Answers
Given:
Total invested amount = $9000
One account = 5%
Another account = 6%
Find-:
Invested amount of each equation
Explanation-:
Let in 5% account invested amount is x
then amount in 6% account is (9000-x)
Then,
[tex]5\%\text{ of }x+6\%\text{ of }(9000-x)=510[/tex]Then the value of "x" is:
[tex]\begin{gathered} \frac{5}{100}\times x+\frac{6}{100}\times(9000-x)=510 \\ \\ 0.05x+0.06(9000-x)=510 \\ \\ 0.05x+(0.06\times9000)-0.06x=510 \end{gathered}[/tex]The "x" is:
[tex]\begin{gathered} 0.05x-0.06x+540=510 \\ \\ -0.01x=510-540 \\ \\ -0.01x=-30 \\ \\ x=\frac{-30}{-0.01} \\ \\ x=3000 \end{gathered}[/tex]The value of x is 3000 the mean amount in 5% invested amount is 3000.
6% invested amount is:
[tex]\begin{gathered} =9000-3000 \\ \\ =6000 \end{gathered}[/tex]So each account invested amount is:
[tex]\begin{gathered} 5\%\rightarrow3000 \\ \\ 6\%\rightarrow6000 \end{gathered}[/tex]Related Questions
Write and solve an equation that represents the following math sentence.
Twenty-nine equals the sum of 11.5 and the quotient of a number and 2.5.
29 equals 11.5 plus m over 2.5; m = 43.75
29 equals 11.5 plus m over 2.5; m = 7
29 = 11.5 + 2.5m; m = 43.75
29 = 11.5 + 2.5m; m = 7
Answers
The algebraic expression which correctly represents the word phrase and it's solution are respectively; 29 equals 11.5 plus m over 2.5; m = 43.75.
What is the algebraic expression which correctly represents the given word phrase?It follows from the task content that the algebraic expression of which represents the word phrase is to be determined.
First, the quotient of a number, m and 2.5 can be represented algebraically as; m/2.5.
Therefore, since; Twenty-nine equals the sum of 11.5 and the quotient of a number and 2.5, we have;
29 = 11.5 + (m/2.5)
The solution is therefore as follows;
29 -11.5 = (m/2.5)
17.5 = (m/2.5)
m = 2.5 × 17.5
m = 43.75.
Therefore, the correct answer choice is; 29 equals 11.5 plus m over 2.5; m = 43.75.
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What is the area of the triangle 9 2 12
Answers
The given diagram is a traingle with base 12 units, height 4 units, and one side 9 units.
Since base (b) and height (h) are known, we can use the following formula for the area (A) of the triangle,
[tex]A=\frac{1}{2}bh[/tex]Substitute the values and simplify the expression,
[tex]\begin{gathered} A=\frac{1}{2}\times12\times4 \\ A=6\times4 \\ A=24 \end{gathered}[/tex]Thus, the area of the given triangle is 24 square units.
Would the inverse of this graph be a function? Why or why not?
Answers
We will have the following:
*First: We would determine the piecewise function that describes the graph.
Since we can see that the function increases by a factor of 2 and decreases by the same factor we would have:
[tex]f(x)=\begin{cases}2x\colon x\ge0\land x\le4 \\ \\ -2x+16\colon x>4\land\le8\end{cases}[/tex]This is:
*Second: We calculate the inverse of the piecewise function:
[tex]f^{-1}(x)=\begin{cases}\frac{x}{2}\colon x\ge0\land x\le4 \\ \\ -\frac{x-16}{2}\colon x>4\land x\le8\end{cases}[/tex]That is:
From this we can see that the inverse of that graph would in fact represent a function, a non-continuous function. [It will represent a function as long as it follows the parameters stablished in the first point]
7Lines a and bare parallel cut by transversal line t solve for the value of x25x + 4a3x + 14
Answers
These angles measure the same they are interior alternate angles.
3x + 14 = 5x + 4
Solve for x
3x - 5x = 4 - 14
Simplify like terms
-2x = -10
x = -10/-2
Result
x = 5
you pick a marble and flip a coin how many outcomes are possible
Answers
Solution
A coin has two possible outcome
We have 5 marbles
[tex]2\times5=10[/tex]The final answer
[tex]10[/tex]Use the rules of significant figures to answer the following question:43.5694 * 22.07A. 961.58B. 961C. 961.577D. 961.7
Answers
we have that
43.5694 * 22.07=961.576658
therefore
the answer is
961.577 -----> 6 figures
(remember that 43.5694 has 6 figures)
option C
PLS HELP ME ASAP!!!!
Answers
The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.
What is meant by data set?A data set is a group of figures or values related to a specific topic. a list of words, numbers, or symbols, the values of which are frequently the outcomes of an investigation or observation. There are typically multiple variables in data sets.
A dataset is an organized group of data typically connected to a certain body of work. An organized collection of data kept as several datasets is called a database.
In an ordered data set, the median is the value in the middle. The mean is calculated by dividing the sum of all values by the total number of values. The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.
Therefore, the correct answer is option c) The northbound cars were generally faster because the median for the northbound cars is greater than the median for the southbound cars.
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What needs to occur for a geometric series to converge?
Answers
Given a Geometric Series:
[tex]\sum_{n\mathop{=}1}^{\infty}a\cdot r^{n-1}[/tex]Where "r" is the ratio.
By definition:
[tex]undefined[/tex]How many gallons of the water are in the filled tank? You must show work with dimensional analysis using the above fact.
Answers
From the question, we can deduce the following:
Length = 5.6 meters
Width = 7.3 meters
Height = 4.5 meters
Where:
1 ft = 0.3048 m
1 cubic foot = 7.48 gallons
Let's find the amount of gallons of water in the tank if the tank is filled to 1 foot below the top of the tank.
Let's first sketch the tank.
We have:
Now, let's find the volume of the tank(total amount of water it can carry).
Apply the formula:
[tex]V=l\times w\times h[/tex]Thus, we have:
[tex]\begin{gathered} V=5.6\times7.3\times4.5 \\ \\ V=183.96m^3 \end{gathered}[/tex]Now, to find the amount of water presently in the tank since it is filled 1 ft below the top of the tank, we have:
[tex]\begin{gathered} V=5.6\times7.3\times(4.5-0.3048) \\ \\ V=5.6\times7.3\times4.1952 \\ \\ V=171.5m^3 \end{gathered}[/tex]Therefore, the volume of the water in the tank is 171.5 cubic meters.
Now, let'c convert from cubic meters to gallons.
Where:
1 foot = 0.3048 m
[tex]1meter=\frac{1}{0.3048}=3.28\text{ feet}[/tex]Thus, we have:
[tex]\begin{gathered} 1\text{ cubic meter = 3.28}^3=35.29\text{ cubic f}eet \\ \\ 171.5\text{ cubic meters = 171.5 x 35.29 = }6052.235\text{ cubic fe}et \end{gathered}[/tex]Now, to convert from cubic feet to gallons, where:
1 cubci foot = 7.48 gallon
We have:
[tex]6052.235\times7.48=45273.86\text{ gallons}[/tex]Therefore, there are 45273.86 gallons of water filled in the tank.
Simplify completely.a.4x212 xwhen x +0.b. (2t)(3t)(t)c. (3x² - 4x +8)+(x² +6x-11)d. (3x² + 4x – 8) - (x² + 6x +11)
Answers
The expression in 4a) is given below
[tex]\frac{4x^2}{12x}[/tex]Collecting similar terms using the division rule of indices, we will have
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]The above expression therefore becomes
[tex]\begin{gathered} \frac{4x^2}{12x} \\ =\frac{4x^2}{12x^1} \\ =\frac{1}{3}\times x^{2-1} \\ =\frac{1}{3}\times x \\ =\frac{x}{3} \end{gathered}[/tex]Hence,
The final answer = x/3
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
If angle a measures 42 degrees, then what other angles would be congruent to angle a and also measure 42 degrees?
Answers
If angle "a" measures 42° the the other angles that will be congruent to angle "a" and also measure 42° will be angle d, angle e and angle h .
In the question ,
a figure is given ,
From the figure we can see that 2 parallel lines are cut by a transversal .
So ,
angle a = angle d .......because vertically opposite angles .
angle a = angle e ...because corresponding angles are equal in measure
also
angle e = angle h .... because vertically opposite angles .
Therefore , If angle "a" measures 42° the the other angles that will be congruent to angle "a" and also measure 42° will be angle d, angle e and angle h , the correct option is (a) .
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A student rolled 2 dice. What is the probability that the first die landed
on a number less than 3 and the second die landed on a number
greater than 3?
Answers
So the first dice can get either 1 or 2 and the second dice can have 4 5 or 6
So we need any one of these outcomes
(1,4) (1,5) (1,6) (2,5) (2,6) (2,4)
Clearly total no of outcomes is 36 (6x6)
Thus probability= 6/36 = 1/6
A local video game store sells used games and new games. A new game costs$64, including tax. A used game costs $43, including tax. Luis bought 3 more used games than new games. Luis spent $343. How many used games did Luis purchase?
Answers
Given:
new game cost - $ 64
used game cost - $ 43
Luis spent $ 343
Required:
Number of used games Luis purchased
Solution
Let: x be the number of new games Luis bought
x + 3 be the number of used games Luis bought
Total cost = $ 343
Total Cost = (No. of new games bought)(Cost of new games) + (No. of used games bought)(Cost of used games)
$ 343 = ( x ) ( $ 64 ) + ( x + 3 ) ( $ 43 )
343 = 64x + 43 ( x + 3 )
343 = 64x + 43x + 129
343 - 129 = 107x
214 = 107x
2 = x
x = 2
x be the number of new games Luis bought 2
x + 3 be the number of used games Luis bought 2 + 3 = 5
Answer:
Luis purchased 5 used games
To check:
Substitute x into the equation,
343 = x ( 64 ) + (x + 3 ) (43)
343 = 2 ( 64 ) + (2 + 3)(43)
343 = 2 (64) + (5) (43)
343 = 128 + 215
343 = 343
The computed value of x satisfies the equation, Our answer is correct.
Find the value of f(4) for the func
f(x) = -3(x + 2)
f(4) = (Simplify your answer.)
Answers
Answer: f(4) = -18
Step-by-step explanation:
f(4) = -3(4 + 2)
= -3(6)
= -18
Solve for a.5a== ✓ [?]2aPythagorean Theorem: a2 + b2 = c2=
Answers
ANSWER
a = √21
EXPLANATION
This is a right triangle, so we have to apply the Pythagorean Theorem to find the value of a.
We know the length of the hypotenuse which is 5, and the length of one of the legs, which is 2. The Pythagorean Theorem for this problem is,
[tex]a^2+2^2=5^2[/tex]Subtract 2² from both sides,
[tex]\begin{gathered} a^2+2^2-2^2=5^2-2^2 \\ a^2=25-4 \end{gathered}[/tex]And take the square root to both sides,
[tex]\begin{gathered} \sqrt[]{a^2}=\sqrt[]{25-4} \\ a=\sqrt[]{21} \end{gathered}[/tex]Hence, the value of a is √21.
The wholesale price for a chair is 194$ . A certain furniture store marks up the wholesale price by 35%. Find the price of the chair in the furniture store.
Answers
The price of the chair will be 261.9 $ .
One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. For example, 1 percent of 1,000 chickens equals 1/100 of 1,000, or 10 chickens; 20 percent of the quantity is 20/100 1,000, or 200.
If we say, 5%, then it is equal to 5/100 = 0.05.
To solve percent problems, you can use the equation, Percent · Base = Amount, and solve for the unknown numbers. Or, you can set up the proportion, Percent = , where the percent is a ratio of a number to 100. You can then use cross multiplication to solve the proportion.
Based on given conditions formulate
x = 194 ×(35%+1)
x= 194 ×1.35
x = 261.9 $ .
Thus The price of the chair will be 261.9 $ .
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John took 30 minutes to bicycle to his grandmother’s house, a total of 2.5 kilometers. What was his speed in km/hr?
Answers
Answer:
5(km)/1(hr)
Step-by-step explanation:
You multiply the 30 minutes to make one hour, and with that, you also multiply the 2.5 kilometers to get 5. You multiply the 2.5 because we multiply both sides of an equation.
Uniform line movement.
We have that the data is:
Time (t) = 30 m = 0.5 h
Distance (d)= 2.5 km
Speed (v) = ?
Since it asks us for the speed in Km/h, we make a time conversion, from minutes to hours. Knowing that 1 hr = 60 minutes, then
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{30 \not{m}*\left(\frac{1 \ h}{60 \not{m})\right)=0.5 \ h } } \end{gathered}$}}[/tex]
To calculate the speed, divide the distance by the time. We apply the following formula:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{Speed=\frac{Distance}{Time} } \end{gathered}$}}[/tex]
We substitute our data in the formula and solve:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=\frac{d}{t} } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=\frac{2.5 \ km}{0.5 \ h} } \end{gathered}$}}[/tex]
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=5 \ km/h} \end{gathered}$} }}[/tex]
Juan's speed was: 5 km/h.A parents' evening was planned to start at
15h45. There were 20 consecutive
appointments of 10 minutes each and a
break of 15 minutes during the evening. At
what time was the parents evening due to
finish?
C O 19h15
O 19h20
O 19h00
O 20h00
O 19h30
Answers
The time on which parents evening was due to finish was 19 hour 20 minutes.
What is time and its unit?
Time is the ongoing pattern of existence and things that happen in what seems to be an irreversible order from the past, through the present, and into the future.
It is a component quantity of various measurements used to order events, compare the length of events or the time gaps between them, and quantify rates of change of quantities in objective reality or in conscious experience. Along with the three spatial dimensions, time is frequently considered a fourth dimension.
The International System of Units is built upon the seven base units of measurement stipulated by the Système International d'Unités (SI), from which all other SI units are derived. The primary unit of time is the second. The second can be shortened using either the letter S or the letter sec.
20 consecutive appointments of 10 mins = 20 × 10 mins
= 200 min
= 3 hours 20 mins
A break of 15 mins = 3 hours 20 mins + 15 min
= 3 hours 35 mins
The time that the parents evening due to finish = 15h 45 min +3h 35 mins
= 19h 20min
Thus, the time on which parents evening was due to finish was 19h 20min.
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(1 point) The expression 64g4y2 64gʻy2 equals kg"ys where r, the exponent of g, is: and s, the exponent of y, is: and k, the leading coefficient is:
Answers
We are asked to find the final expression in exponent for, of the product of two radical expressions as shown below:
We will be addressing each factor at a time, first in the cubic root, and second in the square root.
Cubic root:
notice that the pure number (64) can be written as the perfect cube of the number 4 since 4^3 = 64. That means that a factor 4 will come out of the cubic root, and no factor 4 will be left in the root.
Now we are going to address the variables g and y which are inside the root, and try to find if they contain any perfect cube expression (perfect cubes will cancel out of the cubic root simplifying then the notation).
We notic that g^4 can be written as g^3 times g, so g^3 will come out of the cubic root as "g", and a factor "g" would be left inside the cubic root. Similarly, the factor y^2 cannot get out of the cubic root because it doesn't have a perfect cube in it.
We are then left with the following expression:
[tex]4g\sqrt[3]{g\cdot y^2}[/tex]Now, we recall the property of fractional exponents associated with roots of a factor:
[tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]Using this, the cubic root can be expressed as fractional exponents, as we show below:
[tex]4g\sqrt[3]{g\cdot y^2}=4g\cdot g^{\frac{1}{3}}\cdot y^{\frac{2}{3}}=4g^{\frac{4}{3}}\cdot y^{\frac{2}{3}}[/tex]Now we proceed to simplify the expression with the square root. This is much simpler, since all factor inside can be written as perfect squares:
64 = 8^2
g^4 = (g^2)^2 (the double square of g)
y^2 is already a perfect square.
Therefore, the square root is simplified entirely and we are left with the following factors:
8 g^2 y
Now we combine via the multiplication what we found for the cubic root and what we found for the square root:
[tex](4\cdot g^{\frac{4}{3}}\cdot y^{\frac{2}{3}})\cdot(8\cdot g^2\cdot y)=32\cdot g^{\frac{10}{3}}\cdot y^{\frac{5}{3}}[/tex]Therefore the power (r) of the factor g is the fraction: 10/3
The power (s) of the factor y is the fraction 5/3
and the constant number "k" is 32.
help pleaseeeeeeeeeeeeeeee
Answers
Answer:
(b) f(2) = 28
(c) f(-2) = -20
Step-by-step explanation:
f(2) = -2^3 + 7 x 2^2 - 2 x 2 + 12 f(-2) = -2^3 + 7 x -2^2 - 2 x -2 + 12
1. Calculate Exponents
-2^3 = -8 -2^3 = -8
2^2 = 4 -2^2 = -4
-8 + 7 x 4 - 2 x 2 + 12 -8 + 7 x -4 - 2 x -2 + 12
2. Multiply (left to right)
7 x 4 = 28 7 x -4 = -28
2 x 2 = 4 2 x -2 = -4
-8 + 28 - 4 + 12 -8 - 28 - (-4) + 12
3. Add (left to right)
-8 + 28 = 20 -8 + -28 = -36
20 - 4 = 16 -36 - (-4)= -32
16 + 12 = 28 -32 + 12 = -20
Andre was trying to write 7^4/7^-3 with a single exponent and write 7^4/7^-3= 7^4-3=7^1 Exploit to Andre what his mistake was and what the answer should be...PLEASE THE ANSWER IS URGENT!!
Answers
Here, we want to get what Andre's mistake was and correct it
To answer this, we are supposed to use the division law of indices
We have this as;
[tex]\frac{a^x}{a^y\text{ }}=a^{x-y}[/tex]Now, in the case of this question, x is 4 and y is -3
So, we have the expression as;
[tex]7^{4-(-3)}=7^{4+3}=7^7[/tex]His mistake is thus adding the exponents instead of subtracting
4/5 × (12÷2+4)-1 what is the value of the expression
Answers
Given the expression
[tex]\frac{4}{5}\cdot(12\div2+4)-1[/tex]To find the value of the expression you have to follow the order of operations:
- Parentheses
- Exponents
- Multiplication/Division
- Addition/ Subtraction
• First, you have to solve the operations inside the parentheses term:
[tex]12\div2+4[/tex]Solve the division first and then the sum:
[tex]12\div2+4=6+4=10[/tex]• Write the result on the original expression:
[tex]\begin{gathered} \frac{4}{5}\cdot(12\div2+4)-1 \\ \frac{4}{5}\cdot10-1 \end{gathered}[/tex]• The next step is to solve the multiplication and finally solve the difference
[tex]\frac{4}{5}\cdot10-1=8-1=7[/tex]The value of the expression is 7
The sum of the squares of three consecutive odd numbers is 83. Find the numbers.
Answers
In order to represent three consecutive odd numbers, we can use the expressions "x", "x+2" and "x+4".
If we add the square of each number, the result is 83, so we can write the following inequality:
[tex]\begin{gathered} x^2+(x+2)^2+(x+4)^2=83\\ \\ x^2+x^2+4x+4+x^2+8x+16=83\\ \\ 3x^2+12x+20=83\\ \\ 3x^2+12-63=0\\ \\ x^2+4x-21=0 \end{gathered}[/tex]Let's solve this quadratic equation using the quadratic formula, with a = 1, b = 4 and c = -21:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4a}c}{2a}\\ \\ x=\frac{-4\pm\sqrt{16+84}}{2}\\ \\ x=\frac{-4\pm10}{2}\\ \\ x_1=\frac{-4+10}{2}=\frac{6}{2}=3\\ \\ x_2=\frac{-4-10}{2}=\frac{-14}{2}=-7 \end{gathered}[/tex]If we assume the numbers are positive, the numbers are 3, 5 and 7.
(The other result, with negative numbers, would be -7, -5 and -3).
Solve the system [tex]\left \{ {{5x1 + 5x2 = 5} \atop {2x1 + 3x2 = 4}} \right.[/tex]
Answers
The solution for the given system of equations is x[1] = -1 and x[2] = 2.
What is system of equations?A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.
Given are the following equations as -
5 x[1] + 5 x[2] = 5
2 x[1] + 3 x[2] = 4
Assume that -
x[1] = a
x[2] = b
Then, we can write the equations as -
5a + 5b = 5
2a + 3b = 4
Now -
5a + 5b = 5
5(a + b) = 5
a + b = 1
a = 1 - b
So, we can write -
2a + 3b = 4
as
2(1 - b) + 3b =4
2 - 2b + 3b = 4
b = 4 - 2
b = 2 = x[2]
Then
a = 1 - 2
a = -1 = x[1]
Therefore, the solution for the given system of equations is x[1] = -1 and x[2] = 2.
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Please help! I can also change the vent graph to different kinds as well.
Answers
Answer:
See below and attached Venn Diagram3
Step-by-step explanation:
No need to change Venn diagrams It is perfectly clear
We will represent the different sets of people using letters A and B for convenienceThat total number of people who "Had Drowsiness" is represented by the maroon circle to the left. )Note some of those participants also belong to the category had Nausea)We will represent the set of all people who had drowsiness as A and the number of people in that set as n(A) = 95 (given)Similarly, the total number of people who had nausea is represented by the aquamarine circle to the right. (Note that some of these people also had drowsiness) We will represent the set of all people who had nausea as B and the number of people in that set as n(B) = 77 (given)The number of people who had both drowsiness and nausea is the intersection area of the two i.e. the Venn diagram area in the middle which overlaps both the circles. This is represented as A and B and we are given that this number n(A and B) = 58This is the number that would go into the center box in the Venn DiagramThe number of people who had drowsiness but not nausea is the total number of people who had drowsiness - number of people who had both side effectsThis would be n(A) - n(A and B) = 95 - 58 = 37This would be the number that would go into the box on the leftThis is referred to as set difference denoted by A - B i.e. the set of all elements in a but not in B. So we say n(A-B) = 37Similarly the number of people experiencing nausea but not drowsiness would be set difference B-A and the number of such people would be 77 - 58 = 19This number would go into the box on the rightIf we add up all the boxes we get the total number of people who had drowsiness or nausea or both as n(A or ) = 37 + 58 + 19 = 114You can also arrive at this number by the formula
n(A or B) = n(A) + n(B) - n(A and B)
= 95 + 77 - 58 = 114We subtract n(A and B)= 58 because when
we add n(A) and n(B) we are adding this chunk twice so we need to adjust by removing the duplicate additionIn addition to all these values you will see a box that is outside of any of the circles but inside the circle. This represents the number of people who had no side effects.This number would be 161 - 114 = 47
The completed Venn Diagram is attached for your convenience
If the Manufacturing Overhead account is closed proportionally to Work in Process, Finished Goods, and Cost of Goods Sold, the related entry will include a ________.
Answers
If the Manufacturing Overhead account is closed proportionally to Work in Process, Finished Goods, and Cost of Goods Sold, the related entry will include a Credit to cost of goods sold for $12000
How to solve for the costThe cost of a good is the total amount that was used in the purchase of a particular good form the market.
we have the manufacturing overhead to be = 30000 dollars
the work in progress = 30000 x 25 %
= 30000 x 0.25
= 7500
The finished goods = 30000 x 35 %
= 30000 x 0.35
= 10500
The cost of good sold = 30000 - 10500 - 7500
= 12000
Hence the cost of good sold is 12000
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complete questionManufacturing overhead applied $ 150,000
Actual amount of manufacturing overhead costs 120,000
Amount of overhead applied during the year that is in:
Work in Process $ 37,500 25 %
Finished Goods 52,500 35 %
Cost of Goods Sold 60,000 40 %
Total overhead applied $ 150,000 100 %
If the Manufacturing Overhead account is closed proportionally to Work in Process, Finished Goods, and Cost of Goods Sold, the related entry will include a ________.
debit to Cost of Goods Sold for $12,000
credit to Cost of Goods Sold for $12,000
credit to Cost of Goods Sold for $30,000
debit to Work in Process for $7,500
For people over 50 years old, the level of glucose in the blood (following a 12 hour fast) is approximately normally distributed with mean 85 mg/dl and standard deviation 25 mg/dl ("Diagnostic Tests with Nursing Applications", S. Loeb). A test result of less than 40 mg/dl is an indication of severe excess insulin, and medication is usually prescribed.
What is the probability that a randomly-selected person will find an indication of severe excess insulin?
Suppose that a doctor uses the average of two tests taken a week apart (assume the readings are independent). What is the probabiltiy that the person will find an indication of severe excess insulin?
Repeat for 3 tests taken a week apart:
Repeat for 5 tests taken a week apart:
Answers
Using the normal distribution and the central limit theorem, it is found that:
There is a 0.0359 = 3.59% probability that a randomly-selected person will find an indication of severe excess insulin.Considering the mean of two tests, there is a 0.0054 = 0.54% probability that the person will find an indication of severe excess insulin.Three tests: 0.0009 = 0.09%.Five tests: 0% probability.Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the following rule:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score score is positive or negative.From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X in the distribution of interest.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The mean and the standard deviation of the glucose levels are given, respectively, by:
[tex]\mu = 85, \sigma = 25[/tex]
The probability of a reading of less than 40 mg/dl(severe excess insulin) is the p-value of Z when X = 40, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (40 - 85)/25
Z = -1.8.
Z = -1.8 has a p-value of 0.0359.
For the mean of two tests, the standard error is:
s = 25/sqrt(2) = 17.68.
Hence, by the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (40 - 85)/17.68
Z = -2.55.
Z = -2.55 has a p-value of 0.0054.
For 3 tests, we have that:
s = 25/sqrt(3) = 14.43.
Z = (40 - 85)/14.43
Z = -3.12.
Z = -3.12 has a p-value of 0.0009.
For 5 tests, we have that:
s = 25/sqrt(5) = 11.18.
Z = (40 - 85)/11.18
Z = -4.03
Z = -4.03 has a p-value of 0.
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Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west at 18 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later?
mi/h
Answers
The rate at which the distance between the two cars increased four hours later is 30 mi/h.
How to determine the rate?First of all, we would determine the distances travelled by each of the cars. The distance travelled by the first car after four (4) hours is given by:
Distance, x = speed/time
Distance, x = 24/4
Distance, x = 6 miles.
For the second car, we have:
Distance, y = speed/time
Distance, y = 18/4
Distance, y = 4.5 miles.
After four (4) hours, the total distance travelled by the two (2) cars is given by this mathematical expression (Pythagorean theorem):
z² = x² + y²
Substituting the parameters into the mathematical expression, we have;
z² = 6² + 4.5²
z² = 36 + 20.25
z² = 56.25
z = 7.5 miles.
Next, we would differentiate both sides of the mathematical expression (Pythagorean theorem) with respect to time, we have:
2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt)
Therefore, the rate of change of speed (dz/dt) between the two (2) cars is given by:
dz/dt = [x(dx/dt) + y(dy/dt)]/z
dz/dt = [6(24) + 4.5(18)]/7.5
dz/dt = [144 + 81]/7.5
dz/dt = 225/7.5
dz/dt = 30 mi/h.
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Answer:
30 mi / hr
Step-by-step explanation:
First find out how far the cars are apart after 4 hours
24 * 4 = 96 mi = y
18 * 4 = 72 mi = x
Now use the pythagorean theorem
s^2 = ( x^2 + y^2 ) shows s = 120 miles apart at 4 hours
Now s^2 = x^2 + y^2 Differentiate with respect to time ( d / dt )
2 s ds/dt = 2x dx/ dt + 2y dy / dt
ds/dt = (x dx/dt + y dy/dt)/s
= (72(18) + 96(24)) / 120
ds/dt = 30 mi/hr
Find all the values of x where the tangent line is horizontal.3f(x) = x³ - 4x² - 7x + 12X=(Use a comma to separate answers as needed. Type an exact answer, using radicals
Answers
Given the function:
[tex]h(x)=x^3-4x^2-7x+12[/tex]Find the first derivative:
[tex]h^{\prime}(x)=3x^2-8x-7[/tex]The first derivative gives us the slope of the tangent line to the graph of the function. When the tangent line is horizontal, the slope is 0, thus:
[tex]3x^2-8x-7=0[/tex]This is a quadratic equation with coefficients a = 3, b = -8, c = -7.
To calculate the solutions to the equation, we use the quadratic solver formula:
[tex]$$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$$ [/tex]Substituting:
[tex]x=\frac{-(-8)\pm\sqrt{(-8)^2-4(3)(-7)}}{2(3)}[/tex]Operate:
[tex]\begin{gathered} x=\frac{8\pm\sqrt{64+84}}{6} \\ \\ x=\frac{8\pm\sqrt{148}}{6} \end{gathered}[/tex]Since:
[tex]148=2^2\cdot37[/tex]We have:
[tex]\begin{gathered} x=\frac{8\pm2\sqrt{37}}{6} \\ \\ \text{ Simplifying by 2:} \\ \\ x=\frac{4\pm\sqrt{37}}{3} \end{gathered}[/tex]There are two solutions:
[tex]\begin{gathered} x_1=\frac{4+\sqrt{37}}{3} \\ \\ x_2=\frac{4-\sqrt{37}}{3} \end{gathered}[/tex]A baseball team has home games on Wednesday and Saturday. The two games together earn $4920.00 for the team. Wednesday's game generates $880.00 less than Saturday's game. How much money did Wednesday's game generate?
Answers
Wednesday's game generated $2020
Explanations:Let the amount generated by Wednesday's game be x
Let the amount generated by Saturday's game be y
The two games together earn $4920 for the team. That is,
x + y = 4920....................(1)
Wednesday's game generates $880 less than Saturday's game
x = y - 880.................(2)
Make y the subject of the formula in equation (2)
y = x + 880..................(3)
Substitute equation (3) into equation (2)
x + x + 880 = 4920
x + x = 4920 - 880
2x = 4040
Divide both sides by 2
2x/2 = 4040/2
x = 2020
Wednesday's game generated $2020