The linear function that is represented by which table has the same slope as the graph? On a coordinate plane, a line goes through points (0, negative 3) and (2, 1). A 2-column table with 5 rows. Column 1 is labeled x with entries negative 25, negative 21, negative 17, negative 13, negative 9. Column 2 is labeled y with entries negative 9, negative 7, negative 5, negative 3, negative 1. A 2-column table with 5 rows. Column 1 is labeled x with entries negative 25, negative 21, negative 17, negative 13, negative 9. Column 2 is labeled y with entries 9, 7, 5, 3, 1. A 2-column table with 5 rows. Column 1 is labeled x with entries negative 9, negative 7, negative 5, negative 3, negative 1. Column 2 is labeled y with entries negative 25, negative 21, negative 17, negative 13, negative 9. A 2-column table with 5 rows. Column 1 is labeled x with entries 1, 3, 5, 7, 9. Column 2 is labeled y with entries negative 9, negative 13, negative 17, negative 21, negative 25.
Answers
Answer:
c
step-by-step explanation:
ok the slope of the line is 2
and so by using the formula y1+y2/x1+x2 we can get the ration of each table
the first table is -9+-7/-25+-21
this can be simplified to -16/-46 which is about 0.347
using this formula for each table you can find the answer .
im
too lazy to do the rest
Answer:
It's C
Step-by-step explanation:
I did the quiz, see Arjinoodles for a detailed explanation.
Related Questions
the sum of 3 consecutive even integers is 228
Answers
Here we will use algebra to find three consecutive integers whose sum is 228. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 228. Therefore, you can write the equation as follows:
(X) + (X + 1) + (X + 2) = 228
To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:
X + X + 1 + X + 2 = 228
3X + 3 = 228
3X + 3 - 3 = 228 - 3
3X = 225
3X/3 = 225/3
X = 75
Which means that the first number is 75, the second number is 75 + 1 and the third number is 75 + 2. Therefore, three consecutive integers that add up to 228 are 75, 76, and 77.
75 + 76 + 77 = 228
We know our answer is correct because 75 + 76 + 77 equals 228 as displayed above.
Answer:
74, 76, 78
Step-by-step explanation:
The numbers are even and consecutive so they are 2x, 2x+2 and 2x+4 because any number multiplied by 2 is always even and they are even CONSECUTIVE,. So 2 and 4
Now their sum is given as 228 so,
2x+2x+2+2x+4= 228
6x+6= 228
6x= 228-6= 222
x= 222/6
= 37
So the numbers are:
2x= 37*2= 74
2x+2= 74+2= 76
2x+4= 74+4= 78
A man starts with an initial velocity of 3.50 m/s and accelerates for a distance of 205
m over 28.7 s. What is the acceleration of the man?
Answers
Answer:
[tex] X= v_i t + \frac{1}{2}a t^2 [/tex]
And from this equation we can solve for a like this:
[tex] 205m = 3.5m/s *(28.7s) +\frac{1}{2}a (28.7s)^2[/tex]
And solving for a we got:
[tex] 104.55m = \frac{1}{2}a (28.7s)^2[/tex]
[tex] a = \frac{2*104.55m}{(28.7s)^2)}= 0.254 m/s^2[/tex]
Step-by-step explanation:
For this case we have the velocity , distance and time given:
[tex] v = 3.5 m/s, d=205m, t =28.7s[/tex]
And we know from kinematics that he velocity can be expressed like this:
[tex] v_f = v_i +a t[/tex]
We also know that the distance is given by:
[tex] X= v_i t + \frac{1}{2}a t^2 [/tex]
And from this equation we can solve for a like this:
[tex] 205m = 3.5m/s *(28.7s) +\frac{1}{2}a (28.7s)^2[/tex]
And solving for a we got:
[tex] 104.55m = \frac{1}{2}a (28.7s)^2[/tex]
[tex] a = \frac{2*104.55m}{(28.7s)^2)}= 0.254 m/s^2[/tex]
A human gene carries a certain disease from the mother to the child with a probability rate of 34%. That is, there is a 34% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has three children. Assume that the infections of the three children are independent of one another. Find the probability that at least one of the children get the disease from their mother.
Answer the following questions:
State the complement of the event "At least one of the children get the disease from their mother".
Find the probability of the complement. Round your answer to four decimals
Find the probability that at least one of the children get the disease from their mother.
Answers
Answer:
The probability that at least one of the children get the disease from their mother is 0.7125.
Step-by-step explanation:
We are given that a human gene carries a certain disease from the mother to the child with a probability rate of 34%.
Suppose a female carrier of the gene has three children. Assume that the infections of the three children are independent of one another.
Let Probability that children get the disease from their mother = P(A) = 0.34
SO, Complement of the event "At least one of the children get the disease from their mother"= P(A') = 1 - P(A)
where A' = event that children do not get the disease from mother.
So, P(A') = 1 - P(A) = 1 - 0.34 = 0.66
Now, probability that at least one of the children get the disease from their mother = 1 - Probability that none of the three children get disease from their mother
= 1 - P(X = 0)
= 1 - (0.66 [tex]\times[/tex] 0.66 [tex]\times[/tex] 0.66)
= 1 - 0.2875 = 0.7125
Which statement could be an interpretation of the graph’s x-intercept or y-intercept?
On a coordinate plane, a line goes through points (0, 800) and (400, 0).
Answers
Answer:
[tex] m=\frac{y_2 -y_1}{x_2 -x_1} =\frac{0-800}{400-0}= -2[/tex]
And then we can find the y intercept using one point for example (0,800) and we have:
[tex] 800= -2*0+ b[/tex]
[tex] b= 800[/tex]
And our model would be:
[tex] y = -2x +800[/tex]
And the x intercept would be if y=0 then
[tex] 0 =-2x +800[/tex]
[tex] x =400[/tex]
x intercept =400 represent the value of x when y =0
y intercept = 800 represent the value of y when x =0
Step-by-step explanation:
We have the following points given:
(0, 800) and (400, 0)
If we want to find the x intercept and y intercept we need to remember that we need to set a linear model given by:
[tex] y=mx +b[/tex]
Where
[tex] m=\frac{y_2 -y_1}{x_2 -x_1} =\frac{0-800}{400-0}= -2[/tex]
And then we can find the y intercept using one point for example (0,800) and we have:
[tex] 800= -2*0+ b[/tex]
[tex] b= 800[/tex]
And our model would be:
[tex] y = -2x +800[/tex]
And the x intercept would be if y=0 then
[tex] 0 =-2x +800[/tex]
[tex] x =400[/tex]
x intercept =400 represent the value of x when y =0
y intercept = 800 represent the value of y when x =0
Answer:
And then we can find the y intercept using one point for example (0,800) and we have:
And our model would be:
And the x intercept would be if y=0 then
x intercept =400 represent the value of x when y =0
y intercept = 800 represent the value of y when x =0
Step-by-step explanation:
We have the following points given:
(0, 800) and (400, 0)
If we want to find the x intercept and y intercept we need to remember that we need to set a linear model given by:
Where
And then we can find the y intercept using one point for example (0,800) and we have:
And our model would be:
And the x intercept would be if y=0 then
x intercept =400 represent the value of x when y =0
y intercept = 800 represent the value of y when x =0
Step-by-step explanation:
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none select none. When m<7=m<4
Answers
Answer:
Option (2). None
Step-by-step explanation:
A quadrilateral ABCD has been given with a property,
m∠7 = m∠4
Option (1). AB║ DC
For AB║DC, angle 7 and angle 3 should measure the same.
(By the property of alternate angles)
Therefore, by the given property we can not deduce AB║DC.
Option (3). AD║BC
For AD║BC, angle 7 and angle 3 must be equal in measure.
(By the property of alternate angles)
Therefore, by the given property we can not deduce AD║DC
Option (2). None will be the answer.
The window above the doorway in Angelica's house is shaped like a semicircle with a diameter of 36 inches.
How much glass was used to make the window? Use 3.14 for π
Answers
Answer:
[tex]508.68[/tex] [tex]in^{2}[/tex]
Step-by-step explanation:
[tex]\pi r^{2} (1/2)[/tex]
[tex](3.14)(18^{2})(1/2)[/tex]
[tex]12717/25 = 508.68[/tex]
Results of 99% confidence intervals are consistent with results of two-sided tests with which significance level? Explain the connection. A 99% confidence interval is consistent with a two-sided test with significance level alphaequals nothing because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval ▼ contains does not contain the value in the null hypothesis.
Answers
Answer:
Yes, they are consistent.
A 99% confidence interval is consistent with a two-sided test with significance level alpha=0.01 because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval does contains the value in the null hypothesis.
Step-by-step explanation:
Yes, they are consistent.
A 99% confidence interval is consistent with a two-sided test with significance level alpha=0.01 because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval does contains the value in the null hypothesis.
The critical values of the confidence level are equivalent to the critical values in the hypothesis test. In the case that the conclusion of the test is to not reject the null hypothesis, the test statistic falls within the acceptance region: its value is within the critical values of the two-sided test.
Then, it is also within the critical values of the confidence interval and the sample mean (or other measure) will be within the confidence interval bounds.
Assume Shelley Kate decides to take her social security at age 63. What amount of social security benefit will she receive each month, assuming she is entitled to $720 per month
Answers
She will receive a lot more money because she is already retired from work already and will win as bit more money
Please help me with this math problem
Answers
Answer:
see below
Step-by-step explanation:
5x - 6y = 21
Let x = 0 and solve for y to find the y intercept
-6y = 21
Divide by -6
y = 21/-6 = -7/2
The y intercept is (0,-7/2)
5x - 6y = 21
Let y = 0 and solve for x to find the x intercept
5x = 21
Divide by 5
y = 21/5 = 21/5
The x intercept is (21/5,0)
Answer:
x=4.2 (x-intercept)
y=-3.5 (y-intercept)
Step-by-step explanation:
To find the x-intercept, we know that y=0. To find the y-intercept, we know that x=0. All we have to do is plug in 0 into either x or y to find the x-intercept and y-intercept.
X-intercept
5x-6(0)=21
5x-0=21
5x=21
x=4.2
Y-intercept
5(0)-6y=21
0-6y=21
-6y=21
y=-3.5
Place a lien company sells t-shirts at $5 and shirt shorts with six if total sales were 1,040. and people bought four times as many t-shirts and shorts what was the total number of t-shirts and shorts sold
Answers
Answer:
Number of shorts = 40
Number of t-shirt = 160
Step-by-step explanation:
Let number of t-shirts = t
Let number of shorts = s
Price of each t-shirt = $5
Total price of t-shirts = 5t
Price of each shorts = $6
Total price of shorts = 6s
So,
5t+ 6s = 1,040...............Eq1
Given:
Number of t-shirt = 4 (number of shorts)
So, t = 4s ................Eq2
From Eq1 and Eq2
5t+ 6s = 1,040
5(4s) +6s = 1,040
20s + 6s = 1,040
26s = 1,040
Number of shorts = 40
Number of t-shirt = 4(number of shorts)
Number of t-shirt = 4(40)
Number of t-shirt = 160
On a number line, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with number a. For example b= 11/4 when a= -11/4
A) b=-a
B) -b=-a
C) b-a=0
D) b(-a)=0
Answers
Answer:
B and A
Step-by-step explanation:
So based on the facts given, we know that b and a both have the same abasolute value. It does not matter whether a or b is negative or positive.
eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
So, we do 3.142*2squared
Which gives you 12.568
so the area of the circle is 12.568 metres squared
Solution,
Radius=2 m
Area =pi r^2
= 3.142*(2)^2
=12.568 m^2
hope it helps
Good luck on your assignment
A candy bar and a piece of bubble gum together cost $1.10. The candy bar costs a dollar more than the bubble gum. How much does the candy bar cost, in dollars?
Answers
Answer:
$1.05
Step-by-step explanation:
Say the price of a piece of bubble gum is x. This means that we can represent our scenario with the equation (x+1)+x=1.10, with (x+1) representing the price of a candy bar. We can then solve from there.
(x+1)+x=1.10 - Given
2x+1=1.10 - Simplify
2x=0.10 - Subtract From Both Sides (sorry, I forgot the name of this property)
x=0.05 - Divide From Both Sides
So now we have the price of the piece of bubble gum, but we want the cost of the candy bar. Fortunately, we know it costs one dollar more than the piece of bubble gum, so just do 0.05 + 1. This means our candy bar costs $1.05.
The candy bar cost, in dollars, is $1.05
Say the price of a piece of bubble gum is x.
This means that we can represent our scenario with the equation (x+1)+x=1.10, with (x+1) representing the price of a candy bar.
We can then solve from there.
We have given that,
(x+1)+x=1.10
Simplify above expression
2x+1=1.10
2x=0.10 - Subtract From Both Sides
x=0.05 - Divide From Both Sides
So now we have the price of the piece of bubble gum, but we want the cost of the candy bar.
What is the cost?Cost is the value of money that a company had to spend to produce its goods or services.
Fortunately, we know it costs one dollar more than the piece of bubble gum, so just do 0.05 + 1. This means our candy bar costs $1.05.
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Help me plzzz with my hw
Answers
Answer:
w || n and n ⊥ m
Step-by-step explanation:
To find out which statement is true, recall the following:
1. 2 lines are said to be parallel to each other if they do not intersect at any given point and are of the same distant apart. Parallel is denoted by ||
2. 2 lines are said to be perpendicular if both lines intersect at a right angle. It is denoted by ⊥
==>From the diagram given, we can see that w and n are of the same distant apart and they do not intersect at any given point.
Also, we can see that n and m intersect at point X to at right angle.
Therefore, we can conclude that w || n and n ⊥ m
Daniel, Clarence, and Matthew split a $20.20 dinner bill so that Daniel pays half of what
Clarence pays. If Daniel pays $6.06, what is the ratio of Clarence’s pay to Matthew’s
pay?
Answers
Answer:
8.80$
Step-by-step explanation:
Total 20.20. 6.06 x 2=12.12. 20.20-12.12=8.80$
Mathew paid 8.80$
Clarence paid 12.12$
Daniel paid 6.06$
Suppose that T is a one-to-one transformation, so that an equation T(u)=T(v) always implies u=v. Show that if the set of images {T(v1)......T(vp)} is linearly dependent, then {v1......vp} is linearly dependent. This fact shows that a one-to-one linear transformation maps a linearly independent set onto a linearly independent set (because in this case the set of images cannot be linearly dependent).
Answers
Answer:
Step-by-step explanation:
The objective is to Show that if the set of images {T(v1)......T(vp)} is linearly dependent, then {v1......vp} is linearly dependent.
Given that:
[tex]\mathbf{[T(v_1) +T(v_2) ...T(v_p)]}[/tex] is linearly dependent set
Thus; there exists scalars [tex]\mathbf{k_1 , k_2 ... k_p}[/tex] ; ( read as "such that") [tex]\mathbf{k_1 T(v_1) +k_2T(v_2) ...k_pT(v_p)=0}[/tex]
[tex]\mathbf{= T(k_1 v_1 +k_2v_2 ...k_pv_p)=0}[/tex]
T = 0 (for the fact that T is linear transformation)
[tex]\mathbf{k_1 v_1 +k_2v_2 ...k_pv_p=0}[/tex] (due to T is one-one)
NOTE: Not all Ki's are zero;
Thus;
[tex]\mathbf{[v_1,v_2 ...v_p] }[/tex] is linearly dependent
It negation also illustrates that :
If [tex]\mathbf{[v_1,v_2 ...v_p]}[/tex] is also linearly independent then [tex]\mathbf{[T(v_1),T(v_2) ...T(v_p)]}[/tex] is also linearly independent.
For the transformation to be a translation, which statements must be true? Select four options.
Answers
Answer:
BD = DB'
CG = GC'
m∠EFA = 90°
The line of reflection, EH, is the perpendicular bisector of BB', AA', and CC'.
Step-by-step explanation:
Hope this helps
Correct me if this is wrong
100 thousands equal to ---lakhs
Answers
Answer:one lakh....
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thnk me...
Answer:
1 Lakh = 100 Thousands
Step-by-step explanation:
which of the following expressions is equal to 2X^2 +8
Answers
Answer:
The question is not clear.
Step-by-step explanation:
Normally it helps to rewrite 8 as
8 = 2 * 2 * 2 = 2³
However the question is not clear.
There are no following expressions given...
By 2X^2 +8,
do you mean 2*x² + 8, or do you mean 2*x^(2 + 8)
or did you perhaps mean 2^(x+8)
Next time, please add a picture.
Answer:
(2x-4i)(x+2i)
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time.
(a) Find the probability that at least 13 flights arrive late .
Answers
Answer:
The probability that at least 13 flights arrive late is 2.5196 [tex]\times 10^{-6}[/tex].
Step-by-step explanation:
We are given that Southwest Air had the best rate with 80 % of its flights arriving on time.
A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time.
The above situation can be represented through binomial distribution;
[tex]P(X = x) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.........[/tex]
where, n = number of trials (samples) taken = 18 Southwest flights
r = number of success = at least 13 flights arrive late
p = probability of success which in our question is probability that
flights arrive late, i.e. p = 1 - 0.80 = 20%
Let X = Number of flights that arrive late.
So, X ~ Binom(n = 18, p = 0.20)
Now, the probability that at least 13 flights arrive late is given by = P(X [tex]\geq[/tex] 13)
P(X [tex]\geq[/tex] 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18)
= [tex]\binom{18}{13}\times 0.20^{13} \times (1-0.20)^{18-13}+ \binom{18}{14}\times 0.20^{14} \times (1-0.20)^{18-14}+ \binom{18}{15}\times 0.20^{15} \times (1-0.20)^{18-15}+ \binom{18}{16}\times 0.20^{16} \times (1-0.20)^{18-16}+ \binom{18}{17}\times 0.20^{17} \times (1-0.20)^{18-17}+ \binom{18}{18}\times 0.20^{18} \times (1-0.20)^{18-18}[/tex]
= [tex]\binom{18}{13}\times 0.20^{13} \times 0.80^{5}+ \binom{18}{14}\times 0.20^{14} \times 0.80^{4}+ \binom{18}{15}\times 0.20^{15} \times 0.80^{3}+ \binom{18}{16}\times 0.20^{16} \times 0.80^{2}+ \binom{18}{17}\times 0.20^{17} \times 0.80^{1}+ \binom{18}{18}\times 0.20^{18} \times 0.80^{0}[/tex]
= 2.5196 [tex]\times 10^{-6}[/tex].
Is a sinusoid a function whose values repeat based on position of a point that moves around a circle
Answers
Answer:
yes
Step-by-step explanation:
One way to describe a sine function is that it is the y-coordinate of a point on the unit circle that is θ radians counterclockwise from the x-axis:
y = sin(θ)
__
Another way to describe the sine function is that it is the solution to the differential equation for undamped "simple harmonic motion."
y'' + y = 0; y'(0) = 1, y(0) = 0
y = sin(x)
Answer:
True
Step-by-step explanation:
Linek 5
Linem
Line
Linen
-5
Which line has a slope of -3?
A. line j
B. line k
C. line m
D. linen
Answers
Will pick brainliest! I need help with this, actual effort in answering is much appreciated.
Answers
Answer:
option 2
Step-by-step explanation:
4^2=16/8=2. 4^2=16/16=1. 2-1=1
please help with math, it’s easy!! explantion needed!
Answers
Answer:
1
Step-by-step explanation:
The quadratic relation is a perfect square:
y = (7x +3)²
so has one zero, where the factor is zero:
7x +3 = 0
7x = -3
x = -3/7
_____
It is useful to have handy reference to the form of the square of a binomial:
(a +b)² = a² +2ab +b²
Here, your first clue is that 49x² and 9 are both perfect squares: (7x)² and (3)². It is easy to check that the middle term is twice the product of these roots:
2(7x)(3) = 42x . . . . matches the middle term
So, the given expression is equivalent to ...
y = (7x +3)²
You roll a die with the sample space S = {1, 2, 3, 4, 5, 6}. You define A as {1 ,4, 6}, B as {1, 3, 4, 5, 6}, C as {1, 5}, and D as {2, 3, 5) 5}. Determine which of the following events are exhaustive and/or mutually exclusive
Exhaustive Mutually exclusive
a. A and B (Click to select) (Click to select)
b. A and C Click to select) (Click to select)
c. A and D (Click to select) (Click to select)
d. Band C (click to select) (click to select)
Answers
Answer:
Step-by-step explanation:
Recall that two events A,B are called mutually exclusive if and only if [tex]A\cap B = \emptyset [/tex] (their intersection is empty). They are exhaustive if they are mutually exclusive and their union is the sample space.
Based on this
a) Note that [tex]A\cap B = \{1,6\}[/tex], so they are not mutually exclusive nor exhaustive.
b) [tex]A\cap C = \{1\}[/tex] so they are not mutually exclusive nor exhaustive.
c) [tex]A\cap D = \emptyset [/tex], so they are mutually exclusive. Note that [tex]A\cup D = \{1,2,3,4,5,6\}=S[/tex]. Then they are exhaustive.
d) [tex]B\cap C = \{1,5\}[/tex], so they are not mutually exclusive nor exhaustive.
Label the parts of the triangle. Leg leg altitude hypothenuse right angle.
Answers
1)The longest side is the hypotenuse
2)The line segment in the within the triangle is the altitude.
3)The arrow pointing the uppermost angle is right angle.
4)The bottommost line segment is the leg.
5)The arrow below the arrow pointing the right angle is also the leg.
HOPE IT HELPS!!!!
PLEASE MARK BRAINLIEST!!!!
Refer to the provided image.
What is a right-angled triangle?A triangle with one of its angles to be 90°. That is if a triangle has one right angle then the triangle is a right-angled triangle.
What is the hypotenuse of a right-angled triangle?A right-angled triangle's hypotenuse is the longest side. It's the side that's on the opposite side of the right angle.
What is a leg of a right-angled triangle?A leg of a right-angled triangle is the side that is adjacent to the right angle.
What is the altitude of a right-angled triangle?The height of the right-angled triangle when the hypotenuse is considered as the base is called the Altitude of the right-angled triangle.
How to solve it?Considering the definitions above label the figure accordingly.
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Which equation is equivalent to One-fourth + x =Negative StartFraction 5 over 4 EndFraction? Select all that apply.
Answers
Options:
(A)x = StartFraction 6 over 4 EndFraction
(B)x = Negative StartFraction 6 over 4 EndFraction
(C)x minus one-fourth = negative StartFraction 5 over 4 EndFraction
(D)x = negative three-halves
(E)x = negative three-fourths
Answer:
(B)x = Negative StartFraction 6 over 4 EndFraction
[tex]-\dfrac{6}{4}[/tex]
(D)x = negative three-halves
[tex]-\dfrac{3}{2}[/tex]
Step-by-step explanation:
We want to determine which fraction is equivalent to
[tex]\dfrac{1}{4}+x=-\dfrac{5}{4}\\$First, we collect like terms$\\x=-\dfrac{5}{4}-\dfrac{1}{4} \\\\=\dfrac{-5-1}{4}\\=-\dfrac{6}{4}\\x=-\dfrac{6}{4}[/tex]
This value of x is the result in Option B.
Reducing [tex]-\dfrac{6}{4}[/tex] to its lowest form:
[tex]-\dfrac{6}{4}=-\dfrac{3}{2}[/tex] which is Option D.
Therefore, the correct options are: B and D
find the mean of x,2x,3x,4x,5x
Answers
Answer:
Mean = 3x
Step-by-step explanation:
Mean = [tex]\frac{SumOfObservations}{No. OfObservations}[/tex]
Mean = [tex]\frac{x+2x+3x+4x+5x}{5}[/tex]
Mean = [tex]\frac{15x}{5}[/tex]
Mean = 3x
The mean, also known as the average of x, 2x, 3x, 4x, and 5x is 3x as per the concept of Simplifying.
To find the mean of x, 2x, 3x, 4x, and 5x, we need to add up all the values and divide by the total number of values.
In this case, we have five values.
Mean = (x + 2x + 3x + 4x + 5x) / 5
Simplifying the numerator:
Mean = (15x) / 5
Mean = 3x
Therefore, the mean of x, 2x, 3x, 4x, and 5x is 3x.
The mean, also known as the average, represents the central tendency of a set of values. In this case, the mean is 3x, which indicates that on average, the values x, 2x, 3x, 4x, and 5x are three times the value of x.
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What must Bill McGuire invest today to receive an annuity of $12,000 for four years semiannually at a 10% annual rate? All withdrawals will be made at the end of each period.
Answers
Answer:
$77,558.55
Step-by-step explanation:
A fix periodic payment for specific period of time.
We need to calculate the present value annuity to determine the value of investment today.
Present value of annuity = P x ( 1 - ( 1 + r )^-n / r )
where
P = Periodic payment = $12,000
r = interest rate = 10% / 2 = 5%
n =numbers of payment = 4 years x 2 = 8 payments
Placing values in the formula
Investment Value today = $12,000 x ( 1 - ( 1 + 5% )^-8 / 5% )
Investment Value today = $77,558.55
Suppose a box of Cracker Jacks contains one of 5 toy prizes: a small rubber ball, a whistle, a Captain America decoder ring, a race car, or a magnifying glass. Each prize is equally likely to be in a box. Question 1. How many boxes of Cracker Jacks would you expect to buy until you obtain a complete set of prizes
Answers
Answer:
11.42 boxes
Step-by-step explanation:
For the first box bought, there is a 100% chance of getting a unique toy (since you still don't have any). E₁ = 1.
After that, there is a 4 in 5 chance of getting a unique toy from the next box, the expected number of boxes required is:
[tex]E_2 = (\frac{4}{5})^{-1} = 1.25[/tex]
For the next unique toy, there is now a 3 in 5 chance of getting it:
[tex]E_3 = (\frac{3}{5})^{-1} = 1.67[/tex]
Following that logic, there is a 2 in 5 chance of getting the 4th unique toy:
[tex]E_4 = (\frac{2}{5})^{-1} = 2.5[/tex]
Finally, there is a 1 in 5 chance to get the last unique toy:
[tex]E_5 = (\frac{1}{5})^{-1} = 5[/tex]
The expected number of boxes to obtain a full set is:
[tex]E=E_1+E_2+E_3+E_4+E_5\\E=1+1.25+1.67+2.5+5\\E=11.42\ boxes[/tex]