The number of motor cycles produced last year is 135,000.
The number of motor cycles expected to produce is 145,000.
Therefore, the percentage of increase is,
[tex]\frac{(145000-135000)}{135,000}\times100[/tex]That is,
[tex]\begin{gathered} \frac{10000}{135000}\times100=\frac{10}{135}\times100 \\ =7.4 \end{gathered}[/tex]Therefore, the percentage of increase is 7.4%
the table below shows the minimum volume of water needed to fight a typical fire in rooms of various sizes. Find the rate of change. Explain the meaning of rate of change. Include the units in your answer.
Since the volume of water depends on the floor area, the floor area is the independent variable while the minimum water volume is the dependent variable.
Let x represents the floor area
Let y represent the miminum volume of water
The rate of change is the ration of the change in y to the change in x
Let the rate of change be represented by dy/dx
[tex]\begin{gathered} \frac{dy}{dx}=\text{ }\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]Considering the first two rows of the table, since the rate of change does not differ despite the rows picked
[tex]\begin{gathered} x_1=25,y_1=39,x_2=50,y_2=78 \\ \frac{dy}{dx}=\text{ }\frac{78-39}{50-25} \\ \frac{dy}{dx}=\frac{39}{25} \\ \frac{dy}{dx}=1.56 \end{gathered}[/tex]Every quadrilateral with opposite angles supplementary can be inscribed in a circle.TrueFalseIf a triangle is inscribed in a circle, the center of the circle is called the circumcenter.TrueFalse
Explanation
The Inscribed Quadrilateral Theorem states that a quadrilateral can be inscribed in a circle if and only if the opposite angles of the quadrilateral are supplementary
Answer 1: True
Also, Given a triangle, the circumscribed circle is the circle that passes through all three vertices of the triangle. The center of the circumscribed circle is the circumcenter of the triangle, the point where the perpendicular bisectors of the sides meet.
Answer 2: True
Arithmetic and Geometric Sequences. The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
From the information provided, observe that the three terms are connected by a common ratio.
The first term is multiplied by a value denoted as letter r (common ratio) to derive the second term. The second term is also multiplied by r to derive the third term, and so on.
Therefore;
[tex]\begin{gathered} 5\times r=4 \\ r=\frac{4}{5} \\ 4\times r=\frac{16}{5} \\ r=\frac{16}{5}\text{ / }\frac{4}{1} \\ r=\frac{16}{5}\times\frac{1}{4} \\ r=\frac{4}{5} \end{gathered}[/tex]From the above calculation, the common ratio is 4/5. Therefore, the 10th term in the sequence shall be;
[tex]\begin{gathered} T_n=a\times r^{n-1} \\ \text{Where;} \\ a=5,r=\frac{4}{5},n=\text{nth term} \\ T_{10}=5\times(\frac{4}{5})^{10-1} \\ T_{10}=5\times(\frac{4}{5})^9 \\ T_{10}=5\times\frac{262144}{1953125} \\ T_{10}=\frac{262144}{390625} \end{gathered}[/tex]The 10th term is as shown above. To round this figure to the nearest thousandth, we need to convert this fraction into a decimal.
Hence we would have;
[tex]\begin{gathered} T_{10}=\frac{262144}{390625} \\ T_{10}=0.67108864 \\ T_{10}\approx0.671\text{ (to the nearest thousandth)} \end{gathered}[/tex]Billy used four colors to divide 4.20 by 4. Which model shows 4.20/4?
Given that Billy used four colours to divide 4.20 by 4
To Determine: The model that shows this division
Solution:
It can be observed that 1 represents 100 small boxes
Dividing 4.20 by 4 would give
[tex]\frac{4.20}{4}=1.05[/tex]1.05 would be represented by small boxes
[tex]1.05\times100=105[/tex]If we used colours, then each of the colours would have 105 boxes
From the above explanation, the model that shows 4.20/4 is OPTION D
Write an equation in slope-intercept form of the line that passes through the point (5,2) and is parallel to 2y+4x=5
• We are given 2y +4x = 5
This can be rewritten as :
2y = -4x +5
y = -4/2x +5/2
y = -2x +5/2
• A line parallel to this line will also have the exact, same slope
Therefore m = -2
in order to find the equation , we will use the following formula
y = mx +c , where m = -2 :
y = -2x + c , at point (5;2)
2 = -2(5) +c
2 +10 = c
Therefore c = 12
finally;
y = -2x +12 is our equation .
RewritingInstructions: Rewrite the equation in Slope-Intercept Form.y-2=-5(x- 2)Check
In general, the slope-intercept form of a linear equation is
[tex]\begin{gathered} y=mx+b \\ m,b\rightarrow\text{ constants} \end{gathered}[/tex]Thus, in our case,
[tex]\begin{gathered} y-2=-5(x-2) \\ \Rightarrow y-2=-5x+10 \\ \Rightarrow y=-5x+12 \end{gathered}[/tex]The answer is y=-5x+12Complete the table and answer the questions below.a) without graphing, which equation from above has the steepest line? How do you know?b) without graphing, which equation describes a decreasing line? How do you know?
The values on the table are:
[tex]\begin{gathered} y=x-3 \\ \Rightarrow slope\colon m=1 \\ \Rightarrow y-axis\colon b=-3 \\ y=\frac{1}{5}x+2 \\ \Rightarrow slope\colon m=\frac{1}{5} \\ \Rightarrow y-axis\colon b=2 \\ y=-2x \\ \Rightarrow slope\colon m=-2 \\ \Rightarrow y-axis\colon b=0 \end{gathered}[/tex]a) the steepest slope is m=-2 (from the third option). We can see this because in the first option, the rate of change is 1 and in the second option is 1/5. Then for each increase of x, the value of y will be modified but not as much as in the equation y=-2x.
b)the equation y=-2x represents a decreasing line, since the slope is negative.
Consider the equation. Determine whether the graph of the equation is wider or narrower than the graph of Y=1/2x^2+1
It's important to observe that the number that multiples the x is 1/2, that is, it's less than zero.
5. What is the sum of 3 5/24, 6 7/24, and 9 9/24?,A. 14²/3B. 14 1/8C. 18 7/8D. 13 1/2
To answer this question, we can realize that we have mixed fractions. Then we need to add integers and fractions separately as follows:
1. We have:
[tex]3\frac{5}{24}+6\frac{7}{24}+9\frac{9}{24}[/tex]2. And this expression is equivalent to:
[tex]3+\frac{5}{24}+6+\frac{7}{24}+9+\frac{9}{24}[/tex]3. Now, we can add the integer parts, and the fractional parts separately as follows:
[tex](3+6+9)+(\frac{5}{24}+\frac{7}{24}+\frac{9}{24})[/tex]4. Therefore:
[tex]18+\frac{5+7+9}{24}=18+\frac{21}{24}[/tex]5. We finally need to simplify the fraction, and then we will have:
[tex]\begin{gathered} \frac{21}{24}=\frac{\frac{21}{3}}{\frac{24}{3}}=\frac{7}{8} \\ 18+\frac{7}{8}=18\frac{7}{8} \end{gathered}[/tex]In summary, therefore, we have that the sum of the above fractions is:
[tex]18\frac{7}{8}[/tex][Option C.]
3. Factor 3x from 12x2 + 15x 3
SOLUTION
In this question, we are meant to factor
[tex]\begin{gathered} 3xfrom12x^2+15x^3 \\ \text{Next, we factor in this manner,} \\ 3\text{ x ( }4x+5x^2\text{ )} \\ \text{CONCLUSION : The correct solution is 3 x ( 4 x + 5 x }^2\text{ )} \end{gathered}[/tex]The perimeter of a rectangular picture frame can be represented by the expression 6x,where x is one of the side lengths. Rewrite the expression as the sum of the four side lengths.
Perimeter is formed by 4 side lengths.
Divide perimeter in 4 parts
x= side length
P = 6x = x + x + 4x
then length of the other sides lengths is= 2x
So then ANSWER IS
P= x + x + 2x + 2x
1) Compare the following numbers. Choose the correct inequality symbol 10 pointsto go in the circle. *Remember the inequality symbol “eats” the biggernumber!√8 + 3 ? 8 + √3
√8 + 3 ? 8 + √3
√8 is between √4 (= 2) and √9 (= 3), then
√8 + 3 < 3 + 3 = 6
Therefore,
√8 + 3 < 8 + √3
Which statement best explains the relationship betweenlines AB and CD?
GIven:-
An graph with two parallel lines.
To find:-
The given condition which sutis it.
Now we find two points form the line.
The points from the line AB is,
[tex](-4,-2),(4,4)[/tex]The points from the line CD is,
[tex](0,-3),(4,0)[/tex]Now the slope of AB is,
[tex]\frac{4+2}{4+4}=\frac{6}{8}=\frac{3}{4}[/tex]Now the slope of CD is,
[tex]\frac{0+3}{4}=\frac{3}{4}[/tex]The both slopes are equal so we have,
They are parallel because the slopes are equal.
Nolan just drove at a constant rate for 5 hours here is now 340 miles from where he started. A. At what rate was he driving? B. Nolan has another 204 miles to go. If he continues to drive at the same rate, how long will it take him?
A) 68 mph. B) 3h
1) Gathering the data
time: 5 hours
Space= 340 miles
A) To find the rate, we can calculate it by simply writing a quotient between the Space and the time, (since Nolan is constantly moving
[tex]V=\frac{340}{5}=68\text{ mph}[/tex]So Nolan was at 68 mph
B) We can find out by setting a proportion since it's been said that the speed is constant. 340 miles have already been driven there are 204 miles to go.
340------5 hours
204 ---- x
340x = 204 *5 Divide both sides by 340
x=3
So it will take more 3 hours so that Nolan can finish his trip.
which represents the inverse of the fuction f(x)=4x?a. h(x) = x + 4xb. h(x) = x - 4c. h(x) = 3/4xd. h(x) = 1/4x
If we want to calculate the inverse, we have to solve for x the following equation
[tex]\begin{gathered} y=4x \\ x=\frac{y}{4} \end{gathered}[/tex]Therefore the inverse function is
[tex]h(x)=\frac{1}{4}x[/tex](b) A company has 39 salespeople. A boardmember at the company asks for a list of the topsalespeople, ranked in order of effectiveness. How many such rankings are possible?0ExplanationCheck
Since 1 person cannot be in the top 4 salespeople more than once, then, we use combinations instead of permutations.
[tex]39C4=\frac{39!}{4!(39-4)!}[/tex]Simplify the expression,
[tex]39C4=\frac{39!}{4!35!}[/tex][tex]\begin{gathered} 39C4=\frac{39\ast38\ast37\ast36}{4\ast3\ast2\ast1} \\ 39C4=\frac{1974024}{24} \\ 39C4=82251 \end{gathered}[/tex]answer:
The 4 top list can be arranged in 82251 ways
ZA and ZB are supplementary angles. If mZAZB = (7x – 26)°, then find the measure of ZA.
the sum of two supplementary angles is 180 degrees
[tex]m\angle A+m\angle B=180[/tex]7x+10+7x-26 = 180
14x = 180 + 16
x = 196/14
x = 14
so the value of m7x+10
= 7(14) + 10
= 98 + 10
= 108
m
what percentage of college graduates believe their education was useful for helping them grow personally and intellectually, but not useful for helping them develop specific skills and knowledge for the workplace?Write your answer as a percentage
We get the following from the given table.
The percentage of college graduates who believes their education was helping them grow personally and intellectually =62 % + 31 %= 93 %
The percentage of college graduates who believes their education was useful for helping them develop specific skills and knowledge for the workplace = 49%+25%= 84 %
The percentage of college graduates who does not believe their education was useful for helping them develop specific skills and knowledge for the workplace=100-84=16%
The percentage of college graduates believes their education was helping them grow personally and intellectually and does not believe useful for helping them develop specific skills and knowledge for the workplace=the least value of 93 and 16 is 16 %.
Hence the required percentage is 16%.
A model airplane is built at a scale of 1 inch to 32 feet. If the model plane is 8 inches long, the actual length of the airplane is blank feet.
If the model plane is built at a scale of 1 inch to 32 feet
let x be the actual length of the airplane
1/32 = 8/x
cross-multiply
x = 32 times 8
x = 256 inches
The Fighting Irish won 7 games, lost 2 and tied 1. What percent of their games did they win?
N = Total number of games = 7
W = games won = 7 + 2 + 1 = 10
% games they won = W/N = 7/10 = 0.7 = 70%
What is the equation of the graphed function?A. f(x) = -1/3x + 1B. f(x) = 3x + 1C. f(x) = 1/3x + 1D. f(x) = -3x + 1
If (x,y) is a point in the graph of a line then its coordinates x and y form a solution to the equation of that line. In slope-intercept form this equation looks like this:
[tex]y=mx+b[/tex]What we are going to do here is choose two points from the line in the picture and use them and the expression above to construct two equations for m and b.
As you can see (0,1) and (3,0) are part of the line so we have the following two equations:
[tex]\begin{gathered} 1=m\cdot0+b \\ 0=3m+b \end{gathered}[/tex]From the first equation we get b=1. If we use this value of b in the second equation we obtain the following:
[tex]\begin{gathered} 0=3m+b=3m+1 \\ 0=3m+1 \end{gathered}[/tex]We can substract 1 from both sides:
[tex]\begin{gathered} 0-1=3m+1-1 \\ -1=3m \end{gathered}[/tex]Then we divide both sides by 3:
[tex]\begin{gathered} -\frac{1}{3}=\frac{3m}{3} \\ m=-\frac{1}{3} \end{gathered}[/tex]Then we have this equation for the line in the picture (we take y=f(x)):
[tex]f(x)=-\frac{1}{3}x+1[/tex]AnswerThen the answer is option A.
The perpendicular bisectors of a triangle are congruent. Their common point is the:
Given
The perpendicular bisector of the triangle are concurrent. Their common point is the .........
Find
Complete the statement
Explanation
The three angle bisector of triangel are concurrent in a point equidistant from the sides of the triangle.
The point of concurrency of the angle bisectors of a triangle is known as
circumcenter.
Final Answer
Hence , the correct option is C
a farmer wants to build a fence in the shape of a parallelogram for his animals. The perimeter of the fence will be 600 feet, and the North/South fences are half of the length of the West/East fences. If fences are sold in 5 foot segments, how many fence segments does the farmer need to buy ?
Let's use the variable L to represent the length and W to represent the width.
If the perimeter is 600 ft, we have:
[tex]\begin{gathered} P=2L+2W\\ \\ 2L+2W=600\\ \\ L+W=300 \end{gathered}[/tex]The width is half the length, so we have:
[tex]\begin{gathered} W=\frac{L}{2}\rightarrow L=2W\\ \\ 2W+W=300\\ \\ 3W=300\\ \\ W=\frac{300}{3}\\ \\ W=100\text{ ft}\\ \\ L=200\text{ ft} \end{gathered}[/tex]Now, if each fence segment is 5 ft, we number of segments needed is:
[tex]\begin{gathered} \text{ fences for W1: }\frac{100}{5}=20\\ \\ \text{ fences for W2: }\frac{100}{5}=20\\ \\ \text{ fences for L1:}\frac{200}{5}=40\\ \\ \text{ fences for L2:}\frac{200}{5}=40\\ \\ \\ \\ \text{ total:}20+20+40+40=120\text{ fence segments} \end{gathered}[/tex]Which ordered pair does not lie on the graph of Y=x/4+5?A (-8,3)B (-4,6)C (12,8)D (20,10)
Answer
B (-4, 6)
Step-by-step explanation
Given the expression:
[tex]y=\frac{x}{4}+5[/tex]Substituting x = -8, we get:
[tex]\begin{gathered} y=\frac{-8}{4}+5 \\ y=-2+5 \\ y=3 \end{gathered}[/tex]Then, the point (-8, 3) lies on the line.
Substituting x = -4, we get:
[tex]\begin{gathered} y=\frac{-4}{4}+5 \\ y=-1+5 \\ y=4 \end{gathered}[/tex]Then, the point (-4, 6) does not lie on the line, the point (-4, 4) does.
In ∆MNO , o = 790cm. < O=50° and
Using the law of sines:
[tex]\begin{gathered} \frac{o}{\sin(O)}=\frac{m}{\sin (M)} \\ \frac{790}{\sin(50)}=\frac{m}{\sin (25)} \\ m=\frac{790\cdot\sin (25)}{\sin (50)} \\ m=435.834278 \end{gathered}[/tex][tex]\begin{gathered} \frac{o}{\sin(O)}=\frac{n}{\sin (N)} \\ \frac{790}{\sin(50)}=\frac{n}{\sin (105)} \\ n=\frac{790\cdot\sin (105)}{\sin (50)} \\ n=515.6358793 \end{gathered}[/tex]Using the heron formula:
[tex]\begin{gathered} s=\frac{790+435.834278+515.6358793}{2} \\ s=870.7350787 \\ so\colon \\ A=\sqrt[]{870.7350787(870.7350787-790)(870.7350787-435.834278)(870.7350787-515.6358793)} \\ \end{gathered}[/tex][tex]\begin{gathered} A=104194.335 \\ A=104194cm^2 \end{gathered}[/tex]1. This is a two part question. If you are going 65 kilometers per hour how many meters per second are you traveling? a) What conversions will you use to solve this problem? b) Complete the conversion. Show your work. Make sure to include units
The value of 65 km/hr in meter/second will be 18.05 m/sec by the method of "To convert km/hr to m/s ,multiply the quantity by 5/18."
What is kilometer per hour?A derived unit for both speed and velocity, kilometers per hour is a measurement that takes length in kilometers and time in hours. Although kph or kmph are also occasionally used, km/h is the correct abbreviation for this unit.
a. 65 KM/hour to metre/second
=65*5/18
=18.05 m/second
b. To convert km/hr to m/s ,multiply the quantity by 5/18.
as 1 KM=1000 m
1 hour=3600 seconds
x* 1000/3600
x*5/18
According to the formula "To convert km/hr to m/s, multiply the quantity by 5/18," 65 km/hr will equal 18.05 m/s.
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Jim and Carla are scuba diving. Jim started out 8 feet below the surface. He descended 18 feet, rose 5 feet,and descended 9 more feet. Then he rested. Carla started out at the surface. She descended 16 feet, rose 5feet, and descended another 18 feet. Then she rested. Which person rested at a greater depth? Completethe explanation.
To solve this question, we need to use integers to express different altitudes. We can sketch each situation as follows:
To find the depth at which each person rested, we need to algebraically sum all these altitudes.
Jim:
-8 -18 + 5 - 9 = -30. He rested at 30 feet below the surface.
Carla:
-16 + 5 - 18 = -29. She rested at 29 feet below the surface.
Therefore, Jim rested at a greater depth (30 feet below the surface).
The radius of a circle is 8 miles. What is the area of a sector bounded by a 180° arc?Give the exact answer in simplest form. ____ square miles.
Radius r:
r = 8 miles
Area of a circle:
A = π * r²
The area of a 180° arc is the half of the area of the entire circle:
A_arc = (π * r²)/2
Solving:
A_arc = 32π square miles
Find the unit rate.
576 passengers in 144 cars =
Save answer
passengers per car
The unit rate is 4 passengers per car
We need to find the unit rate.
576 passengers in 144 cars
rate = 576/144
rate = 4 passengers per car
Therefore, the unit rate is 4 passengers per car
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she has 78 inches of thread that she cut into 2 pieces. One piece is twice as long as the other piece. How long is each piece?
Answer:
One piece is 26 inches long while the other is 52 inches long.
We let:
x = one piece of the thread
2x = the other piece of the thread
Since the thread is 78 inches long,
2x + x = 78
Solve for x:
[tex]2x+x=78\Rightarrow3x=78[/tex][tex]\frac{3x}{3}=\frac{78}{3}\Rightarrow x=26[/tex]Since one piece of the thread is 26 inches long, the other piece would be:
[tex]2x=2(26)=52[/tex]The other piece would be 52 inches long.