type of round solid figure that has no edges or vertices. The surface of a sphere is continuous, and it encloses a fixed volume of space.
The formula for the volume of a sphere is:
V = (4/3) × π × r³
where r is the radius of the sphere.
In this case, the radius of the beach ball is 4 feet, so we can substitute this value into the formula:
V = (4/3) ×π × (4)³
V = (4/3) × π × 64
V = 268.08 cubic feet (rounded to two decimal places)
Therefore, it will take approximately 268.08 cubic feet of air to fill the giant beach ball.
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I NEED HELP ASAP. ITS DUE TODAY AND IM STUCKKKKKKK
Answers
The expression for the area of the triangle is given as follows:
A = 1.5x^4 + x³ - 0.5x².
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:
A = 0.5bh.
The dimensions for this problem are given as follows:
b = 3x² - x.h = x² + x.Hence the area of the triangle is given as follows:
A = 0.5(3x² - x)(x² + x)
A = 0.5(3x^4 + 3x³ - x³ - x²)
A = 0.5(3x^4 + 2x³ - x²)
A = 1.5x^4 + x³ - 0.5x².
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Sam decides to build a square garden. If the area of the garden is 9x^2 - 24x + 16 square feet, what is the length of the garden?
Answers
The length of the square garden is s = ( 3x - 4 ) feet
Given data ,
Let the length of the square garden be s
Now , The area of a square is given by the formula A = s², where s is the length of one side of the square.
We are given that the area of the garden is:
A = 9x² - 24x + 16
To find the length of the garden, we need to take the square root of the area:
s = √(A)
Substituting the given expression for A, we get:
s = √(9x² - 24x + 16)
We can simplify this expression by factoring the quadratic under the square root sign:
s = √[(3x - 4)(3x - 4)]
Using the property that the square root of a product is equal to the product of the square roots, we can simplify further:
s = (3x - 4)
Hence , the length of the garden is 3x - 4 feet
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What function is inverse of the exponential function y=(1. 5)^x
Answers
Answer:
[tex]y = {1.5}^{x} [/tex]
[tex] ln(y) = ln( {1.5}^{x} ) [/tex]
[tex] ln(y) = x ln(1.5) [/tex]
[tex]x = \frac{ ln(y) }{ ln(3) - ln(2) } [/tex]
[tex]y = \frac{ ln(x) }{ ln(3) - ln(2) } [/tex]
a jet tank is in the shape of a rectangular prism. The tank is 18 inches wide, 12 inches deep and 23 inches tall How many squares inches of glass was used to make the tank if there is no top.
Answers
The tank used 3,528 square inches of glass to make, assuming that there is no overlap or waste in the glass cutting process.
The tank has four vertical rectangular sides, a bottom, and no top. Since there is no top, we do not need to include the area of any glass for the top of the tank.
The area of each rectangular side is given by multiplying the height by the width. The area of the bottom is given by multiplying the length by the width. Therefore, the total area of glass used to make the tank is:
Area = 2(height x width) + 2(height x length) + (length x width)
Substituting the given values, we get:
Area = 2(23 x 18) + 2(23 x 12) + (18 x 12)
Area = 1,656 + 1,656 + 216
Area = 3,528
Therefore, the tank used 3,528 square inches of glass to make, assuming that there is no overlap or waste in the glass-cutting process.
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What is 1/2% to decimal
Answers
Answer: 0.5
Step-by-step explanation:
1/2% is equal to 50 out of 100, or 50/100.
So you turn that into a decimal (fifty one hundredths).
0.50
You can get rid of the 0 at the end.
0.5
Hope this helps!!! :)
two different missiles are shot simultaneiously at a practice target. if the probability of the first one hitting the target is 1 4 and of the second one hitting is 2 5 , what is the probability that (a) both missiles will hit, (b) at least one will hit?
Answers
(a) The probability that both missiles will hit the target is 1/10.
(b) The probability that at least one missile will hit the target is 11/20.
To find the probability that both missiles will hit, we multiply the individual probabilities of each missile hitting
P(both missiles hit) = P(first missile hits) × P(second missile hits)
P(both missiles hit) = (1/4) × (2/5)
P(both missiles hit) = 2/20
P(both missiles hit) = 1/10
So the probability that both missiles will hit the target is 1/10.
(b) To find the probability that at least one missile will hit, we need to find the probability that both missiles miss and then subtract that from 1 (since the probability of either missile hitting is the complement of both missiles missing)
P(at least one missile hits) = 1 - P(both missiles miss)
P(at least one missile hits) = 1 - P(first missile misses) × P(second missile misses)
P(at least one missile hits) = 1 - (3/4) × (3/5)
P(at least one missile hits) = 1 - 9/20
P(at least one missile hits) = 11/20
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12. Jenny's water bottle holds 1.3 liters of water. How many milliliters of water does the water bottle hold? milliliters
Answers
Answer:
1300 milliliters
Step-by-step explanation:
There are 1000 milliliters in one liter. so 1.3 liters would be 1300. 1.3 x 1000 = 1300.
Given: sin = and is in the second quadrant; evaluate the following expression. cos 2 = -7/9 -1/9 1/9
Answers
Trigonometric ratios allow us to determine the value of Cos²θ to be = 5/9. As a result, choice D is the best one.
Define trigonometric ratios?Triangle side ratios are known as ratios of trigonometry. These ratios demonstrate how a right triangle's edges to angles ratio functions in mathematics. The sine, cosine, and tangent trigonometric ratios are the fundamental three. The sin, cos, and tan functions can be used for calculating the other significant trig ratios, cosec, sec, and cot.
Here in the question,
Sinθ = 2/3
Now,
Cos²θ = 1 - Sin²θ
= 1- (2/3) ²
= 1 - 4/9
= (9-4)/9
= 5/9
Therefore, the value of Cos²θ = 5/9.
Option D is the correct option.
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The complete question is:
Given: sinθ = 2/3 and is in the second quadrant; evaluate the following expression: cos²θ
a). -7/9
b). -1/9
c). 1/9
d). 5/9
A mother is 25 years older than her daughter If the daughter's age is x years? (a) Express the mother's age in terms of x (b) Find x when the daughter's is one third of her mother's age
Answers
a) The linear equation is:
y = 25 + x
b) When the daughter's is one third of her mother's age we will have x = 12.5
How to express the mother's age in terms of x?We know that the mother is 25 years older than the daughter, so, if the daughter's age is x, the mother's age can be defined as the linear equation:
y = 25 + x
b) When the daughter's age is one third of her mother's, we have:
x = (1/3)*y
3x = y
Replacing that in the equation above we will get:
3x = 25 + x
3x - x = 25
2x = 25
x = 25/2 = 12.5
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A 35 foot ladder is set against the side of a house so that it reaches up 21 feet. If Elijah grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 17 ft.) Round to the nearest tenth of a foot.
Answers
Answer:
[tex] {21}^{2} + {x}^{2} = {35}^{2} [/tex]
[tex] {x}^{2} =784[/tex]
[tex]x = 28[/tex]
[tex] {y}^{2} + {32}^{2} = {35}^{2} [/tex]
[tex] {y}^{2} = 201[/tex]
[tex]y = \sqrt{201} = 14.18[/tex]
The ladder will reach about 14.2 feet up the side of the house.
obability and Sampling: End-of-Unit
Assessment (B)
Illustrative
iM
İM Mathema
Do not use a calculator. A standard number cube has the numbers 1 through 6 on its
faces.
1. Elena would like to know the average speed that people drive on her street. She
tracks the speed of 30 random cars that drive through with a speedometer. The
mean of Elena's sample is 30 miles per hour, and the MAD (mean absolute deviation)
is 3.
Select all the true statements.
A. Elena would be more likely to get an accurate estimate of the mean speed of
the population by sampling 60 cars instead of sampling 30 cars.
B. The median speed of the sample must be between 25 and 35 miles per hour.
C. Another random sample of 30 cars is likely to have a mean between 24 and 36
miles per hour.
D. The mean speed of these 30 cars is likely to be the same as the mean speed of a
second sample of 30 cars.
E. The mean speed of these random 30 cars is likely to be the same as the mean of
all cars that drive in a residential area.
Answers
The true statements are:
A. Elena would be more likely to get an accurate estimate of the mean speed of the population by sampling 60 cars instead of sampling 30 cars.
C. Another random sample of 30 cars is likely to have a mean between 24 and 36 miles per hour.
What is Mean Absolute Deviation (MAD)?Mean Absolute Deviation (MAD) is a measure of variability in a set of numerical data. It is calculated by finding the average absolute difference between each data point and the mean of the dataset.
Elena would be more likely to get an accurate estimate of the mean speed of the population by sampling 60 cars instead of sampling 30 cars. This statement is true. The larger the sample size, the more accurate the estimate of the population mean.Another random sample of 30 cars is likely to have a mean between 24 and 36 miles per hour. This statement is true. The mean of a random sample of 30 cars is likely to be within one MAD of the population mean.Learn about mean here https://brainly.com/question/1136789
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A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 6 grams and the amount of gold in each necklace is 24 grams. The jeweler made a total of 16 bracelets and necklaces using 258 grams of gold. Determine the number of bracelets made and the number of necklaces made.
Answers
Using a system of equations, the number of bracelets made and the number of necklaces made are:
Bracelets = 7Necklaces = 9.What is a system of equations?A system of equations is two or more equations that can be solved simultaneously or at the same time.
Simultaneous equations can be solved concurrently.
Quantity of gold in each bracelet = 6 grams
Quantity of gold in each necklace = 24 grams
The total number of bracelets and necklaces made = 16
The total quantity of gold used in making the 16 pieces = 258 grams
Let the number of bracelets made = x
Let the number of necklaces made = y
Equations:x + y = 16 ...Equation 1
6x + 24y = 258 ...Equation 2
Multiply Equation 1 by 6:
6x + 6y = 96 ...Equation 3
Subtract Equation 3 from Equation 2:
6x + 24y = 258
-
6x + 6y = 96
18y = 162
y = 9
x = 7 (16 - 9)
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what is the answer to the following questions 32 − 14
Answers
Answer:
Step-by-step explanation:
18
Stanley has $13,800 in a savings account that earns 14% annually. The interest is not
compounded. How much will he have in total in 6 months?
Answers
Answer:
$14,766.00
Step-by-step explanation:
Interest = principle x rate x time
I = 13800 (.14)(.5)
I = 966
Total:
Principle plus interest
13800 + 966 = 14,766
Helping in the name of Jesus.
A shirt costs $18 and is 15% off. How much money do you save?
Answers
Answer:$2.7 would be saved
Step-by-step explanation:
Multiply 18 by .15 which gives you 2.7 which is the answer.
Jayla's math certificate is 19 centimeters tall and 29 centimeters wide. Jayla wants to put the certificate in a fancy frame that costs $0.03 per centimeter. How much will it cost to frame Jayla's math certificate?
Answers
Answer: It will cost $2.88 to frame Jayla's math certificate with the fancy frame.
Step-by-step explanation: To calculate the cost of framing Jayla's math certificate, we need to determine the perimeter of the certificate, which is the sum of the lengths of all four sides.
Perimeter = 2 × (height + width)
Perimeter = 2 × (19 + 29)
Perimeter = 2 × 48
Perimeter = 96 centimeters
So the perimeter of the certificate is 96 centimeters.
To find the cost of framing, we need to multiply the perimeter by the cost per centimeter of the fancy frame:
Cost = perimeter × cost per centimeter
Cost = 96 × $0.03
Cost = $2.88
Therefore, it will cost $2.88 to frame Jayla's math certificate with the fancy frame.
In a math class with 25 students, a test was given the same day that an assignment
was due. There were 15 students who passed the test and 16 students who completed
the assignment. There were 6 students who failed the test and also did not complete
the assignment. What is the probability that a student who completed the homework
passed the test?
Answers
Answer:
Let's first calculate the number of students who passed the test and completed the assignment. We know that 15 students passed the test and 6 students who failed the test and did not complete the assignment. Therefore, there are 25 - 15 - 6 = 4 students who failed the test but completed the assignment.
Now we can calculate the probability that a student who completed the homework passed the test by dividing the number of students who passed the test and completed the assignment by the total number of students who completed the assignment.
The number of students who passed the test and completed the assignment is 15 - 6 = 9. The total number of students who completed the assignment is 16 - 6 = 10. Therefore, the probability that a student who completed the homework passed the test is 9/10 or 0.9.
Step-by-step explanation:
a fair coin is tossed three times, and the events a and b are defined as follows: a: 5at least one head is observed.6 b: 5the number of heads observed is odd.6 a. identify the sample points in the events a, b, a b, ac , and a b. b. find p1a2, p1b2, p1a b2, p1ac 2, and p1a b2 by summing the probabilities of the appropriate sample points. c. use the additive rule to find p1a b2 . compare your answer with the one you obtained in part b. d. are the events a and b mutually exclusive? why?
Answers
The evaluated solution for the given question comprises of sample point of a that are {HHT, HTH, THH, HHHT, HHTH, HTHH, THHH} , the event probability is 0.875 and the probability of implementing a, b is 3/4 below under the condition of a fair coin is tossed three times, and the events a and b are defined.
a) Points sample for event a: {HHT, HTH, THH, HHHT, HHTH, HTHH, THHH}
Points sample for event b: {HTT, THT, TTH, HHH}
Points sample for event a b: {HTT, THT, TTH, HHH, HHT, HTH, THH}
Points sample for event ac: {TTT}
Points sample for event a c: {TTT, HHHH}
b) Event a probability= 7/8 = 0.875
Event b probability= 1/2 = 0.5
Event ab probability = 3/8 = 0.375
Event ac probability = 1/8 = 0.125
Event a c probability = 1/16 + 1/8 = 0.1875
c) Probability of a b implementing additive rule
P(a b) = P(a) + P(b) - P(a ∩ b)
P(a ∩ b) = P(a) + P(b) - P(a b)
P(a ∩ b) = (7/8) + (1/2) - (3/8)
P(a ∩ b) = 9/8 - 3/8
P(a ∩ b) = 6/8
P(a ∩ b) = 3/4
d) Hence, events a and b are not mutually exclusive due to the lack of chances of having common sample points {HHH}.
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The standard deviation of the data displayed in this dot-plot is most likely to be... (a) 20 (b) 5 (c) 11 (d) 8 (e) 15 Make a choice and explain your reasoning. Note: just a choice without explanations will not be accepted.
Answers
Based on the spread of the dots in the dot-plot, the standard deviation of the data is most likely to be (c) 11.
The dot-plot displays a unimodal distribution with a moderate to large spread of the data.
The spread of the data is roughly from 0 to 40, with most of the dots being between 10 to 30.
The spread of the dots, it is unlikely that the standard deviation of the data is as small as 5 or 8.
Similarly.
It is unlikely that the standard deviation is as large as 20 or 15 as there are a significant number of data points that lie within the 20-30 range.
Based on the spread of the dots in the dot-plot, the standard deviation of the data is most likely to be around 11.
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When children roll a die for a game, their probability of rolling a 5 is 17%. This is an example of which type of probability?
Answers
The probability of rolling a 5 when playing a game with a die is an example of empirical probability.
Empirical probability is determined through observation and experimentation, by counting the number of times an event occurs and dividing it by the total number of trials. In this case, the children have likely rolled the die multiple times and recorded the number of times a 5 was rolled.
They then calculated the probability of rolling a 5 by dividing the number of times a 5 was rolled by the total number of rolls. Empirical probability is commonly used in fields such as science and statistics, where data is gathered through experimentation and observation.
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1. Ignoring commission, 512 shares of Targa Resources (TRGP) were purchased for $2,790.40 at the close
for the week. Find the close price for the week. Then, find the quarterly dividend payment per share if
the annual dividend amount paid was $40.96.
Answers
The quarterly dividend payment per share based on the question above will be: $0.02.
The close price for the week will be: $5.45.
What is the dividend?For one to find the closing price for the week, we have to divide the total cost of the shares by using the number of shares that was bought so it will be:
Close price = Total cost / Number of shares
= $2,790.40 / 512
= $5.45
To know the quarterly dividend payment per share, we have to calculate the annual dividend payment per share before we can get it so it will be:
Annual dividend per share = Total annual dividend / Number of shares
= $40.96 / 512
= $0.08
From the question, the dividend was paid quarterly, we then divide the annual dividend per share by 4 so as to get the quarterly dividend per share:
Quarterly dividend per share = Annual dividend per share / 4
= $0.08 / 4
= $0.02
Hence the quarterly dividend payment per share will be: $0.02.
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See text below
Ignoring commission, 512 shares of Targa Resources (TRGP) were purchased for $2,790.40 at the clos for the week. Find the close price for the week. Then, find the quarterly dividend payment per share if the annual dividend amount paid was $40.96. (7pts)
EARNINGS
52-WEEK
TICK
VOL.
WEEK'S
LATEST
THIS NEXT DIV
High Low
Name
Sym.
100s
Yld.
P/E Last Chg.
Year
Year
Year
Amt
8.50
3.20
Targa Resources
TRGP
412574 1.8
PO
dd
+0.41
0.25
0.18
0.12
the cheese head in the image is a triangular prism. the base of the triangle is 12 and the height of the triangle is 8 in. the 3-d is 4 in. what is the volume of the cheese head
Answers
The volume of the cheese head is 192 cubic inches.
Explain the term volume
Volume refers to the amount of space that an object or substance occupies in three dimensions. It is typically measured in units such as cubic meters or cubic feet. The volume of an object can be calculated using various formulas, depending on its shape and dimensions.
According to the given information
The volume V of a triangular prism is given by the formula:
V = (1/2) * b * h * L
In this case, the base of the triangle is 12 inches, the height of the triangle is 8 inches, and the length of the prism (depth of the 3D shape) is 4 inches. Substituting these values into the formula, we get:
V = (1/2) * 12 * 8 * 4
V = 192 cubic inches
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There is a spinner with 14 equal areas, numbered 1 through 14. If the spinner is spun one time, what is the probability that the result is a multiple of 3 or a multiple of 4?
Answers
Answer:
Okay, let's solve this step-by-step:
There is a spinner with 14 equal areas, numbered 1 through 14
We want to find the probability that the result is a multiple of 3 or a multiple of 4
There are 14 possible outcomes (numbers 1 through 14) when the spinner is spun.
Of these 14 numbers:
4 are multiples of 3: 3, 6, 9, 12
4 are multiples of 4: 4, 8, 12, 16
However, 12 is also a multiple of both 3 and 4, so we have counted it twice.
We need to subtract 1 from each to account for this:
Multiples of 3: 3
Multiples of 4: 4
So there are 3 possible multiples of 3 and 3 possible multiples of 4.
In total, there are 3 + 3 = 6 possible multiples of 3 or 4.
To calculate probability:
Probability = (Number of favorable outcomes) / (Total possible outcomes)
= 6 / 14
= 3/7
Converting to a percent: 3/7 = 42.9%
Rounded to the nearest whole percent: 43%
Therefore, the probability that the result is a multiple of 3 or a multiple of 4 is 43%.
Step-by-step explanation: