I’ve been working on these similar questions but coming to this question. I found myself being stuck.
Answers
Solution:
If the variation in pressure is P pounds per square inch, then the Loudness L in decibels is;
[tex]L=20\log _{10}(121.3P)[/tex]When L=115 decibels;
[tex]\begin{gathered} 115=20\log _{10}(121.3P) \\ \text{Divide both sides by 20;} \\ \frac{115}{20}=\frac{20\log_{10}(121.3P)}{20} \\ \log _{10}(121.3P)=5.75 \end{gathered}[/tex]But from the logarithmic law, we have;
[tex]\log _ba=c\leftrightarrow a=b^c[/tex]Thus,
[tex]\begin{gathered} \log _{10}(121.3P)=5.75 \\ 121.3P=10^{5.75} \\ 121.3P=562341.33 \end{gathered}[/tex][tex]\begin{gathered} \text{Divide both sides by 121.3;} \\ \frac{121.3P}{121.3}=\frac{562341.33}{121.3} \\ P\cong4635.95 \end{gathered}[/tex]FINAL ANSWER:
[tex]4636.0\text{ pounds per square inch.}[/tex]Related Questions
Pls help me with this I will give brainless thank u <3
Answers
15.sum,neg
16.sum,neg
17.diff,neg
18.sum,neg
19.sum,pos
20.neg
21.pos
22.neg
23.pos
24.neg
I just finished my other 2 questions and I need help with this one now, I don't understand the letters really. please help
Answers
So, c(x) = 8.25x + 1500
the marginal cost doubles so, (8.25 x) will be 2 * (8.25x )
And the fixed cost decreased by 30%
so, 1500 will be (1 - 30%) of 1500
so, (1 - 30%) of 1500 = 70% of 1500 = 0.7 * 1500 = 1050
So, k(x) = 2 * (8.25x) + 1050
K(x) = 16.5 x + 1050
Cobalt-60 has a half-life of about 5 years. After 20 years, how many grams of a2,076 gram sample will remain? Round to the hundredths place, if answer doesn'thave a tenths place then use a zero so the answer does.
Answers
Solution:
The formula for half-life is given below as
[tex]N(t)=N_0(\frac{1}{2})^{\frac{t}{\frac{t1}{2}}}[/tex]Where the given values are
[tex]\begin{gathered} N_0=2076g \\ t=20years \\ t^{\frac{1}{2}}=5years \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} N(t)=N_{0}(\frac{1}{2})^{\frac{t}{\frac{t\times1}{2}}} \\ N(t)=2076\times(\frac{1}{2})^{\frac{20}{5}} \\ N(t)=2076\times(\frac{1}{2})^4 \\ N(t)=\frac{2076}{16} \\ N(t)=129.75g \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow129.75g[/tex]Assume your salary is $24,000 per year and $50 for each computer you sell. What function represents your total pay for one year? Be sure to indicate any domain restrictions.
Answers
Let x represent the total amount of computers you sell in one year.
Since you get $50 for each computer, then, you would get 50x for x computers.
Additionally, your base salary is $24,000. Then, add 50x and 24,000 to find your total salary in a year.
If f(x) is a function that represents your salary depending on the amount of computers you sell, then:
[tex]f(x)=50x+24000[/tex]Notice that the amount of computers that you sell cannot be a negative number. Then, you must take into account the following restriction:
[tex]x\ge0[/tex]Therefore, the answer is:
[tex]f(x)=50x+24000\text{ for }x\ge0[/tex]Give the digits in the ones place and the hundredths place.
12.86
Please help ASAP
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Need help with a math word problem for homework. Thank you in advance
Answers
Given:
A client is making a 10-lb bag of trail mix
The chocolates cost $4 per pound and mixed nuts cost $7 per pound
the client has a budget of $6.1 per pound
We will use the variables c and n to represent the number of pounds for chocolates and nuts
So, we have the following system of equations:
[tex]\begin{gathered} c+n=10\rightarrow(1) \\ 4c+7n=6.1\cdot10\rightarrow(2) \end{gathered}[/tex]Solving the system by substitution method
From equation (1)
[tex]c=10-n\rightarrow(3)[/tex]substitute with (c) from equation (3) into equation (2)
[tex]\begin{gathered} 4(10-n)+7n=6.1\cdot10 \\ \end{gathered}[/tex]solve the equation to find (n)
[tex]\begin{gathered} 4\cdot10-4n+7n=6.1\cdot10 \\ -4n+7n=6.1\cdot10-4\cdot10 \\ 3n=21 \\ n=\frac{21}{3}=7 \end{gathered}[/tex]Substitute with (n) into equation (3) to find (c)
[tex]c=10-7=3[/tex]so, the answer will be:
The number of pounds of chocolates = c = 3 pounds
The number of pounds of nuts = n = 7 pounds
The radius of a circle is 8 inches. What is the area?Give the exact answer in simplest form. _____ square inches. (pi, fraction)
Answers
Given:
Radius of circle is 8 inches.
The objective is to find the area of the circle.
The formula to find the area of the circle is,
[tex]\begin{gathered} A=\pi r^2 \\ =\pi\times8\times8 \\ =64\pi \\ =201in^2 \end{gathered}[/tex]Hence, the area of the circle is 201 square inches.
How do I graph a line with a equation in slope intercept form?An example is y=-3x+3, how do I graph this?
Answers
we have
y=-3x+3
to graph a line we need at least two points
so
Find out the intercepts
y-intercept (value of y when the value of x is zero)
For x=0
y=-3(0)+3
y=3
y-intercept is (0,3)
x-intercept (value of x when the value of y is zero)
For y=0
0=-3x+3
3x=3
x=1
x-intercept is (1,0)
therefore
Plot the points (0,3) and (1,0)
and join them to graph the line
see the attached figure to better understand the problem
Question 5 Fill in the table. First Integer Next Integers Give four consecutive odd integers: The simplified sum of the second and forth integers are Question Help: Message instructor Submit Question
Answers
The four consecutive odd integers
If the first integer is given to be x
Then the next three are:
x + 2, x+ 4 and x+ 6
The sum of the second and forth integers :
x+2 + x+ 6 = 2x + 8
Hence, the sum of the second and forth integers are: 2x+8
During the spring, Mr. Salina's grass grows at a rate of 1.5 inches per week. During a rainy stretch in the summer, his grass grew a total of 8 inches in 4 weeks.
Answers
Based on the growth rate of Mr. Salina's grass per week in the summer, and in spring, the relationship is not proportional.
How are relationships proportional?When relationships are said to be proportional, it means that they increase or decrease by the same rate.
In the spring, Mr. Salina's grass grows at a rate of 1.5 inches per week.
In the rainy stretch of summer, this rate goes to:
= Total number of inches / Number of weeks
= 8 / 4
= 2 inches per week
This means that the relationship is not proportional and one rate is higher than the other.
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im not sure the steps to this math problem, from step one to step three
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The equation of the second line is written in standard form. To know the slope of this line, we can rewrite its equation in slope-intercept form by solving for y.
[tex]\begin{gathered} ax+by=c\Rightarrow\text{ Standard form} \\ y=mx+b\Rightarrow\text{ Slope-intercept form} \\ \text{ Where m is the slope and b is the y-intercept} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} 4x-5y=-10 \\ \text{ Subtract 4x from both sides of the equation} \\ 4x-5y-4x=-10-4x \\ -5y=-10-4x \\ \text{Divide by -5 from both sides of the equation} \\ \frac{-5y}{-5}=\frac{-10-4x}{-5} \\ y=\frac{-10}{-5}-\frac{4x}{-5} \\ y=2+\frac{4}{5}x \\ \text{ Reorganize} \\ y=\frac{4}{5}x+2 \\ \text{ Then} \\ $$\boldsymbol{m=\frac{4}{5}}$$ \end{gathered}[/tex]Now, two lines are perpendicular if their slopes satisfy the following equation:
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ \text{ Where }m_1\text{ is the slope of the first equation and} \\ m_2\text{ is the slope of the second equation} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} m_2=\frac{4}{5} \\ m_1=-\frac{1}{\frac{4}{5}_{}} \\ m_1=-\frac{\frac{1}{1}}{\frac{4}{5}_{}} \\ m_1=-\frac{1\cdot5}{1\cdot4} \\ $$\boldsymbol{m}_{\boldsymbol{1}}\boldsymbol{=-\frac{5}{4}}$$ \end{gathered}[/tex]Step 2Since we already have a point on the line and its slope, then we can use the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1)\Rightarrow\text{ Point-slope formula} \\ \text{ Where } \\ m\text{ is the slope and} \\ (x_1,y_1)\text{ is a point through which the line passes} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} (x_1,y_1)=(6,3) \\ m=-\frac{5}{4} \\ y-3=-\frac{5}{4}(x-6) \\ \text{ Apply the distributive property} \\ y-3=-\frac{5}{4}\cdot x-\frac{5}{4}\cdot-6 \\ y-3=-\frac{5}{4}x+\frac{5}{4}\cdot6 \\ y-3=-\frac{5}{4}x+\frac{30}{4} \\ \text{ Add 3 from both sides of the equation} \\ y-3+3=-\frac{5}{4}x+\frac{30}{4}+3 \\ y=-\frac{5}{4}x+\frac{30}{4}+\frac{12}{4} \\ y=-\frac{5}{4}x+\frac{30+12}{4} \\ y=-\frac{5}{4}x+\frac{42}{4} \\ \text{ Simplify} \\ y=-\frac{5}{4}x+\frac{21\cdot2}{2\cdot2} \\ y=-\frac{5}{4}x+\frac{21}{2} \end{gathered}[/tex]Step 3Therefore, the equation of the line that passes through the point (6,3) that is perpendicular to the line 4x - 5y = -10 is
[tex]$$\boldsymbol{y=-\frac{5}{4}x+\frac{21}{2}}$$[/tex]find the ranges of values for which x²-5+6<0
Answers
Answer:
The range of values of x for which the function is < 0 is:
2<x<3.
Step-by-step explanation:
x²-5x+6<0
First find the critical points:
x^2 - 5x + 6 = 0
(x - 2)(x - 3) = 0.
x = 2, 3.
The critical points are 2 and 3.
Make a table of values:
x x<2 2<x<3 x >3
x -2 < 0 >0 >0
x -3 <0 <0 >0
(x - 2)(x - 3) >0 <0 >0
I was wondering if you could help me with this problem. I am not sure where to start solving it. Thank you.
Answers
As shown at the graph, we need to find x and y
The angles (x+1) and (2y+1) are vertical
so, x + 1 = 2y + 1
so,
x = 2y eq.(1)
And the sum of the angles (x+1) , (3x + 4y) and (71 - 3y) are 180
So,
(x+1) + (3x + 4y) + (71-3y) = 180
x + 1 + 3x + 4y + 71 - 3y = 180
4x + y = 180 - 1 - 71
4x + y = 108
Substitute with x from eq (1) with 2y
4 * 2y + y = 108
8y + y = 108
9y = 108
y = 108/9 = 12
x = 2y = 2 * 12 = 24
So, x = 24 and y = 12
32. Challenging. Read this one very carefully. Carla runs a small business where she makes artificial flower arrangements. A customer has placed a large order for 100 identical arrangements. Carla has made a list of supplies that she needs to make the entire order. Each arrangement needs a plastic molding. It will cost Carla $3.25 for each plastic molding. She also needs 4 packages of colored netting, which sell for $15.00 each. However, the company she orders from has a special on the netting packages. If you buy 3 packages of netting, you get a package for free. Polyester fabric is another item she will need. She needs 180 square feet of polyester fabric that sells for $5.20 per square yard. Lastly she needs artificial stems. She will need 6 stems per arrangement and they are sold in packs of 10. The cost for one pack of artificial stems is $2.50. if Carla sells each arrangement for $20.00,How much money will Carla make off the order once she subtracts her expenses for the supplies.
Answers
Substract expenses
Carlas expenses are
1. 100 Arrangements
2. Plastic molding PM = 3.25
3. Colored netting CN = 15
4. Four packages netting = 3 packages
5. 180 feet2 ,. 1 yard2=5.20
6. 10 stems = 2.5x10 = $25
7. Arrangement price AP = 20.00
Then substract
20 minus 3.25 = 16.75
16.75 x100= $1675
4. 4 packages nettingx 15 = $60 - $15 = $45
5. Now
In 180 feet2 ,there are 60 yards2
then polyester price is 60x5.2= $312
6. She needs 100x6= 600 stems
600/10 = 60 packs
60 packs x 2.50= $150
Then answer is
Carla's money = 1675 - 45 - 312 - 150 = $1168 dollars
For which value(s) of x will the rational expression below equal zero? Che all that apply. (x - 5)(x+2) x + 1 A.-5 B. 2 c. 1 1 D. -1 E. 5 F. -2
Answers
The rational expression we have is:
[tex]\frac{(x-5)(x+2)}{x+1}[/tex]For a rational expression to be equal to 0, the numerator of the expression has to be equal to 0.
The numerator is: (x-5)(x+2)
That has to be equal to 0:
[tex](x-5)(x+2)=0[/tex]Here, we apply the zero product property, which tells us that if a product is equal to 0, one of the two elements, or the two elements, are equal to 0:
[tex]\begin{gathered} x-5=0 \\ x+2=0 \end{gathered}[/tex]We solve the two equations, and get the two values that will make the rational equation equal to 0:
[tex]\begin{gathered} x=5 \\ x=-2 \end{gathered}[/tex]Answer:
E. 5
F. -2
Given the formula for the nth term, state the first 5 terms of each sequence.t1= 800, tn= -0.25tn-1
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
t1 = 800
tn = - 0.25 tn-1
Step 02:
sequence:
t1 = 800
t2 = -0.25 (800) = - 200
t3 = -0.25 (-200) = 50
t4 = -0.25 (50) = -12.5
t5 = - 0.25 (-12.5) = 3.125
The answer is:
t1 = 800
t2 = - 200
t3 = 50
t4 = -12.5
t5 = 3.125
How is the input force different from the output force?
Responses
The input force is all of the energy applied to the situation, and the output force is the result.
The input force is all of the energy applied to the situation, and the output force is the result.
The input force is applied to the problem, and the output force is the movement that results.
The input force is applied to the problem, and the output force is the movement that results.
The output force is applied to the simple machine, and the input force is the force the simple machine applies to an object.
The output force is applied to the simple machine, and the input force is the force the simple machine applies to an object.
The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object.
The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object.
Answers
The input force different from the output force is D. The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object."
What is a simple machine?A simple machine is a mechanical device that alters the magnitude or direction of a force. In general, they are the most basic systems that exploit mechanical advantage to multiply force.
A simple machine is a mechanical device that adjusts the direction or amplitude of a force. According to Newton's third law, if object A exerts a force on object B, object B will exert a force of same size and opposite direction on object A.
In that situation, the input force is done by object A, and the output force is done by object B as a reaction.
With this in mind, we can see that the proper answer is: "The input force is applied to the simple machine, and the output force is the force applied to an item."
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The line 3x + 4y - 7 = 0 is parallel to the line k . x + 12y + 3 = 0. What is the value of k?
Answers
The function is solved below
What is a function?
The function is instantly given a name, such as a, in functional notation, and its description is supplied by what it does to the input x, using a formula in terms of x. Instead of sine, put sine x. (x). Leonhard Euler invented functional notation in 1734. Some commonly used functions are represented with a symbol made up of many letters (usually two or three, generally an abbreviation of their name). In this scenario, a roman font is typically used, such as "sine" for the sine function, rather than an italic font for single-letter symbols. A function is also known as a map or a mapping, however some writers distinguish between "map" and "function."
The function can be written as
3x+4y-7 = 0
or, y = (-3/4)x + 7/4
so, slope = -3/4
and other function is
kx+12y+3 = 0
or, y = (-k/12)x - 1/4
so, slope = -x/12
Given the lines are parallel, so slopes are equal
i.e., -3/4 = -k/12
or, k = (3/4)12 = 9
Hence, the value of k is 9.
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Sq root of z +3 + Sq root of Z -2 = 5
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A random variable X follows a normal distribution with a mean of 150 and a standard deviation of sigma. If we know that P(120 < X < 180) = 0.95, then, according to the 68-95-99.7 rule, the value of sigma is approximately:
a.
20
b.
15
c.
40
d.
30
e.
60
Answers
The value of sigma according to the 68-95-99.7 rule is 15.
What is the 68-95-99.7 rule?This is the informal term that is used in statistics to remember the percentage of values that are in the interval of a distribution in statistics.
We have the mean = 150
the interval is given as P(120 < X < 180)
based on this rule, 95 percent of the data lies in the u - 20 and u + 20 region
Such that we would have
u - 2α < x < u + 2α = 0.95
we have
u - 2α = 120
150 - 2α = 120
2α = 150 - 120
2α = 30
divide through by 2
α = 15
Sigma is given as 15
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Find a if (10-a )×2 +(2a×2)+(4a+7)=48
Answers
First step: Simplify everything
[tex]2(10-a) + 4a + 4a+7 = 48[/tex]
Next: Distribute required values
[tex]20-2a+4a+4a+7=48[/tex]
Next: Time to add like terms
[tex]6a = 21[/tex]
Final Step: Divide 6 on both sides to isolate variable
[tex]a = \frac{21}{6}[/tex]
Thus, the value "a" = [tex]\frac{21}{6}[/tex]
Hope this helps :)
Matthew filled two 20 oz. water bottles before he left home. At the end of the day, he has less than 8 oz. left. Write an inequality to determine how much water, z, Matthew drank.
Answers
Given data:
The expression for the inequality is,
[tex]\begin{gathered} 2(20)-z<8 \\ 40-z<8 \end{gathered}[/tex]Thus, the second inequality is correct.
U Last Saturday V. Tomo los restaurant sold 85 cheese pizzes and 54peperon p2205 Wechple was cut into elchihs, how many peces ofpedid hosilinona nlgh?2Adeleydiverlor the realanddeliverpiznes ot 5-13 ke arrivedback at therestaurant 6 45. How many manutes wesheoulding p2205 ?3 Tomola hoz 158 ounces domaSouce The uses 9 aunces of louce bonepi? how many plazos canhe moke with mesouce behet?41 Au months ago the restaurar had 2 258pizobe in their warehouse Today they have749 boxen led. How many pizza bazea haether
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Answer : The amount of boxes of pizzas used is 2009 boxes
A few months ago, the company has 2, 758 boxes of pizzas in the warehouse
Today, they have 749 boxes of pizzas in the warehouse
To calculate the amount left
The amount used = 2758 - 749
The amount of boxes used = 2009 boxes
In an art classroom, 8 students can sit around 1 table, and 48 students can sit around 6 tables. What is the relationship between the number of students to tables? (Do not reduce the ratios to their lowest terms.)
Answers
Answer: 8/1 = 6/48
Step-by-step explanation: um thats the answer bye
The relationship between the number of students to tables or the ratio of students to number of tables is 8 to 1.
According to question,
We have the following information:
In an art classroom, 8 students can sit around 1 table, and 48 students can sit around 6 tables.
Now, we will find the relationship between the number of students and the number of tables or in simple words, ratio.
So, we have:
8 students = 1 table
48 students = 6 tables
It can be rewritten by dividing both the sides by 6 as 8 students to 1 table.
It means that there are 8 students for 1 table.
Hence, the relationship between the number of students to the number of tables is 8 to 1.
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A cat is stuck in the tree and the fire department needs a ladder to rescue the cat. The fire truck available has a 95-foot ladder, which starts 8 feet above ground. Unfortunately, the fire truck must park 75 feet away from the tree. If the cat is 60 feet up the tree, does the cat get rescued? If not, what ladder length is need to allow the cat to be rescued?
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Draw the given scenario
STEP 2: Describe how to answer the question
The question forms a right angle triangle. where the height of the cat on the tree is the opposite side of the triangle. The distance between the cat and the tree is the adjacent side of the triangle .
Recall the 95 foot ladder can only start 8 feet above the ground .The diagram is represented above:
The ladder height should be the hypotenuse of the triangle.
using Pythagoras's theorem,
[tex]hypotenuse^2=opposite^2+adjacent^2[/tex]STEP 3: Write the given sides
[tex]\begin{gathered} adjacent=75fto \\ opposite=52ft \\ hypotenuse=x\text{ ft} \end{gathered}[/tex]STEP 4: find x
[tex]\begin{gathered} x^2=75^2+52^2 \\ x^2=5625+2704 \\ x^2=8329 \\ x=\sqrt{8329}=91.26335519 \\ x\approx91.26ft \end{gathered}[/tex]The expected length of the ladder should be approximately 91.26ft. Since the ladder is 95 foot, therefore the cat will be rescued with the given ladder.
Please see the picture below,PART BUse the real zeros to factor f
Answers
Explanation:
The polynomial is given below as
[tex]f(x)=x^4+2x^3-7x^2-8x+12[/tex]Given in the question above the real zeros are gotten below as
[tex]x=-3,-2,1,2[/tex]Concept:
To figure out the factor form of the polynoimial, we will equate each zero to x below as
[tex]\begin{gathered} x=c \\ (x-c) \end{gathered}[/tex]Therefore,
The factored form of the polynomial will be
[tex]\begin{gathered} f(x)=x^{4}+2x^{3}-7x^{2}-8x+12 \\ x=-3,x=-2,x=1,x=2 \\ f(x)=(x+3)(x+2)(x-1)(x-2) \end{gathered}[/tex]Hence,
Using the real zeros of f(x) , the factored form of the polynomial is
[tex]\Rightarrow f(x)=(x+3)(x+2)(x-1)(x-2)[/tex]find the value of XA. 11√ 41inB. 11 inC. 33 inD. 35 in
Answers
From the diagram provided, we have a right angled triangle with the hypotenuse (side facing the right angle) given as 55, while one of the other two sides is given as 44.
We shall apply the pythagoras' theorem as follows;
[tex]c^2=a^2+b^2[/tex]Where,
c = hypotenuse,
a and b = the other sides.
Therefore, we'll now have;
[tex]\begin{gathered} c^2=a^2+b^2 \\ 55^2=44^2+c^2 \\ 3025=1936+c^2 \end{gathered}[/tex]Next step, we'll subtract 1936 from both sides of the equation;
[tex]\begin{gathered} 3025-1936=1936-1936+c^2 \\ 1089=c^2 \end{gathered}[/tex]Add the square root sign to both sides of the equation;
[tex]\begin{gathered} \sqrt[]{1089}=\sqrt[]{c^2} \\ 33=c \end{gathered}[/tex]ANSWER
Therefore, the correct answer is option C, that is 33 inches.
Equipment was purchased for $50,000. The equipment is expected to be used 15,000 hours over its useful life and has a residual value of $10,000. In the first two years of operation, the equipment was used for 2,700 hours and 3,300 hours, respectively. Using the activity-based method, what is the equipment’s accumulated depreciation at the end of the second year?
Answers
The equipment’s accumulated depreciation at the end of the second year is $16,000.
What is the accumulated depreciation?Depreciation is the process used in expensing the cost of an asset. The activity based method allocates the depreciation expense using the number of hours the asset was used. Accumulated depreciation is the sum of the depreciation over a period of time.
Depreciation expense using the activity based method = (cost of the asset - residual value) x (number of hours used in a year / total number of hours)
Depreciation expense in year 1 = ($50,000 - $10,000) x (2,700 / 15,000)
$40,000 x 0.18 = $7,200
Depreciation expense in year 2 = ($50,000 - $10,000) x (3,300 / 15,000)
$40,000 x 0.22 = $8,800
Accumulated depreciation = $8,800 + $7,200 = $16,000
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if (11,13) is an ordered pair of the function F(x), which of the following is an ordered pair of the inverse of F(x)
Answers
Given:
There are given that the ordered pair is:
[tex](11,13)[/tex]Explanation:
According to the question:
We need to find the inverse of the given ordered pair.
Then,
To find the inverse of the given relation, we need to switch the x and y-coordinates.
Then,
The inverse is:
[tex](11,13)\rightarrow(13,11)[/tex]Final answer:
Hence, the correct option is C.
How many and what type of solution(s) does the equation have?6p2 = 8p + 32 rational solutions1 rational solutionNo real solutions2 irrational solutions
Answers
We are going to solve the question using the quadratic formula
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{(b^2}-4ac)}{2a} \\ \text{where the quadratic equation is ax}^2+bx+c=0 \end{gathered}[/tex]The quadratic equation given is
[tex]\begin{gathered} 6p^2=8p+3 \\ 6p^2-8p-3=0 \\ \text{where a=6} \\ b=-8 \\ c=-3 \end{gathered}[/tex]By substitution we will have,
[tex]\begin{gathered} p=\frac{-(-8)\pm\sqrt[]{(-8)^2}-(4\times6\times-3)}{2\times6} \\ p=\frac{8\pm\sqrt[]{64+72}}{12} \\ p=\frac{8\pm\sqrt[]{136}}{12} \\ p=\frac{8\pm\sqrt[]{4\times34}}{12} \\ p=\frac{8\pm2\sqrt[]{34}}{12} \\ p=\frac{2(4\pm\sqrt[]{34)}}{12} \\ p=\frac{4\pm\sqrt[]{34}}{6} \\ p=\frac{4+\sqrt[]{34}}{6}\text{ or p=}\frac{4-\sqrt[]{34}}{6} \end{gathered}[/tex]Therefore,
With the roots gotten from the quadratic equation, we can therefore deduce that the solutions to the equation 6p²=8p+3 will give 2 irrational roots.
The correct answer is OPTION D