Answers
Answer: 5/6
Step-by-step explanation:
First, you find the common denominator of the two:
3/6 + 2/6
Now you can easily add the two:
5/6
Answer:
See below.
Step-by-step explanation:
We are asked to Add Fractions.
What are Fractions?
Fractions are parts of a single whole number.
To make adding these fractions similar, we should have a common denominator.
[tex]\frac{Numerator}{Denominator}[/tex]
When we add common denominators, they remain the same. This makes adding fractions much easier.
Let's identify the common denominator by finding the Least Common Multiple. (LCM)
What is the LCM?
The LCM is the smallest common multiple that 2 numbers have. A multiple is the product of that number.
An Example of Multiples:
[tex]4; 4 \times 1, 4 \times 2, 4 \times 3, 4 \times 4, 4 \times 5, 4 \times 6.\\4; 4, 8, 12, 16, 20, 24.[/tex]
An Example of the LCM:
[tex]4; 4, 8, 12, 16, 20, [24], 28\\6; 6, 12, 18, [24], 30, 36, 42. \\The \ LCM \ is \ 24.[/tex]
Let's use the example above as a guide, but for our values in the denominator.
[tex]2; 2, 4, [6], 8, 10, 12, 14.\\3; 3, [6], 9, 12, 15, 18, 21.\\The \ LCM \ is \ 6.[/tex]
Our Denominators will be 6.
Multiply both the Numerator and the Denominator by the number needed to make the denominator 6.
[tex]\frac{1 \times 3}{2 \times 3}=\frac{3}{6} \\\frac{1 \times 2}{3 \times 2} = \frac{2}{6}[/tex]
Add:
[tex]\frac{3}{6} + \frac{2}{6} = \frac{5}{6} \\[/tex]
Our final answer is [tex]\frac{5}{6} .[/tex]
Related Questions
Please show detailed algebraic work.
Answers
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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Please Answer the question.
Answers
Make both fractions have equal denominators: 2/5 = 6/15
To find the middle, just list them out: 6/15, 7/15, 8/15
7/15 is the exact middle of them.
2/5 = 3x2/15 = 6/15 , 8/15
So, between 2/5 and 8/15 is 7/15
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
Answers
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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Can anyone help with this question? I’m stumped.
Answers
The fewest number of cards you will have to look at the back of to know what color the back of each card is 2
How to determine the number of cardsTo determine the color of the back of each card, we need to observe the color of the opposite side.
We can start by looking at the two-sided white card.
Since both sides of the card are white, no matter which side we look at, we can't determine the color of the back of the card.
So, we have to move on to the other cards.
Next, we can look at the two-sided black card. If we look at either side of this card, we know that the back of the card must also be black.
So, we have determined the color of the back of this card by looking at just one side.
The above means that, in the worst-case scenario, we will have to look at three cards, but we only need to look at two sides of each card
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What is the solution set of the quadratic inequality 6x² +1≤0?
O {X| X = R}
{XIX--1}
© {x1x=1}
Answers
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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Jose's age is 7 years less than 2/3 of his dad's age. If Jose's dad is d years old, write an expression that determines how old Jose is. (No spaces in the expression when typing into solution)
If Jose's dad is 30 years old, how old is Jose?
Answers
The expression that determines hοw οld Jose is, in terms of his dad's age, is [tex]\frac{2}{3}d - 7[/tex]
What are Linear equatiοns?Linear equatiοns are equatiοns whοse highest pοwer οf the variables is 1. The graph οf a linear equatiοn is a straight line.Let J be Jοse's age. Accοrding tο the prοblem, Jοse's age is 7 years less than 2/3 οf his dad's age.
We can express this mathematically as:
J = (2/3)d - 7
where d is Jοse's dad's age.
Therefοre, the expressiοn that determines hοw οld Jοse is, in terms οf his dad's age, is [tex]\frac{2}{3}d - 7[/tex]
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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.
Answers
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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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
Answers
If we plug in x = 0, we get:
y = 1.5(3)^0 = 1.5
However, from the table we can see that when x = 0, y = 2. Therefore, option A is not correct.
B) y = 3(1.5)^x
If we plug in x = 1, we get:
y = 3(1.5)^1 = 4.5
This matches the second value in the table. Let's check the other values:
- When x = 0, y = 3 (matches the first value)
- When x = 2, y = 6.75 (matches the third value)
Therefore, option B is correct.
C) y = 3(0.5)^x
If we plug in x = 0, we get:
y = 3(0.5)^0 = 3
However, from the table we can see that when x = 0, y = 2. Therefore, option C is not correct.
D) y = 0.5(3)^x
If we plug in x = 1, we get:
y = 0.5(3)^1 = 1.5
This does not match the second value in the table. Therefore, option D is not correct.
Therefore, the correct equation that models the exponential data given by the table is:
y = 3(1.5)^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?
Answers
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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ο Δ Δ Δ Δ 2
A
52. Last month, 200 people each donated between 2 and 5
food items to the Downtown Food Bank, according to the
information in the bar graph below.
Which of the
following statements about the mean, median, and mode
of the data must be true?
F.
G.
H.
1.
K.
Number of Donors
100
80
60
40
20
0
2 3
4 5
Number of Food Items Donated
The mean number of food items donated is equal
to the median number of food items donated.
The mode number of food items donated is equal
to the median number of food items donated.
The median number of food items donated is
greater than the mode number of food items
donated.
The mode number of food items donated is greater
than the median number of food items donated.
The mean number of food items donated is greater
than the median number of food items donated.
Answers
Answer:
Step-by-step explanation:
To determine which statement must be true about the mean, median, and mode of the data, we need to analyze the bar graph provided.
We see that the data is not normally distributed, but rather skewed to the right. Therefore, the mean will be greater than the median, as the mean is affected by outliers and extreme values, which in this case will pull it towards the higher end.
Furthermore, since there is no single value that appears more frequently than any other, there is no mode for this data set.
Therefore, the statement that must be true is:
The mean number of food items donated is greater than the median number of food items donated. (Option K)
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Reuben and his wife are each starting a saving plan. Reuben will initially set aside $50 and then add $50. 85 every week to the savings. The amount A (in dollars) saved this way is given by the function =A+50. 85N50, where N is the number of weeks he has been saving.
His wife will not set an initial amount aside but will add $70. 55 to the savings every week. The amount B (in dollars) saved using this plan is given by the function =B70. 55N.
Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N. Simplify your answer as much as possible
Answers
Answer:
T=50+86.49N
Step-by-step explanation:
you just have to combine A and B.
Total (T)=A(50+30.65N)+B(55.85N) thank just open the prentices and add 30.65N and 55.85N=86.49N. so total is initial savings+ weekly savings by both.
complete the steps to solve the equation -16x - 13= -157
Answers
Answer: no
Step-by-step explanation:
The measure of ∠N is (15x +47) °. If x=8, find the measure of∠N, then classify the angle
Answers
So 167 degrees it’s an obtuse angle
Please help.
Subject is geometry
Answers
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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simplify the square root of 2 divided by 125
Answers
Answer:
20√2
Step-by-step explanation:
20√2 = 28.284...
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
Answers
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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Can someone help me with this
Answers
Answer: f(x)=90
Step-by-step explanation:
f(x)=-(-9)^2-(9) substitute -9 for x
f(x)=9^2+9 simplify negatives
f(x)=81+9 simplify exponents
f(x)=90 add
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."
Answers
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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Standard postage relates to letters between a weight of 0 to 5 . The letters have a probability distribution for the weight f(x)=(3/125) x2 for 0 < x < 5
What is the probability of getting a score less than 4.3?
Answers
The probability of getting a score less than 4.3 for standard postage is 0.77
In this scenario, f(x) = (3/125) x^2 is a probability density function for the weight of a letter, x, for standard postage where x ∈ (0,5). Thus, the integral of the probability density function between two bounds would give the probability of the event occurring. The probability of getting a score less than 4.3 can be calculated as follows:Pr(X < 4.3) = ∫_0^4.3(3/125) x^2 dx= [(3/125) * (1/3) * 4.3^3] - [(3/125) * (1/3) * 0^3]= 0.77
Thus, the probability of getting a score less than 4.3 for standard postage is 0.77.
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Raymond works for a pharmaceutical company that is testing the effectiveness of a new medication
Answers
The exponential function that gives the amount of medication y in the body after x hours is:
[tex]y = 400(\frac{2}{3} )^x[/tex]
What is an exponential function?
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth. When the input variable x appears as an exponent in the formula f(x) = aˣ, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x. A constant serves as the exponent in an exponential function, but not the other way around (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
The complete question is given below.
The initial value of the medication = 400 mg
This is the value of a.
a = 400
b is the growth or decay factor in the exponential function formula.
In this question, it is the decay factor.
b = 1-r
where r is the decay rate = 1/3
b = 1-1/3 = 2/3
The exponential function is given by the formula:
y = abˣ
[tex]y = 400(\frac{2}{3} )^x[/tex]
Therefore the exponential function that gives the amount of medication y in the body after x hours is:
[tex]y = 400(\frac{2}{3} )^x[/tex]
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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.
Answers
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.
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
Answers
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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9 ( 7 ℎ − 4 k ) + 10 k − 5 ( 6 k − 7 ℎ )
Answers
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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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.
Answers
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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In the equation below, when the value of d is decreased by 2, how does g change? 4g = 8d + 20
Answers
Answer:
Therefore, when the value of d is decreased by 2, the value of g changes by -3. In other words, g decreases by 3.
Step-by-step explanation:
We can start by solving the given equation for g:
4g = 8d + 20
g = (8d + 20) / 4
g = 2d + 5
So, we know that g is a function of d and is equal to 2d + 5.
Now, if we decrease the value of d by 2, we get:
d' = d - 2
Substituting this value of d' in the equation for g, we get:
g' = 2d' + 5
g' = 2(d - 2) + 5
g' = 2d - 4 + 5
g' = 2d + 1
Therefore, when the value of d is decreased by 2, the value of g changes by -3. In other words, g decreases by 3.
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
Answers
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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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.)
Answers
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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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?
Answers
men × hours × length of wall = constant
We know that six men can build a 150 m wall in ten hours. Therefore, we can write:
6 × 10 × 150 = constant
Simplifying this equation, we get:
constant = 9000
Now, we can use this constant to find the number of men needed to build a 200 m wall in four hours. We can write:
men × 4 × 200 = 9000
Simplifying this equation, we get:
men = 9000 / (4 × 200) = 11.25
Since we can't have a fraction of a person, we need to round up to the nearest whole number. Therefore, we need 12 men to build a 200 m wall in four hours.
Three friends are eating enormous freeze pops on a hot summer day. Benjamin has a strawberry freeze pop that has a density of 0.8 pounds per cubic inch. His freeze pop is shaped like a square pyramid with a 1.5 inch side and a height of 2 inches. Kendra has a giant grape freeze pop which has a density of 0.2 pounds per cubic inch. The freeze pop is a cylinder which has a radius of 1 inch and a height of 4 inches. Luke has a giant cherry freeze pop, which has a density of 0.05 pounds per cubic inch and is also shaped like a cylinder which has a radius of 1.5 inches and a height of 3 inches. Answer the following questions.
1. Who is eating the largest mass of freeze pop? Round to the nearest tenth of a pound.
2. How many more pounds of freeze pop does Kendra have compared to Luke? Round your answer to the nearest tenth.
3. If all three freeze pops were the same size, which flavor would you prefer, based on the densities? Explain why.
Answers
Hence, in answering the stated question, we may say that As a result, cylinder Kendra has approximately 1.45 pounds more freeze pop than Luke.
what is cylinder?The cylinder, which is frequently a three-dimensional solid, is one of the most basic curved geometric forms. In elementary geometry, it is called a prism with a circle as its basis. A cylinder is also defined as an infinitely curved surface in several modern domains of geometry and topology. A "cylinder" is a three-dimensional object with curved sides and round tops and bottoms. A cylinder is a three-dimensional solid figure with two identical circle bases linked by a curving surface at the cylinder's height, which is determined by the distance between the bases from the centre. Cold beverage cans and toilet paper wicks are both examples of cylinders.
1.5 cubic inches = 1/3 * 2.25 * 2
1.5 * 0.8 = 1.2 lbs.
* radius2 * height = * 12 * 4 = 4 cubic in.
Kendra's freeze pop has the following mass:
4 * 0.2 = 0.8 lbs.
The volume for Luke's freeze pop is:
*1.52 x 3 = 6.75 cubic inches
And the majority is:
6.75 * 0.05 = 0.3375 lbs
1.2 pound Benjamin
Kendra weighs 0.8 2.51 pounds.
Luke: 0.3375 1.06 lbs.
As a result, Kendra is consuming the most freeze pop, weighing around 2.51 pounds.
We may deduct Luke's mass from Kendra's to figure out how many more pounds of freeze pop Kendra has than Luke:
2.51 - 1.06 1.45 lbs.
As a result, Kendra has approximately 1.45 pounds more freeze pop than Luke.
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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 -
Answers
Answer:
x=(2+sqrt(-16))/2=1+2i=1.0000+2.0000i
Step-by-step explanation:
Step by Step Solution
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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.