Remember that
The formula for the number of independent pairwise comparisons is k(k-1)/2, where k is the number of conditions
In this problem
k=15
substitute
15(15-1)/2=105
therefore
The answer is 105Sheridan Company purchased a truck for $79,000. The company expected
the truck to last four years or 120,000 miles, with an estimated residual
value of $12,000 at the end of that time. During the second year the truck
was driven 45,000 miles. Compute the depreciation for the second year
under each of the methods below and place your answers in the blanks
provided.
Units-of-activity
Double-declining-balance
The depreciation in year 2 using the units of activity method is $23,125.
The depreciation in year 2 using the double declining balance is $19,750.
What is the depreciation in year 2?
Depreciation is when the value of an asset declines as a result of wear and tear.
Deprecation in year 2 using the units of activity method = (miles driven in year 2 / total miles) x (cost of the asset - salvage value)
Deprecation = (45,000 / 120,000) x ($79,000 - $12,000)
Deprecation = $23,125
Deprecation using the double declining method = (2/ useful life) x cost of the asset
Depreciation in year 1 = (2/4) x 79,000 = $39,500
Book value in year 2 = 79,000 - $39,500 = $39,500
Depreciation in year 2 = (2/4) x $39,500 = $19,750
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Kirby wants to run a total of 7 5/8 miles every Tuesday and Thursday. If he runs 4 4/16 miles onTuesday and 3 3/8 miles on Thursday, will he meet his goal for this week? Explain.
Given:
Kirby wants to run a total of 7 5/8 miles every Tuesday and Thursday.
If he runs 4 4/16 miles on Tuesday and 3 3/8 miles on Thursday,
Then, the total miles he will cover is,
[tex]\begin{gathered} 4\frac{4}{16}+3\frac{3}{8}=4\frac{1}{4}+3\frac{3}{8} \\ =\frac{17}{4}+\frac{27}{8} \\ =\frac{34}{8}+\frac{27}{8} \\ =\frac{61}{8} \\ =7\frac{5}{8} \end{gathered}[/tex]Since, he will cover total of 7 5/8 miles.
So, he will meet his goal for this week.
11.) SOLVE the equation for w by using "factoring by grouping". YOUMUST SHOW ALL STEPS of the grouping process, especially theFIRST STEP of grouping to receive FULL CREDIT. (10 pts)2w3 + 5w2 - 32w - 80 = 0
ANSWER:
w = -5/2, w = 4 and w = -4
STEP-BY-STEP EXPLANATION:
We have the following equiation:
[tex]2w^3+5w^2-32w-80=0[/tex]We solve with the help of factoring by grouping
[tex]\begin{gathered} (2w^3+5w^2)+(-32w-80)=0 \\ w^2\cdot(2w+5)-16\cdot(2w+5)=0 \\ (2w+5)\cdot(w^2-16)=0 \\ 2w+5=0\rightarrow w=-\frac{5}{2} \\ (w^2-16)=0\rightarrow w^2=16\rightarrow w=\pm4\rightarrow w=4,w=-4 \end{gathered}[/tex]The solutions are w = -5/2, w = 4 and w = -4
which of the following Roots would be between 8 and 7
To find which of the following roots is between "8" and "7" we can calculate the root of which numbers result in 8 and 7. To do this we will power them by 2, this is done because power is the oposite operation to the root. Doing this gives us:
[tex]\begin{gathered} 8^2=64 \\ 7^2=49 \end{gathered}[/tex]So the root of 64 is 8 and the root of 49 is 7. We need to find the number that is between 49 and 64.
From the options the only one that qualifies is 52. The correct option is b.
- 23 = -9+7(v - 3)could I please get some help
we have
- 23 = -9+7(v - 3)
apply distributive property right side
-23=-9+7v-21
combine like terms
-23=7v-30
Adds 30 both sides
-23+30=7v-30+30
7=7v
Divide by 7 both sides
7/7=7v/7
1=v
v=1which values are in the domain of the function F(X)= -6x + 11 with a range of (-37 ,-25, -13, -1)? select all that apply a)1b)4c)8d)5e)2f)6g)3h)7
Answers:
2
4
6
8
Explanation:
The domain of the function with a range {-37, -25, -13, -1} will be the set of values of x when f(x) is -37, -25, -13, and -1. So, to find the correct answers, we need to solve the following equations:
If f(x) = -37, we get:
[tex]\begin{gathered} f(x)=-6x+11 \\ -37=-6x+11 \\ -37-11=-6x+11-11 \\ -48=-6x \\ \frac{-48}{-6}=\frac{-6x}{-6} \\ 8=x \end{gathered}[/tex]If f(x) = - 25, we get:
[tex]\begin{gathered} -25=-6x+11 \\ -25-11=-6x+11-11 \\ -36=-6x \\ \frac{-36}{-6}=\frac{-6x}{-6} \\ 6=x \end{gathered}[/tex]If f(x) = - 13, we get:
[tex]\begin{gathered} -13=-6x+11 \\ -13-11=-6x+11-11 \\ -24=-6x \\ \frac{-24}{-6}=\frac{-6x}{-6} \\ 4=x \end{gathered}[/tex]If f(x) = -1, we get:
[tex]\begin{gathered} -1=-6x+11 \\ -1-11=-6x+11-11 \\ -12=-6x \\ \frac{-12}{-6}=\frac{-6x}{-6} \\ 2=x \end{gathered}[/tex]Therefore, the domain is the set of the values of x: {2, 4, 6, 8}
What is the worst part of being a girl?
Answer:
men.
Step-by-step explanation:
just men
Answer:
is this really a question?...
Step-by-step explanation:
Find the value of x.
Answer:
this is very simple
Step-by-step explanation:
the answer of this question is x=12 only
-3x+5y=-8 solve for x and y
ANSWER
The set of equations has no solution
EXPLANATION
-3x + 5y = -8 ------ equation 1
6x - 10y = 16 -------- equation 2
These two equations can be solve simultaneously either by substitution method or elimination method
To solve for the value of x and y, we will be using the elimination method
-3x + 5y = -8
6x - 10y = 16
Let us eliminate x first.
We need to make the coefficient of x in both equation equal
Hence, multiply equation 1 by 2 and equation 2 by 1
-3x*2 + 5y*2 = -8 x 2
6x * 1 - 10y * 1 = 16 x 1
-6x + 10y = -16 ------------ equation 3
6x - 10y = 16 -------------- equation 4
To eliminate x , add equation 3 and 4 together
-6x + 6x + 10y + (-10y) = -16 + 16
-6x + 6x + 10y - 10y = -16 + 16
0 + 0 = 0
0 = 0
Hence, the set of equations has no solution
A town's population is 52,525. About 75 people move out of the town each month. Each month, 200 people on average move into town. A nearby town has a population of 56,375. It has no one moving in and an average of 150 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation Then solve the equation and answer the question.
The required equation to model the given situation is 52,525 - 75x +200x = 56,375 - 150x. the value of x = 14; the populations will be equal in 14 months.
Let x represents the number of months, the first town's population rise is 75x and its drop is 200x. The population of the second town has decreased by 150x.
We want to find m such that the increases and decreases equalize the populations of the towns. In each case, we add the increases and subtract the decreases from the base population.
As per the given situation, the required equation would be as:
52,525 - 75x +200x = 56,375 - 150x
Rearrange the terms likewise and apply the arithmetic operation,
150x + 200x - 75x = 56,375 - 52,525
275x = 3850
x = 3850 / 275
x = 14
Thus, the required equation to model the given situation is 52,525 - 75x +200x = 56,375 - 150x. the value of x = 14; the populations will be equal in 14 months.
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Consider the following set of equations:Equation M: 3y = 3x + 6Equation P: y = x + 2Which of the following best describes the solution to the given set of equations? No solutionOne solutionTwo solutionsInfinite solutions
Solution
Given
Equation M: 3y = 3x + 6
Equation P: y = x + 2
Plot the graph of the two equation
The graph of the two equations are the same. With the same slope and intercept
The graph is shown below
Conclusion:
Because the graph of the equatons are thesame, the system of equations have Infinite solutions
The answer is Infinite solutions
Window45°Apartment450BenchNoah can see a bench in the nearby play area through his window inhis apartment at a 45° angle of depression.If the floor of the apartment that Noah is standing is 25 feet abovethe ground level, what is the horizontal distance from the apartmentto the bench in the play area?
Given:
The angle of depression of the bench with respect to Noah, θ=45° .
The height of the apartment or the height at which Noah is standing with respect to the ground, h=25 feet.
Let x be the horizontal distance from the apartment to the bench.
Now, using trigonometric property in the above triangle,
[tex]\begin{gathered} \tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan \theta=\frac{h}{x} \end{gathered}[/tex]Substitute the values and solve the equation for x.
[tex]\begin{gathered} \tan 45^{\circ}=\frac{25\text{ ft}}{x} \\ 1=\frac{25\text{ ft}}{x} \\ x=25\text{ ft} \end{gathered}[/tex]Therefore, the horizontal distance from the apartment to the bench is 25 ft.
A van with seven people drove 422 miles six hours. About how many miles did they travel each hour?
Distance travelled by van in six hours is 422 miles.
Determine the distance travelled by the van in one hour.
[tex]\begin{gathered} \frac{422}{6}=70.333 \\ \approx70.3\text{ miles} \end{gathered}[/tex]So, they travel approximately 70.3 miles in each hour.
Question 2 Find the area of the figure below. Ty below. 24 yd 24 yd 24 yd 40 yd
Answer:
1536 yd²
Explanation:
To find the area of the figure, we need to divide the figure into 2 rectangles as:
So, the area of the first rectangle is equal to:
[tex]\begin{gathered} \text{Area = Base x Height } \\ \text{Area = 24 yd x 24 yd} \\ \text{Area = 576 yd}^2 \end{gathered}[/tex]In the same way, the area of the second rectangle is:
[tex]\begin{gathered} \text{Area = Base x Height } \\ \text{Area = 40 yd }\times24\text{ yd} \\ \text{Area = 960 yd}^2 \end{gathered}[/tex]So, the area of the figure is:
576 yd² + 960 yd² = 1536 yd²
Therefore, the answer is 1536 yd²
48 feet wide . the sides of the roof meet to form a right angle and both sides of the roof are the same length. find the length of the roof rafters find x
Given the image in the question, it can be seen that the roof forms a right angled triangle. Therefore, we can get the length of the roof rafters (x) by using the Pythagoras theorem.
Step 1: We define the Pythagoras theorem and state our parameters
[tex]\begin{gathered} \text{hypotenuse}^2=opposite^2+adjacent^2 \\ \text{hypotenuse}=48ft,\text{ adjacent=opposite=}xft \end{gathered}[/tex]Step 2: We substitute the values into the theorem to solve for x
[tex]\begin{gathered} 48^2=x^2+x^2 \\ 2x^2=2304 \\ x^2=\frac{2304}{2} \\ x^2=1152 \\ x=\sqrt[2]{1152} \\ x=33.9411255 \\ x\approx33.94ft \end{gathered}[/tex]Hence, the length of the roof rafters (x) is 33.94ft to the nearest hundredth.
Determine whether each number is a solution of the given inequality.5b - 7>13
Solve for b:
Add 7 to both sides:
[tex]\begin{gathered} 5b-7+7>13+7 \\ 5b>20 \end{gathered}[/tex]Divide both sides by 5:
[tex]\begin{gathered} \frac{5b}{5}>\frac{20}{5} \\ b>4 \end{gathered}[/tex]Answer:
b > 4
The bookstore is selling 4 books for $10 in a clearance sale. If Regina has $28 to spend, how many books can she purchase in the clearance sale?
The bookstore is selling 4 books for $10 in a clearance sale. If Regina has $28 to spend, how many books can she purchase in the clearance sale?
In this problem
Applying proportion
we have
4/10=x/28
solve for x
x=(4/10)*28
x=11.2
therefore
answer is 11 booksIf P(6,-2). O(-2,8), R(-4, 3), and S(-9, y). find the value of y so that PO perpendicular to RS.please?
Answer:
y = - 1
Explanation:
Two lines are perpendicular if the product of their slopes is equal to -1.
Additionally, we can calculate the slope of a line with two points (x1, y1) and (x2, y2) as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]If we replace (x1, y1) by P(6, -2) and (x2, y2) by O(-2, 8), we get that the slope of PO is equal to:
[tex]m=\frac{8-(-2)}{-2-6}=\frac{8+2}{-8}=\frac{10}{-8}=-1.25[/tex]In the same way, if we replace (x1, y1) by (-4, 3) and (x2, y2) by (-9, y), we get that the slope of RS is equal to:
[tex]m_{}=\frac{y-3}{-9-(-4)}=\frac{y-3}{-9+4}=\frac{y-3}{-5}[/tex]Then, the product of these two slopes should be equal to -1, so we can write the following equation:
[tex]-1.25\cdot(\frac{y-3}{-5})=-1[/tex]So, solving for y, we get:
[tex]\begin{gathered} (-5)(-1.25)\cdot(\frac{y-3}{-5})=(-5)(-1) \\ -1.25(y-3)=5 \\ y-3=\frac{5}{-1.25} \\ y-3=-4 \\ y=-4+3 \\ y=-1 \end{gathered}[/tex]Therefore, the value of y is equal to -1
Plot the point given by the following polar coordinates on the graph below. Each circular grid line is 0.5 units apart.(2, -1)
In polar coordinates we must have two things to plot a point, it's the radius and the angle
If we use a negative angle, it just means that we are doing the rotation clockwise.
Therefore the point (2, -π) is
We do a 2 units long line and rotate is by -π, the result is
We estimate that the population of a certain, in t years will be given byp (t) = (2t² + 75) / (2t² + 150) million habitantsAccording to this hypothesis:What is the current population?What will it be in the long term?Sketch the population graph
Given that the population can be represented by the equation;
[tex]P(t)=\frac{2t^2+75}{2t^2+150}[/tex]The current population (Initial population) is the population at time t=0;
Substituting;
[tex]t=0[/tex][tex]\begin{gathered} P(0)=\frac{2t^2+75}{2t^2+150}=\frac{2(0)^2+75}{2(0)^2+150}=\frac{75}{150} \\ P(0)=0.5\text{ million} \end{gathered}[/tex]Therefore, the current population of the habitat is;
[tex]0.5\text{ million}[/tex]The long term population would be the population as t tends to infinity;
[tex]\begin{gathered} \lim _{t\to\infty}P(t)=\frac{2t^2+75}{2t^2+150}=\frac{2(\infty)^2+75}{2(\infty)^2+150}=\frac{\infty}{\infty} \\ \lim _{t\to\infty}P(t)=\frac{4t}{4t}=1 \end{gathered}[/tex]Therefore, the long term population of the habitat is;
[tex]P(\infty)=1\text{ million}[/tex]What is the probability that the spinner lands on blue?
Answer:
Concept:
The total number of angles in a circle is
[tex]\begin{gathered} =360^0 \\ =120^0+60^0+180^0=360^0 \end{gathered}[/tex]The angle of the sector that represents blue is
[tex]=60^0[/tex]To calculate the probability, we will use the formula below
[tex]\begin{gathered} P(\text{blue)}=\frac{n(\text{blue)}}{n(S)} \\ n(\text{blue)}=60^0,n(S)=360^0 \\ P(\text{blue)}=\frac{n(\text{blue)}}{n(S)}=\frac{60}{360} \\ P(\text{blue)}=\frac{1}{6} \end{gathered}[/tex]Hence,
The final answer is = 1/6
hunter says that there should be a decimal point in the quotient below after 6. is he correct? use number sense to explain your answer. 69.48 ÷ 7.2= 965
Solution
For this case we can do this:
[tex]undefined[/tex]Jaron made a trip of 450 miles in 8hours. Before noon he averaged 60 miles per hour , and afternoon he averaged 50 miles per hour. At what time did he begin his trip and when did he end it?
Data:
Total distance: 450 miles
Total time: 8 h
Average 60 mi/h before noon
Average 50 mi/h afternoon
The relationship between the time, speed (average) and distance is drescribed in the next equations:
[tex]\begin{gathered} s=\frac{d}{t} \\ \\ d=s\times t \\ \\ \end{gathered}[/tex]Then, if you multiply the speed and the time you get the distance:
time before noon: b
time afternoon: a
[tex](60\times b)+(50\times a)=450[/tex]The sum of a and b is the total time:
[tex]a+b=8[/tex]Use the next system of equations to find a and b:
[tex]\begin{gathered} 60b+50a=450 \\ a+b=8 \end{gathered}[/tex]1. Solve a in the second equation:
[tex]\begin{gathered} \text{Subtract b in both sides of the equation:} \\ a+b-b=8-b \\ \\ a=8-b \end{gathered}[/tex]2. Substitute the a in first equation by the value you get in first step:
[tex]60b+50(8-b)=450[/tex]3. Solve b:
[tex]\begin{gathered} 60b+400-50b=450 \\ 10b+400=450 \\ \\ \text{Subtract 400 in both sides of the equation:} \\ 10b+400-400=450-400 \\ 10b=50 \\ \\ \text{Divide both sides of the equation into 10:} \\ \frac{10}{10}b=\frac{50}{10} \\ \\ b=5 \end{gathered}[/tex]4. Use the value of b=5 to solve a:
[tex]\begin{gathered} a=8-b \\ a=8-5 \\ a=3 \end{gathered}[/tex]Then, Jaron begin his trip 5 hours before noon ( at 7:00) and end it 3 hours afternoon (at 15:00)A boat is heading towards a lighthouse, whose beacon-light is 135 feet above the water. The boat's crew measures the angle of elevation to the beacon, 4 deg What is the ship's horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary .
The ship's horizontal distance from the lighthouse is: 1930.59 feet.
What is tangent or tan in trigonometry?
The ratio of the side opposite the angle we know or want to know over the side next to that angle is known as the tangent, which is sometimes abbreviated as T-A-N. The side touching the angle that is NOT the hypotenuse, or the side opposite the right angle, is the neighboring side.
Given in the question,
Height of lighthouse = 135 feet,
angle of elevation = 4 degree,
We know that, tan Θ = perpendicular/ base
Here, height is perpendicular and distance is base,
Putting the values,
tan4° = 135/B
B = 1930.59 feet
Therefore, distance is 1930.59 feet.
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Answer:The answer is 1930.59
Step-by-step explanation:
Choose the expression that is equivalent to 9w² +3/5(20w² - 15w+10)+2w
The correct answer or equivalent expression is 21w² - 7w + 6.
What is the equivalent of an expression?X-terms and constants should be combined with any other like and similar terms on either side of the equation. By putting the terms in the same order, with the x-term usually comes before the constants. The two phrases or equation are equal if and only if each of their terms is the same.
It is given in the question that 9w² +[tex]\frac{3}{5}[/tex](20w² - 15w+10)+2w
⇒ 9w² + [tex]\frac{3}{5}[/tex] (20w² - 15w+10)+ 2w
⇒ 9w² + [tex]\frac{3}{5}[/tex] × 5 (4w² - 3w+2) + 2w
⇒ 9w² + 3(4w² - 3w+2) + 2w
⇒ 9w² + 12w² - 9w + 6 + 2w
⇒ 21w² - 7w + 6
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Please explain why the lowest value is at four why it’s not at six?
Solution
- The lowest value of the sinusoidal function is usually gotten using the formula:
[tex]\begin{gathered} L=M-A \\ where, \\ M=\text{ The value of the midline} \\ A=\text{ The Amplitude or highest value} \end{gathered}[/tex]- The question says that the sea falls 6ft below sea level and rises 6ft above sea level.
- The midline M represents the sea level and the rise of 6ft represents the amplitude.
- Thus, the above equation can be rewritten as:
[tex]L=M-6[/tex]- The formula for finding the peak of the sinusoidal is:
[tex]\begin{gathered} U=M+A \\ where, \\ U=\text{ The Peak or height of the water} \end{gathered}[/tex]- We can similarly rewrite the equation as:
[tex]U=M+6[/tex]- We have been given the peak height of the water to be 16. Thus, U = 16. Thus, we can find the midline (M) as follows:
[tex]\begin{gathered} U=M+6 \\ put\text{ }U=16 \\ 16=M+6 \\ \text{ Subtract 6 from both sides} \\ M=16-6=10 \end{gathered}[/tex]- Thus, the midline (M) is at 10ft. This also implies that the sea level is at 10 ft.
- Thus, we can find the lowest value or low line as follows:
[tex]\begin{gathered} L=M-6 \\ \text{ We know that }M=10 \\ \\ \therefore L=10-6=4ft \end{gathered}[/tex]Final Answer
The lowest value or Low line is at 4ft
To the nearest centimeter, find the surface area of a hemisphere with 15 inch diameter
Given:
The diameter of the hemisphere is 15 inches.
To find:
The surface area of a hemisphere.
Explanation:
The radius of the hemisphere is
[tex]r=\frac{15}{2}inches[/tex]Using the formula of the surface area of a hemisphere,
[tex]\begin{gathered} S.A=2\pi r^2 \\ =2\times3.14\times(\frac{15}{2})^2 \\ =353.25 \\ \approx353square\text{ }inches \end{gathered}[/tex]Final answer:
The surface area of the hemisphere is 353 square inches.
1. Find the area of the triangle below. 13 in9in7in18 in63 inches squared91 inches squared126 inches squaredO 45.5 inches squared
ANSWER:
63 square inches
STEP-BY-STEP EXPLANATION:
We have the formula to calculate the area of the triangle is the following:
[tex]A=\frac{b\cdot h}{2}[/tex]Replacing:
[tex]\begin{gathered} A=\frac{7\cdot18}{2} \\ A=63 \end{gathered}[/tex]The area equals 63 square inches
for a function f(x)=x^2, write an equation for that function stretched vertically by a factor of 4, and shifted 2 units to the right
the initial function is:
[tex]f(x)=x^2[/tex]to stretch the fuction vertically we have to divide by 4 y so:
[tex]\begin{gathered} \frac{f(x)}{4}=x^2 \\ f(x)=4x^2 \end{gathered}[/tex]now to move two units to the right we have to rest 2 in the x so:
[tex]f(x)=4(x-2)^2[/tex]a triangle has side lengths for 8 in and 7 in select all the possible lengths for the third side 6 inches 15 inches 7 inches 20 inches 9 inches
To answer this question, we need to take into account the triangular inequality, that is, in a triangle, the sum of two sides must be greater than one side of the triangle. That is:
[tex]a+b>c,b+c>a,a+c>b[/tex]We can see that two of the sides are:
a = 8 in, and b = 7 in, then, we have:
a + b = 8 + 7 = 15. Therefore:
[tex]15>6,\text{ and 15>7,15>9}[/tex]Therefore, the possible lengths for the third side are:
• 6 inches
,• 7 inches
,• 9 inches