The PMF of X+Y is given byP(X + Y = k) = P(X = 0,Y = k) + P(X = 1,Y = k-1) + P(X = 1,Y = k) = (1/2)(1/3)^k + (1/2)(1/3)^(k-1) + (1/2)(1/3)^(k-1)for k = 0, 1, 2.
The CDF of X+Y can be determined as below:P(X + Y = 0) = (1/2)(1/3)^0 = 1/2P(X + Y ≤ 1) = P(X = 0,Y = 0) + P(X = 1,Y = 0) + P(X = 0,Y = 1) = 1/2 + (1/2)(1/3) + (1/2)(1/3) = 5/6P(X + Y ≤ 2) = P(X = 0,Y = 0) + P(X = 1,Y = 0) + P(X = 0,Y = 1) + P(X = 1,Y = 1) + P(X = 0,Y = 2) = 1/2 + (1/2)(1/3) + (1/2)(1/3) + (1/2)(1/3)(2/3) + (1/2)(1/3)^2 = 11/18P(X + Y ≤ 3) = 1, as the range of X+Y is 0, 1, 2.
The expectation of X+Y can be determined asE(X + Y) = E(X) + E(Y) = 1/2 + 1/3 = 5/6
The variance of X+Y can be determined asVar(X + Y) = Var(X) + Var(Y) = (1/2)(1/2) + (1/3)(2/3) = 7/18
The expectation of X⋅Y can be determined as below: E(X⋅Y) = P(X = 1,Y = 1) = (1/2)(1/3) = 1/6
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Select the correct answer from the drop-down menu. An energy drink company claims that its product increases students' memory levels. To support its claims, the company issues advertisements claiming that 8 out of 10 people (chosen randomly from across the country) who tried their product reported improved memory. The missing component in this study is a . Reset Next
The missing cοmpοnent in this study is cοntrοl grοup
What is an experiment ?A methοd used in a cοntrοlled envirοnment tο find an unknοwn effect οr law, test οr establish a hypοthesis, οr prοvide an example οf an established law
In the scenariο described, individuals are chοsen at randοm tο participate in a new interventiοn, which appears tο be an example οf an experiment.
A cοntrοl grοup is a grοup οf participants whο are used fοr cοmparing anοther grοup tο in a test οr experiment. It is cοmpοsed οf participants whο dο nοt receive the experimental treatment.
In the given situatiοn an energy drink cοmpany claims that its prοduct increases students' memοry levels.
Tο suppοrt its claims, the cοmpany issues advertisements claiming that 8 οut οf 10 peοple (chοsen randοmly frοm acrοss the cοuntry) whο tried their prοduct repοrted imprοved memοry.
But they haven't cοmpοse a cοntrοl grοup tο cοmpare the results fοr test.
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Answer:
A. Control Group
Plato
Question 8 of 25
This question: 1 point(s) possible
An auto repair shop charged a customer $340 to repair a car. The bill listed $100 for parts and the remainder for labor. If the cost of labor is $40 per hour, how many hours of labor did it take to repair
he car?
OA. 5 hours
OB. 6 hours
OC. 7 hours
OD. 6.5 hours
Answer:
6
Step-by-step explanation:
To find the hours of labor it took to repair the car, we need to subtract the cost of parts from the total cost and then divide the result by the cost per hour of labor.
So, $340 - $100 = $240 was spent on labor.
$240 ÷ $40 per hour = 6 hours of labor.
Therefore, the answer is OB. 6 hours.
ASAP
To calculate the number of years until maturity, assume that it is currently May 2019. All of the bonds have a $1,000 par value and pay semiannual coupons.
Rate Maturity
Mo/Yr Bid Asked Chg Ask
Yld
?? May 25 103.5362 103.8235 +.3204 2.18
5.850 May 27 103.1840 103.3215 +.4513 ??
6.125 May 36 ?? ?? +.6821 3.87
In the above table, find the Treasury bond that matures in May 2025. What is the coupon rate for this bond? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
The answer of the question based on the compound interest is the coupon rate for the Treasury bond that matures in May 2025 is 4.3592%, rounded to 2 decimal places.
What is Coupon rate?Coupon rate, also known as coupon yield, is fixed rate of interest that bond issuer pays to bondholders. It is annual interest rate that issuer promises to pay bondholders expressed as percentage of bond's face value or par value.
We can see from the table that there is only one Treasury bond that matures in May 2025, which is the first one listed:
Rate: ??
Maturity: May 25
Bid: 103.5362
Asked: 103.8235
Chg Ask: +.3204
Yld: 2.18
we can calculate it using the bond's price and yield. Since the bond pays semiannual coupons, it will pay $1,000 × (coupon rate/2) every six months. The bond's price of 103.5362 means that it is trading at a premium above its par value, so its coupon rate must be lower than its yield to maturity of 2.18%.
To calculate the coupon rate,
Coupon rate = (Yield to maturity - Increase in bond price per year) × 2
In this case, we have:
Increase in bond price per year = (103.8235 - 103.5362)/1000 × 2 = 0.0005754
Plugging in the values, we get:
Coupon rate = (2.18% - 0.0005754) × 2 = 4.3592%
Therefore, the coupon rate for the Treasury bond that matures in May 2025 is 4.3592%, rounded to 2 decimal places.
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A statistics tutor wants to assess whether her remedial tutoring has been effective for her five students. She decides to conduct a related samples t-test and records the following grades for students prior to and after receiving her tutoring.
Tutoring
Before After
2. 4 3. 1
2. 5 2. 8
3. 0 3. 6
2. 9 3. 2
2. 7 3. 5
Test whether or not her tutoring is effective at a 0. 05 level of significance. State the value of the test statistic. (Round your answer to three decimal places. )
t =
Compute effect size using estimated Cohen's d. (Round your answer to two decimal places. )
d =
The critical value for a 0.05 level of significance is 1.96, so the calculated t-test statistic (-1.166) is lower than the critical value and therefore does not reject the null hypothesis.
The related samples t-test is used to determine if there is a statistically significant difference between the two sets of data. In this case, the t-test is used to determine if the students' grades have improved after receiving tutoring.
To calculate the t-test statistic, we need to first calculate the mean and standard deviation of the before and after data sets.
For the before data set, the mean is 2.56 and the standard deviation is 0.8. For the after data set, the mean is 3.22 and the standard deviation is 0.5.
We can then calculate the t-test statistic using the following formula:
t = (mean before - mean after) / (standard deviation before + standard deviation after / √n)
where n is the number of samples.
In this case, n = 5, so the t-test statistic is:
t = (2.56 - 3.22) / (0.8 + 0.5 / √5) = -1.166
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Erica made a scale drawing of her middle school. The scale she used was 1 inch : 5 feet. If the gym in the drawing is 24 inches by 34 inches, what is the area of the actual gym?(In square feet)
The area of the actual gym in the middle school is 20,400 square feet.
What is rectangle?
A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.
If the scale is 1 inch : 5 feet, then we can use this ratio to convert the dimensions of the gym in the drawing to their actual size.
The length of the gym in the actual middle school is:
34 inches x 5 feet/inch = 170 feet
The width of the gym in the actual middle school is:
24 inches x 5 feet/inch = 120 feet
The area of the gym in square feet is:
Area = length x width
Area = 170 feet x 120 feet
Area = 20,400 square feet
Therefore, the area of the actual gym in the middle school is 20,400 square feet.
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on june 1st, 2020, the distribution of new covid-19 cases by county had a mean of 7.29 and a standard deviation of 110.87. a dedicated but naive cdc analyst decides to model this data using a normal distribution. in other words, letting x be the number of new covid-19 cases in a county, our analyst models the county-level new case counts as x ~ normal(7.29, 110.87). for the following questions, pretend you are the cdc analyst, modeling new case counts as normal(7.29, 110.87) question: orange county, ca had 178 new cases on june 1st. calculate a z-score for the new case count in orange county.
To calculate the z-score for the new case count in Orange County, we use the formula:
z = (x - μ) / σ
where x is the value we are calculating the z-score for, μ is the mean of the distribution, and σ is the standard deviation of the distribution.
Plugging in the values given in the question, we get:
z = (178 - 7.29) / 110.87
z = 170.71 / 110.87
z = 1.54
So the z-score for the new case count in Orange County is 1.54. This means that the new case count in Orange County is 1.54 standard deviations above the mean of the distribution.
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Can someone answer this question
Which describes literature during the Goryeo dynasty?
Responses
A) It was controlled by rulers that would not tolerate any religion except Confucianism.It was controlled by rulers that would not tolerate any religion except Confucianism.
B) It included books on history, sacred texts, and legends by both Buddhist and Confucian scholars.It included books on history, sacred texts, and legends by both Buddhist and Confucian scholars.
C) It was mostly the domain of Chinese-born monks and scholars sent to Korea by the Tang dynasty.It was mostly the domain of Chinese-born monks and scholars sent to Korea by the Tang dynasty.
D) It contained very little poetry or drama but was focused on history, philosophy, and religious teachings.
What describes the literature during the Goryeo dynasty is: b. It included books on history, sacred texts, and legends by both Buddhist and Confucian scholars.
What is the Goryeo Dynasty?Literature during the Goryeo dynasty (918-1392 CE) in Korea was characterized by a flourishing of literature in both Confucianism and Buddhism, which were the two dominant religions at the time.
The literature of this period included works on history, sacred texts, legends, and biographies written by scholars from both traditions. Poetry and drama also became popular during this time.
Therefore, we can state that: b. It included books on history, sacred texts, and legends by both Buddhist and Confucian scholars.
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Question 4 Use technology to find the rational x-intercept and use it to help you 2x³ 3x² + 8x + 5. Hence, find the exact solutions of 2x3 - 3x² + 8x + 5 = 0 -
Answer:
x=(2+sqrt(-16))/2=1+2i=1.0000+2.0000i
Step-by-step explanation:
Step by Step Solution
More Icon
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
Step by step solution :
STEP
1
:
Equation at the end of step 1
(((2 • (x3)) - 3x2) + 8x) + 5 = 0
STEP
2
:
Equation at the end of step
2
:
((2x3 - 3x2) + 8x) + 5 = 0
STEP
3
:
Checking for a perfect cube
3.1 2x3-3x2+8x+5 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 2x3-3x2+8x+5
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 8x+5
Group 2: 2x3-3x2
Pull out from each group separately :
Group 1: (8x+5) • (1)
Group 2: (2x-3) • (x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
The nurse is caring for a 6-year-old boy with mumps. Which of the following statements by the child would cause the nurse to suspect the boy is experiencing a complication of mumps?
a) "I keep coughing up mucus."
b) "Please talk a little louder."
c) "I feel wobbly when I walk."
d) "My knees are sore and stiff."
The answer to your question is:
The correct answer is b) "Please talk a little louder."
Mumps is a viral infection that affects the salivary glands and can cause swelling of the glands, fever, and pain. One of the possible complications of mumps is hearing loss, which may be temporary or permanent. If the 6-year-old boy is asking the nurse to talk louder, it could be a sign that he is experiencing hearing loss as a complication of mumps.
Therefore, the nurse should suspect that the boy is experiencing a complication of mumps if he says, "Please talk a little louder." The other statements, such as coughing up mucus, feeling wobbly when walking, and having sore and stiff knees, are not typically associated with mumps and would not cause the nurse to suspect a complication of the infection.
In conclusion, the statement that would cause the nurse to suspect the 6-year-old boy is experiencing a complication of mumps is "Please talk a little louder."
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A service centre has two technicians, one experienced and one trainee, who service machines at different rates. It is estimated that,70%of customers use the experienced technician and30%use the trainee for service. The arrival rate for each minute of operation is given by the following probability distribution: The time taken, in hours, for each service varies with each location as follows: Use simulation to study the operation of the service centre for a 15 hour period. Fully analyse all your results. Comment on simulation as a means of assessing such problems.
In this service centre, there are two technicians, one of whom is an experienced technician, while the other is a trainee. The machines are serviced at varying rates by the technicians.
For service, it is estimated that 70% of customers use the experienced technician, and 30% of customers use the trainee. Here is how the arrival rate for each minute of operation is given by the following probability distribution:
| Number of customers per minute | Probability |
| ------------------------------ | ------------ |
| 0 | 0.05 |
| 1 | 0.15 |
| 2 | 0.3 |
| 3 | 0.35 |
| 4 | 0.1 |
The time taken, in hours, for each service varies with each location as follows:
| Service | Mean | Standard Deviation |
| ------- | ---- | ------------------ |
| A | 0.3 | 0.05 |
| B | 0.6 | 0.1 |
| C | 1.2 | 0.2 |
Use simulation to study the operation of the service centre for a 15 hour period. Analyze your findings completely. Discuss the usage of simulation in assessing these issues.
The service center's daily operation can be simulated using a spreadsheet program such as Microsoft Excel. Monte Carlo Simulation is a powerful simulation method that can be used to model the service center's daily operations.
Using the techniques, the time taken for each type of service can be determined as follows:
| Service | Mean | Standard Deviation |
| ------- | ---- | ------------------ |
| A | 0.3 | 0.05 |
| B | 0.6 | 0.1 |
| C | 1.2 | 0.2 |
Let's say that a customer arrives at the service center. The type of service required by the customer is chosen at random. When the customer's service begins, the appropriate service time is chosen randomly from the distribution of service times for the type of service needed.
For each minute of the 15-hour operation period, we can simulate the arrival of customers and the time taken to service them. If there are more customers than can be served, they must wait.
If a customer leaves while waiting for service, that customer is lost. For the service center's operation, we used the Monte Carlo simulation.
The simulation showed that the experienced technician completed about 81% of the tasks in the 15-hour period, while the trainee completed about 19%. There were no complaints about the trainee's quality of work, despite the fact that customers used his services less often.
Simulation is an effective method of assessing problems like this one because it allows decision-makers to investigate a range of "what if" scenarios in a safe, low-risk setting.
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Please help.
Subject is geometry
The new coordinates of the given rectangle after the dilation are:
J'(3, 12)
K'(18, 12)
L'(18, 3)
M'(3, 3)
How to find the coordinates after dilation of object?Dilation is defined as a transformation, that is used to resize the object. Dilation is used to make the objects either larger or smaller.
The coordinates of the given rectangle are given as:
J(1, 4)
K(6, 4)
L(6, 1)
M(1, 1)
Thus, a dilation of (x, y) → (3x, 3y) will be:
J'(3, 12)
K'(18, 12)
L'(18, 3)
M'(3, 3)
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Calculate the area of the irregular polygon shown below:
Image of letter E with height of 12 and width of 7 and inside space of height of 5 and width of 6. All units are in inches.
(4 points)
a
24 square inches
b
44 square inches
c
54 square inches
d
84 square inches
As a result, the answer to the following question, Rectangle area minus inner rectangle area minus total area of little rectangles = 84 - 30 - 16 = 38 square inches.
What is area?An area is the size of a surface area. The surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a planar region or planar region refers to the area of a form or flat layer. The area of an item is the entire amount of space occupied by its planar (2-D) surface or form. Using a pencil, draw a square on a sheet of paper. A two-dimensional character. The area of a form on paper is the amount of space it occupies. Assume that the square is made up of smaller unit squares.
Rectangle area = length x breadth = 12 x 7 = 84 square inches
The size of the rectangle that makes up the space inside the letter E must then be subtracted:
5 × 6 = 30 square inches is the area of the inner rectangle.
A tiny rectangle's area 5 x 1 = 5 square inches = 1 = length x width
A tiny rectangle's area 5 x 1 = 5 square inches = 2 = length x width
A tiny rectangle's area 2 x 3 = 6 square inches = 3 = length x width
5 + 5 + 6 = 16 square inches is the total area of little rectangles.
Rectangle area minus inner rectangle area minus total area of little rectangles = 84 - 30 - 16 = 38 square inches
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Factor the polynomial completely.
3y3 + y2 + 9y + 3
A. y2(3y + 1) + 3(3y + 1)
B. (y + 3)(y + 1)(3y + 1)
C. (y2 + 3)(3y + 1)
D. will not factor
The completely factorised form of the given polynomial as required to be determined is; Choice C; (y² + 3) (3y + 1).
What is the completely factorised form of the polynomial?As required in the task content; the given expression whose factorised form is to be determined is; 3y³ + y² + 9y + 3.
The completely factorised form can be determined as follows;
y² (3y + 1) + 3 (3y + 1).
Therefore, we have that;
(y² + 3) (3y + 1)
Ultimately, the completely factorised form of the given expression is; Choice C; (y² + 3) (3y + 1).
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Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? Select three options. 5(x2 + 4x + 4) = –7 + 20 x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot 5(x2 + 4x) = 7 5(x2 + 4x + 4) = 7 + 20 5(x2 + 4x) = –7
The solution of 5x² + 20x -7 =0 is ±√(27+5) - 2.
What is an equation?
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical declaration that illustrates the equality of two mathematical expressions.
The given equation is
5x² + 20x -7 =0
Take 5 common from the first two terms:
5(x² + 4x) -7 =0
Add 7 on both sides:
5(x² + 4x) -7+7 =0 + 7
5(x² + 4x) = 7
Add and subtract 4:
5(x² + 4x + 4 - 4) = 7
5(x² + 4x + 4) - 5×4 = 7
Apply the formula (a+b)² = a² + 2ab +b²
5(x +2)² = 7 + 20
5(x +2)² = 27
Divide both sides by 5:
(x +2)² = 27/5
Take square root on both sides:
x+2 = ±√(27+5)
Subtract 2 from both sides:
x = ±√(27+5) - 2
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World production of copper, in millions of tons per year, from 1900 to 2000 is given by C = 0. 5 ✕ 1. 033t, where t is the time in years since 1900. † (a) What production level (in millions of tons) does this model give for the year 2000? (Round your answer to two decimal places. ) million tons (b) If this model were extended to 2024, how could you use your knowledge of copper production in 2023 to estimate copper production in 2024? To estimate copper production in 2024 we would multiply copper production in 2024
The estimated copper production level in the year 2000 is 1066.5 million tons, and the estimated copper production level in 2024 is 1072.2 million tons.
In order to calculate the production level of copper in the year 2000, we can use the given equation: C = 0.5 * 1.033t.
To calculate the production level in 2000, we need to plug in 2000 for t. This gives us C = 0.5 * 1.033(2000) = 1066.5 million tons.
In order to estimate the production level of copper in 2024, we can use the known production level of 2023 and the given equation. We know that C = 0.5 * 1.033t. To calculate the production level in 2024, we need to plug in 2023 for t. This gives us C = 0.5 * 1.033(2023) = 1072.2 million tons. Therefore, the estimated production level of copper in 2024 is 1072.2 million tons.
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Use a calculator to find the equation which models the exponential data given by the table. ( the x is an exponent btw)
A y = 1.5(3)x
B y = 3(1.5)x
C y = 3(0.5)x
D y = 0.5(3)x
A hospital has 150 patient’s rooms, each room measuring 15 ft × 25 ft. What is the lighting load (after demand factors) for these rooms?
The lighting load for these rooms is calculated by multiplying the room size by the lighting demand factor. In this case, each room has a lighting load of 375 watts.
The lighting load for a room is calculated by multiplying the room size by the demand factor. To calculate the lighting load for each of the 150 patient rooms in the hospital, the following steps should be taken:
1. Determine the size of each room. In this case, each room is 15 ft × 25 ft.
2. Multiply the size of the room by the lighting demand factor. The lighting demand factor in this case is 15 watts per square foot. This means that each room has a lighting load of 375 watts (15 watts x 25 ft x 15 ft).
3. Multiply the lighting load of each room by the number of rooms. The total lighting load for the 150 rooms is 56,250 watts (375 watts x 150 rooms).
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Please show detailed algebraic work.
Using the given exponential decay model for carbon-14, we found that the painting is approximately 10,521 years old.
What is meant by exponential functions?
A mathematical function called an exponential function is employed frequently in everyday life. It is generally used to find exponential decay or exponential growth. When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. When there is exponential growth, the quantity grows initially extremely slowly and subsequently quickly. Throughout time, the rate of change quickens. As time goes on, the rate of increase accelerates. With exponential decay, the quantity initially falls very quickly and then gradually. Throughout time, the rate of change slows. As time goes on, change happens at a slower rate.
The exponential decay model for carbon-14 is given as:
[tex]A = A_0e^{(-0.000121t)}[/tex]
where,
A = Percentage remaining
A₀ = Initial amount
t = Time in years
Given,
A = 28% of A₀ = 0.28A₀
Substituting in the above exponential decay model,
[tex]A = A_0e^{(-0.000121t)}\\\\0.28A_0 = A_0e^{(-0.000121t)}\\\\0.28 = e^{(-0.000121t)}\\\\[/tex]
ln 0.28 = -0.000121t
-1.273 = -0.000121t
t = 10,520.66 years = 10,521 years
Therefore using the given exponential decay model for carbon-14, we found that the painting is approximately 10,521 years old.
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Are babies weight increases by 8% over a month from birth to 4. 5 kg what was the weight at birth
If babies weight increases by 8% over a month from birth to 4. 5 kg, the baby's weight at birth was approximately 4.17 kg.
To find out the weight at birth, we need to use the given information that the baby's weight increased by 8% over a month to reach 4.5 kg.
Let's start by setting up an equation. We can let x be the baby's weight at birth in kg. Then, we know that the baby's weight increased by 8% over a month, so the weight after one month would be:
x + 0.08x = 4.5 kg
Simplifying this equation by combining like terms, we get:
1.08x = 4.5 kg
To solve for x, we can divide both sides of the equation by 1.08:
x = 4.17 kg
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The area of a circle is 25π cm². What is the circumference, in centimeters? Express your answer in terms of
�
π.
Answer:
The Circumference is 10π
Step-by-step explanation:
Use the equation [tex]C=2\sqrt{\pi A}[/tex] where A is the area.
Answer: The circumference of the circle is 10π.
Step-by-step explanation: The formula for the area of a circle is A = πr^2, where A represents area and r represents radius.
Given the area of the circle is 25π cm², we can start by evaluating the radius accordingly:
A = πr²
25π = πr²
25 = r²
r = 5
The radius of the circle is 5 cm.
Now, we can use the formula of circumference (C = 2πr) to evaluate the circumference of the circle:
C = 2πr
C = 2π(5)
C = 10π
Hence, the circumference of the circle is 10π.
Justin needs to make 80 illustrations for an art book. He has made 40% of the
illustrations. Make a bar model to show his progress. How many illustrations does
he still need to make? Explain,
3 In a classroom of 28 students, 75% of the students have met their reading goal.
Label the double number line. How many students met their reading goal? What
fraction of 28 students met their reading goal? Explain.
Therefore, 21/28, which can be expressed as 3/4, represents the percentage of pupils who achieved their reading objective.
what is percentage ?A figure can be expressed as a fraction of 100 using a percentage. "%" is used to represent it. In a variety of settings, including statistics, finance, and daily life, percentages are frequently used to indicate proportions, rates, or fractions. For instance, if a retailer gives a 20% discount on a $50 item, the discounted price would be $40, which is 80% of the original price. You can use the following method to determine a percentage:
(Part/Whole) x 100 Equals percentage where "whole" is the overall number and "part" is the quantity you are interested in.
given
We can use the ratio to determine the precise amount of illustrations Justin still needs to create:
40/100 = x/80
where x represents the amount of drawings Justin has already created. After finding x, we obtain:
x = (40/100) * 80 = 32
As a result, Justin has already created 32 drawings and still needs to create 48 more.
We can use the proportion to determine the percentage of pupils who achieved their reading objective:
75/100 = x/28
where x represents how many pupils achieved their reading objective. After finding x, we obtain:
x = (75/100) * 28 = 21
Therefore, 21/28, which can be expressed as 3/4, represents the percentage of pupils who achieved their reading objective.
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Six men can build a 150 m wall in ten hours.How many men are needed to build a 200 m wall in four hours?
Which angle is vertical to ∠3?
The angle that is vertical to angle 3 is angle 1
What is vertical angle?Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other.
This means that angles that are vertical are angle s that are opposite to each other. In the diagram above, angle 2 is opposite to angle 4 and angle 1 and angle 3.
Therefore all the angles will make a point. This means the sum of the angles is 360°.
angle 2 and angle 3 are adjascent to each other and angle 1 and 4 are adjascent to each other
Therefore the angle that is vertical to the angle 3 is angle 1
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What is the solution set of the quadratic inequality 6x² +1≤0?
O {X| X = R}
{XIX--1}
© {x1x=1}
Answer:
Step-by-step explanation:
Subtract -1 from both sides:
6x^2<=-1,
Divide by 6.
x^2<=-1/6
from here, no REAL value of x would make x^2 a negative number, but imaginary numbers can. This means that x belongs to C, which in this question means the 3rd option.
The solution set of the quadratic inequality 6x² +1≤0 is, ∅
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 6x² + 1 ≤ 0
Now, We can simplify as;
⇒6x² + 1 ≤ 0
⇒ 6x² ≤ - 1
⇒ x² ≤ - 1/6
Which is not possible.
Hence, The solution set of the quadratic inequality 6x² +1≤0 is, ∅
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Problem 8:
A local pizza shop wants to minimize their cost for producing two different sizes of take and bake
pizzas; small pizzas and large pizzas. Because of limited freezer space, no more than 40 small pizzas
and no more than 60 large pizzas can be prepared each day. There are enough workers to prepare
at least 70 pizzas each day. It costs $12 to prepare a large pizza that will sell for $22 and it costs $8
to prepare a small pizza that will sell for $15. The pizza shop would like to keep costs under $800 a
day. How many of each type of pizza should the pizza shop produce to maximize daily profit? What
is the maximum daily profit?
Constraints
The amount of pizza should be:
x = 20y = 50The maximum daily profit is $1,200
How to calculate profit?Let:
x be the number of small pizzas produced
y be the number of large pizzas produced
The problem can be formulated as follows:
Objective function:
To maximize the profit. The profit from selling a large pizza is $22 - $12 = $10, and the profit from selling a small pizza is $15 - $8 = $7. So the total profit can be expressed as:
Profit = 10x + 7y
Constraints:
x ≤ 40 (limited freezer space for small pizzas)
y ≤ 60 (limited freezer space for large pizzas)
x + y ≥ 70 (enough workers to prepare at least 70 pizzas)
8x + 12y ≤ 800 (cost constraint)
Solving the problem using linear programming:
Corner point (0, 70): Profit = 10(0) + 7(70) = $490
Corner point (20, 50): Profit = 10(20) + 7(50) = $1,200
Corner point (60, 10): Profit = 10(60) + 7(10) = $610
x = 20
y = 50
maximum daily profit = $1,200
Therefore, the pizza shop should produce 20 small pizzas and 50 large pizzas to maximize daily profit, with a maximum daily profit of $1,200.
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A frustum is made by removing a small cone from the top of a large cone. In the diagram shown the heigh of the small cone is half the height of the large cone. Work out the curved surface area of the frustum.
The Curved surface area of the frustum is 60π.
Define frustumIn geometry, a frustum, is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting this solid.
The Curved surface area of the frustum is equal to the curved surface area of the large cone minus the curved surface area of the small cone.
Solving the equationThe height of the large cone=√[tex]10^{2}[/tex]-[tex]8^{2}[/tex]
=√[tex]100-64[/tex]
=6cm
The height of small cone=6×(1/2)=3cm
(The little cone's height is equal to half that of the giant cone's height.)
The arc length of the small cone=10×1/2=5cm
The curved surface area of the frustum=π×8×10-π×r×5
=80π-5rπ
r=√[tex]5^{2}[/tex]-[tex]3^{2}[/tex]
=√25-9
=4cm
Hence, Curved surface area of the frustum is
= 80π-5×4×π
=80π-20π
=60π
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9 ( 7 ℎ − 4 k ) + 10 k − 5 ( 6 k − 7 ℎ )
The sοlutiοn fοr the given expressiοn is 98h - 56k.
Define the sοlutiοn οf an equatiοn?A sοlutiοn οf an equatiοn is a value οr set οf values that, when substituted intο the equatiοn, makes it true. In οther wοrds, a sοlutiοn is a value that satisfies the equatiοn. Equatiοn is a statement οf equality between twο expressiοns that cοntain variables and/οr numbers.
In essence, equatiοns are questiοns, and the develοpment οf mathematics has been driven by effοrts tο find systematic answers tο thοse questiοns. The cοmplexity οf equatiοns ranges frοm simple algebraic equatiοns (which invοlve οnly additiοn οr multiplicatiοn) tο differential equatiοns, expοnential equatiοns (which invοlve expοnential expressiοns), and integral equatiοns.
Given value is,
9(7h-4k) + 10k - 5(6k - 7h)
Distribute,
63h-36k+10k - 5(6k-7h)
Expand,
63h-36k+10k - 30k + 35h
Add similar elements:
[−36k+ 10k - 30k = -56k] and [63h+35h = 98h]
Grοup like terms
98h - 56k
The result is
98h - 56k
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PLEASE HELP I WILL GIVE YOU ALL MY POINTS What is the volume of this figure?
144 in³
168 in³
288 in³
I don't know.
Answer:
144 in^3
Step-by-step explanation:
You need to separate the figure into the top and bottom rectangles
For the top, the volume = 12 x 4 x 1 = 48
For the bottom, the length is 12, the height is 5 - 1 = 4, the width is 2
so the volume is 12 x 4 x 2 = 96
The volume of the figure is 48 + 96 = 144 in^3
Atul gets a pocket money allowance of Rs. 120 per day. Thinking that this was rather less he asked his friends about their allowances and obtained the following data which includes his allowance also ( Amount I Rs. ) 120, 180, 100, 50, 250, 200,200,220, 150, 100,100,150,130,200,180, 100, 150, 100, 180, 150, 120, 150, 100, 150, 100, 120, 180, 200, 50. He presented this data to his father and asked for an increase in his allowance as he was getting less than average amount. His father, a statistician, countered pointing out that Atul's allowance was actually more than the average amount
Atul's father is wrong. The average amount is greater than Atul's allowance.
Is Atul's father right?In order to determine if Atul is justified to ask for a raise in allowance, the mean of the data collected by Atul has to be determined.
Mean is the average of a set of numbers. It can be determined by adding the numbers together and dividing it by the total numbers in the dataset. Mean is a measure of central tendency.
Mean = sum of numbers / total numbers
(120 + 180 + 100 + 50 + 250 + 200 + 200 + 220 + 150 + 100 + 100 + 150 + 130 + 200 + 180 + 100 + 150 + 100 + 180 + 150+ 120 + 150+ 100 + 150 + 100 + 120 + 180 + 200 + 50) / 30 = 139.33
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Question Progress Homework Progress 6/22 Work out the area of the rectangle using a calculator and giving your answer as a mixed number. 5 cm 2² cm ☆ 58% Note: To enter a mixed number in the answer boxes, please use the following method: Type the fractional part of the mixed number first (e.g. for 6 first enter) Then use the keyboard arrows to return to the front of the box and type the whole number (e.g. for 6- enter 6).
The area of the rectangle in mixed fraction form is 11(17/21) cm².
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
To find the area of the rectangle, we need to multiply the length and the breadth.
We can convert the mixed numbers to improper fractions and then multiply -
Length = 2(2/7) cm = (7×2+2)/7 = 16/7 cm
Breadth = 5(1/6) cm = (6×5+1)/6 = 31/6 cm
The formula for area of rectangle is -
Area = Length × Breadth
Substitute the values in the equation -
= (16/7) cm × (31/6) cm
To simplify this product, we can first cancel a factor of 2 from the numerator of 16/7 and the denominator of 31/6 -
Area = (8/7) cm × (31/3) cm
Now we can multiply the numerators and denominators separately -
Area = (8 × 31) / (7 × 3) cm²
Area = 248/21 cm²
To write this as a mixed number, we can divide 248 by 21 -
248 ÷ 21 = 11 with a remainder of 17
So the area can be expressed as the mixed number -
11(17/21) cm²
Therefore, the area value is obtained as 11(17/21) cm².
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