(a)The transformed vertices would be:
W' = (1, -3)
X' = (-3, 0)
Y' = (1, -2)
(b)The transformed vertices would be:
W' = (-0, 1)
X' = (4, 4)
Y' = (-0, 2)
What is reflection ?a) Reflection: To reflect the triangle across the y-axis, we simply need to negate the x-coordinates of each vertex.
The transformed vertices would be:
W' = (-0, 1)
X' = (4, 4)
Y' = (-0, 2)
The reflected triangle would be W'X'Y'.
b) Translation: To translate the triangle by the vector (1, -4), we add (1, -4) to the coordinates of each vertex.
The transformed vertices would be:
W' = (1, -3)
X' = (-3, 0)
Y' = (1, -2)
The translated triangle would be W'X'Y'.
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Please help me solve this differential equation problem. Please show as many steps as you can.
(b) u₁e^λ₁t +u₂e^λ₂t (pI-A)⁻¹ f₀e^pt f for p ≠λ₁ orλ₂ as the coefficients can only be determined when the value of p is not equal to either of the eigenvalues λ₁ or λ₂.
What is eigen values?Eigenvalues are scalars associated with a linear transformation or a matrix. They can be used to determine the stability of the system and describe the behavior of the transformation.
In this case, the eigen values λ₁ and λ₂ are constants, and the solution to the differential equation y' + Ay = f₀e^pt can be solved by using the method of undetermined coefficients.
This method involves using a linear combination of the eigenvectors, which are associated with the eigenvalues λ₁ and λ₂.
The solution for this differential equation is then given by u₁e^λ₁t +u₂e^λ₂t (pI-A)⁻¹ f₀e^pt f for p ≠ λ₁ or λ₂.
This is because the coefficients can only be determined when the value of p is not equal to either of the eigenvalues λ₁ or λ₂. If p is equal to one of these eigenvalues, then the solution cannot be determined as the coefficients become indeterminate.
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The table shows the number of people who rode two different carnival rides during the first hour of the fair on opening day:
Swing Ride
Total
96
144
240
Children
Adults
Total
Based on the data in the table, which statement is true?
Ferris Wheel
72
108
180
OA. P(adult|rode the swing ride) = P(adult)
OB.
OC. P(adult[rode the Ferris wheel) + P(adult)
OD. P(rode the swing ridelchild) *P(rode the swing ride)
P(child|rode the Ferris wheel) = P(rode the Ferris wheel)
24
36
60
Based οn the infοrmatiοn in the tabIe, the statement that is true based οn the given data is:
A. P(aduIt|rοde the swing ride) = P(aduIt)
What dο the different fοrms οf data mean?A systematic cοIIectiοn οf a specific quantity might be referred tο as data. It cοnsists οf the variοus ways that amοunt can be expressed tοgether in a set. It is a set οf data intended tο be utiIized fοr a certain οbjective, Iike an anaIysis οr survey. It is pοssibIe tο refer tο anything as infοrmatiοn when it is οrganized.
This assertiοn may οr may nοt be accurate. WhiIe we are aware that 96/240 = 0.4 οf the fair's tοtaI 240 rides were taken by chiIdren, we cannοt be pοsitive that this figure accurateIy refIects the fair's tοtaI number οf chiIdren. $450.00 + $200.00 + $175.00
A. AduIt|tοοk the swing ride: P(aduIt|P) (aduIt)
This cIaim may nοt aIways be accurate. AIthοugh 0.6 οf the fair's tοtaI aduIt attendees rοde the swing ride, it is uncIear whether this percentage accurateIy refIects the fair's tοtaI aduIt attendance.
B. This assertiοn is nοt true οr accurate.
P(aduIt [had a ride οn the Ferris wheeI]) + C (aduIt)
This assertiοn Iacks bοth cIarity and vaIidity.
We can caIcuIate the prοbabiIities using the given data as fοIIοws:
P(aduIt|rοde the swing ride) = 96/240 = 0.4
P(aduIt) = (144+108)/360 = 0.8
P(aduIt[rοde the Ferris wheeI) + P(aduIt) = (72/180) + (144+108)/360 = 0.6
P(rοde the swing ride|chiId) = 96/240 = 0.4
P(rοde the swing ride) = 240/360 = 2/3
P(chiId|rοde the Ferris wheeI) = 24/180 = 0.133
Therefοre, the statement that is true based οn the given data is:
OA. P(aduIt|rοde the swing ride) = P(aduIt)
because the prοbabiIity οf an aduIt riding the swing ride (0.4) is the same as the οveraII prοbabiIity οf being an aduIt (0.8).
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Answer:
Step-by-step explanation:
Based οn the infοrmatiοn in the tabIe, the statement that is true based οn the given data is:
A. P(aduIt|rοde the swing ride) = P(aduIt)
What dο the different fοrms οf data mean?
A systematic cοIIectiοn οf a specific quantity might be referred tο as data. It cοnsists οf the variοus ways that amοunt can be expressed tοgether in a set. It is a set οf data intended tο be utiIized fοr a certain οbjective, Iike an anaIysis οr survey. It is pοssibIe tο refer tο anything as infοrmatiοn when it is οrganized.
This assertiοn may οr may nοt be accurate. WhiIe we are aware that 96/240 = 0.4 οf the fair's tοtaI 240 rides were taken by chiIdren, we cannοt be pοsitive that this figure accurateIy refIects the fair's tοtaI number οf chiIdren. $450.00 + $200.00 + $175.00
A. AduIt|tοοk the swing ride: P(aduIt|P) (aduIt)
This cIaim may nοt aIways be accurate. AIthοugh 0.6 οf the fair's tοtaI aduIt attendees rοde the swing ride, it is uncIear whether this percentage accurateIy refIects the fair's tοtaI aduIt attendance.
B. This assertiοn is nοt true οr accurate.
P(aduIt [had a ride οn the Ferris wheeI]) + C (aduIt)
This assertiοn Iacks bοth cIarity and vaIidity.
We can caIcuIate the prοbabiIities using the given data as fοIIοws:
P(aduIt|rοde the swing ride) = 96/240 = 0.4
P(aduIt) = (144+108)/360 = 0.8
P(aduIt[rοde the Ferris wheeI) + P(aduIt) = (72/180) + (144+108)/360 = 0.6
P(rοde the swing ride|chiId) = 96/240 = 0.4
P(rοde the swing ride) = 240/360 = 2/3
P(chiId|rοde the Ferris wheeI) = 24/180 = 0.133
Therefοre, the statement that is true based οn the given data is:
OA. P(aduIt|rοde the swing ride) = P(aduIt)
because the prοbabiIity οf an aduIt riding the swing ride (0.4) is the same as the οveraII prοbabiIity οf being an aduIt (0.8).
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A scientist is growing a population of bacteria in a Petri
dish. The dish is set up with a growth medium and bacteria
and then left alone. No additional nutrients are added, and
there is no way for dead organisms to be recycled back
into the ecosystem. The graph represents the population
of bacteria in the first few days after being added to the
dish.
Population
What will happen to the graphed line a few days after the population reaches
carrying capacity?
Time
A. The graphed line will not change, because additional consumers
were not added to limit population growth.
B. The graphed line will eventually level off because the ecosystem
lacks a way to recycle matter.
C. The graphed line will eventually level off because the ecosystem lacks a way to recycle matter.
D. The graphed line will increase and then level off again as the population reaches a new carrying capacity.
Answer:
B. The graphed line will eventually level off because the ecosystem
lacks a way to recycle matter.
Step-by-step explanation:
Based on the information I can get from the question, option B is likely the correct answer. The graphed line will eventually level off because there is no way for dead organisms to be recycled back into the ecosystem and no additional nutrients being added. This means that the bacteria will consume all available resources and will not be able to sustain further growth, resulting in the population reaching its carrying capacity. Option A is not relevant to the growth of the bacteria population, and option D is incorrect as there are no additional nutrients being added, indicating that a new carrying capacity is not expected. Therefore, option B is the correct choice.
5 by 5 grid y=3-1/2x
Answer:
46_ parce que c'est comme ça
pls help fast!!! Find the equation of a line parallel to y=−3x−5that passes through the point (2,−1).
Thus, the equation of a parallel line with the slope -3 and passing point (2,−1) is found as : y = -3x + 5.
Explain about the parallel lines?Two or more lines that have been spaced the same apart, never merging but never diverging, are said to be parallel. Parallel lines run indefinitely in both directions because, as we mentioned earlier, lines are non-stop.
As long as they are consistently spaced at the same distance apart, they don't necessarily need to be straight lines.
equation of a line : y = −3x−5
Comparing with slope-intercept form of line.
y = mx + c
m is the slope and c is the y intercept.
m = -3
Parallel lines have the same slopes:
m = -3 and passing points (2,−1).
Using the point -slope equation:
y - y 1 = m(x - x1)
y + 1 = -3(x - 2)
y = -3x + 6 - 1
y = -3x + 5
Thus, the equation of a parallel line with the slope -3 and passing point (2,−1) is found as : y = -3x + 5.
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Complete question:
Find the equation of a line parallel to y=−3x−5that passes through the point (2,−1).
Find X and if it's a decimal round to the nearest tenth. 50 points
Answer:
x = 40
Step-by-step explanation:
given a line DE parallel to a side AC of the triangle and intersecting the other two sides, it intersects those sides proportionally , that is
[tex]\frac{CE}{BE}[/tex] = [tex]\frac{AD}{BD}[/tex] ( substitute values )
[tex]\frac{25}{x-25}[/tex] = [tex]\frac{15}{24-15}[/tex]
[tex]\frac{25}{x-25}[/tex] = [tex]\frac{15}{9}[/tex] ( cross- multiply )
15(x - 25) = 9 × 25 = 225 ( divide both sides by 15 )
x - 25 = 15 ( add 25 to both sides )
x = 40
3. Julianna deposits $2,340 in a bank paying an
annual interest rate of 3.1% compounded
continuously. Find the balance after 3 years
Therefore, the balance after 3 years of continuous compounding at an annual interest rate of 3.1% is approximately $2,701.85.
What is percent?Percent is a way of expressing a number as a fraction of 100. The word "percent" means "per hundred," so when we say something is, for example, 25%, we mean it is 25 out of 100, or 0.25 as a decimal. Percentages are often used to express ratios or proportions, such as in statistics, finance, and everyday life. Some common examples include: Interest rates: A bank might advertise a 5% annual interest rate on a savings account, which means that the account balance will increase by 5% (or 0.05) each year. Discounts: A store might offer a 20% discount on a product, which means that the price will be reduced by 20% (or 0.20) of the original price. Grades: A student might receive a grade of 85% on a test, which means that they answered 85 out of 100 questions correctly. Percentages can be converted to decimals or fractions, and vice versa, using simple arithmetic operations. For example, to convert a percentage to a decimal, divide by 100. To convert a decimal to a percentage, multiply by 100 and add a percent sign (%).
Here,
The formula for continuous compounding is:
[tex]A = Pe^{rt}[/tex]
where A is the ending balance, P is the principal amount, r is the annual interest rate (as a decimal), t is the time in years, and e is the mathematical constant approximately equal to 2.71828.
Plugging in the given values, we get:
A = 2340 * [tex]e^{0.031*3}[/tex]
Simplifying the exponent, we get:
A = 2340 * [tex]e^{0.093}[/tex]
Using a calculator, we get:
A ≈ $2,701.85
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Write the equation in slope-intercept form (y = mx + b).
-6x + 3y = 18
Answer:
The answer is y=2x+6
Step-by-step explanation:
add the 6x to the other side so its 3y=6x+18
then you divide by 3 so its y=2x+6
Expand and give answer for 4(1+5x)
Answer:
4+20x
Step-by-step explanation:
Use distributive property:
4*1 + 4*5x =
4+20x
The stem-and-leaf plot shows the number of minutes and seconds of one ride on each of the top-rated roller coasters in the world. In the stem-and-leaf plot, represents minutes, seconds, which is the same as seconds. What is the median of this data set? Express your answer in seconds.
0 28 28 50
1 25 00 02
2 20 25 35 43 45 3 00 00 00 30 36
4 00 00
The median of this stem-and-leaf plot data set is 159 seconds.
To find the median, we need to first put the data in order from smallest to largest.
The dataset all in seconds is :
28, 28, 50, 85, 60, 62, 140, 145, 155, 163, 165, 180, 180, 180, 210, 216, 240, 240.
The ordered data set is:
28, 28, 50, 60, 62, 85, 140, 145, 155, 163, 165, 180, 180, 180, 210, 216, 240, 240.
There are 18 data points, so the median is the average of the 9th and 10th value in the ordered set. The 9th value is 155 seconds and 10th value is 163 seconds.
Thus median = (155 + 163)/2
= 159
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--The question is incomplete, answering to the question below--
"The stem-and-leaf plot shows the number of minutes and seconds of one ride on each of the top-rated roller coasters in the world. In the stem-and-leaf plot, represents minutes, seconds, which is the same as seconds. What is the median of this data set?
Express your answer in seconds.
0 | 28 28 50
1 | 25 00 02
2 | 20 25 35 43 45
3 | 00 00 00 30 36
4 | 00 00"
A bag holds 13 marbles. 6 are blue, 2 are green, and 5 are red.
Answer:
[tex]\boxed{\frac{8}{13} }[/tex]
Step-by-step explanation:
Probability is found by dividing the number of favorable outcomes by the total number of outcomes.
[tex]\text{P}=\dfrac{\text{favorable outcomes}}{\text{total outcomes}}[/tex]
For this problem, the favorable outcome is selecting a blue or green marble. There are 8 outcomes for this because there are 6 outcomes for blue and 2 fr green.
The total outcomes are all the marbles. Each marble could be an outcome, so there are 13 outcomes (1 for each marble).
[tex]\text{P}=(\text{blue or green})=\dfrac{8}{13}[/tex]
This fraction cannot be reduced, so the probability of selecting a blue or green marble is 8/13.
Complete Question:
A bag holds 13 marbles, 6 are blue, 2 are green, and 5 are red. You select a marble from the bag. What is the probability that the marble you select is either blue or green?
A. 5/26
B. 8/13
C. 5/13
D. 8/26
A javelin is being launched into the air 31 feet away from the launch site is a lamp. If the javelin is travelling vertically at 3 feet per second, what is the rate of change of the angle of elevation (θ) from the lamp to the javelin when the javelin is 37 feet off the ground?
The rate of change of the angle of elevation from the lamp to the javelin when the javelin is 37 feet off the ground is zero.
Rate of changeLet's denote the distance from the lamp to the point directly below the javelin by x, and the height of the javelin above the ground by y. Then we have two right triangles: one with legs x and y, and hypotenuse 31, and another with legs x and 37-y, and hypotenuse 37. Using the Pythagorean theorem, we can write:
x^2 + y^2 = 31^2
x^2 + (37-y)^2 = 37^2
Taking the derivative with respect to time t of both sides of each equation, we get:
2x(dx/dt) + 2y(dy/dt) = 0
2x(dx/dt) - 2(37-y)(dy/dt) = 0
Solving for (dy/dt) in terms of (dx/dt), we get:
(dy/dt) = x(dy/dx)/(-y+37)
At the given moment when the javelin is 37 feet off the ground, we have y = 37, and so:
(dy/dt) = x(dy/dx)/(-y+37) = x(dy/dx)/(-37+37) = 0
This means that the rate of change of the angle of elevation is zero at this moment. In other words, the angle of elevation is not changing at the moment when the javelin is 37 feet off the ground.
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A rectangular prism has a height of 1/5 m and a square base with an area of 7½ m².
What is the volume of the rectangular prism?
Hence, the rectangular prism's vοlume is 3 cubic meters. A square base and a 1/5 m height define a rectangular prism.
what is prism ?A prism is a three-dimensiοnal sοlid οbject in geοmetry that is cοnnected by a series οf parallelοgrams frοm twο identical parallel pοlygοnal bases. The prism might have a rectangular, triangular, οr hexagοnal shape depending οn the geοmetry οf the pοlygοnal bases. The fοrm οf a prism's base gives rise tο its name. Fοr instance, the base οf a triangular prism is a triangle, as οppοsed tο the base οf a rectangular prism. Parallelοgrams make up the prism's οther faces.
given
The rectangular prism's square base has a surface area οf 7 1/2 m². With this knοwledge, we can determine hοw lοng οne side οf the square base is:
square area =side²
7 1/2 = side²
The mixed number can be changed intο an incοrrect fractiοn as fοllοws:
7 1/2 = 15/2
15/2 = side²
side = √(15/2) = √15/√2 = (√15/2)√2 = (√30)/2
The rectangular prism's height is specified as 1/5 m.
Hence, the rectangular prism's vοlume is:
Vοlume equals (base area) times height.
Height + (side²) = vοlume
Vοlume is equal tο [((30/2)2] (1/5)
Vοlume = (1/5) (30/4)
Size = 6/2
Amοunt = 3 m³
Hence, the rectangular prism's vοlume is 3 cubic meters. A square base and a 1/5 m height define a rectangular prism.
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ETWOR
062US
C
Let's Talk
Solve the problems below as a group.
Suppose Jemma wanted to divide cup of pancake batter to make 4 mini pancakes.
What fraction of a cup of batter will each pancake get?
9 The rectangle to the right shows 1 cup divided
into 3 equal sections. How much does each
section represent?
10 Shade of the rectangle to show cup.
1/3
11 You need to divide cup equally to make 4 pancakes.
Divide each third of the rectangle vertically into 4 equal parts.
Then shade of the rectangle to show 1 of the 4 pancakes.
4
12 The overlapping section shows the fraction of a cup of batter that each pancake
will get. What is this fraction?
1
3
13
÷4=
14 What multiplication equation also solves of ?
4
15 How is 4 related to
÷ X
x ¹?
1
3
4
hood
Jemna has to devide [tex]1[/tex] cup pancake in [tex]4[/tex] mini pan cakes so that the batter be distributed in a fraction of [tex]\frac{1}{4}[/tex] th form
[tex]9[/tex]. The rectangle will be [tex]\frac{1}{3}[/tex] in fraction.
[tex]10[/tex]. Out of [tex]3 boxes[/tex] [tex]1[/tex] should be shaded.
[tex]11[/tex]. [tex]\frac{1}{3}[/tex] of [tex]4[/tex]
[tex]13[/tex]. [tex]\frac{1}{12}[/tex]
[tex]14[/tex]. [tex]\frac{1}{12}[/tex]
[tex]15[/tex] In division the value gets reciprocate ÷[tex]\frac{1}{3}[/tex][tex]\frac{4}{1}[/tex] = [tex]\frac{1}{3}[/tex]* [tex]\frac{1}{4}[/tex] by changing into multiplication.
What do you mean by fraction?Fractions are referred to as the components of a whole in mathematics. A single item or a collection of objects can be the whole. When we cut a slice of cake in real life from the entire cake, the portion represents the fraction of the cake.
[tex]9[/tex]. To calculate how much of a cup of dough will go into each pancake, divide [tex]1[/tex]÷[tex]4[/tex] to get [tex]\frac{1}{4}[/tex]
Let's now examine the rectangle that depicts a cup divided into three equally sized parts. Divide 1 by 3 to determine how much each portion represents as [tex]\frac{1}{3}[/tex]
[tex]10[/tex]. Out of [tex]3 boxes[/tex] [tex]1[/tex] should be shaded
[tex]11[/tex]. [tex]\frac{1}{3}[/tex] of [tex]4[/tex]
[tex]13.\frac{1}{12}= \frac{1}{3}[/tex]÷[tex]4[/tex][tex]=\frac{1}{3} *\frac{1}{4}[/tex]
[tex]14[/tex] Same as previous one
[tex]15[/tex] In division the value gets reciprocate ÷[tex]\frac{1}{3}[/tex][tex]\frac{4}{1}[/tex] = [tex]\frac{1}{3}[/tex]* [tex]\frac{1}{4}[/tex] by changing into multiplication.
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Now that you have mastered multiplying fractions by whole numbers, let's solve the
problem in the Real-World Connection.
Uma made sand art using green, red, blue, pink, and white sand. She used of 2/3
a cup of each color. How much sand did she use in all?
Answer:
10/3
Step-by-step explanation:
2/3+2/3+2/3+2/3+2/3=10/3
What is the equation of the line that has a slope of -1 and passes through the point (4,1) in slope-intercept form?
y=-1x-4
y = -1x +5
y=-1x-5
y = -1x +3
Answer:
[tex]1 = - 1(4) + b[/tex]
[tex]1 = - 4 + b[/tex]
[tex]b = 5[/tex]
[tex]y = - 1x + 5[/tex]
Please help with this answer, I will give brainliest to whoever answers correctly.
Answer:
2cos(3ẞ/2)(sin(7ẞ/2) + cos(19ẞ/2))
Step-by-step explanation:
We can use the identity for the sum of two sines to rewrite the expression as follows
sin 4ẞ + sin 10ẞ = 2sin(7ẞ/2)cos(3ẞ/2)
Similarly, we can use the identity for the sum of two cosines to rewrite the expression as follows
22ẞ + sin 16ẞ = 2cos(19ẞ/2)cos(3ẞ/2)
Therefore, we have
sin 4ẞ + sin 10ẞ + 22ẞ + sin 16ẞ = 2sin(7ẞ/2)cos(3ẞ/2) + 2cos(19ẞ/2)cos(3ẞ/2)
Factoring out the common factor of cos(3ẞ/2), we get
sin 4ẞ + sin 10ẞ + 22ẞ + sin 16ẞ = 2cos(3ẞ/2)(sin(7ẞ/2) + cos(19ẞ/2))
Therefore, the expression can be expressed as a product of 2cos(3ẞ/2) and the sum of sin(7ẞ/2) and cos(19ẞ/2).
What is arc mBC?
Inscribed angles
Answer:
[tex]\textsf{B.} \quad m\overset{\frown}{BC}=56^{\circ}[/tex]
Step-by-step explanation:
To find the measure of arc BC, first calculate the measures of arc ABC and arc BCD.
Definitions:
A chord is a straight line joining two points on the circle.An inscribed angle is the angle formed (vertex) when two chords meet at one point on a circle.An intercepted arc is the arc that is between the endpoints of the chords that form the inscribed angle.Inscribed Angle TheoremThe measure of an inscribed angle is half the measure of the intercepted arc.
Therefore, we can use the inscribed angle theorem to calculate the measures of arcs ABC and BCD:
[tex]\boxed{\begin{aligned}\angle ADC&=\dfrac{1}{2} \overset{\frown}{ABC}\\\\\implies 70^{\circ}&=\dfrac{1}{2} \overset{\frown}{ABC}\\\\ \implies \overset{\frown}{ABC}&=140^{\circ}\end{aligned}}[/tex] [tex]\boxed{ \begin{aligned}\angle BAD&=\dfrac{1}{2} \overset{\frown}{BCD}\\\\\implies 98^{\circ}&=\dfrac{1}{2} \overset{\frown}{BCD}\\\\ \implies \overset{\frown}{BCD}&=196^{\circ}\end{aligned}}[/tex]
The sum of the arcs is 360°. Therefore:
[tex]\overset{\frown}{ABC}+\overset{\frown}{CD}+\overset{\frown}{AD}=360^{\circ}[/tex]
Substitute the given measure of arc AD and the found measure of arc ABC and solve for arc CD:
[tex]\implies 140^{\circ}+\overset{\frown}{CD}+80^{\circ}=360^{\circ}[/tex]
[tex]\implies \overset{\frown}{CD}=140^{\circ}[/tex]
The measure of arc BCD is the sum of arcs BC and CD. Therefore:
[tex]\overset{\frown}{BC}+\overset{\frown}{CD}=\overset{\frown}{BCD}[/tex]
To find the measure of arc BC, substitute the found measures of arc CD and arc BCD and solve for BC:
[tex]\implies \overset{\frown}{BC}+140^{\circ}=196^{\circ}[/tex]
[tex]\implies \overset{\frown}{BC}=56^{\circ}[/tex]
Therefore, the measure of arc BC is 56°.
500g packet of beans cost £1.55
Answer: The packet is better value for money is a 125 g packet of beans which costs £0.36.
Step-by-step explanation:
The better value for money of a packet of beans can be calculated as follows?
The first step we can check on the first packet value for money by calculating the costs of 1 g of beans as follows :
(1/500) x £1.55 = £0,003
In the second step we can check on the second packet value for money by calculating the costs of 1 g of beans as follows :
(1/125) x £0.36 = £0,0028.
Hence, the better value for money between those two packets of beans is the second packet of beans which is given 125 g and costs £0.36
When John waters, his plants each day he keeps track of how many liters he uses. He measures in 1/8 liter amounts, and never uses more than 1 L the amount he uses each day varies, but he figures that if all the amounts work evened out he uses 1/2 L a day how did John decide this?
Use the following financial information to find the entry you would make on an income statement for INCOME BEFORE TAXES for the year ended December 31, 2011: Gross Sales, $223,000; Sales Returns and Allowances, $11,200; Sales Discounts, $1,800; Merchandise Inventory, January 1, 2011, $67,600; Merchandise Inventory, December 31, 2011, $78,300; Net Purchases, $84,000; Freight In, $950; Salaries, $107,200; Rent, $19,500; Utilities, $1,450; Insurance, $2,150; and Income Tax, $14,900.
INCOME BEFORE TAXES for the year ended December 31, 2011 is $669.
how to find gross profit ?Gross Profit = Gross Sales - Sales Returns and Allowances - Sales Discounts - Cost of Goods Sold
Cost of Goods Sold = Beginning Inventory + Net Purchases + Freight In - Ending Inventory
Cost of Goods Sold = $67,600 + $84,000 + $950 - $78,300 = $74,250
Gross Profit = $223,000 - $11,200 - $1,800 - $74,250 = $135,750
Operating Expenses = Salaries + Rent + Utilities + Insurance = $107,200 + $19,500 + $1,450 + $2,150 = $130,300
Income Before Taxes = Gross Profit - Operating Expenses - Income Tax
Income Before Taxes = $135,750 - $130,300 - $14,900 = $669
Therefore, the entry for INCOME BEFORE TAXES for the year ended December 31, 2011 is $669.
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An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 3 ft long with a diameter of 1.8 ft. Suppose oil is drained at a rate of 1.7 ft³ per minute. If the tank starts completely full, how many minutes will it take to empty the tank? Use the value 3.14 for pi, and round your answer to the nearest minute. Do not round any intermediate computations.
Answer:
4 minutes
Step-by-step explanation:
You want to know how long it takes to drain a cylindrical tank 1.8 ft in diameter and 3 ft long at the rate of 1.7 ft³/minute. (π = 3.14)
VolumeThe volume of a cylinder can be found using the formula ...
V = (π/4)d²h . . . . . . . diameter d, height h
Then the volume of the oil tank is ...
V = 3.14/4(1.8 ft)²(3 fft) = 7.6302 ft³
TimeThe time it takes to empty the tank is found by dividing the volume by the rate:
(7.6302 ft³)/(1.7 ft³/min) ≈ 4.49 min ≈ 4 min
It will take about 4 minutes to empty the tank.
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Tests show that the lives of light bulbs are
normally distributed with a mean of 750 hours
and a standard deviation of 75 hours. Find
the probability that a randomly selected light
bulb will last between 675 and 900 hours.
525 600 675 750 825 900 975
P = [?]%
Hint: use the 68 - 95 - 99.7 rule.
Enter
Answer: like three out of a thousand, would be likely to last less than 525 hours or more than 975 hours.
Step-by-step explanation:
normal distribution is shaped like a bell curve with the average (mean) at the center.
A light bulb in your problem is most likely to last about 750 hours. One standard deviation up from that would be 750 + 75, which is 825 hours, and one standard deviation down is 750 - 75, which is 675 hours.
According to the empirical rule, the interval from the average to +1 standard deviation (750 to 825) and the interval from the average to -1 standard deviation (675 to 725) each have a 34.1% probability.
From +1 to +2 standard deviations and -1 to -2 standard deviations (825 to 900 and 600 to 675) the probability is 13.5% for each interval.
From +2 to +3 standard deviations and -2 to -3 standard deviations (900 to 975 and 525 to 600) the probability is 2.1% for each interval.
These percentages are the same for any normal distribution problem. If you add up the chances you can find the probability a light bulb will last an increasing range of times centered around the average:
Within one standard deviation of the average: 68.3% (chance it will last 675 to 825 hours)
Within two standard deviations of the average: 95.4% (chance it will last 600 to 900 hours)
Within three standard deviations of the average: 99.7% (chance it will last 525 to 975 hours)
And only a very few, like three out of a thousand, would be likely to last less than 525 hours or more than 975 hours.
Which of the following expressions is equal to 9?
4 x (one-half x 6) ÷ 3
6 ÷ (one-fourth x 3 x one and one-fourth)
8 + (one-third x 6) ÷ 5
10 − (one-fifth x 10) + 1
the companies bounce zone and jump world run many trampoline parks around the country. the box plots show the number of trampolines at their park. which conclusion is best supported by the box plots?
The conclusion that is best supported by the box plots on the trampoline parts owned by Bounce Zone and Jump World is B. For both companies, about 25% of the parks have 21 or fewer trampolines.
What does the box plot show ?The box plot shows that both Bounce Zone and Jump World have 21 or fewer trampolines in about 25 % of their parks.
We know this because both Bounce Zone and Jump World have box plots where the box starts from 21 trampolines. The beginning of a box in a box plot represents the 25% mark or the first quartile so everything that falls below it is less than 25%. Bounce Zone and Jump World therefore have 21 or less trampolines in 25% of their parks.
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The options for the question is:
Bounce Zone has more parks than Jump World.For both companies, about 25% of the parks have 21 or fewer trampolines.Jump World has a park with 25trampolines, but Bounce Zone does not.For both companies, about half the parks have more than 26 trampolines.What is the measure of each interior angle of the regular polygon pictured below? If necessary, round to the nearest tenth.
[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=5 \end{cases}\implies 5\theta =180(5-2) \\\\\\ 5\theta =180(3)\implies 5\theta =540\implies \theta =\cfrac{540}{5}\implies \theta =108[/tex]
How can I solve this?
Answer: x= −6
x=4
Step-by-step explanation:
Which economic system has no government involvement in the market? a. capitalism b. communism c. socialism d. No economic system is free from government involvement. Please select the best answer from the choices provided A B C D Mark this and return
Answer: D is correct.
Step-by-step explanation:
The economic system that has no government involvement in the market is d. No economic system is free from government involvement.
In reality, there is no government intervention because at some point the government will comes in , this could actually be minimal, only in the free market is where there is no government intervention.
It should be noted that in this free market, there is an unregulated system of economic exchange, where the act of taxes collection as well as quality controls, has no economic interventions which can be attributed to the government. Because of this, option D is correct.
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Write an equation for the translation of y=4/x
that has the given asymptotes.
X=-2
Y=7
Answer:y=4/x−4−3
Step-by-step explanation:Explanation:
translation of 4 units right
translation of 3 units down
y=f(x)→y=f(x−4)−3
Find the area of a circle with diameter = 16 units.
Answer: ;)
The area of a circle is 64 square units
Step-by-step explanation:
Area of a circle a=64 square units in terms of
Step-by-step explanation:
Given that the diameter of a circle is 16
That is d=16
Therefore radius r=8
Now to find the area of a circle :Area of a circle square units
Substitute r=8 we get
Area of a circle
Therefore the area of a cicle is 64 square units
Area of a circle a=64 square units in terms of