To determine the optimal number of matted and unmatted pictures to maximize the company's profit, we can set up a linear programming problem.
Let's denote:
- x: the number of matted pictures
- y: the number of unmatted pictures
The objective is to maximize the profit, which can be expressed as:
Profit = 40x + 35y
We need to consider the following constraints:
1) The number of pictures completed each day cannot exceed 36:
x + y ≤ 36
2) The total man-hours of labor cannot exceed 80:
4x + 2y ≤ 80
3) The number of pictures cannot be negative:
x, y ≥ 0
Now we can solve this linear programming problem to find the optimal values for x and y.
First, let's graph the feasible region defined by the constraints:
```
x + y ≤ 36
4x + 2y ≤ 80
x, y ≥ 0
```
The feasible region is the area of the graph that satisfies all the constraints.
Next, we need to evaluate the objective function (Profit = 40x + 35y) at the vertices of the feasible region to find the maximum profit.
We can use different methods such as the corner-point method or the simplex method to determine the vertices and evaluate the profit at each vertex.
Thus, once we find the vertex that yields the maximum profit, we will have the optimal values for x and y.
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50 POINTS TO BEST ANSWER
A function is shown below where b is a real number.
f(x)=x²+bx+118
The minimum of the function is 37.
Create an equivalent equation of the function in the form f(x)=(x-h)²+k.
Type your numerical answers below for h and k. Use the hyphen (-) for the negative sign if
necessary.
h=
k=
I did some research and found that for quadratic equations in the form of [tex]y = ax^2 + bx + c[/tex], you can find the minimum value using the equation [tex]$\text{minimum} = c - \frac{b^2}{4a}[/tex] .
We can substitute our given values in the formula and get the following: [tex]$37 = 118 - \frac{b^2}{4}$[/tex] .
We can go ahead and solve it, and get the following:
[tex]-81 = -\frac{b^{2}}{4}[/tex]
[tex]324 = b^2[/tex]
[tex]\pm{18} = b[/tex]
Now we know that the equation is either [tex]$f(x)=x^2+18x+118$[/tex] or [tex]$f(x)=x^2-18x+118$[/tex] .
We will solve using both equations, but we will solve the one with a positive b-value first. Substituting [tex]f(x)[/tex] for [tex]$37$[/tex], the minimum or y-value of the vertex, we can now solve for the x-value of the vertex.
We have:
[tex]37 = x^2+18x+118[/tex]
[tex]0=x^2+18x+81[/tex]
[tex]0=(x+9)^2[/tex]
[tex]x+9=0\\x=-9[/tex]
Doing the same thing with the second equation, we get:
[tex]37 = x^2-18x+118[/tex]
[tex]0=x^2-18x+81[/tex]
[tex]0=(x-9)^2[/tex]
[tex]x-9=0\\x=9[/tex]
After all of this, we know our vertex's x-values are either [tex]9[/tex] or [tex]-9[/tex], and that our y-value is [tex]37\\[/tex].
We can conclude that our k-value (y-value of the vertex in vertex form) is [tex]37[/tex], and our h-value (x-value of the vertex in vertex form) is [tex]9[/tex] or [tex]-9[/tex].
Conclusion: [tex]h = -9, 9[/tex]
[tex]k=37[/tex]
A rocket is launched in the air. Its height in feet is given by h= -16t^2 + 56t where t represents the time in seconds after launch. What is the appropriate domain for this Solution?
The domain of the function (t) in h = - 16t² + 56t should be greater than
or equal to 43.5 seconds as the height of the rocket can not be negative.
Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given that;
A rocket is launched into the air. Its height in feet is given by
h = - 16t² + 72t.
Where t represents time in seconds and h represents the height in feet.
We know that height can not be negative.
h ≥ 0.
So, - 16t² + 56t ≥ 0.
- 16t² ≥ -56t.
16t² ≥ 56t.
16t ≥ 56.
t ≥ 56/16.
t ≥ 3.5 seconds.
Therefore, the domain of the function (t) in h = - 16t² + 56t should be greater than or equal to 3.5 seconds.
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For which equation would x = 3 be a solution?
8 - x = 11
x + 7 = 4
5 + x = 9
x - 2 = 1
Giving out 60 points and will mark brainliest
Answer:
Step-by-step explanation:
lets solve all the equations and check:
1 ) 8 - x = 11
-x = 11 - 8
x = -3 ------------- not this one
2 ) x + 7 = 4
x = 4 - 7
x = -3 -------------not this one
3 ) 5 + x = 9
x = 9 - 5
x = 4 ------------- not this one
4 ) x - 2 = 1
x = 1 + 2
x = 3 ----------- this is the correct option
hope this helps!
Add and simplify: 9sqrt(x)+3root(3)(x)+sqrt(9x)
Group of answer choices
12sqrt(x)+sqrt(9x)
18sqrt(x)+3root(3)(x)
12sqrt(x)+3root(3)(x)
15sqrt(x)
Answer:
C
Step-by-step explanation:
[tex]9\sqrt{x} + 3\sqrt{3x} + \sqrt{9x} \\= \sqrt{x} ( 9 + 3\sqrt{3}+3)\\ = 12\sqrt{x} + 3\sqrt{3x}[/tex]
5. A student project asked an SRS of 172 college freshman at a large university "Would you
report cheating if you witnessed it in class?" Only 19 students responded "yes".
Calculate the 97% confidence interval.
a. Point Estimate =
b. Margin of Error z
p(1-P)
n
c. Confidence Interval=
pue
The 97% confidence interval for the proportion of college freshmen who would report cheating if they witnessed it in class is (0.0728, 0.1482).
The point estimate is the proportion of students who responded "yes" out of the total sample.
In this case, the point estimate is 19/172, which is approximately 0.1105.
b. Margin of Error:
To calculate the margin of error, we need the standard deviation. Since we don't have the population standard deviation, we'll use the formula for the estimated standard deviation of a proportion:
Margin of Error (ME) = z√[(p(1 - p)) / n]
Where z is the z-score corresponding to the desired confidence level. For a 97% confidence level, the z-score is approximately 1.96, p is the point estimate of the proportion and n is the sample size.
Using the given values, we can calculate the margin of error:
ME = 1.96√[(0.1105(1 - 0.1105)) / 172]= 0.0377
c. Confidence Interval:
The confidence interval is calculated by subtracting and adding the margin of error from the point estimate.
Confidence Interval = Point Estimate ± Margin of Error
Confidence Interval = 0.1105 ± 0.0377
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The length of the longer leg of a right triangle is 20cm more than twice the length of the shorter leg. The length of the hypotenuse is 22cm more than twice the length of the shorter leg. Find the side lengths of the triangle.
the square root of 50
Answer:
The square root of 50 is approximately 7.07.
Answer:
7.07106781187...
Step-by-step explanation:
its an irrational number
If sing, which of the following are possible for the same value of a?
A. sec9 =
B. cose =
C. cose =
√5
3
D. sece=
√5
3
and tang =
and tang
8=-2 and 1
-7/5
3
and tang =
tang =
-7/5
25
Like
SUBMIT
The possible trigonometric ratios for the angle θ are given as follows:
A. [tex]\sec{\theta} = \frac{3}{\sqrt{5}}[/tex] and [tex]\tan{\theta} = \frac{2}{\sqrt{5}}[/tex]
B. [tex]\cos{\theta} = \pm \frac{\sqrt{5}}{3}[/tex] and [tex]\tan{\theta} = \frac{2}{\sqrt{5}}[/tex]
How to obtain the trigonometric ratios?The sine for the angle θ is given as follows:
sin(θ) = 2/3.
The identity relating the sine and the cosine is given as follows:
sin²(θ) + cos²(θ) = 1.
Hence the cosine of the angle is given as follows:
cos²(θ) = 1 - 4/9
cos²(θ) = 5/9
[tex]\cos{\theta} = \pm \frac{\sqrt{5}}{3}[/tex]
The tangent is given by the division of the sine by the cosine, hence it is calculated as follows:
[tex]\tan{\theta} = \frac{2}{\sqrt{5}}[/tex]
(if the cosine is negative, the tangent is then negative, as the sine is positive).
The secant is the division of one by the cosine, that is, it is the inverse fraction of the cosine, hence:
[tex]\sec{\theta} = \frac{3}{\sqrt{5}}[/tex]
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Can I have help please thank u
Answer:
A = 30 cm
B = 14 cm
C = 15 cm
D = 41 cm
Step-by-step explanation:
You can find A by multiplying 10 times 6 (because the other side of the square is ten and the side of A already has that 4 there it would be 6) which would be 60, then since it is a right triangle, you can divide that by two and get 30.
You can find B by multiplying 4 by 7 (because the other part of that side of the square is 3 so that part would be 7) which would be 28, then since it is a right triangle, you can divide that by two and get 14.
You can find C by multiplying 10 times 3 and getting 30, then since it is a right triangle, you can divide that by two and get 15.
You can find D by multiplying 10 by 10 (because it is a square) then you'll get 100 from that. Then you can subtract the rest of the triangles from it which would be 100 minus 30 minus 14 minus 15 and you would get 41 which would be triangle D.
Hope this helps!! Let me know if you need more explanation
Find the y-intercept and the slope of the line.
-8x -4y =5
Given statement solution is :- The slope (m) of the line is -2, and the y-intercept (b) is -5/4.
To find the y-intercept and slope of the line represented by the equation -8x - 4y = 5, we need to rearrange the equation into slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Let's begin by isolating the term with y:
-8x - 4y = 5
Subtract -8x from both sides:
-4y = 8x + 5
Next, divide both sides of the equation by -4 to solve for y:
y = (-8/4)x - (5/4)
Simplifying further:
y = -2x - 5/4
Now we can identify the slope and the y-intercept:
The slope (m) of the line is -2, and the y-intercept (b) is -5/4.
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If side a measures 30 feet and side b measures 40 feet, how many feet of flowers will be planted along side c, the hypotenuse of the triangle? Show your work.
Answer:
You dont have to tell me to show my work twice
Step-by-step explanation:
To find the length of side c (the hypotenuse), we will use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (a and b) is equal to the square of the hypotenuse (c).
In this case, a = 30 feet and b = 40 feet. Therefore:
c^2 = a^2 + b^2
c^2 = 30^2 + 40^2
c^2 = 900 + 1600
c^2 = 2500
c = √2500
c = 50 feet
So the length of side c (the hypotenuse) is 50 feet. To find out how many feet of flowers will be planted along side c, we need to know the perimeter of the triangle (the sum of the lengths of all three sides). The perimeter is:
Perimeter = a + b + c
Perimeter = 30 + 40 + 50
Perimeter = 120 feet
Therefore, 120 feet of flowers will be planted along side c.
Answer: Here, side a = 30ft.
side b = 40ft.
Hence according to, Pythagoras theorem,
h²=p²+b²
where, h= hypotenuse of the triangle
b= base of the triangle
p= perpendicular of the triangle
Step-by-step explanation:
hypotenuse c {according to question} - c=[tex]\sqrt{a^{2} + b^{2}[/tex]
therefore, c=[tex]\sqrt{30^{2} + 40^{2} }[/tex] = 50ft. will be the answer.
Hypotenuse means the longest side of the triangle or in other words the side opposite to the 90° angle of the triangle.
write an equation for the line that passes through (4, -5) and (3, -2)
Answer:
y = - 3x + 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, - 5 ) and (x₂, y₂ ) = (3, - 2 )
m = [tex]\frac{-2-(-5)}{3-4}[/tex] = [tex]\frac{-2+5}{-1}[/tex] = [tex]\frac{3}{-1}[/tex] = - 3 , then
y = - 3x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (3, - 2 )
- 2 = - 3(3) + c = - 9 + c ( add 9 to both sides )
7 = c
y = - 3x + 7 ← equation of line
100 Points! State the amplitude, period, and phase shift for each function. Then graph the function. Photo attached. Thank you!
hello
the answer to the question is:
y = a tan(bx – c) + d
a = 1, b = 1, c = π/2
the midline is y = d, so y = 0 and there's no vertical shift
the vertical stretch is 1, so label the y-axis so the inflection point of the curve is 1 above the midline, 1, and the other inflection point is 1 below the midline, −1
the period is:
T = π/b ----> T = π
the phase shift is:
PS = c/b ----> PS = π/2
and also, there's no amplitude for tangent and cotangent, there is only the vertical stretch that takes the place of an amplitude
Determine which of the given points are solutions to the given equation.
2x^2 + y = 4
I. (3, -14) II. (-3, 14) III. (-3, -14)
The points that are solutions to the equation [tex]2x^2 + y = 4[/tex] are:
I. (3, -14)
III. (-3, -14)
To determine which of the given points are solutions to the equation [tex]2x^2 + y = 4[/tex], we need to substitute the x and y values of each point into the equation and check if the equation holds true.
Let's evaluate each point one by one:
I. (3, -14)
Substituting x = 3 and y = -14 into the equation:
[tex]2(3)^2 + (-14) = 4[/tex]
18 - 14 = 4
4 = 4
Since both sides of the equation are equal, the point (3, -14) is a solution to the equation.
II. (-3, 14)
Substituting x = -3 and y = 14 into the equation:
[tex]2(-3)^2 + 14 = 4[/tex]
18 + 14 = 4
32 = 4
Since the equation is not satisfied (32 is not equal to 4), the point (-3, 14) is not a solution to the equation.
III. (-3, -14)
Substituting x = -3 and y = -14 into the equation:
[tex]2(-3)^2 + (-14) = 4[/tex]
18 - 14 = 4
4 = 4
Since both sides of the equation are equal, the point (-3, -14) is a solution to the equation.
In summary, the points that are solutions to the equation [tex]2x^2 + y = 4[/tex]are:
I. (3, -14)
III. (-3, -14)
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The first shelf on Hannah’s bookshelf hoods an equal number of fiction and nonfiction. If Hannah’s selects 5 books randomly, what is the probability that 3 of the books will be fiction and 2 will be nonfiction
Answer:
The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
Step-by-step explanation:
What is probability?
Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true.
To find which 2 books describe a pair of dependent events:
A pair of two dependent events are simply those in which the selection of the second item is contingent on the selection of the first item, causing the probability to change.
Because the sample size is lowered when the initial item is taken without replacement, choosing the exact same item reduces the chance.
Now, in regard to the question, this means that for two of the occurrences to be independent, they must be on the same shelf and of the same type of book, so that the second book cannot be selected until the first one is.
Option D, where both books are on the same shelf and are of the same type, is the only option that fulfills this requirement.
Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
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Roger sprinted 89 yards. Lara sprinted 270 feet.
Who sprinted the longer distance? How much
greater? Show your work.
Answer: Lara
Step-by-step explanation:
convert yards into feet
yards*3= feet
89 yards * 3 = 267 feet
Since 270 is greater than 267 Lara. Lara's distance is greater by 3 feet since 270-267 is 3
A manager notes that there is a .125 probability that any employee will arrive late for work. What is the probability that no more than one person in a six-person department will arrive late for work on any given day?
Answer:
21
Step-by-step explanation:
Need help solving this question
The proportion that correctly defines θ is BC/PC = DE/PE = θ.
option C.
What is the length of the arcs?The length of the arcs is calculated as follows;
Length of arc = (θ/360) x 2πr
where;
r is the radius of the circleθ is the central angle of the arcFor sector PCB, the length of the arc is given as;
(θ/360) x 2π(PC) = BC
(θ/360) x 2π = BC/PC
θ = BC/PC ------- (1)
Note: 2π radian = 360⁰
For sector PED, the length of the arc is given as;
(θ/360) x 2π(PE) = DE
(θ/360) x 2π = DE/PE
θ = DE/PE ------- (2)
Compare the two equations as follows;
BC/PC = DE/PE = θ
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I need help can someone help me
Answer:
x ≈ 12.7
Step-by-step explanation:
since the triangle is isosceles then the 2 legs are congruent, both 9
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
x² = 9² + 9² = 81 + 81 = 162 ( take square root of both sides )
x = [tex]\sqrt{162}[/tex] ≈ 12.7 ( to the nearest tenth )
Answer:
Solution is in the attached photo.
Step-by-step explanation:
This question tests on the concept of triangles, as this is an isosceles triangle, the other 2 unknown angles are the same, as well as the sine rule.
The Glen Oaks Village Co-op is represented by s shares. Sage owns r shares. Express the percent of shares he owns algebraically.
What is the slope-intercept form of this equation? Show all your work.
-8x + 2y = 14 HELP FAST!!!
Answer: y=4x+7
Step-by-step explanation:
-8x+2y=14
Convert to y=kx+b
2y=8x+14
y=4x+7
four times the quantity of 6 minus a number is 8
Answer:
The original number was 4.
Step-by-step explanation:
We can construct an equation to model the given situation, using a variable x to represent the original number:
"the quantity of 6 minus a number"
[tex](6 - x)[/tex]
"four times the quantity"
[tex]4(6 - x)[/tex]
"is 8"
[tex]4(6 - x) = 8[/tex]
We can solve for x in this equation.
[tex]4(6 - x) = 8[/tex]
↓ applying the distributive property ... [tex]A(B+C) = AB + AC[/tex]
[tex]24 - 4x = 8[/tex]
↓ adding 4x to both sides
[tex]24 = 8 + 4x[/tex]
↓ subtracting 8 from both sides
[tex]16 = 4x[/tex]
↓ dividing both sides by 4
[tex]4 = x[/tex]
[tex]\boxed{x = 4}[/tex]
So, the original number was 4.
34. The scores on a psychology exam were normally distributed with a mean of 57 and a standard deviation of 8. A failing grade on the exam was anything 2 or more standard deviations below the mean. What was the cutoff for a failing score? Approximately what percentage of the students failed?
The passing score cutoff is 39, and 22.22% of the students failed.
Using the generic formula =
Z = score - mean / standard deviation
According to the question, the results of a psychology test had a mean of 57 and a standard deviation of 9, and they were normally distributed.
Anything 2 or more standard deviations below the mean on the test was considered a failing grade,
hence z = 2/9 = 0.222.
Additionally, the falling cut-off score is determined by using the formula: Falling cut-off = mean - 2 x standard deviation,
or 57 - 2 x 9 = 39.
Hence the passing score cutoff is 39, and 22.22% of the students failed.
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A school district has eight elementary schools, four middle schools, and two high schools. The district’s IT manager wishes to survey teachers regarding the use of technology in the classroom. Which of the following designs would create appropriate strata?
All the teachers at the district’s junior high buildings are asked to complete a survey on the topic.
Two teachers are chosen from only one grade level at random to complete a survey on the topic.
Four teachers from each school in the district are chosen at random to complete a survey on the topic.
All the high school teachers in the district are asked to complete a survey on the topic.
The option that would create an appropriate strata is given as follows:
Four teachers from each school in the district are chosen at random to complete a survey on the topic.
How are samples classified?Samples may be classified as follows:
A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.An appropriate strata is created when stratified sampling is used that is, the population is divided into groups(each school in the district), and then an equal amount(four teachers from each school) is surveyed.
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mariah bought a package of 8 cupcakes. She and her friend ate 5 of the cupcakes.
What fraction of the cupcakes did they eat and what fraction of the cupcakes were left?
Answer:
The fraction of cupcakes they ate is:
5 / 8
The fraction of cupcakes left is:
3 / 8
I need the answer for this question
The solution is; C. x² + 2x - 1 = 3 equation could be solved using this application of the quadratic formula.
Here,
Quadratic formula: x = -b±√b²-4ac/2a [ +/- is ± ]
You can find the value of a, b, c --> ax² + bx + c = 0
we have,
x = -2±√2² - 4×1× -4 / 2×1
Since this is not simplified, you can find a, b, c:
a = 1
b = 2
c = -4
A.) x² + 1 = 2x − 3 Make the equation into ax² + bx + c = 0.
Subtract 2x on both sides, and add 3 on both sides to set the equation equal to 0
x² + 1 - 2x + 3 = 2x - 2x - 3 + 3
x² - 2x + 4 = 0
a = 1
b = -2
c = 4 This is not the answer because b = 2 not -2, and c = -4 not 4
B.) x² - 2x − 1 = 3 Subtract 3 on both sides to set the equation = 0
x² - 2x - 4 = 0
a = 1
b = -2
c = -4 This is not the answer because b = 2 not -2
C. x² + 2x - 1 = 3 Subtract 3 on both sides to set the equation = 0
x² + 2x - 4 = 0
a = 1
b = 2
c = -4 This is your answer
D. x² + 2x - 1 = -3 Add 3 on both sides to set the equation = 0
x² + 2x + 2 = 0
a = 1
b = 2
c = 2
This is not the answer because c = -4 not 2
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complete question:
Which equation could be solved using this application of the quadratic formula?
x = -2±√2² - 4×1× -4 / 2×1
There are 400 employees. If there is one manager for every 9 engineers. Find the number of managers in company.
answer is 45
400/9 = 44.44...
so with the extra employees you need another manager.
Answer:
40 managers
Step-by-step explanation:
If there is one manager for every 9 engineers, we can assume that each manager is responsible for a group of 9 engineers. To determine the number of managers in the company, we need to divide the total number of engineers by 9.
First, we need to determine the total number of engineers in the company. Since there is one manager for every 9 engineers, the ratio of engineers to managers is 9:1. This means that for every 10 people (9 engineers and 1 manager), there is 1 manager. So we can find the total number of groups of 10 people by dividing the total number of employees by 10:
400 employees / 10 = 40 groups of 10 people
This means that there are 40 groups of 10 employees (1 manager and 9 engineers) in the company. Since there is 1 manager in each group, the total number of managers in the company is equal to the number of groups:
Number of managers = Number of groups = 40
Solve the proportional equation below
The solution to the proportional equation 5/8 = 8/a is a = 64/5 or a = 12.8.
To solve the proportional equation 5/8 = 8/a, we can cross-multiply.
Cross-multiplying means multiplying the numerator of the first fraction by the denominator of the second fraction and vice versa.
We have:
5 × a = 8 × 8
5a = 64
To isolate the variable a, we divide both sides of the equation by 5:
a = 64/5
We may cross-multiply the proportional equation 5/8 = 8/a to find the solution.
Cross-multiplication is the process of multiplying the denominator of the second fraction by the first fraction's numerator, and vice versa.
We possess
5 × a = 8 × 8 5a = 64
We divide both sides of the equation by 5 to identify the variable a:
a = 64/5.
We may cross-multiply to find the solution to the proportional equation 5/8 = 8/a.
Cross-multiplication is the process of multiplying one fraction's numerator by another's denominator and vice versa.
There are:
5 × a = 8 × 8 5a
= 64
By multiplying both sides of the equation by 5, we may separate the variable a:
a = 64/5.
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Divide 20 in the ratio 4:1
Answer:
16 and 4
Step-by-step explanation:
To divide 20 in the ratio 4:1, we need to divide the quantity into 5 parts (4 parts for the first ratio and 1 part for the second ratio) and then allocate the parts accordingly.
The total number of parts is 4+1=5. So, each part represents 20/5 = 4.
To find the share of the first ratio, we multiply the first ratio (4) by the number of parts it represents (4). So, the first share is 4*4 = 16.
To find the share of the second ratio, we multiply the second ratio (1) by the number of parts it represents (1). So, the second share is 1*4 = 4.
Therefore, the quantities in the ratio 4:1 that add up to 20 are 16 and 4, respectively.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
(B) sin(60°) = 4/x
Step-by-step explanation:
You want an equation for finding the hypotenuse of a 30°-60°-90° triangle with the middle-length side being 4 units.
SineThe trig relation between the side opposite and angle and the hypotenuse of the right triangle is ...
Sin = Opposite/Hypotenuse
ApplicationIn this triangle, this relation means ...
sin(60°) = 4/x . . . . . matches choice (B)
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Additional comment
The middle-length side is opposite the middle length angle.
This is a "special" right triangle with sides in the ratios 1 : √3 : 2. The length x will be 4(2/√3) = (8/3)√3. It can be useful to remember the side length ratios for this triangle.
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