Answers
Given:
1 counsellor for every 9 campers.
Lets' determine the type of variation and write the equation.
Here, we can see that for every 9 campers, there is one extra counsellor. This means that as the number of campers increase, the number of counsellors will also increase.
Since one variable as the other increases, this is a direct variation.
Hence, we have the equation which represents the direct variation below:
y = 9x
Where x represents the number of counsellors and y represents the number of campers.
ANSWER:
Direct variation.
y = 9x
Related Questions
So I joined a ged class and this is apparently a “high school level” math problem, maybe for people in advanced classes but not regular. Anyway, I need help with solving this. Also the greater than sign with the problem that I’m doing has like an underline under it, which I think means greater than or equal to 3x + 9 > - x + 19
Answers
Given the inequality:
[tex]3x+9\ge-x+19[/tex]Solve for x:
[tex]\begin{gathered} 3x+x\ge19-9 \\ 4x\ge10 \\ x\ge\frac{10}{4} \\ \\ x\ge\frac{5}{2} \end{gathered}[/tex]so, the answer will be:
[tex]\begin{gathered} x\ge\frac{5}{2} \\ x\in\lbrack\frac{2}{5},\infty) \end{gathered}[/tex]Which systems of inequalities represents the number of apartments to be built
Answers
Given that:
- The office building contains 96,000 square feet of space.
- There will be at most 15 one-bedroom units with an area of 800 square feet. The rent of each unit will be $650.
- The remaining units have 1200 square feet of space.
- The remaining units will have two bedrooms. The rent for each unit will be $900.
Let be "x" the number of one-bedroom apartments and "y" the number of two-bedroom apartments.
• The words "at most 15 one-bedroom units" indicates that the number of these apartments will be less than or equal to 15 units:
[tex]x\leq15[/tex]• You know that the remaining units are two-bedroom apartments. And the number of them is greater than or equal to zero. Then, you can set up the second inequality to represent this:
[tex]y\ge0[/tex]• You know the area of each one-bedroom apartment, the area of each two-bedroom apartment, and the total area that the office building contains. The sum of the areas of the apartments must be less than or equal to the total area of the office building.
Then, the inequality that represents this is:
[tex]800x+1200y\leq96,000[/tex]• Therefore, you can set up this System of Inequalities to represent that situation:
[tex]\begin{gathered} \begin{cases}x\leq15 \\ \\ y\ge0 \\ \\ 800x+1200y\leq96,000 \\ \end{cases} \\ \end{gathered}[/tex]Hence, the answer is: Last option.
Pats normal pulse rate is 80 beats minute. How many times does it beat in 3/4 of a minute?
Answers
The number of times that pat pulse rate maintains the given ratio in 3/4 of a minute is 60 times.
What are the ratio and proportion?The ratio is the division of the two numbers.
Proportion is the relation of a variable with another. It could be direct or inverse.
For example, a/b, where a will be the numerator and b will be the denominator.
As per the given,
Pat's normal pulse rate is 80 beats per minute.
So, 80 beats → 1 minute
Multiply both sides by 3/4
80 × 3/4 beats → 1 × 3/4 minute
(3/4) minute → 60 beats.
Hence "The number of times that pat pulse rate maintains the given ratio in 3/4 of a minute is 60 times".
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What is the area of the composite figure?o 52.5 cm^2o 60 cm^2o 40 cm^265 cm^2
Answers
we have that
The area of the composite figure is equal to the area of a rectangle plus the area of a right triangle
so
step 1
Find out the area of the rectangle
A=L*W
A=8*5
A=40 cm2
step 2
Find out the area of the right triangle
A=(1/2)(b)(h)
where
b=8-(2+1)=8-3=5 cm
h=5 cm
A=(1/2)(5)(5)
A=12.5 cm2
therefore
the total area is
A=40+12.5=52.5 cm2
52.5 cm2g(x)= x^2 + 2hx) = 3x - 2Find (g+ h)(-3)
Answers
Given the following functions;
f(x) = x^2 + 2
g(x) = 3x - 2
(g+h)(x) = g(x)+h(x)
(g+h) = x^2 + 2 + 3x - 2
(g+h) = x^2+3x + 2-2
(g+h) = x^2 + 3x
To get (g+h) (-3), we will subtitute x = -3 into the resulting function as shown;
(g+h) (-3) = (-3)^2+3(-3)
(g+h) (-3) = 9 - 9
(g+h) (-3) = 0
Hence the value of the expression (g+h) (-3) is 0
Calculate the slope (2,-5) and (4,3)
Answers
Answer:
Slope = 4
Step-by-step explanation:
The slope of a line can be calculated using the following formula:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
From the question can put the points as:
(2, -5) as (x1, y1)
and
(4, 3) as (x2, y2)
Therefore, we can put in the values into the formula to solve for the slope.
[tex] \frac{3 - ( - 5)}{4 - 2} \\ = \frac{3 + 5}{2} \\ = \frac{8}{2} \\ = 4[/tex]
Now , using the formula of slope,m = [tex] y_2-y_1/x_2-x_1[/tex]
=> 3-(-5)/4-2
=> 8/2
=> 4
Hence the required slope of given two ordered pairs is 4
The average American man consumes 9.6 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.8 grams. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible. a. What is the distribution of X? X - NO b. Find the probability that this American man consumes between 9.7 and 10.6 grams of sodium per day. C. The middle 10% of American men consume between what two weights of sodium? Low: High:
Answers
The variable of interest is
X: sodium consumption of an American male.
a) This variable is known to be normally distributed and has a mean value of μ=9.6grams with a standard deviation of δ=0.8gr
Any normal distribution has a mean = μ and the variance is δ², symbolically:
X~N(μ ,δ²)
For this distribution, we have established that the mean is μ=9.6grams and the variance is the square of the standard deviation so that: δ² =(0.8gr)²=0.64gr²
Then the distribution for this variable can be symbolized as:
X~N(9.6,0.64)
b. You have to find the probability that one American man chosen at random consumes between 9.7 and 10.6gr of sodium per day, symbolically:
[tex]P(9.7\leq X\leq10.6)[/tex]The probabilities under the normal distribution are accumulated probabilities. To determine the probability inside this interval you have to subtract the accumulated probability until X≤9.7 from the probability accumulated probability until X≤10.6:
[tex]P(X\leq10.6)-P(x\leq9.7)[/tex]Now to determine these probabilities, we have to work under the standard normal distribution. This distribution is derived from the normal distribution. If you consider a random variable X with normal distribution, mean μ and variance δ², and you calculate the difference between the variable and ist means and divide the result by the standard deviation, the variable Z =(X-μ)/δ ~N(0;1) is determined.
The standard normal distribution is tabulated. Any value of any random variable X with normal distribution can be "converted" by subtracting the variable from its mean and dividing it by its standard deviation.
So to calculate each of the asked probabilities, you have to first, "transform" the value of the variable to a value of the standard normal distribution Z, then you use the standard normal tables to reach the corresponding probability.
[tex]P(X\leq10.6)=P(Z\leq\frac{10.6-9.6}{0.8})=P(Z\leq1.25)[/tex][tex]P(X\leq9.7)=P(Z\leq\frac{9.7-9.6}{0.8})P(Z\leq0.125)[/tex]So we have to find the probability between the Z-values 1.25 and 0.125
[tex]P(Z\leq1.25)-P(Z\leq0.125)[/tex]Using the table of the standard normal tables, or Z-tables, you can determine the accumulated probabilities:
[tex]P(Z\leq1.25)=0.894[/tex][tex]P(Z\leq0.125)=0.550[/tex]And calculate their difference as follows:
[tex]0.894-0.550=0.344[/tex]The probability that an American man selected at random consumes between 10.6 and 9.7 grams of sodium per day is 0.344
c. You have to determine the two sodium intake values between which the middle 10% of American men fall. If "a" and "b" represent the values we have to determine, between them you will find 10% of the distribution. The fact that is the middle 10% indicates that the distance between both values to the center of the distribution is equal, so 10% of the distribution will be between both values and the rest 90% will be equally distributed in two tails "outside" the interval [a;b]
Under the standard normal distribution, the probability accumulated until the first value "a" is 0.45, so that:
[tex]P(Z\leq a)=0.45[/tex]And the accumulated probability until "b" is 0.45+0.10=0.55, symbolically:
[tex]P(Z\leq b)=0.55[/tex]The next step is to determine the values under the standard normal distribution that accumulate 0.45 and 0.55 of probability. You have to use the Z-tables to determine both values:
The value that accumulates 0.45 of probability is Z=-0.126
To translate this value to its corresponding value of the variable of interest you have to use the standard normal formula:
[tex]a=\frac{X-\mu}{\sigma}[/tex]You have to write this expression for X
[tex]\begin{gathered} a\cdot\sigma=X-\mu \\ (a\cdot\sigma)+\mu=X \end{gathered}[/tex]Replace the expression with a=-0.126, μ=9.6gr, and δ=0.8gr
[tex]\begin{gathered} X=(a\cdot\sigma)+\mu \\ X=(-0.126\cdot0.8)+9.6 \\ X=-0.1008+9.6 \\ X=9.499 \\ X\approx9.5gr \end{gathered}[/tex]The value of Z that accumulates 0.55 of probability is 0.126, as before, you have to translate this Z-value into a value of the variable of interest, to do so you have to use the formula of the standard normal distribution and "reverse" the standardization to reach the corresponding value of x:
[tex]\begin{gathered} b=\frac{X-\mu}{\sigma} \\ b\cdot\sigma=X-\mu \\ (b\cdot\sigma)+\mu=X \end{gathered}[/tex]Replace the expression with b=0.126, μ=9.6gr, and δ=0.8gr and calculate the value of X:
[tex]\begin{gathered} X=(b\cdot\sigma)+\mu \\ X=(0.126\cdot0.8)+9.6 \\ X=0.1008+9.6 \\ X=9.7008 \\ X\approx9.7gr \end{gathered}[/tex]The values of sodium intake between which the middle 10% of American men fall are 9.5 and 9.7gr.
How do I find the linear equation for this? (y=mx+b)
Answers
Okay, here we have this:
Considering the provided table, we are going to find the corresponding linear equation, so we obtain the following:
To do this we will start using the information in the slope formula, then we have:
m=(y2-y1)/(x2-x1)
m=(190-(-30))/(19-9)
m=220/10
m=22
Now, let's find the y-intercept (b) using the point (9, -30):
y=mx+b
-30=(22)9+b
-30=198+b
b=-30-198
b=-228
Finally we obtain that the linear equation is y=22x-228
Answer:
Step-by-step explanation:
These are the two methods to finding the equation of a line when given a point and the slope: Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. Use the m given in the problem, and the b that was just solved for, to create the equation y = mx + b.
Could you please help with
Answers
The angle measures
m WXZ = 180 - 90 - 24
mWXZ = 66°
Question 9 of 30 Find the surface area of the polyhedron below. The area of each base is 65 cm2 7 cm 2 cm 12 cm 2 cm 2cm 3 cm 4 cm
Answers
The approach is to find the area of the individual sides and add all up
Besides the base, we can identify about 6 rectangles.
area of a rectangle, A = base x height
[tex]\begin{gathered} \text{All the rectangles have a height of 12cm as se}en\text{ in the diagram,} \\ \text{Therefore area is area of 2 bases + area of rectangles.} \end{gathered}[/tex][tex]\begin{gathered} =2(65)\text{ + (4}\times12\text{)+(3}\times12\text{) +(2}\times12\text{)+(2}\times12\text{)+(2}\times12\text{)+(7}\times12\text{)} \\ =130+\text{ 48 + }36\text{ + 24 + 24 + 24 + 84} \\ =370\text{ sq cm} \end{gathered}[/tex]the table below shows the height of trees in a park. how many trees are more than 8m tall but not more than 16m tall?
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the question is y=4m=2x=3solve for b
Answers
y=mx+b
replacing y=4, m=2, x=3 in the equation:
4=2(3)+b
then
b=4-2(3)=4-6=-2b=-2sorry you have to zoom in to see better. its a ritten response.
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A: height is increasing from 0-2 interval.
B: Height remains the same on 2-4
C: 4-6 the height is decreasing the fastest, because the slope is the steepest on that interval.
D: Baloon would be on the ground at 16 seconds, and will not fall down further. that is the way it is in real-world (constraint).
Please Help!!
Karen was computing the volume of a rectangular prism where v=lwh. In her case w=h. After she multiplied l and w she realized she made w 1/3 larger than it should have been. Since w=h, she lowered the third number by 1/3 of itself and continued to multiply to get the final answer. Betty, who did the same problem with the correct numbers, showed that Karen was off by 12 cubic yards. The correct volume of the prism is __ cu. yds.
Answers
The correct volume of the rectangular prism as calculated by Betty is 108 cubic yards
What is a rectangular prism?A rectangular prism is cuboid and an hexahedron that has 6 faces.
The formula for finding the volume of the rectangular prism is V = l•w•h
Where;
l = Length
w = Width
h = Height
The measurement of the prism, for which Karen is calculating the volume gives;
w = h
The amount larger Karen found that she made the width, which gives;
Width of the cube Karen used = (1 + 1/3) × w
Therefore;
h = (1 + 1/3) × w
The volume becomes;
V' = l × (1 + 1/3) × w × (1 - 1/3) × w = l•w²•(1²-1/3²)
V' = l•w²•(8/9)
The amount by which the volume increased, dV = 12 yd³
Which gives;
l•w²•(8/9) = l•w•h - 12 = l•w² - 12
l•w²•(8/9) - l•w² + 12 = 0
l•w²•(8/9) - l•w² + 12 = 0
l•w²/9 = 12
V = l•w² = 12 × 9 = 108
The correct volume of the prism is 108 cubic yards
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What is the value of the expression? (9 1/2−3 7/8) + (4 4/5−1 1/2)
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By algebra properties, the sum of four mixed numbers is equal to the mixed number [tex]8\,\frac{37}{40}[/tex].
How to simplify a sum of mixed numbers
In this problem we find a sum of four mixed numbers. The simplification process consists in transforming each mixed number into a fraction and apply algebra properties. Then,
[tex]9 \,\frac{1}{2}[/tex] = 9 + 1 / 2 = 18 / 2 + 1 / 2 = 19 / 2
[tex]3\,\frac {7}{8}[/tex] = 3 + 7 / 8 = 24 / 8 + 7 / 8 = 31 / 8
[tex]4\,\frac{4}{5}[/tex] = 4 + 4 / 5 = 20 / 5 + 4 / 5 = 24 / 5
[tex]1 \,\frac{1}{2}[/tex] = 1 + 1 / 2 = 2 / 2 + 1 / 2 = 3 / 2
(19 / 2 - 31 / 8) + (24 / 5 - 3 / 2)
(76 / 8 - 31 / 8) + (48 / 10 - 15 / 10)
45 / 8 + 33 / 10
450 / 80 + 264 / 80
714 / 80
357 / 40
320 / 40 + 37 / 40
8 + 37 / 40
[tex]8\,\frac{37}{40}[/tex]
The sum of mixed numbers is equal to [tex]8\,\frac{37}{40}[/tex].
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Select the correct answerVector u has its initial point at (15, 22) and its terminal point at (5, 4). Vector v points in a direction opposite that of u, and its magnitude is twicethe magnitude of u. What is the component form of v?OA V=(-20, 36)OB. V=(-20, 52)Ocv = (20, 36)ODV= (20, 52)
Answers
Answer
Option C is correct.
v = (20, 36)
Explanation
If the initial and terminal points of a vector are given, the vector itself is obtained, per coordinate, by doing a terminal point coordinate minus initial point coordinate.
u = [(5 - 15), (4 - 22)]
u = (-10, -18)
Then, we are told that vector v points in the opposite direction as that of vector u and its magnitude is twice that of vector u too.
In mathematical terms,
v = -2u
v = -2 (-10, -18)
v = (20, 36)
Hope this Helps!!!
A. Determine the slope intercept equation of each line given two points on the line 1. (1, -3) and (-2, 6)
Answers
ANSWER
y = -3x
EXPLANATION
We have to determine the slope-intercept form of the equation of the line.
The slope-intercept form of a linear equation is given as:
y = mx + c
where m = slope
c = y intercept
First, we have to find the slope:
[tex]m\text{ = }\frac{y2\text{ - y1}}{x2\text{ - x1}}[/tex]where (x1, y1) and (x2, y2) are two points the line passes through.
Therefore:
[tex]\begin{gathered} m\text{ = }\frac{6-(-3)}{-2-1}=\frac{6+3}{-3}=\frac{9}{-3} \\ m=-3 \end{gathered}[/tex]Now, we have to use the point-slope method to find the equation:
y - y1 = m(x - x1)
=> y - (-3) = -3(x - 1)
y + 3 = -3x + 3
y = -3x + 3 - 3
y = -3x
That is the slope intercept form of the equation.
A production applies several layers of a clear acrylic coat to outdoor furniture to help protect it from the weather. If each protective coat is 2/27 inch thick, how many applications will be needed to build up 2/3 inch of clear finish.
Answers
We know that
• Each protective coat is 2/27 inches thick.
,• We need to fill 2/3 inches of this protective coat.
To solve this problem, we need to know the total number of the application needed to fill 2/3 inches. We can form the following expression
[tex]\frac{2}{27}x=\frac{2}{3}[/tex]We solve for x
[tex]x=\frac{2\cdot27}{3\cdot2}=\frac{27}{3}=9[/tex]Therefore, we need 9 applications in total.12345678912345678900[tex]11447 \times \frac{333}{999} \times {141}^{2} - x \times y = \sqrt[255]{33} [/tex]Jardin De Ronda. updtCHECK EQUATION in QUESTION ! UPDT 2 :) `!!!z
Answers
test
some text with formatting
0. primo
,1. secondo
,2. terzo
• good
,• better
,• the best
jiohoh oj; lkippomklok∛
yespl
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=)
Brody received a $13.25 tip on a meal that cost $109. What percent of the meal costwas the tip?Round answer to the nearest whole percent.
Answers
Explanation
To find the percentage of the tip we will use the formula below.
[tex]\text{\%Tip}=\frac{\text{Tip(\$)}}{Cost\text{ of meal}}\times100[/tex][tex]\begin{gathered} \text{ \%Tip =}\frac{\text{13.25}}{109}\times100 \\ =13\text{\%} \end{gathered}[/tex]Answer: 13%
I think I’m off to a good start but I’m still confused
Answers
The radius is given 3.5 ft and height is given 14 ft.
ExplanationTo find the surface area of cylinder,
Use the formula.
[tex]S=2\pi rh+2\pi r^2[/tex]Substitute the values.
[tex]\begin{gathered} S=2\pi r(h+r) \\ S=2\times3.14\times3.5(14+3.5) \\ S=384.65ft^2 \end{gathered}[/tex]The volume of cylinder is determined as
[tex]V=\pi r^2h[/tex]Substitute the values
[tex]\begin{gathered} V=3.14\times3.5^2\times14 \\ V=538.51ft^3 \end{gathered}[/tex]AnswerThe surface area of cylinder is 384.65 sq.ft.
The volume of cylinder is 538.51 cubic feet.
1. Which expression is equivalent to 2 x (5 x 4)?a. 2+ (5 x 4)b. (2 x 5) x 4c. (2 x 5) x 4d. (5 x 4) x (2 X4)
Answers
We are given the following expression
[tex]2\times(5\times4)[/tex]Recall the associative property of multiplication
[tex]a\times(b\times c)=(a\times b)\times c[/tex]The associative property of multiplication says that when you multiply numbers, you can group the numbers in any order and still you will get the same result.
So, if we apply this property to the given expression then it becomes
[tex]2\times(5\times4)=(2\times5)\times4[/tex]Therefore, the following expression is equivalent to the given expression.
[tex](2\times5)\times4[/tex]a relationship between decimal, fraction, or 3 Three students wrote percentage. Maggie wrote 75% = Bieber wrote 0.05 = 50% Lee Yung wrote == 0.375 Whích students wrote a correct equation? A. All the above B. None of the above C. Beiber and Lee Yung only D. Lee Yung only 8
Answers
To change decimal or fraction to percent multiply them by 100
Example: 1/4 x 100% = 25%, 0.2 x 100% = 20%
Let us check the answer of the 3 students
Maggie wrote 75% = 3/5
Since
[tex]\frac{3}{5}\times100=\frac{300}{5}=60[/tex]Then 3/5 = 60%, not 75%
Maggie is wrong
Bieber wrote 0.05 = 50%
Let us check
0.05 x 100% = 5%, not 50%
Bieber is wrong
Yung wrote 3/8 = 0.375
Let us check
[tex]\begin{gathered} \frac{3}{8}\times100=\frac{300}{8}=\frac{\frac{300}{2}}{\frac{8}{2}}=\frac{150}{4} \\ \frac{150}{4}=\frac{\frac{150}{2}}{\frac{4}{2}}=\frac{75}{2}=37.5 \end{gathered}[/tex]Since 0.375 x 100% = 37.5%
Yung is right
The answer is Lee Yung only
The answer is D
Jeff has a job at baseball park selling bags of peanuts .he get paid $12 a game and 1.75 per bag of peanuts they sell .how many bags if peanuts does he need to sell in order to earn $54 in one
Answers
Let x be the number of peanut bags Jeff sells. Since he earns $1.75 per bag the total amount he earns for selling x bags is:
[tex]1.75x[/tex]Now, to this we have to add the $12 he gets paid, then the total amount he earns is:
[tex]1.75x+12[/tex]To find out how many bags he has to sell to earn $52 we equate the expression above with the amount and solve for x:
[tex]\begin{gathered} 1.75x+12=54 \\ 1.75x=54-12 \\ 1.75x=42 \\ x=\frac{42}{1.75} \\ x=24 \end{gathered}[/tex]therefore he has to sell 24 bags to earn $54.
1 mile= 1,760 yards.1 kilometer= 1,000 metersIf Jose walked 2 miles this morning, about how many kilometers did he walk?
Answers
1 mile= 1.609 km
Then,
2*1.609=3.218 km
He walked 3.218 kilometers
differentiate t^4 In(8cost)
Answers
⇒It is way more appropriate if I use the product rule. That states that:
⇒f(x)g(x)=f'(x)g(x)+f(x)g'(x)
[tex]t^{4} In(8cos(t))\\=4t^{3}In(8cos(t))+t^{4} \frac{1}{8cos(t)} *(0cos(t)+8*(-sin(t))*1)\\=4t^{3}In(8cos(t))+\frac{t^{4}-8sin(t)}{8cos(t)}[/tex]
Note:
Given F(x)=In(x)
⇒[tex]F'(x)=\frac{1}{x}[/tex]
Goodluck
Answer:
t^3 (4 ln(cos8t) - t tant)
Step-by-step explanation:
Using the Product Rule:
dy/dt = t^4 * d(ln(8cost) / dt + ln(8cost) * d(t^4)/dt
= t^4 * 1/ (8cost) * (-8sint) + 4t^3 ln(8cost)
= -8t^4 sint / 8 cost + 4t^3 ln(8cost)
= -t^4 tan t + 4t^3 ln(8cost)
= t^3 (4 ln(cos8t) - t tant)
Graph the line y = -4 on the graph below.
Answers
we have the equation
y=-4
This is a horizontal line (parallel to the x-axis) that passes through the point (0,-4)
see the graph below to better understand the problem
Alleen's bi-weekly gross pay is $829.70. She sees that $174.25 was deducted for taxes. What percent of Alleen's bi-weekly gross pay has been withheld for tax? Round to the nearest whole percent. (1 point)
O 21%
20%
2%
O 1%
Answers
calculated the slope (5,-14),(-14,0) help
Answers
the slope can be calculated using the next formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where
(5,-14)=(x1,y1)
(-14,0)=(x2,y2)
then we substitute the values
[tex]m=\frac{0+14}{-14-5}=\frac{14}{-19}=-\frac{14}{19}[/tex]the answer is -14/19
([20 + 10.4^2 - 116,870) / (20/ 1/3 x 15 - 10.4/ (116,870/6808))] ^-1
Answers
Answer:
[tex]8\frac{875730264}{8491541359}[/tex]Explanation:
Given the values of the variables below:
• D = 116,870
,• E=1/3
,• L =15
,• M = 20
,• O = 10.4
,• Y = 6,808
We are required to evaluate:
[tex]\begin{gathered} \lbrack(M+O^2-D\div Y)\div(M\div E\cdot L-O\div(D\div Y))\rbrack^{-1} \\ =\mleft(\frac{(M+O^2-D\div Y)}{(M\div E\cdot L-O\div(D\div Y))}\mright)^{-1} \end{gathered}[/tex]Substitute the given values:
[tex]=\mleft(\frac{20+10.4^2-116,870\div6,808}{20\div\frac{1}{3}\cdot15-10.4\div(116,870\div6,808)}\mright)^{-1}[/tex]We simplify using the order of operations PEMDAS.
First, evaluate the parentheses in the denominator.
[tex]=\mleft(\frac{20+10.4^2-116,870\div6,808}{20\div\frac{1}{3}\cdot15-10.4\div\frac{116,870}{6,808}}\mright)^{-1}[/tex]Next, evaluate the exponent(E): 10.4²
[tex]=\mleft(\frac{20+108.16-116,870\div6,808}{20\div\frac{1}{3}\cdot15-10.4\div\frac{116,870}{6,808}}\mright)^{-1}[/tex]Next, we take multiplication and division together:
[tex]\begin{gathered} =\mleft(\frac{20+108.16-\frac{116,870}{6,808}}{20\times3\times15-10.4\times\frac{6808}{116,870}}\mright)^{-1} \\ =\mleft(\frac{20+108.16-\frac{116,870}{6,808}}{900-\frac{13616}{22475}}\mright)^{-1} \end{gathered}[/tex]Finally, take addition and subtraction and then simplify.
[tex]\begin{gathered} =\mleft(\frac{9445541}{85100}\div\frac{20213884}{22475}\mright)^{-1} \\ =(\frac{9445541}{85100}\times\frac{22475}{20213884})^{-1} \\ =(\frac{8491541359}{68808061136})^{-1} \\ =1\div\frac{8491541359}{68808061136}=1\times\frac{68808061136}{8491541359} \\ \\ =\frac{68808061136}{8491541359} \\ =8\frac{875730264}{8491541359} \end{gathered}[/tex]The result of the evaluation is:
[tex]8\frac{875730264}{8491541359}[/tex]