The inverse of the equation y = 9x² − 4 is found by switching x and y and solving the equation for the new y. The correct inverse function after simplification is y = ±√(x / 9 + 4).
Explanation:To find the inverse of the equation y = 9x2 − 4, you need to switch the roles of x and y and then solve for y once again. Here is a step-by-step explanation:
Replace y with x and x with y to get x = 9y2 − 4.Add 4 to both sides to isolate the perfect square term: x + 4 = 9y2.Divide both sides by 9 to get (x + 4) / 9 = y2.Take the square root of both sides note that there are always two solutions when taking a square root, a positive and a negative: y = ±√((x + 4) / 9).Finally, simplify to express y: y = ±√(x / 9 + 4/9).Comparing the result with the choices given, we find that y = ±√(x / 9 + 4) is the correct inverse function.
solve the following problems using 5-D process part 2
(Describe/Draw, Define, Do, Decide, and Declare)
a. The number of girls in the Spanish Club is four more than twice the number of boys. There are 61 students in the Spanish Club. Find the number of boys and the number of girls in the Spanish Club.
b. Carrie and John went bowling together. They each bowled one game. Carrie knocked down 12 more pins than John did. The sum of their bowling games was 230. What was Carrie's and John's bowling scores?
The two problems are almost identical: you have to set up a system, and then solve it.
In the first case, let [tex]g[/tex] and [tex]b[/tex] be, respectively, the number of girls and boys.
We know that [tex]g=2b+4[/tex] (the number of girls in the Spanish Club is four more than twice the number of boys). Also, we know that [tex]g+b=61[/tex] (there are 61 students in total).
So, we have the system
[tex]\begin{cases}g=2b+4\\g+b=61\end{cases}[/tex]
We can use the first equation to substitute in the second
[tex]g+b=61 \iff (2b+4)+b=61 \iff 3b+4=61 \iff 3b=57 \iff b=19[/tex]
And then solve for [tex]g[/tex]:
[tex]g=2b+4=2\cdot 19+4=38+4=42[/tex]
For the second problem, let [tex]c[/tex] and [tex]j[/tex] be the number of pins knocked down by, respectively, Carrie and John. Just like before, we have the system
[tex]\begin{cases}c=j+12\\c+j=230\end{cases}[/tex]
And you can solve it in the very same way we solved the previous one.
A bookcase has 4 shelves. The bottom shelf has 10 books. Each of the other shelves has 5 more books than the shelf below it. How many books are in the bookcase.
Answer:
70
Step-by-step explanation:
For every positive 2-digit number, x, with tens digit t and units digit u, let y be the 2-digit number formed by reversing the digits of x. Which of the followingexpressions is equivalent to x − y ?a) 9(t − u) b) 9(u − t) c) 9t − u d) 9u − t e) 0
Answer:
a) 9(t - u)
Step-by-step explanation:
x = 10t + u
y = 10u + t
x - y = 10t + u - 10u - t
= 9t - 9u
= 9(t - u)
If the standard deviation of a set of data is zero, what can you conclude about the set of values? The sum of the deviations from the mean is zero. All values are identical. All values are equal to zero. The sum of the values is zero
Answer:
All values are identical.
Step-by-step explanation:
We are given the following in the question:
If the standard deviation of a set of data is zero.
Then, all the values in data are identical.
This can be shown as:
Let all the terms in data be x.
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{nx}{n} = x[/tex]
Sum of squares of differences =
[tex]\displaystyle\sum (x_i - x)^2 = 0[/tex]
[tex]\sigma = \sqrt{\frac{0}{n}} = 0[/tex]
Thus, the correct answer is
All values are identical.
The correct conclusion about the set of values when the standard deviation is zero is that all values are identical.
The standard deviation is a measure of the amount of variation or dispersion in a set of values. A standard deviation equal to zero means that there is no variation at all in the data set. This can only occur if all the values in the set are exactly the same.
To understand why this is the case, let's consider the formula for standard deviation (for a population):
[tex]\[ \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}} \][/tex]
Here, [tex]\( \sigma \)[/tex] is the standard deviation, [tex]\( x_i \)[/tex] represents each value in the data set, [tex]\( \mu \)[/tex] is the mean of the data set, and [tex]\( N \)[/tex] is the number of values in the data set.
Now, let's address the other options:
The sum of the deviations from the mean is zero: This statement is true for any data set, regardless of whether the standard deviation is zero or not. The positive and negative deviations from the mean always sum to zero.All values are equal to zero: This is not necessarily true. The standard deviation can be zero if all values are the same non-zero number.The sum of the values is zero: This is also not necessarily true. The standard deviation is concerned with the variation of the values around the mean, not the sum of the values themselves.In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?
A) 5
B) 4
C) 3
D) 2
E) 0
Step-by-step explanation:
Below is an attachment containing the solution.
Please assist on these problems
Answer:
a) linear. Cost per minute is a constant.
b) f(x) = 40 -0.15x
d) f(100) = 25. The remaining value is $25 after using 100 minutes.
Step-by-step explanation:
a) Since the cost per minute is a constant, the remaining dollar value of the phone decreases by the same amount for each minute used. The cost as a function of minutes used is a linear function with a constant rate of change.
__
b) The value starts at $40 and decreases by $0.15 for each increment of x (minutes used). The function can be written as ...
f(x) = 40 -0.15x
__
d) Put 100 where x is in the function definition and do the arithmetic.
f(100) = 40 -0.15×100 = 40 -15
f(100) = 25
According to the variable and function definitions, x=100 means 100 minutes have been used; f(x) = 25 means the remaining value of the phone is 25 dollars.
f(100) = 25 means the phone's remaining value is $25 when 100 minutes have been used.
Match each function formula with the corresponding transformation of the parent function y = –x 2 – 1. 1. y = –x2 – 1 Translated right by 1 unit 2. y = –(x – 1)2 – 1 Reflected across the x-axis 3. y = x2 + 1 Translated down by 1 unit 4. y = –x2 Reflected across the y-axis 5. y = –(x + 1)2 – 1 Translated left by 1 unit 6. y = –x2 – 2 Translated up by 1 unit
Answer:
1. f₁(x)=-x²+2x-2
2. f₂(x)=-x²+6x-10
3. f₃(x)=-x²-2
4. f₄(x)=-x²+10x-26
5. f₅(x)=-x²-2x-2
6. f₆(x)=-x²
Step-by-step explanation:
1. we have that f(x) is translated right by 1 unit , also
according to the graph f(x) has a vertex P(0,-1) then P₁ ( 1,-1) to f₁(x) therefore y-y₁ = -(x-x₁)² ⇒ y-y₁ = -(x-x₁)² ⇒ y+1 = -(x-1)² ⇒ y=-(x²-2x+1)-1 =-x²+2x-2
2. f(x) is reflected across the x-axis 3, same as in 1., P₂(3,-1) to f₂(x)
y+1 = -(x-3)² ⇒ y=-(x²-6x+9)-1 =-x²+6x-10
3. f(x) is translated down by 1 unit, P₃(0,-2) to f₃(x)
y+2 = -(x)² ⇒ y=-x²-2
4. f(x) is reflected across the y-axis 5, P₄(5,-1) to f₄(x)
y+1 = -(x-5)² ⇒ y=-(x²-10x+25)-1 =-x²+10x-26
5. f(x) is translated left by 1, P₅(-1,-1) to f₅(x)
y+1 = -(x+1)² ⇒ y=-(x²+2x+1)-1 =-x²-2x-2
6. f(x) is translated up by 1 unit, P₆(0,0) to f₆(x)
y+0 = -(x+0)² ⇒ y=-x²
In a network of 40 computers, 5 hold a copy of a particular file. Suppose that 7 computers at random fail. Let F denote the number of computers that fail and have a copy of the file. A) What is E[F]?B) What is the range of F? C) What is the probability that F = 2?
Answer:
a. E(F)=0.875
b. 99.9976%
c. P(X=2)=0.1683
Step-by-step explanation:
a. We notice that this is a binomial distribution with the probability of success;
[tex]p=\frac{5}{40}=0.125[/tex]
#We are given the sample size, n=7. The Expected value is calculated as:
[tex]E(X)=np\\\\E(F)=np , n=7, p=0.125\\\\E(F)=7\times 0.125\\\\=0.875[/tex]
Hence the expectation, E(F)=0.875
b. To calculate the probability of the range of F, we need to calculate all possible outcomes of F in the given sample;
[tex]P(X\leq 5)=1-P(X=6)-P(X=7)\\\\=1-{7\choose 6}(0.125)^6(1-0.125)^1-{7\choose 7}(0.125)^7(1-0.125)^0\\\\=1-0.000023365-0.000000476\\\\=0.999976158\\\\=99.9976\%[/tex]
Hence, the range of F is 99.9976%
c. The probability that F=2 is calculated using the binomial distribution function as:
[tex]P(X=2)={7\choose 2}(0.125)^2(1-0.125)^5\\\\=0.1683[/tex]
Hence, the probability of F=2 is 0.1683
Using the hypergeometric distribution, it is found that:
a) E(F) = 0.875
b) The range is {0, 1, 2, 3, 4, 5}
c) 0.1741 = 17.41% probability that F = 2.
The computers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.In this problem:
There are 40 computers, hence [tex]N = 40[/tex].Of those computers, 7 fail, hence [tex]n = 7[/tex].5 of the computers hold a copy, hence [tex]k = 5[/tex].Item a:
The expected value of the hypergeometric distribution is:
[tex]E(F) = \frac{nk}{N}[/tex]
Hence:
[tex]E(F) = \frac{35}{40} = 0.875[/tex]
Item b:
The range is the possible values that F can assume, which is from 0 to k, hence 0 to 5.
Item c:
The probability is P(X = 2), applying the hypergeometric distribution.
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,40,7,5) = \frac{C_{5,2}C_{35, 5}}{C_{40,7}} = 0.1741[/tex]
0.1741 = 17.41% probability that F = 2.
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A ball slides up a frictionless ramp. It is then rolled without slipping and with the same initial velocity up another frictionless ramp (with the same slope angle). In which case does it reach a greater height, and why
Answer:
Rolling case achieves greater height than sliding case
Step-by-step explanation:
For sliding ball:
- When balls slides up the ramp the kinetic energy is converted to gravitational potential energy.
- We have frictionless ramp, hence no loss due to friction.So the entire kinetic energy is converted into potential energy.
- The ball slides it only has translational kinetic energy as follows:
ΔK.E = ΔP.E
0.5*m*v^2 = m*g*h
h = 0.5v^2 / g
For rolling ball:
- Its the same as the previous case but only difference is that there are two forms of kinetic energy translational and rotational. Thus the energy balance is:
ΔK.E = ΔP.E
0.5*m*v^2 + 0.5*I*w^2 = m*g*h
- Where I: moment of inertia of spherical ball = 2/5 *m*r^2
w: Angular speed = v / r
0.5*m*v^2 + 0.2*m*v^2 = m*g*h
0.7v^2 = g*h
h = 0.7v^2 / g
- From both results we see that 0.7v^2/g for rolling case is greater than 0.5v^2/g sliding case.
A ball will reach a greater height when it slides up a frictionless ramp and is then rolled without slipping up another frictionless ramp with the same slope angle.
Explanation:A ball will reach a greater height when it slides up a frictionless ramp and is then rolled without slipping up another frictionless ramp with the same slope angle. This is because, when the ball slides up, it gains potential energy which is then converted to kinetic energy as it rolls up the second ramp. The ball will reach a greater height because it retains some of the initial energy it gained from sliding up the first ramp.
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giving out brainliest !!
Three runners Dave, Edith, and Foley all start at the same time for a 24 km race, and each of them runs at a constant speed. When Dave finishes the race, Edith is 8 km behind, and Foley is 12 km behind. When Edith finishes the race, how far behind is Foley, in km?
Answer:
4 Km behind.
Step-by-step explanation:
1. Draw a graph
2. make Dave Edith and Foley
3. 8-0 is 8 and 12-8 is 4
The speed is the distance covered by an object at a particular time. When Edith finishes the race, the distance by which Foley is behind is 6 km.
What is speed?The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Let the time in which Dave finishes the race be represented by t. Therefore, in time t Dave completed 24 km.
Given that When Dave finishes the race, Edith is 8 km behind. Therefore the distance that Edith will cover in time t is 16 km. Now, the speed of Edith will be,
Speed of Edith = 16 km /t
Also, When Dave finishes the race, Foley is 12 km behind. Therefore the distance that Edith will cover in time t is 12 km. Now, the speed of Edith will be,
Speed of Edith = 12 km /t
Now, the time it will take for Dave to finish the rest of 8 km distance is,
Time = 8 km / (16 km/t)
= 0.5 t
Further, the distance that Edith will cover in time 0.5t is,
Distance = 0.5t × 12km/t
= 6 km
Therefore, the distance that will be left for Foley is 6 km.
Hence, When Edith finishes the race, the distance by which Foley is behind is 6 km.
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Two trains continuously travel between Washington D.C. and Baltimore which are 120 miles apart. The trains start simultaneously, with train A starting in Washington DC and train B starting in Baltimore, and travel at 30 and 90 mph respectively. If the station turnaround times are negligible, what is the distance between the point where the trains meet for the first time and the point where they meet for the second time?
Answer:
Step-by-step explanation:
Two train traveling in opposite direction
Distance apart the train is 120miles
Train A
Speed =30mph
Train B
90mph
What is common to the train is the same time, they will meet at the same time
Let assume they meet at distance x from from Washington
Then A has travelled x mile distance
Then, B has travelled 120-x mile distance
Time for train A to get to x,, = time for train B to get 120-x
Time=distance/speed
da/Sa=db/Sb
Let da be distance of train A
And db be distance of train B
Sa be speed of train A
Sb be speed of train B
Then,
da/Sa=db/Sb
x/30=120-x/90
Cross multiply
90x=3600-30x
90x+30x=3600
120x=3600
Then, x=3600/120
x=30miles
Then will meet at 30miles from Washington
Second part of the questions
Train B is faster than train A
Train B has already travelled 90miles while train B travels 30 miles
This shows that train A will not get to Baltimore before train B catch up
Then, let train A travel y distance
Then B will have to complete the 30 miles and then with another 30 miles that A has travel and then y
Total distance B travel will be
db=30+30+y
db=60+y
And da=y
Therefore,
da/Sa=db/Sb
y/30=60+y/60
Cross multiply
60y=1800+30y
60y-30y=1800
30y=1800
Then, y=1800/30
y=60miles
That means they will meet at 60miles from both Washington and Baltimore, or they are at mid points
Define a function called isSenior that takes a parameter containing an integer value and returns True if the parameter is greater than or equal to 65, and False otherwise.
Answer:
So if the parameter 's value is 7 or 803 or 141 the function returns true . But if the parameter 's value is -22 or -57, or 0, the function returns false .
My Code:
bool is Positive ( int x ) {
if ( x > 0 )
{
return true;
}
else {
return false ;
}
}
Oliver read for 450 minutes this month. His goal is to read for 10% more minutes next month. If Oliver meets his goal,how many minutes will he read in all during the two months
Answer:
Oliver read in two months = 945 minutes
Step-by-step explanation:
Oliver read in this month = 450 minutes
Goal for the next month = 10 % more than this month = [tex]\frac{110}{100}[/tex] × 450
⇒ Oliver read in next month = 495 minute
⇒ Oliver total read in two months = 450 + 495 = 945 minutes
Thus Oliver read in two months = 945 minutes
Answer:
Oliver will read 945 minutes in 2 months.
Step-by-step explanation:
Given:
Number of minutes read this month = 450 mins
Percent of minutes to read next month = 10%
We need to find the number of minutes he read in two months.
Solution:
First we will find the number of minutes he read in next month.
number of minutes he read in next month is equal to Number of minutes read this month plus Percent of minutes to read next month multiplied by Number of minutes read this month.
framing in equation form we get;
number of minutes he read in next month = [tex]450+\frac{10}{100}\times 450 =450+45 =495\ mins[/tex]
Now number of minutes he read in two months is equal to sum of Number of minutes read this month and number of minutes he read in next month.
framing in equation form we get;
number of minutes he read in two months = [tex]450+495 = 945\ mins[/tex]
Hence Oliver will read 945 minutes in 2 months.
identify the type of function shown in the graph.
The type of Function shown in the graph
Step-by-step explanation:
1.The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular x value. The y value of a point where a vertical line intersects a graph represents an output for that input x value.
2.Different types of graphs depend on the type of function that is graphed. The eight most commonly used graphs are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal. Each has a unique graph that is easy to visually differentiate from the rest.
3.we can represent a function using a graph. Graphs display many input-output pairs in a small space. The visual information they provide often makes relationships easier to understand. We typically construct graphs with the input values along the horizontal axis and the output values along the vertical axis.
Answer:
y= 1/2 csc (x)
Step-by-step explanation:
probably
Find the missing side length BM. Round your answer to the nearest tenth.
Length of side BM is 30 yd
Step-by-step explanation:
Step 1: Find the value of ∠S using the property that sum of angles of a triangle is 180°⇒ ∠B + ∠M + ∠S = 180°
⇒ 35° + 102° + ∠S = 180°
∴ ∠S = 180° - 137° = 43°
Step 2: Use the law of sines to find the length of BM.Law of sines ⇒ a/sin A = b/sin B = c/sin C
Here, let BM be a then, sin A = sin S = sin 43° = -0.83
Also, b = 18 yd, then sin B = sin 35° = -0.43
⇒ BM/-0.83 = 18/-0.43
⇒ BM = -0.83 × 18/-0.43 = 14.94/0.43 = 34.74 yd = 30 yd (rounded to nearest tenth)
Answer:
Step-by-step explanation:
Looking at the triangle, to determine BM, we would apply the sine rule. It is expressed as
a/SinA = b/SinB = c/SinC
Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. From the triangle, m∠S = 180 - (102 + 35) = 43°
Therefore, applying the rule,it becomes
18/Sin35 = BM/Sin43
Cross multiplying, it becomes
BM × Sin 35 = 18 × Sin 43
BM × 0.5736 = 18 × 0.6820
0.5736BM = 12.276
Dividing the left hand side and the right hand side of the equation by 0.5736, it becomes
0.5736BM/0.5736 = 12.276/0.5736
BM = 21.4
Brandy set her watch 4 seconds behind and it falls behind another 1 second every day. How many days had it been since brandy last set her watch if the watch is 22 seconds behind?
Answer:
18 days
Step-by-step explanation:
Let x represent number of days.
We have been given that Brandy's watch falls 1 second every day. So Brandy's watch will fall [tex]1x[/tex] seconds behind in x days.
We are also told that Brandy set her watch 4 seconds behind, so Brady's watch will be behind by total [tex]x+4[/tex] seconds in x days.
Since Brady's watch is 22 seconds behind, so we will equate [tex]x+4[/tex] by 22 to solve for x as:
[tex]x+4=22[/tex]
[tex]x+4-4=22-4[/tex]
[tex]x=18[/tex]
Therefore, Brandy set her watch 18 days ago.
Answer:
Its been 19 days since brandy last set her watch as the watch is 22 seconds behind.
Step-by-step explanation:
We are given the following in the question:
Brandy set her watch 4 seconds behind and it falls behind another 1 second every day.
Thus, this forms an arithmetic progression.
4, 5, 6, 7, ...
First term, a = 4
Common difference, d = 1
The [tex]n^{th}[/tex] terms is 22. We have to find the value of n.
The [tex]n^{th}[/tex] terms of A.P is given by
[tex]a_n = a + (n-1)d[/tex]
Putting values, we get,
[tex]22 = 4 + (n-1)1\\18 = n-1\\n = 19[/tex]
Thus, its been 19 days since brandy last set her watch as the watch is 22 seconds behind.
Ms.Perkins needs to order art supplies for the entire school.She would like to get at least 8,000 piece construction paper has 495 pieces , about how many pack will she need!
To find out how many packs of construction paper Ms. Perkins will need, divide the total number of pieces needed by the number of pieces in each pack. Using long division, we find that she will need at least 16 packs of construction paper.
Explanation:To find out how many packs of construction paper Ms. Perkins will need, we can divide the total number of pieces she needs (8,000) by the number of pieces in each pack (495). This will give us the number of packs required.
Using long division, we divide 8,000 by 495:
First, we divide 8,000 by 495 to get 16 with a remainder of 40.We then bring down the next digit, 0, making the new dividend 400.We divide 400 by 495, getting 0 with a remainder of 400.Finally, we bring down the 0, making the new dividend 4000. We divide 4000 by 495, getting 8 with a remainder of 40.Since the remainder is less than 495, we stop here. Therefore, Ms. Perkins will need at least 16 packs of construction paper.
Two welders worked a total of 46 h on a project. One welder made $34/h, while the other made $39/h. If the gross earnings of the two welders was $1,669 for the job, how many hours did each welder work?
Answer:
x = 25 Total worked hours by welder winning 34 $ /h
y = 21 Total worked hours by welder winning 39 $ /h
Step-by-step explanation:
Let call
"x" numbers of hours worked by welder winning 34 $/h
"y" numbers of hours worked by welder winning 39 $/h
Then according to problem statement
x + y = 46 ⇒ y = 46 - x
1669 = 34*x + 39*y ⇒
We got a two equation system, solving
1669 = 34*x + 39* ( 46 - x ) ⇒ 1669 = 34*x + 1794 - 39*x
1669 - 1794 = - 5*x ⇒ -125 = - 5*x
x = 125/5 ⇒ x = 25
And as y = 46 - x y = 46 - 25 ⇒ y = 21
Harold catches fish throughout the day at unpredictable intervals. Which reinforcement schedule is this?a. variable interval b. variable ratio c. fixed interval d. fixed ratio
Answer:
The correct answer to the question is
a. variable interval
Step-by-step explanation:
In a variable interval, the time at which reinforcement or reward is gained occurs at an unpredictable time. That is the animal gets a reinforcement on the grounds of an unpredictable time period.
An example of a variable interval is the catching of fish whereby the fisher catches fishes at an unpredictable time throughout the day.
The result of a variable interval is a controlled but stable response rate. In the case in the question, constant monitoring of the fishing device is important
The reinforcement schedule described is a variable interval schedule where the reinforcement occurs at unpredictable intervals of time.
Explanation:The reinforcement schedule described in the question is a variable interval schedule.
Variable interval refers to a schedule in which the reinforcement (in this case, catching fish) occurs at unpredictable intervals of time. Harold catches fish throughout the day, but the intervals between catching fish are inconsistent and unpredictable.
Examples of variable interval schedules include waiting for a bus that arrives at different times or checking your phone for new messages throughout the day.
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The workers in a factory are organized into five-person teams. When conducting a work-environment survey, a researcher randomly selected 10 teams to obtain a total sample of 50 workers. The researcher used ____ sampling.
Answer:
cluster sampling
Step-by-step explanation:
ideal groups of objects are naturally chaos arranged in groups, and randomly selected. Unlike class sampling, with homogeneously arranged groups and only a few randomly selected objects from each group, in cluster sampling, each group is allocated in a chaotic and all objects in the group become part of the sample.
x + 4y – 12 = 0 x = 3y – 7 Which of the following is the resulting equation?
-7y – 19 = 0
y – 5 = 0
7y + 19 = 0
7y – 19 = 0
Answer:
The answer to your question is 7y - 19 = 0
Step-by-step explanation:
Data
Equation l x + 4y - 12 = 0
Equation ll x = 3y - 7
Process
1.- Substitute equation ll in equation l
3y - 7 + 4y - 12 = 0
2.- Group like terms
(3y + 4y) + (-7 - 12) = 0
3.- Simplify like terms
7y - 19 = 0
4.- Result
7y - 19 = 0
The amount of time it takes for a student to complete a statistics quiz is uniformly distributed (or, given by a random variable that is uniformly distributed) between 32 and 64 minutes. One student is selected at random. Find the probability of the following events.
A. The student requires more than 59 minutes to complete the quiz.
Probability =
B. The student completes the quiz in a time between 37 and 43 minutes.
Probability =
C. The student completes the quiz in exactly 44.74 minutes.
Probability =
Answer:
(A) 0.15625
(B) 0.1875
(C) Can't be computed
Step-by-step explanation:
We are given that the amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 32 and 64 minutes.
Let X = Amount of time taken by student to complete a statistics quiz
So, X ~ U(32 , 64)
The PDF of uniform distribution is given by;
f(X) = [tex]\frac{1}{b-a}[/tex] , a < X < b where a = 32 and b = 64
The CDF of Uniform distribution is P(X <= x) = [tex]\frac{x-a}{b-a}[/tex]
(A) Probability that student requires more than 59 minutes to complete the quiz = P(X > 59)
P(X > 59) = 1 - P(X <= 59) = 1 - [tex]\frac{x-a}{b-a}[/tex] = 1 - [tex]\frac{59-32}{64-32}[/tex] = [tex]1-\frac{27}{32}[/tex] = 0.15625
(B) Probability that student completes the quiz in a time between 37 and 43 minutes = P(37 <= X <= 43) = P(X <= 43) - P(X < 37)
P(X <= 43) = [tex]\frac{43-32}{64-32}[/tex] = [tex]\frac{11}{32}[/tex] = 0.34375
P(X < 37) = [tex]\frac{37-32}{64-32}[/tex] = [tex]\frac{5}{32}[/tex] = 0.15625
P(37 <= X <= 43) = 0.34375 - 0.15625 = 0.1875
(C) Probability that student complete the quiz in exactly 44.74 minutes
= P(X = 44.74)
The above probability can't be computed because this is a continuous distribution and it can't give point wise probability.
A TRAFFIC LIGHT IS RED FOR 38 SECONDS YELLOW FOR 10 SECONDS AND GREEN FOR ONE MINUTE AND TWELVE SEONDS. IN A CONSTANTLY REPEATING CYCLE, WHAT IS THE PROBABILITY THAT AT THE MOMENT A PASSING PEDESTRIAN GLANCES AT IT, THE LIGHT WILL BE GREEN
At Sara's birthday party, 15 guests are sharing 3/5 of a gallon of Liquid Soap Bubbles. What fraction of the liquid is available for each guest to use for blowing bubbles?
Answer:
Each guest uses [tex]\frac{1}{25}[/tex] of a gallon of liquid soap bubble at Sara's party.
Step-by-step explanation:
We are given the following in the question:
Number of guests at Sara's party = 15
Amount of liquid soap bubble used by 15 guest =
[tex]\dfrac{3}{5}\text{ of a gallon}[/tex]
Fraction of liquid soap bubble available for each guest =
[tex]=\dfrac{\text{Liquid soap bubble used by 15 guest}}{\text{Number of guest}}\\\\=\dfrac{\frac{3}{5}}{15}\\\\=\dfrac{1}{25}[/tex]
Thus, each guest uses [tex]\frac{1}{25}[/tex] of a gallon of liquid soap bubble at Sara's party.
Answer:
1/25 of the gallon each person will get
Step-by-step explanation:
A person’s blood pressure is monitored by taking 3 readings daily. The probability distribution of his reading had a mean of 132 and a standard deviation of 5. Each observation behaves as a random sample. Find the mean of the sampling distribution of the sample mean for the three observations each day.
Answer:
The mean of the sampling distribution of the sample mean for the three observations each day is 132.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 132
Standard Deviation, σ = 5
Each observation behaves as a random sample.
a) Mean of the sampling distribution
[tex]\bar{x} = \mu = 132[/tex]
b) Standard deviation of the sampling distribution
Sample size,n = 3
[tex]s = \dfrac{\sigma}{\sqrt{n}} = \dfrac{5}{\sqrt{3}} = 2.887[/tex]
Thus, the mean of the sampling distribution of the sample mean for the three observations each day is 132.
I need help I have no clue
Answer:
The answer to your question is x = 64; y = 20
Step-by-step explanation:
Angles 2x + 2 and 130° are vertical angles so they measure the same.
2x + 2 = 130
- Solve for x
2x = 130 - 2
2x = 128
x = 128/2
x = 64
Angles 3y - 10 and 50° are vertical angles, so they measure the same.
3y - 10 = 50
3y = 50 + 10
3y = 60
y = 60/3
y = 20
Nolini says that if the denominator is more than twice the numerator, the fraction can always be replaced with a 0. Is she correct? Give an example in your explanation.
Answer:
yes
Step-by-step explanation:
It depends on how accurate you want your answer to be, but basically yes, imagine we set our numerator to be x, and our denominator to be 2x, if we built our fraction we will get that:
[tex]\frac{x}{2x}=\frac{1}{2}[/tex]
If the denominator of a fraction is exactly twice the numerator, then the fraction will be simplified to 1/2 or 0.5.
Now, the greater the denominator is, the closer the fraction will get to zero.
Take for example I had an fraction like this:
[tex]\frac{3}{6}=0.5[/tex]
which approximates to 0. If we made the denominator bigger, let's say 7, we would get:
[tex]\frac{3}{7}=0.43[/tex]
notice the answer is closer to 0 this time, so it's valid to round it to zero. If we made the denominator greater, let's say 25, we would get:
[tex]\frac{3}{25}=0.12[/tex]
and so on. So it is true that if the denominator of a fraction is greater than twice the numerator, we can always replace the fraction with a 0 (depending on how accurate you want your answer to be).
If the denominator is more than twice the numerator, the number is therefore less than halve, 1/2 but cannot always be replaced with a 0.
An example;
Suppose we have a numerator, 2.
Then, we have a denominator which is more than twice the numerator; say 5
The resulting fraction is therefore;
2/5.The fraction 2/5 is definitely less than 1/2 but cannot always be replaced with a 0.
Read more on fractions:
https://brainly.com/question/17220365
a. Money market accounts
b. Single stocks
c. Bonds
d. Mutual funds
e. Fixed annuities
f. Real estate
For this assignment:
1. Put the investments in order by least risk to greatest risk. You can list by letter only (for example: a, b, c, d, e, f).
2. On a second line, order the investments by least return to greatest return. Again, you can list by letter only.
3. Review the sorted lists, and determine the one investment type you would select to start your investment portfolio. Provide a one-paragraph explanation of why you selected the investment along with your expected returns.
Answer:
Investments in order by least risk to greatest risk: A, C, E, D, F, B.
Step-by-step explanation:
What is the value of X in the following parallelogram?
Answer: x = 35
Step-by-step explanation:
In a parallelogram, the opposite sides and the opposite angles are equal and parallel.
Also, the consecutive angles in a parallelogram are supplementary. This means that the sum of the consecutive angles is 180 degrees.
Angle (2x - 10) and angle (2x + 50) are consecutive angles. Therefore,
2x - 10 + 2x + 50 = 180
2x + 2x - 10 + 50 = 180
4x + 40 = 180
4x = 180 - 40 = 140
x = 140/4
x = 35
A rectangular prism 5 feet long by 5 feet high by 6 feet deep and wide 15 tons what was the volume of the average stone how much did it one cubic foot of the stone weigh
Answer:
One cubic foot of the stone weigh 10 tons.
Step-by-step explanation:
There is a mistake in the question, thus it is corrected:
A typical stone on the lowest level of the great pyramid in Egypt was a rectangular prism 5 feet long by 5 feet high by 6 feet deep and weighed 15 tons. What was the volume of the average stone and how much did it one cubic foot of the stone weigh?
Now, to find the volume of average stone and how much one cubic foot of stone weigh.
Dimension of rectangular prism:
Length = 5 feet.
Height = 5 feet.
Width = 6 feet.
Now, to get the volume of stone which was a rectangular prism we put formula:
[tex]Volume=length\times width\times height[/tex]
[tex]Volume=5\times 6\times 5[/tex]
[tex]Volume=150\ cubic\ feet.[/tex]
The volume of the average stone was = 150 cubic feet.
Weight of stone = 15 tons.
Now, to get one cubic foot of the stone weigh we divide the volume of the average stone by weight of stone:
The volume of the average stone ÷ weight of stone
[tex]150\div 15[/tex]
[tex]=10\ tons.[/tex]
Therefore, one cubic foot of the stone weigh 10 tons.