The probability that a defective component will be detected only by the first inspector is 0.19
The probability that a defective component will be detected by exactly one of the two inspectors is 0.38
The probability that all three defective components in a batch escape detection by both inspectors is 0.
It is given that The first inspector detects 81% of all defectives that are present, and the second inspector does likewise.
Therefore P(A)=P(B)=81%=0.81
At least one inspector does not detect a defect on 38% of all defective components.
Therefore, bar P(A∩B)=0.38
As we know:
bar P(A∩B)=1-P(A∩B)=0.38
P(A∩B)=1-0.38=0.62
A defective component will be detected only by the first inspector.
P(A∩barB)=P(A)-P(A∩B)
=0.81-0.62
P(A∩barB)=0.19
The probability that a defective component will be detected only by the first inspector is 0.19
Part (B) A defective component will be detected by exactly one of the two inspectors.
This can be written as: P(A∩barB)+P(barA∩B)
As we know:
P(barA∩B)=P(B)-P(A∩B) and P(A∩bar B)=P(A)-P(A∩B)
Substitute the respective values we get:
P(A∩ barB)+P(bar A∩B)=P(A)+P(B)-2P(A∩B)
=0.81+0.81-2(0.62)
=1.62-1.24
P(A∩ barB)+P(bar A∩B)=0.38
The probability that a defective component will be detected by exactly one of the two inspectors is 0.38
Part (C) All three defective components in a batch escape detection by both inspectors
This can be written as: P(bar A∪ bar B)-P(bar A∩B)-P(A∩ barB)
As we know bar P(A∩B)=P(bar A∪ bar B)=0.38
From part (B): P(bar A∩B)+P(A∩bar B)=0.38
This can be written as:
P(bar A∪ bar B)-P(bar A∩B)-P(A∩bar B)=0.38-0.38=0
The probability that all three defective components in a batch escape detection by both inspectors is 0
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A florist wants to purchase a rain barrel (cylinder shape) for a greenhouse. He wants the barrel to hold atleast 2000 litres of water.
a) Determine the amount each barrel can hold in the table below
b) which should the florist buy to have 200L capacity without going bigger than needed
The volume of Economy Barrel is 785 litres.
The volume of Oceanview Barrel is 1766.25 litres.
The volume of Rainforest Barrel is 2649.375 litres.
The volume of Mountain Flow Barrel is 4710 litres.
The florist should buy Rainforest Barrel to have 2000L capacity without going bigger than needed.
What is volume?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
The radius of Economy Barrel is = 50 cm
The height of Economy Barrel is = 100 cm
The formula for volume of a cylinder is -
Volume = πr²h
Substitute the values into the equation -
Volume = 3.14 × (50)² × 100
Volume = 3.14 × 2500 × 100
Volume = 785000 mL
Now converting it into litres -
785000 / 1000 = 785 Litres
Therefore, Economy barrel can hold 785 litres.
The radius of Oceanview Barrel is = 75 cm
The height of Oceanview Barrel is = 100 cm
The formula for volume of a cylinder is -
Volume = πr²h
Substitute the values into the equation -
Volume = 3.14 × (75)² × 100
Volume = 3.14 × 5625 × 100
Volume = 1766250 mL
Now converting it into litres -
1766250 / 1000 = 1766.25 Litres
Therefore, Oceanview barrel can hold 1766.25 litres.
The radius of Rainforest Barrel is = 75 cm
The height of Rainforest Barrel is = 150 cm
The formula for volume of a cylinder is -
Volume = πr²h
Substitute the values into the equation -
Volume = 3.14 × (75)² × 150
Volume = 3.14 × 5625 × 150
Volume = 2649375 mL
Now converting it into litres -
2649375 / 1000 = 2649.375 Litres
Therefore, Rainforest barrel can hold 2649.375 litres.
The radius of Mountain Flow Barrel is = 100 cm
The height of Mountain Flow Barrel is = 150 cm
The formula for volume of a cylinder is -
Volume = πr²h
Substitute the values into the equation -
Volume = 3.14 × (100)² × 150
Volume = 3.14 × 10000 × 150
Volume = 4710000 mL
Now converting it into litres -
4710000 / 1000 = 4710 Litres
Therefore, Mountain Flow barrel can hold 4710 litres.
Therefore, the florist should go with Rainforest barrel.
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1. Rewrite the equation 5(x-3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true. (2 points) 2. Simplify both sides show you work PLEASE HELP ME!!!!!
Answer:
15 - 3 ?
Step-by-step explanation:
We will start by doing the equation on the left:
5(x-3)
Since we will substitute X for 6 the updated equation will be:
5(6-3)
We will now solve it using bodmas so it will be 6-3 which is 3. Then 3 multiplied by 5 is 15.
We will start by doing the equation on the right:
x + 13
Since we will substitute X for 6 the updated equation will be:
6 + 13
So now to simplify it all it will be:
15x = 6 + 13
Take a factor out of the square root : root of 7x^2
The required simplified value of the given root is given as x√7.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given expression,
= √7x²
= √7 × (x²)¹/²
= x√7
Thus, the required simplified value of the given root is given as x√7.
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I dont know how to do this problem...
Answer:
Option B
Step-by-step explanation:
Refer the the picture for working
Please help me with this question.
The trigonometric function, the identity is verified.
is trigonometric function?
The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
Here the given identity is,
=> [tex](cos \theta-5sin\theta)^2+(5cos\theta+sin\theta)^2=26[/tex]
Now using formula [tex](a-b)^2=a^2-2ab+b^2[/tex] and [tex](a+b)^2=a^2+2ab+b^2[/tex] then L.H.S
=> [tex]cos^2\theta-10cos\theta sin\theta+25sin^2\theta + 25cos^2\theta+10cos\theta sin\theta+sin^2\theta[/tex]
=> [tex]25sin^2\theta+25cos^2\theta+sin^2\theta+cos^2\theta[/tex]
=> [tex]25(sin^2\theta+cos^2\theta)+(sin^2\theta+cos^2\theta)[/tex]
We know that [tex]sin^2\theta+cos^2\theta=1[/tex] then,
=> 25(1)+1
=> 25+1
=> 26 = 26
L.H.S = R.H.S
Hence the given identity is verified.
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In right triangle ABC, AC = 4 and BC = 5. A new triangle DEC is formed by connecting the midpoints of AC and BC.
1. What is the area of triangle ABC?
square units
2. What is the area of triangle DEC?
square units
3. Does the scale factor for the side lengths apply to the area as well? (yes/no)
4. What is the scale factor for the area?
*Remember Area = 1/2 (base)*(height)
1. The area of triangle ABC = 10 units²
2. The area of triangle DEC = 2.5 units²
3. No
4. Scale factor = 2
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
The figure is given in the question, as shown
As per the question, the required solution would be as:
1. the area of triangle ABC = 1/2 x 5 x 4 = 20/2 = 10 units²
2. the area of triangle DEC = 1/2 x (5/2) x (4/2) = 20/8 = 2.5 units²
3. No
4. scale factor = 5/(5/2) = 2
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The question seems to be incomplete the missing part has been attached below
Pedro earns $94.50 for 6 hours of work. If he makes a constant hourly wage, which table represents the relationship between the number of hours he works and his total earnings?
please help me
Answer:
The answer is most likely A.
The reason why, is because since the earning in 6 hours is $94.50, so the hourly wage would be, $15.75 because:
94.50/6 = 15.75
Graph B, for the first hour, the amount of dollars is correct, but in 11 hours, it says 25.75, which is not correct so Graph B cannot be it.
Graph C, shows that at hour 1, that it is 15.75 dollars, but at hour 2 16.75, as well with hour 3, 17.75. The graph is showing an increase of 1 dollar per hour, which is not correct so graph C is not it.
Graph D shows that at hour 6, there is $94.50, which is correct, but at hour 12, its 100.50. This is not true because , the hour has increased by 6, and when it increased by 6, the amount of pay increased by 6 as well, which is not the right way in which you would do so.
Option A is correct!
Step-by-step explanation:
Hope it helps! =D
A group of 3 friends buy a nintendo switch each. The nintendo switch is $500. The tax is 10%. How much do you have to pay for ALL of the nintendos.
Answer:
1500
Step-by-step explanation:
Because they are 3 and if everyone pays it will be 1500
well, is three friends so each Nintendo is $500, so that's 3*500 = $1500 total, now let's add the 10% tax to that
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10\% of 1500}}{\left( \cfrac{10}{100} \right)1500}\implies 150~\hfill \underset{\textit{total for all}}{\stackrel{1500~~ + ~~150}{\text{\LARGE 1650}}}[/tex]
A rectangular room is 4 times as long as it is wide and it's perimeter is 40 meters. Find the dimensions of the room:
Length=
Width=
Answer:length=16, width=4
Step-by-step explanation:
P=40m
L=4W
P=L+L+W+W
40=4W+4W+W+W
40=10W
W=4
L=4W
L=4(4)
L=16
find an equation of the plane.the plane through the point (8, 5, 6) and with normal vector 4i 9j 3k
An equation of the plane through the point (8, 5, 6) and with normal vector 4i 9j 3k is 4x + 9y + 3z = 95.
A plane in geometry is a level surface that never ends. Other names for it include a two-dimensional surface. A plane has an unlimited width, an endless length, zero thickness, and no curvature. The flat surfaces of a cube or cuboid, as well as the flat surface of paper, are all true examples of geometric planes, despite the fact that it is difficult to envision a plane in real life.
A point is given that is (8, 5, 6) and is passing through 4i + 9j + 3k so ,
4(x - 8) + 9(y - 5) + 6(z - 6) = 0
4x + 9y + 3z = 95.
A plane is a flat, infinitely long, two-dimensional surface in mathematics. A plane may appear as a subspace of a multidimensional space, such as one of the room's infinitely expanding walls, or it may live independently on its own, such as in the context of Euclidean geometry.
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listen to the following excerpts (x, y, and z) and drag the corresponding letter cards to the correct location on the formal structure bel
After listening to the excerpts we can say that, excerpt z is exposition subject soprano, excerpt x is middle entries episode and excerpt y is closing
In music, a fugue is a contrapuntal compositional technique in two or more voices that is based on a subject (a musical theme) that is introduced at the beginning in imitation (repetition at different pitches) and that recurs frequently throughout the composition.
It should not be confused with a fuguing tune, a type of song that was popularized by early American music and West Gallery music and is primarily restricted to those genres. A fugue typically consists of three main sections: an exposition, a development, and a final entry that features the subject returning in the tonic key of the fugue. Recapitulations are included in some fugues.
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The least common multiple
of 5 and 8
Answer:
40
Step-by-step explanation:
Answer: 40
Step-by-step explanation:
There are 24 hours of dance lessons during the dance convention. Each lesson is dedicated to a genre:1/3 of the time is spent on modern dance 1/4 of the time is spent on tap 3/8 of the time is spent on ballet.what fraction of the time is spent on modern dance and hip-hop
The time is spent on modern dance and hip-hop is, 17/24 hours.
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
We have to given that;
There are 24 hours of dance lessons during the dance convention.
And, 1/3 of the time is spent on modern dance, 3/8 of the time is spent on hip hop.
Hence, The time is spent on modern dance and hip-hop is,
⇒ 1/3 + 3/8
⇒ 8/24 + 9/24
⇒ 17/24 hours
Thus, The time is spent on modern dance and hip-hop is, 17/24 hours
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Can anyone help with this?
Step-by-step explanation:
x = 4
m<ZVW = 36°
m<ZWV = 32°
There are 135 test tubes in 3 boxes. Each box has an equal number of test tubes. Which of the following equations can be used to find the number of test tubes, y , in x boxes
y = 45x is the equations can be used to find the number of test tubes, y , in x boxes.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given, There are 135 test tubes in 3 boxes.
Since, Each box has an equal number of test tubes.
Thus,
Test tubes in each box = 135/3
Test tubes in each box = 45
For expression the number of test tubes, y , in x boxes,
Thus,
In x boxes number of test tubes = 45*x
So,
y = 45x
Therefore, equations can be used to find the number of test tubes, y , in x boxes is y = 45x.
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The point is on the terminal side of an angle in standard position. Find the exact values of the six trigonometric functions of the angle.
(4, -6)
sin θ = cos θ = tan θ = csc θ = sec θ = cot θ =
The exact values of the six trigonometric functions of the angle:
sin θ = -3/ [tex]\sqrt{13}[/tex]
cos θ = 2/ [tex]\sqrt{13}[/tex]
tan θ = -3/2
csc θ = - [tex]\sqrt{13}[/tex] /3
sec θ = [tex]\sqrt{13}[/tex] / 2
cot θ = -2/3
Let us assume that θ be an angle formed with postive x-axis.
Let (x, y) = (4, -6)
This point is on the terminal side of an angle in standard position.
r = [tex]\sqrt{x^2+y^2}[/tex]
r = [tex]\sqrt{4^2+(-6)^2}[/tex]
r = [tex]2\sqrt{13}[/tex]
Now we find the value of trigonometric functions.
We know that 1) sin θ = y/r
sin θ = (-6) / [tex]2\sqrt{13}[/tex]
sin θ = -3/ [tex]\sqrt{13}[/tex]
2) cos θ = x/r
cos θ = 4 / [tex]2\sqrt{13}[/tex]
cos θ = 2/ [tex]\sqrt{13}[/tex]
3) tan θ = y/x
tan θ = (-6) / 4
tan θ = -3/ 2
4) csc θ = 1/( sin θ)
csc θ =1/(-3/ [tex]\sqrt{13}[/tex])
csc θ = -[tex]\sqrt{13}[/tex] / 3
5) sec θ = 1/( cos θ)
sec θ =1/(2/ [tex]\sqrt{13}[/tex])
sec θ = [tex]\sqrt{13}[/tex] / 2
6) cot θ = 1/( tan θ)
cot θ =1/(-3/2)
cot θ = -2 / 3
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My question is about LCM (Least Common Multiple)
So the thing is in this sum, in the first pic as u can see I took 3^2 as it is the least one from the two 3s. But, in the other sum, in the 2nd pic if i take 2 and then when I multiply by 2 the answer turns out wrong but If i multiply it with 2^2 and 3, the answer comes right. But my question is that why is it that I'm taking 2^2 but why not 2? 2 is the least one right and there is already 2^2 so why am I taking 2^2?
Answer:
18a²b²c²12x³y²z²Step-by-step explanation:
You want the least common multiple (LCM) of {6a²b, 9b²c, 3c²a} and of {4x²y²z², 6x³yz, 12xy²z}.
Least common multipleThe LCM of two or more terms is a product that has includes all of the factors of each of the terms. One way to find the LCM is to list the factors of the terms, identify the different ones and the powers of each, then choose the highest power of each of the different factors.
{6a²b, 9b²c, 3c²a}6a²b — factors are ...
23a²b9b²c — factors are ...
3²b²c3c²a — factors are ...
3ac²The distinct factors are ...
2 — power of 1; 1 is the highest power3 — powers of 1 and 2; 2 is the highest powera — powers of 1 and 2; 2 is the highest powerb — powers of 1 and 2; 2 is the highest powerc — powers of 1 and 2; 2 is the highest powerThe product of highest powers is the LCM:
LCM = 2¹·3²·a²·b²·c² = 18a²b²c²
{4x²y²z², 6x³yz, 12xy²z}
The distinct factors are ...
2 — powers of 1 and 2; 2 is the highest power3 — power of 1; 1 is the highest powerx — powers of 1, 2, and 3; 3 is the highest powery — powers of 1 and 2; 2 is the highest powerz — powers of 1 and 2; 2 is the highest powerThe product of the highest powers is ...
LCM = 2²·3¹·x³·y²·z² = 12x³y²z²
__
Additional comment
Sometimes the process of finding the LCM can be confused with finding the GCF (greatest common factor). The GCF will be the product of the lowest of the powers of the distinct factors. That power may be zero for any given factor in any given term.
For example, in the first set of terms, the factor 2 has a power of 0 in the last two terms. The factor 'a' has a power of zero in the second term; b has a power of 0 in the third term; c has a power of 0 in the first term. Then the GCF is ...
2⁰·3¹·a⁰·b⁰·c⁰ = 3 . . . . . GCF of {6a²b, 9b²c, 3c²a}
In the second set of terms, 2 has a power of 1 in the 2nd term; 3 has a power of 0 in the 1st term; x, y, z all have powers of 1 in at least one of the terms. Then the GCF is ...
2¹·3⁰·x¹·y¹·z¹ = 2xyz . . . . . GCF of {4x²y²z², 6x³yz, 12xy²z}
In short, every term must be a factor of the LCM, and the GCF must be a factor of every term.
One way to find the LCM of two terms is to divide their product by their GCF. The process can be repeated to include more terms in the LCM.
Which term is missing when using the square root method
The missing term when using the square root method is the discriminant. The discriminant is a number that is calculated from the coefficients of a quadratic equation.
What is quadratic equation?A quadratic equation is a type of mathematical equation that can be written in the form of ax² + bx + c = 0, where a, b, and c are real numbers, a cannot equal 0. It is called a quadratic equation because it has a second-order term, which is the x² term. This type of equation has two solutions, which are referred to as the roots. These roots can be found by using the quadratic formula, which is x = -b ± √(b² - 4ac) / 2a. This equation can be used to solve a wide variety of problems, including finding the length of a side in a right triangle, calculating the area of a circle, finding the maximum or minimum of a function, and solving systems of linear equations.
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Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of p. EP) .79 (to 2 decimals) op .0288 (to 4 decimals)
The sampling distribution of p is 0.0288 (to 4 decimals).
The sampling distribution of p is a theoretical distribution of the proportion of successes (p) in a sample of a given size, drawn from a population with a known proportion of successes (p). In this case, the proportion of successes is the proportion of complaints involving new car dealers that are resolved, which is given as 0.79 (to 2 decimals).
The standard error of the proportion is given by the formula:
[tex]SE = \sqrt{(p * (1 - p) / n)}[/tex]
where n is the sample size. Plugging in the values, we get:
[tex]SE = \sqrt{(0.79 * (1 - 0.79) / 200)}[/tex] = 0.0288 (to 4 decimals).
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please help, its a problem from ixl.
Answer:
[tex]5x\leq 20[/tex]
[tex]$4[/tex] [tex]dollars[/tex]
Step-by-step explanation:
For the first question, since the maximum cost is $20, it has to be [tex]5x\leq 20[/tex] because less than or equal to 20 is the maximum.
For the second question, we solve:
[tex]5x\leq 20[/tex]
[tex]\frac{5x}{5} \leq \frac{20}{5}[/tex]
[tex]x\leq 4[/tex]
[tex]Answer[/tex] [tex]is[/tex][tex]:[/tex] [tex]4[/tex] [tex]dollars[/tex]
Alice took Peter out for milkshakes. If they each got a shake that cost $7,92 and wanted to tip their waiter 20%, how much should they leave for the tip?
Answer:
Step-by-step explanation:
PLEASE PLEASE HELP!!!!!
Answer:
10 inches
Step-by-step explanation:
The surface area of a cylinder is equal to 2 times the area of the base circles plus the height times the circumference.
[tex]SA=2A+Ch[/tex]
[tex]SA=2\pi r^2+2\pi rh[/tex]
Now substitute given values of radius and surface area
[tex]78\pi =2\pi (3)^2+2\pi (3)h[/tex]
Simplify.
[tex]78\pi =18\pi +6\pi h\\60\pi =6\pi h\\10=h[/tex]
The height is 10 inches.
Determine if S is a function.
S = ((a,5), (b,3), (c,3), (d,3), (e,5)}
S is not a function.
A function is a set of ordered pairs where each input (x-value) corresponds to one and only one output (y-value). In this set, S, there are multiple inputs (a, c, d) that correspond to the same output (3). This means that the input 'a' is not uniquely related to output '5' and 'b' is not uniquely related to output '3', etc. Therefore, S does not qualify as a function.
How do I solve problem number 4?
Downtown Shopping stock photos, pictures and royalty-free images from iStock.
What is public parking?
Public parking means that the Public Parking Spaces shall be available to the general public either for free or at commercially reasonable rates.Parking is private when it belongs to you or when it is in your building for example. It is a parking space that can be a box, garage or surface parking, outside and open, but marked by markings on the ground. If you own a private parking, you have the right to remove any vehicle parked on your parking space.Private parking means land and/or buildings or a part thereof, which is used for parking of motor vehicles under the control of a private individual or agency.Parking spaces are very important to cities. A city must have enough parking spaces to provide their residents and their visitors a place to park their car. Since cars are a main factor in transportation, a city must meet the needs of the drivers.
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The 95% confidence interval for the mean daily income of a parking garage is between $5123.48 and $5134.52, indicating that the average daily income will be within this range.
What is mean?Mean is a form of average that is calculated by adding all of the numbers in a set and then dividing the total number of numbers in the set by the total number of numbers in the set. It is sometimes referred to as the arithmetic average.
Assuming the assumptions given in section a) are correct, the 95% confidence interval for the mean daily income generated by this parking garage may be computed using the method for calculating the confidence interval for a population mean. This confidence interval is computed by taking the sample mean, 5129, and multiplying it by 1.96 times the standard error of the mean, which is the standard deviation divided by the square root of the sample size. As a result, the 95% confidence interval is (5123.48, 5134.52).
This 95% confidence range implies that we can be 95% certain that the average daily income generated by this parking garage will be between $5123.48 and $5134.52. To put it another way, we may be 95% positive that the average daily income in this parking garage is generated.
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Please help me with this
Extra points
Answer:
the answer should be A
Step-by-step explanation:
Kendall puts four-fraction strips in one row, and one
1-fraction strip in the row below it. What is the difference
10
in the lengths of these rows?
The difference in length between the two rows is 3 units.
What exactly is a fraction strip?Fraction strips are rectangular pieces (electronic or paper) that represent distinct sections of the same whole. They may be taken apart and manipulated to demonstrate how different portions can be combined to produce the whole or to compare different fractional quantities for equivalence.
Let's assume that each fraction strip has a length of 1 unit. If Kendall puts four 1-unit fraction strips in one row, then the total length of that row would be 4 units. If Kendall puts one 1-unit fraction strip in the row below it, then the total length of that row would be 1 unit.
The difference in length between these two rows would be the length of the top row minus the length of the bottom row. Substituting the values we found, we get:
4 units - 1 unit = 3 units
Therefore, the difference in length between the two rows is 3 units.
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For what value of x is the rational expression below undefined?
X - 4
4 + x
The required value of x for the rational expression x-4/4+x to become undefined is x = -4
What is a rational expression?Rational expressions are defined as fractions of algebraic expressions, such as ax + b / cx + d.
Here,
A fraction to become undefined must consist of zero in its denominator,
So
Given expression = x - 4 / 4 + x
The above expression can be undefined if and only if 4 + x = 0
x = -4
Thus, the required value of x for the rational expression x-4/4+x to become undefined is x = -4.
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Problem 1: Create a graph of the altitude in kilometers versus the time after launch in seconds. Over the plotted interval, what is the average slope of the line, and what does it represent? Show the calculation for the slope with units and the answer for the slope with the correct units and significant figures. Make sure to circle each data point you select for your slope calculation on the graph.
By using the slope function in Excel, you can verify your response. For this assignment, you must use graph paper if you do not use Excel.
You will calculate the slope for each line (graph) using the slope formula given in problem 1. You can have Excel calculate the slope for you to check your answer.
Problem 2: The distance between the launch gantry and the point directly under the current position of the rocket is called the range. Create a graph of the range of the missile over this time interval. What is the average slope of the plotted line, and what does it represent? (Use proper units for the slope based on the
Problem 3: Graph the rocket's speed over the interval between 192 and 202 seconds. What is the average slope of the line, and what does this represent? (Use proper units for the slope based on the graph.)
This assignment will create a graph for each problem. You must include units for the slope in your calculation and your response. (Recall the expression "rise over run.") In addition, write a statement describing the slope's meaning for each graph.
The average slope of the line is 0.5 and the slope represent the steepness of rocket.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).
Given that, a graph of the altitude in kilometers versus the time after launch in seconds.
From the given table we have (190, 150) and (192, 151).
Slope (m) = (151-150)/(192-190)
= 1/2
= 0.5
Hence, the average slope of the line is 0.5 and the slope represent the steepness of rocket.
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Write an exponential function for the table. X 1 2 3 4 y 6 18 54 162 please l need help
Answer:
y = 2 [tex](3)^{x}[/tex]
Step-by-step explanation:
the standard form of an exponential function is
y = a [tex]b^{x}[/tex]
to find a and b use ordered pairs from the table
using (1, 6 )
6 = a[tex]b^{1}[/tex] , that is
6 = ab → (1)
using (3, 54 )
54 = ab³ → (2)
divide (2) by (1) on both sides
[tex]\frac{54}{6}[/tex] = [tex]\frac{ab^3}{ab}[/tex] , that is
b² = 9 ( take square root of both sides )
b = [tex]\sqrt{9}[/tex] = 3
substitute b = 3 into (1) and solve for a
6 = 3a ( divide both sides b 3 )
2 = a
then the exponential function for the table is
y = 2 [tex](3)^{x}[/tex]
ABCD is a rectangle.
B, E and C are points on the straight line P with the equation x+2y=10
This is about slope intercept form of equation. y = 3x + 66
How to find the equation?We are told that the equation of the straight line L is x + 3y = 18
Now, from the attached image, we can see that the line crosses the x axis at point B and the y axis at point E. These points are known as intercepts.
The x-intercept is when y = 0 while the y intercept is when x = 0. Thus;
x-intercept;
x + 3(0) = 18
x = 18
y-intercept;
0 + 3y = 18
3y = 18
y = 18/3
y = 6
This means we have two coordinates now which are;
B(18, 0) and E(0, 6)
We are told that AE = EB
From midpoint formula between two points, we can say that coordinate of point E is; (x + 18)/2 , (y + 0)/2
where x and y are coordinates of point A.
Thus; (x + 18)/2 = 0
x + 18 = 0
x = -18
Also, (y + 0)/2 = 6
y + 0 = 6 × 2
y = 12
The coordinates of point A are (-18, 6)
The equation of a line in slope intercept form is; y = mx + c
Thus; x + 3y = 18 gives; y = -(1/3)x + 18
where -1/3 is the slope
Line M passes through A and perpendicular to line L. Thus slope of line M = -1/(-1/3) = 3
Equation of Line M is; y - 12 = 3(x - (-18))
⇒ y - 12 = 3x + 54
⇒ y = 3x + 66
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Correct question:
ABCD is a rectangle. A, E and B are points on the straight line L with equation x + 3y = 18. A and D are points on the straight line M. AE = EB. Find the equation for M in the form y = ax + b where a and b are integers
