To find the consecutive even positive integers, we set up an equation based on the given information and solve for the variables.
Explanation:Let's assume the first even positive integer is x. Therefore, the next consecutive even positive integer will be x + 2. According to the problem, the product of these two integers is 782 more than their sum. We can set up the equation as x(x + 2) = x + x + 2 + 782.
Simplifying the equation, we get x^2 + 2x = 2x + 784.
By solving this quadratic equation, we find that the value of x is 26. Therefore, the consecutive even positive integers are 26 and 28.
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A coffee company has found that the marginal cost, in dollars per pound, of the coffee it roasts is represented by the function below, where x is the number of pounds of coffee roasted. Find the total cost of roasting 110 lb of coffee, disregarding any fixed costs.
C'(x)=- 0.018x+ 4.75, for x less than or equal to 200
The total cost of roasting 110 lb of coffee is $765.
How to solve Cost Function?Based on the given function, the marginal cost of roasting x pounds of coffee is:
C'(x) = -0.018x + 4.75 for x ≤ 200.
To find the total cost of roasting 110 lb of coffee, we need to integrate the marginal cost function to get the total cost function C(x), and then evaluate C(110).
However, since we are disregarding any fixed costs, we can assume that the total cost function is simply the integral of the marginal cost function.
Integrating C'(x) = -0.018x + 4.75 with respect to x, we get:
C(x) = -0.009x² + 4.75x + C
where C is the constant of integration. Since we are disregarding any fixed costs, we can assume that C = 0.
Therefore, the total cost of roasting 110 lb of coffee is:
C(110) = -0.009(110)² + 4.75(110) = 765
The total cost of roasting 110 lb of coffee is $765.
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Final answer:
To find the total cost of roasting 110 lb of coffee, integrate the marginal cost function C'(x) = -0.018x + 4.75 over the range of x values. Substitute 110 for x in the total cost function to find the total cost.
Explanation:
To find the total cost of roasting 110 lb of coffee, we need to integrate the marginal cost function over the desired range of x values. The marginal cost function is given by C'(x) = -0.018x + 4.75. Integrating this function will give us the total cost function C(x).
Integrating C'(x) gives C(x) = -0.009x^2 + 4.75x + C, where C is the constant of integration. Since we are disregarding any fixed costs, we can ignore the constant term C.
Now we can substitute 110 for x in the total cost function to find the total cost of roasting 110 lb of coffee: C(110) = -0.009(110)^2 + 4.75(110) = -108.9 + 522.5 = $413.6.
julie spends$5.62 at the store. michael apends 5 times as much as julie. jeremy spends $6.72 more than michal. how much does each person spend.
please help.
Christian has $6 in his wallet and wants to spend it on apples. how many apples can Christian buy
Jackie deposited $315 into a bank account that earned 1.5% simple interest each year.
If no money was deposited into or withdrawn from the account, how much money was in the account after 3 years?
Round your answer to the nearest cent.
need in six minutes or less
Harvey has a fair eight-sided die that has a different number from 1 to 8 on each side. If he rolls the die twice, what is the probability that the second number rolled is greater than or equal to the first number? Express answer as a common fraction.
The probability that the second number rolled is greater than or equal to the first number when rolling a fair eight-sided die twice is 1/16.
Explanation:To find the probability that the second number rolled is greater than or equal to the first number when rolling a fair eight-sided die twice, we need to determine the favorable outcomes and the total number of possible outcomes.
There are 8 possible outcomes for the first roll and 8 possible outcomes for the second roll. However, since the die is fair and has different numbers on each side, the second roll can only be greater than or equal to the first roll for 4 of the outcomes.
Therefore, the probability is 4 favorable outcomes out of 64 total outcomes, which simplifies to a probability of B
Wich symbols makes -3/4 -11/12 a true sentence
The mathematical symbol that makes the expression -3/4 -11/12 true is subtraction.
The student is likely asking which mathematical symbol (operation) would make the expression -3/4 -11/12 a true sentence. The symbols that could apply are addition (+), subtraction (-), multiplication (x), or division (). To determine which symbol makes the sentence true, one would typically compare the result of applying each operation to the numeric values given.
For example, to test addition:
-3/4 + (-11/12) = (-9/12) + (-11/12) = -20/12 = -5/3
To test subtraction:
-3/4 - (-11/12) = (-9/12) - (-11/12) = 2/12 = 1/6
Therefore, subtraction makes the original expression a true one, because subtracting a negative is the same as adding the positive equivalent, which would simplify to an expression that equals 1/6.
How do i find the cost per pound?
The 21st century version of Let’s Make a Deal has five doors instead of three. Two doors have cars behind them and the other three doors have mules. What percentage of doors have cars behind them?
Final answer:
There is a 40% chance that one of the five doors will have a car behind it as there are two doors with cars and five doors in total.
Explanation:
To find the percentage of doors that have cars behind them in the 21st century version of Let’s Make a Deal with five doors, we can use a simple ratio. Since two out of the five doors have cars behind them, we can set up the ratio as 2 cars to 5 total doors.
The calculation for the percentage would be: (Number of doors with cars / Total number of doors) × 100. Plugging in the numbers gives us:
(2 / 5) × 100 = 40%
Therefore, the percentage of doors with cars behind them is 40%.
The amount $0.3994 rounded to the nearest cent
Penny percent. Suppose you flip a coin 100 times, with 53 tosses landing heads up. What percentage of the tosses would be heads? What percentage would be tails?
Three people have a median age of 30 and a mean age of 36. The range of ages is 20 . How old is each person?
Find the inverse of the given function h(x)=log(x)
If 60% of a radioactive element remains radioactive after 400 million years, then what percent remains radioactive after 500 million years? What is the half-life of this element?
The half-life of the element is approximately 542.78 million years.
To find out what percent of the radioactive element remains after 500 million years, we can use the exponential decay formula for radioactive decay:
[tex]\[ N(t) = N_0 \times e^{-kt} \][/tex]
Where:
- [tex]\( N(t) \)[/tex] is the amount of radioactive material remaining at time \( t \)
- [tex]\( N_0 \)[/tex] is the initial amount of radioactive material
- k is the decay constant
- t is the time elapsed
Given that 60% of the radioactive element remains after 400 million years, we know that [tex]\( N(t) = 0.60N_0 \)[/tex] when [tex]\( t = 400 \)[/tex] million years. We also know that [tex]\( N_0 \)[/tex] represents the initial amount of radioactive material, which will cancel out when we're finding the ratio of remaining material, so we don't need its exact value.
Substituting these values into the exponential decay formula:
[tex]\[ 0.60N_0 = N_0 \times e^{-400k} \][/tex]
We can simplify this to find the decay constant k:
[tex]\[ 0.60 = e^{-400k} \][/tex]
Taking the natural logarithm (ln) of both sides to solve for k:
[tex]\[ \ln(0.60) = -400k \][/tex]
[tex]\[ k = \frac{\ln(0.60)}{-400} \][/tex]
Using this value of k, we can find out what percent of the radioactive element remains after 500 million years:
[tex]\[ N(500) = N_0 \times e^{-500k} \][/tex]
[tex]\[ N(500) = N_0 \times e^{-500 \times \frac{\ln(0.60)}{-400}} \][/tex]
Now, to find the half-life of the element, we know that the half-life [tex](\( T_{\frac{1}{2}} \))[/tex] is the time it takes for the amount of radioactive material to decrease by half. In other words, when [tex]\( N(t) = \frac{1}{2}N_0 \),[/tex] we have:
[tex]\[ \frac{1}{2}N_0 = N_0 \times e^{-kT_{\frac{1}{2}}} \][/tex]
[tex]\[ \frac{1}{2} = e^{-kT_{\frac{1}{2}}} \][/tex]
[tex]\[ \ln\left(\frac{1}{2}\right) = -kT_{\frac{1}{2}} \][/tex]
[tex]\[ T_{\frac{1}{2}} = \frac{\ln(2)}{k} \][/tex]
Now, we can calculate both the percentage remaining after 500 million years and the half-life of the element using the calculated value of k. Let's do that.
First, let's calculate the value of \( k \):
[tex]\[ k = \frac{\ln(0.60)}{-400} \][/tex]
[tex]\[ k ≈ \frac{-0.5108}{-400} \][/tex]
[tex]\[ k = 0.001277 \][/tex]
Now, let's use this value of k to find out what percent of the radioactive element remains after 500 million years:
[tex]\[ N(500) = N_0 \times e^{-500k} \][/tex]
[tex]\[ N(500) = N_0 \times e^{-500 \times 0.001277} \][/tex]
[tex]\[ N(500) ≈ N_0 \times e^{-0.6385} \][/tex]
Now, let's find out what percent this is of the original amount [tex](\( N_0 \))[/tex]:
[tex]\[ \frac{N(500)}{N_0} = e^{-0.6385} \][/tex]
[tex]\[ \frac{N(500)}{N_0} ≈ 0.5274 \][/tex]
So, approximately 52.74% of the radioactive element remains after 500 million years.
Now, let's calculate the half-life of the element:
[tex]\[ T_{\frac{1}{2}} = \frac{\ln(2)}{k} \][/tex]
[tex]\[ T_{\frac{1}{2}} = \frac{\ln(2)}{0.001277} \][/tex]
[tex]\[ T_{\frac{1}{2}} = \frac{0.6931}{0.001277} \][/tex]
[tex]\[ T_{\frac{1}{2}} = 542.78 \text{ million years} \][/tex]
So, the half-life of the element is approximately 542.78 million years.
Use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern. –5, –10, –20, –40, . . .
Answer:
Next two number would be –5, –10, –20,–40, –80, –160.
Step-by-step explanation:
Given : –5, –10, –20, –40, . . .
To find : Use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern.
Solution : We have given that
–5, –10, –20, –40, . . .
We can see from given pattern
-5 * 2 = - 10.
- 10 * 2 = - 20 .
-20 * 2 = - 40
So, each number is multiplied by 2 to get next number.
-40 * 2 = - 80 .
- 80 * 2 = - 160 .
Therefore, Next two number would be –5, –10, –20,–40, –80, –160.
Lindsay draws a right triangle and adds the measures of the right angle and one acute angle. Which is a possible sum of the two angles?
Answer:
[tex]90< \gamma< 180[/tex]
Step-by-step explanation:
An acute angle is an angle that measures more than 0º and less than 90º. And a right angle is an angle that measures exactly 90º. Thus:
Let:
[tex]\alpha = Right\hspace{3}angle=90^{\circ}\\\beta= Acute\hspace{3}angle\hspace{10}0^{\circ}<\beta<90^{\circ}\\\gamma= Sum\hspace{3} of\hspace{3} the\hspace{3} two\hspace{3} angles =\alpha +\beta[/tex]
So, in this sense, the sum of the two angles can´t be equal or greater than 180º, since [tex]\beta<90^{\circ}[/tex] , also it has to be at least greater than 90º since [tex]\beta>0^{\circ}[/tex]
Therefore the sum of the two angles is:
[tex]90^{\circ}< \gamma< 180^{\circ}[/tex]
In another words, the sum is greater than 90º and less than 180º
Explain how you can use the basic moves of algebra to transform the equation 5x-3y=12 into 0=12-5x+3y
jonathan goes to th store and purchases 3 pencils for 0 .28 each, and x number of erasers for 0.38each write an expression that shows how much jonathan spent
Keywords
linear equation, variables
Step 1
Define the variables
Let
x-----> number of erasers
y-----> total cost
we know that
[tex]y=3(0.28)+(0.38)x[/tex]
[tex]y=0.84+(0.38)x[/tex] ------> this is the linear equation that represent the situation
therefore
the answer is
[tex]y=0.84+(0.38)x[/tex]
Which of the following groups have terms that can be used interchangeably?
a. critical value, probability, proportion
b. percentage, probability, proportion
c. critical value, percentage, proportion
d. critical value, percentage, probability
Final answer:
The correct answer is option b. percentage, probability, and proportion, because these terms relate to ratios or fractions of a whole and can often be used interchangeably in various statistical contexts. So the correct option is b.
Explanation:
The question is asking which of the following groups contain terms that can be used interchangeably. The correct answer is b. percentage, probability, proportion. These terms can often be used interchangeably because a percentage is a way of expressing a proportion as a number out of 100, and probability is the measure of the likelihood that an event will occur, often expressed as a decimal or a proportion. None of the other options provided (a, c, and d) contain directly interchangeable terms.
Steps:
Understand that the terms percentage, probability, and proportion all relate to ratios or fractions of a whole.Recognize that critical value is a concept used in hypothesis testing and does not equate to any of the other terms mentioned.Choose the answer that includes terms that can be used in similar contexts to express a part of a whole or likelihood.50PTS!
Describe the vertical asymptotes and holes for the graph of y = x-5/x^2 -1
write an expression for the total cost of the three types of tickets and show your work: $8.75, $6.50, $6.50
To find the total cost of three types of tickets priced at $8.75, $6.50, and $6.50, add the prices together, resulting in a total cost of $21.75.
Explanation:To write an expression for the total cost of purchasing three types of tickets with prices $8.75, $6.50, and $6.50, you need to add these values together. Here is the step-by-step process of calculating the total cost:
Identify the cost of each type of ticket: Ticket 1 costs $8.75, and Tickets 2 and 3 each cost $6.50.Add the cost of the three tickets together: $8.75 + $6.50 + $6.50.Calculate the total cost: $8.75 + $6.50 + $6.50 = $21.75.The expression for the total cost of the three tickets is $21.75.
To find the total cost of the three types of tickets, you sum the individual costs to get a total of $21.75.
Explanation:To write an expression for the total cost of the three types of tickets, we sum up the cost of each ticket. The three types of tickets cost $8.75, $6.50, and $6.50 each. Therefore, the expression for the total cost is:
Total Cost = $8.75 + $6.50 + $6.50
To calculate the total cost, we add these prices together:
$8.75 + $6.50 = $15.25
$15.25 + $6.50 = $21.75
So, the total cost of the three tickets is $21.75.
A box contains 17 transistors, 3 of which are defective. If 3 are selected at random, find the probability that
a. All are defective.
b. None are defective.
Express the decimal 2.39 as a percent
The percent of the decimal 2.39 can be expressed as 239%.
What is the percent of the decimal 2.39?To express the decimal 2.39 as a percent, we need to multiply it by 100. This is because a percent is a fraction out of 100.
To do this, we can write 2.39 as 2.39/1 and multiply it by 100/1:
(2.39/1) * (100/1) = 239/1
Therefore, 2.39 as a percent is 239%.
To understand this concept further, let's break it down:
The number 2.39 represents 2 whole units and 0.39 of another unit. When we convert it to a percent, we are essentially comparing it to 100 units.
We can think of the decimal point as moving two places to the right when we multiply by 100. So, 2.39 becomes 239.
Finally, we add the percent symbol (%) to indicate that the value is a percentage.
Therefore, the decimal 2.39 can be expressed in percent as 239%.
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3÷3912.00 carry to the hundreth
a recipe for 1 batch of cookies uses 3/4 cup of sugar. How many cups of sugar are used 1 1/2 batches of these cookies?
The ratio will remain constant. Then the number of cups of sugar used in 1 and 1/2 batches of these cookies will be 1.125.
What are ratio and proportion?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two things are equal.
A recipe for 1 batch of cookies uses 3/4 cup of sugar.
Then the number of cups of sugar used in 1 and 1/2 batches of these cookies will be
We know that the ratio will remain constant. Then we have
1 and 1/2 can be written as 3/2.
Let x be the number of cups of sugar.
Then the ratio will be
[tex]\rm \dfrac{x}{3/2} = \dfrac{3/4}{1}\\\\x = \dfrac{3 \times 3}{2 \times 4}[/tex]
Then we have
x = 9/8
x = 1.125 cups of sugar
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A rectangular room is 4 meters longer than it is wide, and its perimeter is 28 meters. Find the dimension of the room.
Answer: The width of the room = 5 meters
The length of the room = 9 meters
Step-by-step explanation:
Let the w denotes the width of the room , then length of the room will be :-
[tex]\text{length}=4+w[/tex]
The formula of perimeter of rectangle :-
[tex]\text{Perimeter}=2(l+w)\\\\\Rightarrow\ 28=2(4+w+w)\\\\\Rightarrow\ 28=2(4+2w)\\\\\Rightarrow\ 28 =8+4w\\\\\Rightarrow\ 4w=20\\\\\Rightarrow\ w=5[/tex]
Hence, The width of the room = 5 meters
The length of the room = 5+4 = 9 meters
The width of the room is 5 meters, and the length is 9 meters.
Explanation:To find the dimensions of the rectangular room, let's assign variables. Let x be the width of the room. Since the length is 4 meters longer than the width, we can represent the length as x + 4.
Given that the perimeter is 28 meters, we can write an equation: 2(x + 4) + 2x = 28.
Simplifying the equation, we get 4x + 8 = 28. Subtracting 8 from both sides gives 4x = 20. Dividing both sides by 4, we find x = 5. The width of the room is 5 meters, and the length is 5 + 4 = 9 meters.
In a fraternity with 34 members , 18 take mathematics, 5 take both mathematics and physics and 8 take neither mathematics nor physics. How many take physics hit not mathematics?
a guy walks into a store and steals $100 from register, comes back and buys $70 worth of merchandise, pys for it with same $100 and gets $30 cash back. how much did store lose?
$185 with a 6% percent markup
write a 5 digit number that when rounded to the nearest thousand and hundred will have a result that is the same explain
Jonny is jogging along a track. He has already jogged 1 2/3 miles. He plans to jog a total of 3 1/4 miles. How many miles does he have left to jog?