Answer:
270 donuts
Step-by-step explanation:
We need to find the number of donuts they make per hour. To find that, take the known number of donuts divided by the known number of hours.
150/10=15, so 15 donuts per hour.
Now, we multiply 18x15 and find they will have made 270 donuts.
It took Jada's aunt 34 hour to put a puzzle together. It took Jada 213 times as long as her aunt to put the puzzle together.
How long did it take Jada to put the puzzle together?
Enter your answer as a mixed number in simplest form by filling in the boxes.
$$
hours
[tex]1\frac{3}{4}[/tex] hours Jada took to put the puzzle together.
What is Fraction?A fraction represents a part of a whole.
Given that Jada's aunt took 3/4 hour to put a puzzle together.
Jada took [tex]2\frac{1}{3}[/tex] times as long as her aunt to put the puzzle together.
Convert the mixed fraction [tex]2\frac{1}{3}[/tex] to improper fraction
[tex]2\frac{1}{3}[/tex] =7/3
As there is given Jada took [tex]2\frac{1}{3}[/tex] times as long as her aunt to put the puzzle together we have to multiply 7/3 with 3/4
7/3×3/4
7/4
This can be written as mixed fraction
[tex]1\frac{3}{4}[/tex]
Hence, [tex]1\frac{3}{4}[/tex] hours Jada took to put the puzzle together.
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What is ratio short answer?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other
What is an equivalent ratios?
A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.
Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.
Given ratios are 2:1 and 3:1
we can write it as 2/1 and 3/1.
The lcm of 2 and 3 is 6.
Multiply denominator of both ratio with 6, we get
2/6 and 3/6 And we can see both the ratios are not equal.
Hence, there are not equivalent ratios.
4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2
11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)
3:1 and 9:3 are equivalent ratios ------> is true
because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3
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Tv is a medsegment of UWX
if WX=3s+77 and TV=2s+42, what is TV
For the figure shown in the image having TV as the midsegment, the length of TV is 40
What are similar triangles?When the comparable triangles' angles are congruent and their respective sides are proportionate, this is referred to as similar triangles in geometry.
In light of this, if the triangle's corresponding angles are congruent, then the side should be proportionate.
For the given figure, the proportionate sides are
UV and TV, UW and WX
Calculating for s
UV / TV = UW / WX
1 / (-2s + 42) = 2 / (3s + 77)
cross multiplying
3s + 77= 2(-2s + 42)
3s + 77= -4s + 84
collecting like terms
3s + 4s = 84 - 77
7s = 7
s = 1
solving for TV
= -2s + 42
= -2 * 1 + 42
= 40
the value of TV is 40
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the banquet punch is water by volume, apple juice, and the rest is grape juice. if milliliters of grape juice were used to make the punch, then how many milliliters of punch is there total?
The total milliliters of punch is 2x + y.
Total Milliliters Of PunchTo find the total amount of milliliters of punch, we need to add together the amount of water, apple juice, and grape juice used to make it. Since the punch is made up of "water by volume" and "the rest is grape juice," we know that the ratio of water to grape juice is 1 : 1. If we know the amount of grape juice used in milliliters, we can use that to find the amount of water and apple juice used, and then add all three amounts together to find the total amount of milliliters of punch.
Let's say that "x" milliliters of grape juice were used to make the punch. Since the ratio of water to grape juice is 1 : 1, we know that the same amount of water, "x" milliliters, were used. To find the total amount of milliliters of water and grape juice, we add x + x = 2x milliliters.
However, the prompt also mention "apple juice" is also included in the punch, so we need to add the amount of apple juice used in the punch to find the total milliliters of punch. If the amount of apple juice used is "y" milliliters, then the total milliliters of punch is 2x + y.
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The brick will be gold-plated (dipped in gold). Which measure would be used to find the amount of gold needed
To find the amount of gold needed for gold plating a brick, total surface area of the brick would be needed to be calculated, assuming the brick is cuboid or cube shaped.
While dealing with cubes and cuboids, we should know how to find the surface areas and volumes of the two objects. When we either fill these or talk about all the three dimensions of an object, we talk about the volume of the said object. And, when we paint or talk about just the exterior or interior walls of an object, we talk about the surface area of the said object.
When all the six faces of a cube or a cuboid are used, we calculate surface area for all the faces and this is called the total surface area.
Let us look at the different formulas to calculate volume and total surface area of a cube and a cuboid,
Total surface area of a cube (side [tex]a[/tex]) = 6 × (area of each face)
= 6 × [tex]a^{2}[/tex]
Volume of a cube (side [tex]a[/tex]) = [tex]a^{3}[/tex]
Total surface area of a cuboid (length [tex]l[/tex], breadth [tex]b[/tex], height [tex]h[/tex]) = [tex]2 ( lb + lh + bh)\\[/tex]
Volume of a cuboid (length [tex]l[/tex], breadth [tex]b[/tex], height [tex]h[/tex]) = [tex]lbh[/tex]
For plating the brick with anything, gold for instance, total surface area of the brick would be calculated to determine the amount of gold needed as all the walls or faces of the brick would be plated but not the interior volume.
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What is a great way to describe what philosophy means?-( not literally off the web)
I have a question what it means to me and I need help.
Answer:
I think of philosophy as how we view the world and understand it. It is like thinking out of box, questioning our existence, and morals. What is good? What is bad?
Hope this helps :)
Honestly, philosophy is hard to understand
Have a great day
The scatter plot shows the maximum noise level when different numbers of people are in a stadium. the linear model is given by the equation
y = 1.5x +22.7, where y represents maximum noise level and x represents the number of people, in thousands, in the stadium.
the slope of the linear model is 1.5. what does this mean in terms of the maximum noise level and the number of people?
The starting value of the noisy at the y-axis is represented by the equation's 22.7 y-intercept.
How is slope determined?To calculate the % slope, multiply the percent elevation difference between two locations by the distance between them. The change in grade between two places is referred to as a "rise." The distance between the sites is known as the run. Therefore, the formula for percent slope is (increase/jog) x 100.
Given that such scatter plot depicts the stadium's loudest conditions depending on the amount of spectators present The linear model is provided more by equation y=1.5x+22.7, where x is the number of spectators in the stadium, expressed in thousands, and y is the maximum noise level. y=1.5x+22.7
y=1.5x+22.7 is the expression for the highest noise. The gradient in the following equation is 1.5. The starting value of such noise somewhere at y-axis is represented by the y-intercept of something like the equation, which is 22.7.
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mai lee bought a computer for her home office and depreciated it over 5 years using the straight line method. if its initial value was $2350, what is its value 3 years later
In this scenario, if a computer was bought for $2350 and is being depreciated over 5 years, the annual depreciation is $470, and its value 3 years later would be $1410.
The straight-line method of depreciation is a method of calculating the decline in value of an asset over time. Using this method, an asset's value is spread evenly over its useful life.
In this scenario, if the computer was bought for $2350 and is being depreciated over 5 years, the annual depreciation is ($2350 / 5) = $470.
Three years later, the computer's value would be $2350 - ($470 x 3) = $1410. This is because the value of the computer is decreasing by $470 per year, and after three years, the total amount of depreciation would be $470 x 3 = $1410.
It's important to note that the straight-line method of depreciation is a simple method and it does not reflect the real-world scenario in which assets may have a higher value of depreciation in the initial years and less in the later years. But it's easy to calculate and use.
In conclusion, if an asset is depreciated using the straight-line method, its value decreases evenly over its useful life. It's important for businesses to understand the various methods of depreciation and choose the one that best suits their needs.
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find the value of x
(need answered fast)
Answer:
The measure of the third angle of the triangle is 45°.
Step-by-step explanation:
What is a triangle?
A triangle is a polygon with 3 sides.
Given that, the measures of the two angles of a triangle are 50° and 85°.
Let the measure of the third angle be x.
Since the sum of the interior of a triangle is 180°, it follows,
50°+85°+x=180°
135° +x = 180°
x = 180° - 135°
x = 45°
Hence, the measure of the third angle of the triangle is 45°.
Find a formula for the function represented by the integral.\int_{5}^{x}u3 du.Find the formula for the function represented by the integral.\int_{2}^{x^2}(t + 8) dt
As per the concept of integration, the value of the function [tex].\int_{5}^{x}u^{3} du[/tex] is [(x⁴/4) - (625/4)]
The term integration in math is defined as the method of adding or summing up the parts to find the whole and the reverse process of differentiation that is we reduce the functions into parts.
Here we have given that [tex].\int_{5}^{x}u^{3} du[/tex]
And now we have to perform the integration operation on it and then we have to find the simplified version of the function.
As we all know the formula of the integration concept, that is written as,
=> [tex]\int {x^{n}} \, dx =\frac{x^{n+1}}{n+1}[/tex]
Based on these details, we have simplify the expression as,
[tex]= > \mathrm{[\frac{u^{4}}{4}]}_{5}^{x}[/tex]
Now, we have to apply the value of u with the given limit values, then we get the expression like the following,
=> [(x⁴/4) - (5⁴/4)]
When we simplify this one then we get,
=> [(x⁴/4) - (625/4)]
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a committe of e teachers is to be selectewd from a group of 10 t3eachers howo many differnt commitess
The combination is the way to find a number of different committees. The different number of committees is 120.
What is the combination?
A combination is a method of selecting items from a collection where the order of selection is irrelevant.
The combination is defined as "an arrangement of objects in which the order in which the objects are chosen is unimportant." The combination means "selection of things," where the order is irrelevant.
Given that the total number of teachers is 10.
The number of members of the committee is 3.
The formula of combination is nCr = n!/[r!(n-r)!]
Where n is the total number of objects and r is the number of objects those are selected.
In the question, n=10, r=3
The different committees is ₁₀C₃
=10!/3!(10-3)!
=10!/3!7!
=120
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Which of the following equations has 2 as a root ?
A. 2x² - 7x + 6 = 0
B. x² - 4x + 5 = 0
C. x² + 3x - 12 = 0
D. 3x² - 6x - 2 = 0
A. (A)
B. (B)
C. (C)
D. (D)
The equation that has 2 as its root is 2x² - 7x + 6 = 0 (option A)
The roots of a quadratic equation is equal to its solution.
If x = 2 is the solution of an equation, then f(2) = 0.
Let's check for the given functions:
A. 2x² - 7x + 6 = 0
f(2) = 2(2)² - 7(2)+ 6
f(2) = 2(4) - 14 + 6 = 0
Hence, x = 2 is its root.
B. x² - 4x + 5 = 0
f(2) = 2² - 4(2) + 5
f(2) = 4 - 8 + 5 = 1
Since f(2) ≠ 0, hence 2 is not its root.
C. x² + 3x - 12 = 0
f(2) = 2² + 3(2) - 12
f(2) = 4 + 6 - 12 = -2
Since f(2) ≠ 0, hence 2 is not its root.
D. 3x² - 6x - 2 = 0
f(2) = 3(2)² - 6(2) - 2
f(2) = 12 - 12 - 2 = -2
Since f(2) ≠ 0, hence 2 is not its root.
Hence, the correct option is A. 2x² - 7x + 6 = 0
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She simulated 505050 classes of 303030 students where each student selected had a 0.140.140, point, 14 probability of being left-handed. Casey counted how many left-handed students were in each simulated class. Here are her results:
The empirical probability that there are more than 5 left-handed students in a class of 30 is 0.06.
Empirical probability is a sort of experimental probability that is based on historical data. Empirical probability is, then, an illustration of the likelihood of an occurrence occurring based on prior data.
The formula of the empirical probability is:
Experimental probability = number of times an event occurs / total number of outcomes.
In the problem, total number of classes = 50
From the graph, we can read that:
- number of classes with 6 left-handed students = 2
- number of classes with 7 left-handed students = 1
Hence, the empirical probability that there are more 5 left-handed students in a class of 30 is:
Empirical probability = 3/50 = 0.06
Your question is incomplete. Most likely it was:
Casey read a report that said the probability that a randomly selected America is left handed is 14%. she was curious how many left handed students to expect in a class of 30 seconds. she simulated 50 classes of 30 students where each student had a 0.14 probability of being left handed. Casey counted how many left handed students were in each simulated class. here are her results: use her results to estimate the probability that there are more than 5 left handed students in a class of 30 students. (The graph is attached)
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answer the gaps/questions attached
The Venn diagram that indicates the number of students that study a language and the probability of two student chosen study Spanish are as follows;
a) Please find attached the drawing of the completed Venn diagram created with MS Word
b) The probability that two student chosen at random study Spanish is 17/66
What is the probability of an event?The probability of the occurrence of an event is the likelihood that an event takes place from within a number of possible event.
The probability that two student
a) The number of students that study French and Spanish but not German = 18 - 13 = 5
The number of students that study only French = 0
The number of student that study only French and German = 25 - 13 - 5 = 7
Number of students that study only only German = 40 - 19 - 13 - 7 = 1
The number of students that study only Spanish = 100 - 19 - 13 - 5 - 1 - 7 - 41 = 14
Please find attached the completed Venn diagram created with MS Word
b) The number of students that study Spanish = 19 + 13 + 5 + 14 = 51
The probability that the first student chosen studies Spanish = 51/100
The probability that the second student chosen = 50/99
Therefore, the probability that the two student chosen at random, without replacement, study Spanish = (51/100) × (50/99) = 17/66
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tyrone went to the pet store to buy 5 goldfish for his fish tank. he spent less than $15 in all to buy the fish. let x represent how much each goldfish cost. which inequality describes the problem?
Each goldfish cost less than $3.
Now, According to the question:
As per the question information:
Tyrone went to the pet store to buy 5 goldfish for his fish tank.
He spent less than $15 in all to buy the fish.
Let x represent how much each goldfish cost.
which inequality describes the problem?
5x < 15 , 5x ≤ 15
To solve the inequality :
Based on the given condition :
Formulate:
x = 15 ÷ 5
Reduce the fraction :
x = 3
Hence, Each goldfish cost less than $3.
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The given question is incomplete, the complete is :
Tyrone went to the pet store to buy $5 goldfish for his fish tank. He spent less than$15 in all to buy the fish. Let x represent how much each goldfish cost. Which inequality describes the problem?
5x < 15 , 5x ≤ 15
Solve the inequality. Then, complete the sentence to describe the solution. Each goldfish cost less than $
De que numero es 41 el 18% menos
Para calcular el 18% menos de un número, se puede utilizar la fórmula: número original x (1 - porcentaje en decimal). En este caso, para calcular el 18% menos de 41, se puede utilizar la fórmula: 41 x (1 - 0.18) = 41 x 0.82 = 33.62. Entonces, el 18% menos de 41 es 33.62.
Espero que esto ayude :)
Answer:
El número es:
50
Step-by-step explanation:
Porcentaje significa "por cada cien"
18% = 18/100 = 0.18
El número buscado corresponde al 100%
Si es el 18% menos quiere decir que corresponde a:
100 - 18 = 82%
Entonces:
Por regla de tres:
41 es a 82%
A es a 100%
A = 41 * 100 / 82
A = 4100 / 82
A = 50
Comoprobación:
50 - (50*0.18) = 50 - 9 = 41
A student draws portraits for customers. When the price of a picture is $180, the demand is 8 portraits. When the price of a picture is $100, the market is 24 portraits. Which graph best models the demand as a function of the cost? (Please show the steps on the graph)
Answer:
Q = 216 - 0.5P
Step-by-step explanation:
One approach to modeling the demand as a function of the cost is to use a linear demand equation of the form:
Q = a - bP
where Q is the quantity demanded, P is the price, and a and b are constants. To find these constants, we can use the two points given:
When P = $180, Q = 8 portraits, so 8 = a - b * 180
When P = $100, Q = 24 portraits, so 24 = a - b * 100
Solving the system of equations gives us:
a = 216
b = 0.5
So, the demand equation is:
Q = 216 - 0.5P
This represents the demand for portraits as a function of the price, where the demand decreases linearly as the price increases.
In the stock market, changes in value used to be indicated by fractions, which represented portions of $1. A stock had a value of $11.50.
Write and then evaluate an addition expression to find how much the stock is worth after an increase of 1/4.
Enter the correct numbers in the boxes.
The value of the stock after the increase of 1/4(fraction) using the addition expression is equal to $11.75.
In Mathematics, a fraction is defined as the portion/part of the whole thing. A fraction consists of two parts, numerator and denominator. The number on the top is known as the numerator, and the number on the bottom is known as the denominator.
Given,
The initial value of stock = $11.50
Increase in stock ( in fraction) = 1/4
We know that earlier in the stock market the changes in values were indicated by fractions which represent portions of $1
Therefore,
Increase in value of stock = 1/4 * $1
= $0.25
Hence,
Value of stock after increase = $11.50 + $0.25
= $11.75
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0.07 divided by 32.34
Answer:
0.0021645
Step-by-step explanation:
What is a formula answer?
A formula answer is a mathematical expression or equation that provides a specific result or solution to a problem.
A formula is a mathematical equation or expression, or a set of them, which is used to calculate or predict a specific result or solution. They often involve a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
Formulas can be used in a wide range of fields such as science, engineering, finance, and statistics to make calculations and predictions based on known information. They can also be used to simplify complex calculations or to express complex relationships in a clear and concise way. They can be simple or complex, and are often represented using mathematical notation such as equations or graphs.
One example of a formula is the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The formula for the Pythagorean theorem is: c^2 = a^2 + b^2 where c is the length of the hypotenuse and a and b are the lengths of the other two sides. This formula can be used to calculate the length of the hypotenuse in a right-angled triangle, given the lengths of the other two sides.
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pls help super simple!!!
The possible values of the given expression are defined by the inequality below.
1/5 < b/2a < 1/2
How to get the possible values of the expression?Here we want to get the possible values of the expression below:
b/2a
Where we have the restrictions:
4 < a < 5
2 < b < 4
The minimum value of the expression is when a takes it maximum value, and b takes its minimum value, it gives:
2/(2*5) = 2/10 = 1/5
The maximum value of the expression is what we get when a takes its minimum value, and b takes its maximum value:
4/(2*4) = 4/8 = 1/2
These are the bound of the expression, we can write:
1/5 < b/2a < 1/2
These are all the possible values of the expression.
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The base of the triangle, b,is three inches greater than the height. What is the area of the triangle?
Answer:
Step-by-step explanation:
Let the height be h units
then the base is h+3 units
Area = (1/2)(base)(height)
= (1/2)(h)(h+3) or (1/2)(h^2 + 3h)
A scale drawing of a rectangular park had a scale of 1 cm = 90m. What is the actual perimeter of the park in meters?
The actual perimeter is 2934. The perimeter of a rectangle is calculated as P = length + breadth + length + breadth. Alternatively, P = 2(length + breadth).
What is the actual perimeter of the park in meters?Perimeter=2(l + b)
=2[6.3cm +10cm) = 2x16.3 cm 32.6cm
Scale 1 cm = Actual 90m.
32.6cm 32.6x90m
= 2934 m
We sum the lengths of all four sides to determine the perimeter of a rectangle. Because opposing sides of a rectangle are always equal, we must obtain the length and breadth measurements to calculate the perimeter of a rectangle. The perimeter of a rectangle is equal to double the sum of its length and breadth.
To calculate the perimeter, or distance around the rectangle, sum all four side lengths. This may be done quickly by adding the length and breadth and then multiplying the total by two because each side length has two lengths. The perimeter formula is perimeter = (length + width)2.
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A company sells widgets. The amount of profit, y, made by the company, is related to
the selling price of each widget, x, by the given equation. Using this equation, find out
what price the widgets should be sold for, to the nearest cent, for the company to
make the maximum profit.
y=
-3x² +239x-2268
The price of the widgets for which it should be sold to make the maximum profit is $25.4 .
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We know that the quadratic equation ax² + bx + c ,
If a < 0; then the maximum value of the quadratic equation will be at x = -b/2a .
Given;
a company is selling a widget;
the selling price of each widget is = x
the profit made by the company = y
the equation of profit is given as y = −3x² + 152x − 1150 ,
here a = -3 , b = 152 and c = -1150
In the given quadratic equation we can see that;
a < 0 , so , the maximum will be at;
x = -b/2a
x = -152/2(-3)
x = 152/6
x = 25.333
x ≈ 25.4
Hence, the price of the widget will be $25.4
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what is the gcf of 81 and 72
Answer: 9
Step-by-step explanation: It's 9 because both can be divided by 9, as the largest time without going over. As you can see, 81 divided by 9 is 9, and 72 divided by 9 is 8. 8 and 9 are the closest they can be without going over 81 and 72, so it's 9. I hope this helps!
The GCF of the numbers 81 and 72 is 3², which equals 9.
To find the greatest common factor (GCF) of 81 and 72, we can use several methods.
One common approach is to factorize both numbers and identify the common factors.
The prime factorization of 81 is 3⁴, and the prime factorization of 72 is 2³×3².
To find the GCF, we look for the highest power of common prime factors in both numbers.
The highest power of the common prime factor (3) is 3², since it appears as a factor in both numbers.
Therefore, the GCF of 81 and 72 is 3², which equals 9.
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suppose that someone sampled 100 palm trees of the same species, all planted at the same time. they recorded the height for each tree. what shape would you expect the histogram of this data to be?
I expect the histogram be symmetric because, the trees are same species and all are planted at the same time.
The given information is:
Suppose that someone sampled 100 palm trees of the same species, all planted at the same time.
They recorded the height for each tree.
To find the what shape expect the histogram of this data to be?
Now, According to the question:
I expect the histogram be symmetric because, the trees are same species and all are planted at the same time.
There is no tree treated differently during planting or affected by an isolated factor.
Therefore, we should expect the differences in the height of the trees has a normal distribution.
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6x-2y=26 -y+3=x Solve the system by substitution
Step-by-step explanation:
6x-2y = 26 ---(1)
x+y = 3 -------(2)
so, (y = 3-x)
put in equation 1st.,
6x-2(3-x) = 26
6x-6+2x = 26
8x = 32
(x = 4)
so, put x value in equation 2nd,
4+y = 3
(y = -1 ) Answer
Answer:
x = 4
y = -1
Step-by-step explanation:
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Given:
6x-2y=26
-y+3=x
Flip the equation around:
x = 3 - y
6(3-y) - 2y = 26 << Distribute property
18 -6y -2y = 26 << Add liked term
18 -8y = 26
-8y/-8 = 8/-8 << Divide both sides by -8
y = -1
Now, substitute y into the equation also known as -1.
6x - 2(-1) = 26
6x + 2 = 26 << Subtract 2 from 2 and 26 from 2
6x = 24
6x/6 = 24/6 << Divide both sides by 6.
x = 4
Hence, x = 4 and y = -1.
RevyBreeze
Help quickly please! (Worth 20 points) The more hours Randall works, the more wages he earns. Randall's wage is the ___________ variable. The hours he works is the __________ variable. 1. independent; dependent, 2. dependent; independent
Answer:
Randall's wage is the dependent variable. The hours he works is the independent variable.
Step-by-step explanation:
Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation takes about 5 s. The maximum rate of air flow into the lungs is about 0.3 L/s. This explains, in part, why the function f(t) = (3/10)(sin(2πt/5)) has often been used to model the rate of air flow into the lungs. Use this model to find the volume of inhaled air in the lungs at time t.
So, (3/10) ∫(0 to t) sin(2πt/5) dt would find the volume of inhaled air in the lungs at time t.
The function f(t) = (3/10)(sin(2πt/5)) is often used to model the rate of air flow into the lungs because it is cyclic, with a period of 5 seconds, and has a maximum value of 0.3 L/s. This function represents the rate of air flow into the lungs at any given time t.
To find the volume of inhaled air in the lungs at time t, we can integrate the function f(t) with respect to time. The volume of air inhaled at time t is the definite integral of f(t) from the start of inhalation (t = 0) to time t.
∫(0 to t) f(t) dt = (3/10) ∫(0 to t) sin(2πt/5) dt
The definite integral can be solved with proper limits, but the result is not in a closed form that can be expressed in terms of elementary functions.
In order to get the volume of inhaled air in the lungs at time t, we need to know the specific values of t and solve the definite integral with proper limits.
It's worth noting that this model is a simplified one and many other factors like breathing rate, lung capacity, and lung compliance could affect the actual volume of inhaled air in the lungs.
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Amir operates a large lobster boat. The operating cost for the boat is $2.250 each day. At the end of each day, he sells all his freshly caught lobster to either the local restaurant or the local grocery store with the following conditions: • The price per pound that the restaurant is willing to pay follows a triangular distribution with minimum value $1.50, maximum value $5.50, and likeliest value $3.50. • The price per pound that the grocery store is willing to pay is decreasing with more lobsters: $3.85 - 50.0005 * y, where y is the total lobster amount sold in pounds. • The amount of lobster that Amir catches in a single day follows a normal distribution with mean 1,500 pounds and standard deviation sqrt(12,500) pounds. • Amir decides to sell a fixed percentage of lobster to the local restaurant and the rest to local grocery stores. Using either math or simulation, can you help Amir determine what percentage he should choose in order to maximize his expected profit in the long run?
To optimize his long-term predicted profit percentage, he should select 20.567%.
What are an example and a percentage?Both decimal and fractional forms of the expression are acceptable.
Given, The boat's daily running expense is $2,250.
$1.50 is the minimal amount.
a maximum of $5.50
Most likely value is $3.50. Now, each day's conclusion.
More lobsters mean a lower price per pound which the grocery shop will accept ($3.85 - $0.0005). × y,
Amir's daily haul of lobster has a normally distributed with a mean of 1,500 pounds and a standard deviation of 12,500 pounds.
He should therefore select 20.567% to increase his anticipated profit in the long run.
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