A science experiment has a catapult launch a ball. The result of the experiment is shown in the table. experiment is shown in the table.
a. What is the average distance of the 5 attempts? Show your work.
B. How far does the ball have to travel on the sixth attempt so that the average of all 6 of the attempts is 50.9 meters? Explain
please help!!
Answers
The data on the attempts and distances of the science experiment on the launch of a ball by a catapult, presented in a tabular form gives the following;
a. The five attempts have an average distance of 50.58
b. The distance the sixth ball has to travel so as to give an average distance traveled of 50.9 meters is 52.5 meters
What is an average of a data set?An average is a descriptive statistics that tends to describe the values in a dataset. An average or the mean of a dataset is obtained by summing the data values and dividing the result by the number of data points
Please find attached, the Attempt to Distance table obtained from a similar question online
a. The formula for average, [tex] \bar{x} [/tex] of a set of data or observations is presented as follows;
[tex] \displaystyle{\bar x = \frac{Sum \: of \: observations}{Number \: of \: observations}} [/tex]
Mathematically, we have;
[tex] \displaystyle{\bar x = \frac{\sum x}{N}} [/tex]
Which gives from the attached table;
[tex]\displaystyle{\sum {x} =50.7+49.4 +52.3 + 48.9 + 51.6 = 252.9}[/tex]
N = 5
Which gives;
[tex] \displaystyle{\bar x = \frac{252.9}{5} = 50.58}[/tex]
The average distance of the 5 attempts is 50.58 metersb. The distance, d, the ball has to travel on the sixth attempt to get an average of 50.9 meters is found as follows;
The new total number of attempts, N = 6
Which gives;
[tex] \displaystyle{\bar x = 50.9 = \frac{d + 252.9}{6} }[/tex]
6 × 50.9 = d + 252.9
Therefore;
d = 6 × 50.9 - 252.9 = 52.5
The distance the ball has to travel in the sixth attempt to have an overall average of 50.9 meters is 52.5 metersLearn more about the average of a dataset here:
https://brainly.com/question/12636890
#SPJ1
Related Questions
PLEASE HELP- Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 25 gallons of fuel, the airplane weighs 2060 pounds. When carrying 45 gallons of fuel, it weights 2188 pounds. How much does the airplane weigh if it is carrying 60 gallons of fuel?
Answers
The linear function which can be used to represent the situation is y = 6.4x + 1900 and airplane weight if it is carrying 60 gallons of fuel is 2,284 pounds
How to find linear functiony = mx + b
where,
x = the number of gallons and y = the weight of the aircraft in pounds.Now, we can use the two sets of data points given to us to first solve for the slope m as:
m = (2188 - 2060) / (45 - 25)
= 128 / 20
= 6.4
y - yo = m(x - xo)
y - 2060 = 6.4(x - 25)
y - 2060 = 6.4x - 160
y = 6.4x - 160 + 2060
y = 6.4x + 1900
if it is carrying 60 gallons of fuelx = 60
So,
y = 6.4x + 1900
y = 6.4(60) + 1900
y = 384 + 1900
y = 2,284 pounds
Therefore, the weight of the airplane if it is carrying 60 gallons of fuel is 2,284 pounds
Read more on linear function:
https://brainly.com/question/4025726
#SPJ1
[tex] \rm \int_0^ \infty \frac{1}{(1 + {x}^{ \phi} {)}^{ \phi} } dx \\ [/tex]
Answers
Recall that [tex]\phi = 1 + \frac1\phi[/tex].
In the integral, substitute [tex]y=1+x^\phi[/tex], so that [tex]x=(y-1)^{1/\phi} = (y-1)^{\phi-1}[/tex] and [tex]dx = (\phi-1) (y-1)^{\phi-2} \, dy[/tex]. We have
[tex]\displaystyle I = \int_0^\infty \frac{dx}{(1+x^\phi)^\phi} \\\\ ~~~~ = \frac1\phi \int_1^\infty \frac{(y-1)^{\phi-2}}{y^\phi} \, dy[/tex]
Substitute [tex]y=\frac1z[/tex] and [tex]dy=-\frac{dz}{z^2}[/tex] to transform [tex]I[/tex] to
[tex]\displaystyle I = \frac1\phi \int_0^1 \left(\frac1z-1\right)^{\phi-2} z^{\phi-2} \, dz \\\\ ~~~~ = \frac1\phi \int_0^1 (1-z)^{\phi-2} \, dz[/tex]
Finally, substitute [tex]u=1-z[/tex].
[tex]\displaystyle I = \frac1\phi \int_0^1 u^{\phi-2} \, du \\\\ ~~~~ = \frac1\phi \cdot \frac1{\phi-1} = \frac{\phi-1}{\phi-1} = \boxed{1}[/tex]
(b) y = x²+2x9 dx = 11x¹⁰ + 10x¹, where 10 dy is the derived function. dx Find the value of p and the value of q.
Answers
The expression y=[tex]x^{p} +2x^{q}[/tex]. [tex]\frac{dy}{dx}=11x^{10}+10x^{4}[/tex], where dy/dx is derived function. The p and q values are 11 and 5.
Given that,
The expression y=[tex]x^{p} +2x^{q}[/tex]
[tex]\frac{dy}{dx}=11x^{10}+10x^{4}[/tex], where dy/dx is derived function.
Derived function means for any value of the independent variable, the value of another function is the instantaneous rate of change of the specified function at that value of the independent variable.
We have to find the p and q values.
Take expression
y=[tex]x^{p} +2x^{q}[/tex]
[tex]\frac{dy}{dx}=px^{p-1}+2qx^{q-1}[/tex]
[tex]11x^{10}+10x^{4}=px^{p-1}+2qx^{q-1}[/tex]
Here,
we can see p=11 and
2q=10
q=5
Therefore, the p and q values are 11 and 5.
To learn more about derived visit: https://brainly.com/question/25324584
#SPJ1
Hi, I need to send you the question as I have written
Answers
recall the formula for velocity, which involves distance and time:
velocity = distance / time
since the woman's velocity is: 4.5 Km/h, then in order to cover 10 km, we need to find the time in the equation:
4.5 km/h = 10 km / t
multiply both sides by the time (t)
4.5 * t = 10
divide both sides by 4.5 in order to isolate t completely
t = 10 / 4.5
then
t = 2 hours and 0.2222 hours which can be translated into minutes by multiplying this by 60: 40/3 = 13 minutes and 0.33333 minutes. which can be converted into seconds by multiplying it by 60: 20 seconds
Then she will cover that distance in 2 hours, 13 minutes and 20 seconds.
Convert the following phrase into a mathematical expression use x as the variable combine like terms when possible A number multiplied by -8 subtracted from the sum of 8 and two times the number
Answers
ANSWER:
[tex]-8x-(8+2x)[/tex]STEP-BY-STEP EXPLANATION:
We must convert the following statement "A number multiplied by -8 subtracted from the sum of 8 and two times the number" into a mathematical expression.
We know that "a number" would be x.
Therefore:
[tex]-8x-(8+2x)[/tex]Select the correct answer. Based on these segment lengths, which group of segments can form a triangle? A. 3, 10, 14 B. 8, 7, 13 C. 3, 2, 5 D. 20, 7, 13
Answers
Answer:
B
Step-by-step explanation:
By the triangle inequality theorem, the sum of the lengths of the two shorter sides needs to be greater than the length of the longest side.
The position, d, in metres of an object
in motion as it travels is given by:
d= (t + 2) (t + 1.2)
It is the time in seconds.
This is an equation of motion.
By looking at it, we can learn about
how the object started moving.
First, expand the brackets.
t2+2.4+3.2t
The initial height is the constant
(no t) term.
What is the initial height?
Answers
Answer:
2.4m
Step-by-step explanation:
The question has already done most of the work for you. To find the initial height, simply set t = 0 and substitute it into the function.
[tex]d(0) = {0}^{2} + 2.4 + 3.2(0) \\ = 2.4m[/tex]
The quantity of six and a number, times
five
Answers
Mai, Bill, and Dante have a total of $105 in their wallets. Dante has 3 times what Mai has. Bill has $10 more than Mai. How much does each have?
Answers
Answer:
Mai 19
Bill 29
Dante 57
Step-by-step explanation:
assume
mai = X
Bill = Y
Dante = Z
X + Y + Z = 105
Z = 3X
Y = 10 + X
then
X + Y + Z = X + 3X + 10 + X
5X + 10 = 105
5X = 95
X = 19
Y = 29
Z = 57
10 less than the quotient of a number and 2 is -18"
Answers
The representation of the expression is x/2 - 10 = -18
How to translate the algebraic expression?The mathematical statement is given as
"10 less than the quotient of a number and 2 is -18"
In expressions, quotient mean divide i.e. /
So, we have the following representation
"10 less than the quotient of a number and 2 is -18" ⇒ 10 less than a number/2 is -18"
Let the number be x
So, we have
"10 less than the quotient of a number and 2 is -18" ⇒ 10 less than x/2 is -18"
Less than as used here means minus
So, we have
"10 less than the quotient of a number and 2 is -18" ⇒ x/2 - 10 is -18
Rewrite as
"10 less than the quotient of a number and 2 is -18" ⇒ x/2 - 10 = -18
Hence, the expression represented by "10 less than the quotient of a number and 2 is -18" is x/2 - 10 = -18
Read more about expressions at
https://brainly.com/question/4344214
#SPJ1
Can the angle measures of a triangle be 46°, 82°and 50°
Answers
Answer:Explanation:
No
The sum of the interior angles of a triangle is always 180°. in this case, the sum is:
Then,
46 + 82 + 50 = 178
Since 178 and 180 are distinct, 46°, 82°and 50° can't be the angle measures of a triangle.
The set of all numbers greater than or equal to -10 and less than 9
Answers
The The set of all numbers greater than or equal to -10 and less than 9 will be -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8.
How to illustrate the information?It should be noted that from the information, we are to find the set of all numbers greater than or equal to -10 and less than 9.
This simply means the numbers from -10 to 8.
Therefore, the numbers will be -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8.
Learn more about numbers on:
brainly.com/question/17200227
#SPJ1
Mary has 65 roses and 104 tulips. What is
the greatest number of bouquets they can be
divided into if there will be the same number
of roses in each bouquet and the same
number of tulips in each bouquet?
Answers
The greatest number of bouquets they can be divided into if there will be the same number of roses in each bouquet and the same number of tulips in each bouquet is 5.
Given that:-
Number of roses Mary has = 65
Number of tulips Mary has = 104
We have to find the greatest number of bouquets they can be divided into if there will be the same number of roses in each bouquet and the same number of tulips in each bouquet.
HCF (65, 104) = 13
Hence, the groups of 13 roses and 13 tulips will together make a bouquet.
From 65 roses, 65/13 = 5 bouquets can be made.
From 104 tulips, 104/13 = 8 bouquets can be made.
Min (5,8) = 5.
To learn more about HCF, here:-
https://brainly.com/question/17240111
#SPJ1
)) 24 cups 5) 3 cups
Answers
Answer: 12 cups
Explanation
Anna needs 6 pint of milk to produce yoghurt
1 pint = 2 cups
let cups of milk be x
1 pint of milk will give 2 cups
6 pints of milk will give x cups of milk
1 pint = 2cups
6 pints = x cups
Cross multiply
1 * x = 2 * 6
x = 12 cups
Therefore, Anna will need 12 cups of milk to produce a yoghurt.
I need help with this problem
Answers
We have the following function:
[tex]H(t)=10\sin (2\pi(t-\frac{1}{4}))+15[/tex]a) The initial height occurs at t=0. By substituting this value into the function, we get
[tex]H(0)=10\sin (2\pi(0-\frac{1}{4}))+15[/tex]which gives
[tex]\begin{gathered} H(0)=10\sin (-2\pi\frac{1}{4})+15 \\ H(0)=10\sin (-\frac{2\pi}{4})+15 \\ H(0)=10\sin (-\frac{\pi}{2})+15 \end{gathered}[/tex]since sin(-Pi/2) is equal to -1, we have
[tex]H(0)=-10+15[/tex]Then, H(0)= 5, so the height is 5 feets.
b) The car will make a full rotation when the argument is shifted 2Pi:
[tex]H(t)=10\sin (2\pi(t-\frac{1}{4})+2\pi)+15[/tex]at this point H(t) must be equal to 5 feets. Then, we have
[tex]5=10\sin (2\pi(t-\frac{1}{4})-2\pi)+15[/tex]and we must find t. If we move +15 to the left hand side, we obtain
[tex]\begin{gathered} 5-15=10\sin (2\pi(t-\frac{1}{4})-2\pi) \\ \text{then} \\ 10\sin (2\pi(t-\frac{1}{4})-2\pi)=-10 \end{gathered}[/tex]By moving the coefficient 10 the the right hand side, we get
[tex]\begin{gathered} \sin (2\pi(t-\frac{1}{4})-2\pi)=-\frac{10}{10} \\ \sin (2\pi(t-\frac{1}{4})-2\pi)=-1 \end{gathered}[/tex]we can note that when
[tex]\sin \theta=-1\Rightarrow\theta=-90=-\frac{\pi}{2}[/tex]this implies that the argument of our last result is
[tex]2\pi(t-\frac{1}{4})-2\pi=-\frac{\pi}{2}[/tex]By moving 2Pi to the right hand side, we have
[tex]\begin{gathered} 2\pi(t-\frac{1}{4})=-\frac{\pi}{2}+2\pi \\ 2\pi(t-\frac{1}{4})=\frac{3\pi}{2} \end{gathered}[/tex]Now, by moving 2Pi to the right hand side, we have
[tex]t-\frac{1}{4}=-\frac{\frac{3\pi}{2}}{2\pi}[/tex]which gives
[tex]t-\frac{1}{4}=\frac{3}{4}[/tex]so, t is given by
[tex]\begin{gathered} t=\frac{3}{4}+\frac{1}{4} \\ t=1 \end{gathered}[/tex]That is, n 1 minute, the car will take one full rotation.
c) The maximum height of the car ocurrs at t=0.5 min because in one minute it take one full rotation. Then, at t=1/2 we get
[tex]H(\frac{1}{2})=10\sin (2\pi(\frac{1}{2}-\frac{1}{4}))+15[/tex]which gives
[tex]\begin{gathered} H(\frac{1}{2})=10\sin (2\pi(\frac{1}{4}))+15 \\ H(\frac{1}{2})=10\sin (\frac{\pi}{2})+15 \\ H(\frac{1}{2})=10(1)+15 \\ H(\frac{1}{2})=25 \end{gathered}[/tex]that is, the maximum height is 25 feets
7. Write a biconditional for the following conditional. Determine the truth value
of the new statement. If two lines have the same slope, then they are parallel.
Answers
Line AB is parallel to CD, for instance, as indicated by the formula AB ll CD.
How do parallel lines work?
Lines in a plane that are regularly spaced apart are known as parallel lines. Parallel lines don't overlap each other. Perpendicular lines are those that cross at a straight angle of 90 degrees.Only if the slopes of two lines are equal can they be said to be parallel. If two lines have different y-intercepts and equal slopes, they are said to be parallel. In a plane, parallel lines are two lines that never cross (meaning they will continue on forever without ever touching). The equal slopes of parallel lines are a distinctive feature. The rise (change in Y coordinates) over the run (change in X coordinates) of a line, or its steepness, is referred to as the slope of a line. The most typical way to depict parallel lines is with two vertical lines (ll). Line AB is parallel to CD, for instance, as indicated by the formula AB ll CD.Learn more about parallel lines
brainly.com/question/16701300
#SPJ13
Find k with the given information.
m=-3/5 (k,-9) and (1,-6
Answers
Using the slope formula, the value of k in the coordinates of the point given is: k = 6.
How to Find the Slope of a Line?If we are given two points that lie on a line, (x1, y1) and (x2, y2), the formula that is used to find the slope (m) of the line is given as:
Slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = change in y / change in x..
Given the following:
(k, -9) = (x1, y1)
(1, -6) = (x2, y2)
Slope (m) = -3/5
Plug in the values into the formula used for calculating the slope of a line:
(-6 -(-9))/(1 - k) = -3/5
3/(1 - k) = -3/5
Cross multiply and solve for the value of k
-3(1 - k) = 3(5)
-3 + 3k = 15
Add 3 to both sides
-3 + 3k + 3 = 15 + 3 [subtraction property of equality]
3k = 18
Divide both sides by 3
3k/3 = 18/3 [division property of equality]
k = 6
The value of k is: 6. Therefore, the points on the line that have a slope of -3/5 are (6, -9) and (1, -6).
Learn more about the slope of a line on:
https://brainly.com/question/16949303
#SPJ1
Find the length of the arc on a circle with a radius of 2.4 kilometers and is intercepted by a central angle measuring 150°. Leave your answer in terms of π. A. 6π/5kmB. 6 kmC. 12π/5kmD. 2π km
Answers
Given:
The radius of the circle = 2.4 kilometers
The measure of the arc = 150°
The length of the arc is given by the formula:
[tex]A=\theta\cdot r[/tex]Note: we will convert the angle from degrees to radian
So, the length of the arc =
[tex](150\cdot\frac{\pi}{180})\cdot2.4=\frac{150}{180}\cdot2.4\cdot\pi=2\pi[/tex]So, the answer will be option D. 2π km
Can someone help with this question?
Answers
The slope of the line is 2 / 3.
How to find the slope of a line?The slope of a line can be found as follows:
The slope of a line is change in y with respect to change in x.
In other words, the slope of a line is rise over run.
Therefore,
slope = y₂ - y₁ / x₂ - x₁
Using (0, 3)(-3, 1)
Hence,
x₁ = 0
x₂ = -3
y₁ = 3
y₂ = 1
Therefore,
slope = 1 - 3 / -3 - 0
slope = -2 / -3
slope = 2 / 3
learn more on slope here: https://brainly.com/question/23087740
#SPJ1
Hi, can you help me to solve this exercise please. If MK=6 ft, find the length “MKL to the nearest Tenth!
Answers
To find the arc length we need to know the angle subtended by the arc.
From the diagram we notice that angle MNK is of 180°.
We also notice that:
[tex]\begin{gathered} m\angle JNK+m\angle KNL=90 \\ 52+m\angle KNL=90 \\ m\angle KNL=90-52 \\ m\angle KNL=38 \end{gathered}[/tex]Then the angle subtended by the arc MKL is 218°.
Now that we know this we need to remember that the arc length is given by:
[tex]s=2\pi r(\frac{\theta}{360})[/tex]in this case the radius is 3 ft (The radius is half the diameter) then we have that:
[tex]\begin{gathered} s=2\pi(3)(\frac{218}{360}) \\ s=11.4 \end{gathered}[/tex]Therefore the arc length is 11.4 ft.
In geometry,you can use deductive rules to
A
b
c
d
Answers
In geometry, you can use deductive rules to prove conjectures.
What is geometry?Geometry is defined as a subfield of mathematics that examines the measurement and relationships of surfaces, solids, solid surfaces, angles, and points. The calculation of a triangle's angles is a geometry example.
Geometry will categorize, quantify, and lack a counterexample. Once a concept has been defined, it can be utilized in subsequent definitions; for instance, parallel lines can be used in the definition of a parallelogram once they have been defined. classification, counterexample, quantification, and parallelogram.
Given Data
In geometry, you can use deductive rules to
In geometry, you can use deductive rules to prove conjectures.
In geometry, deductive rules can be used to demonstrate whether a particular assertion or conjecture is true or untrue. We narrow down a result proving a statement must be true or untrue by using deductive principles, such as definitions, postulates, and other theorems, in a logical order.
To learn more about geometry, visit:
https://brainly.com/question/3410069
#SPJ9
Match the polar equations to their rectangular forms-
Answers
Applying the rules for the polar equations, the correct pairs are given in the image at the end of the answer.
What are polar equations?
The most well known polar equation rules are given as follows:
For the first pair, when x = 2, we have that:
rcos(θ) = 2.
r = 2/cos(θ)
r = 2 sec(θ), as one divided by the cosine is the secant.
For the second pair, we have that:
x² + y² = 36.
x² + y² = r², hence:
r² = 36
r = 6.
For the third pair, we have that:
x² + y² = 2y
r² = 2rsin(θ).
r²/r = 2sin(θ).
r = 2sin(θ).
For the fourth pair, we have that:
[tex]x = \sqrt{3}y[/tex]
[tex]\frac{y}{x} = \frac{1}{\sqrt{3}}[/tex]
[tex]\frac{y}{x} = \frac{\sqrt{3}}{3}[/tex]
Then the angle theta is given as follows:
θ = arctan(sqrt(3)/3) = pi/6.
For the fifth pair, we have an angle in which the sine and the cosine are equal, hence this angle is of 45º = pi/4.
The image at the end of the answer shows all the matched pairs.
More can be learned about polar equations at https://brainly.com/question/9363127
#SPJ1
A florist sells a dozen roses for $35.40. She sells individual roses for the same unit cost. How much would 18 roses cost?
Answers
Answer: 53.1
Step-by-step explanation: Divide 35.40 by 2 to get 17.7. now add 35.40 with 17.7 and you get 53.1
The analysis of a data set last year produced a line of best fit with equation y = 2.108x - 0.3818. Data was collected from the same sample this year and produced a line of best fit with equation y= 2.107x + 1.7455. Explain the verticalchange in going from last year's data to this year's data.
Answers
The slope of the line has increased, meaning it has become a positive number. This shift means that this year the data points were placed higher than the previous year.
Your teacher wants to put a garden in her backyard with a fence around it. The width needs to be the same size as the shed which is 8ft. If she bought 50 feet of fence and wants the largest garden she can make, what should the length of the garden be? Justify your thinking.
Answers
Th length of the garden when the teacher bought 50 feet of fence is 17 feet.
How to calculate the value?From the information, the width needs to be the same size as the shed which is 8ft and she bought 50 feet of fence and wants the largest garden she can make,
It should be noted that perimeter is calculated as:
= 2(Length + Width)
In this case, the perimeter is 50 feet.
2(Length + Width) = 50
2(Length + 8) = 50
2L + 16 = 50
2L = 50 - 16
2L =34
Divide
L = 34/3
L = 17 feet.
The length is 17 feet.
Learn more about length on:
brainly.com/question/2217700
#SPJ1
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar. y = -x² + 64x - 292
Answers
Answer:
what
Step-by-step explanation:
i think maybe like… actually
Isabelle is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of $9, and her grandmother has pledged $1 per mile. If Isabelle walks a certain distance, the two donors will end up owing the same amount. How much will each donor owe?
Answers
Answer:
9 mileds
Step-by-step explanation:
To pay for a $22,800car, Mai made a down payment of $3,800and took out a loan for the rest. On the loan, she paid monthly payments of $420for 4 years. (a) What was the total amount Mai ended up paying for the car (including the down payment and monthly payments)? (b) How much interest did Mai pay on the loan?
Answers
1. The total amount that was paid for the car will be $23960.
2. The interest that Mai pay on the loan will be $1160.
How to calculate the value?1. From the information, in order to pay for a $22,800 car, Mai made a down payment of $3,800 and took out a loan for the rest and on the loan, she paid monthly payments of $420for 4 years.
The total amount that was paid for the car will be:
= $3800 + ($420 × 4 years)
= $3800 + ($420 × 48)
= $3800 + $20160
= $23960
2. The interest that Mai pay on the loan will be:
= $23960 - $22800
= $1160
Learn more about interest on:
brainly.com/question/25793394
#SPJ1
Please help with the following question:
Answers
Using it's concept, the probabilities are given as follows:
a) Both go off on schedule: 0.30 = 30%.
b) Both go off on schedule: 0.2 = 20%.
What is a probability?A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.
From the text of the problem, the probability of A and not B is of 0.2, that is:
A x (1 - B) = 0.2.
We can multiply the probabilities as the events are independent.
In item a, the probability of neither is of 0.2, hence:
(1 - A) x (1 - B) = 0.2.
From the first equation, we have that:
A = 0.2/(1 - B).
From the second equation, we have that:
(1 - A) = 0.2/(1 - B).
Hence:
A = 1 - A
2A = 1
A = 0.5.
Then we can find B as follows:
(1 - A) x (1 - B) = 0.2.
1 - B = 0.2/0.5
1 - B = 0.4
B = 0.6.
The probability of both is:
A x B = 0.5 x 0.6 = 0.30 = 30%.
For item b, we consider that:
(1 - A) x B = 0.3.
We also have that:
A x (1 - B) = 0.2.
From the first equation:
B = 0.3/(1 - A).
Then, replacing on the second:
A x (1 - 0.3/(1 - A)) = 0.2
Which has a solution of:
A = 0.5, B = 0.4.
Hence the probability of both is:
0.4 x 0.5 = 0.2 = 20%.
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
Question 1 options:
Is the relation in this set of points a function?
{(-2, 6) , (4, 5) , (3, -3) , (6, 9), (4, -4)}
State whether the statement is true of false.
1. The relation is a function.
2. An element from the domain is paired with more than one element from the range.
Answers
Answer:
1.4 Relations and Functions
A relation is a correspondence between two sets. If x and y are two
elements in these sets and if a relation exists between x and y, then x
corresponds to y, or y depends on x.
DEFINITION OF A FUNCTION:
Let X and Y two nonempty sets. A function from X into Y is a relation that
associates with each element of X, exactly one element of Y.
However, an element of Y may have more than one elements of X
associated with it.
That is for each ordered pair (x,y), there is exactly one y value for each x,
but there may be multiple x values for each y. The variable x is called the
independent variable (also sometimes called the argument of the
function), and the variable y is called dependent variable (also
sometimes called the image of the function.) x = y2 is not a function from X into Y, because there
is not exactly one y value for each x.
Solving for y, you get y =
which means there are two possible values for y
Step-by-step explanation: