Answer:
The expected value of the random variable with the given probability distribution = 12 .52
Step-by-step explanation:
Given data
x : 0 1 5 10 1000
p(x) : 0.33 0.32 0.24 0.10 0.01
The expected value of the given random variable of given probability distribution
E(X) = ∑ x p ( X = x)
E(X) = 0 × 0.33 + 1 × 0.32 + 5 × 0.24 + 10× 0.10 + 1000×0.01
E (X) = 12.52
Round the following number to the nearest thousand 2385
By rounding of the following number to the nearest thousand is 2000.
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
'
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
Round the following number to the nearest thousand
2385
= 2000
Thus, by rounding of the following number to the nearest thousand is 2000.
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Find the values
Y = 3x - 7
Y = x - 1
X = Y =
Answer: Y=3x -7
Y=x-1
X=Y=
Step-by-step explanation:
Customer arrivals at a bank are random and independent; the probability of an arrival in any one-minute period is the same as the probability of an arrival in any other one-minute period. Answer the following questions, assuming a mean arrival rate of three customers per minute.
Required:
a. What is the probability of exactly three arrivals in one-minute period?
b. What is the probability of at least three arrivals in a one-minute period?
Answer:
a)0.2240
b)0.5768
Step-by-step explanation:
Given:
µ=3
Poison probability is given by :
[tex]f_k=\frac{\mu^ke^-^\mu}{k!}[/tex]
a) Evaluating at k=3
[tex]f(3)=\frac{3^3e^-^3}{3!} \approx 0.2240[/tex]
b)Evaluating at k=0,1,2:
[tex]f(0)=\frac{3^0e^-^3}{0!} \approx 0.0498[/tex]
[tex]f(1)=\frac{3^1e^-^3}{1!} \approx 0.1494[/tex]
[tex]f(2)=\frac{3^2e^-^3}{2!} \approx 0.2240[/tex]
Use complement rule:
P(x≥3)= 1 - f(0) - f(1) - f(2)= 1- 0.0498 - 0.1494 - 0.2240 =0.5768
Solve the following inequality. |-2x + 1| < 13
Please help!!!!
Answer:
x>−6 and x<7
Step-by-step explanation:
Let's solve your inequality step-by-step.
|−2x+1|<13
Solve Absolute Value.
|−2x+1|<13
We know−2x+1<13and−2x+1>−13
−2x+1<13(Condition 1)
−2x+1−1<13−1(Subtract 1 from both sides)
−2x<12
−2x
−2
<
12
−2
(Divide both sides by -2)
x>−6
−2x+1>−13(Condition 2)
−2x+1−1>−13−1(Subtract 1 from both sides)
−2x>−14
−2x
−2
>
−14
−2
(Divide both sides by -2)
x<7
Answer:
x>−6 and x<7
HELP PLEASE
Find the solution set.
(x - 11)(x - 11) = 0
Answer:
x = 11
Step-by-step explanation:
You are solving for the solution of the variable given (x). Set each parenthesis equal to 0 and simplify:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Add 11 to both sides:
x - 11 = 0
x - 11 (+11) = 0 (+11)
x = 0 + 11
x = 11
Do the same for the other set:
x - 11 = 0
x - 11 (+11) = 0 (+11)
x = 0 + 11
x = 11
~
It has been suggested that night shift-workers show more variability in their output levels than day workers. Below, you are given the results of two independent random samples.
Night Shift (N) Day Shift (D)
Sample Size 9 8
Sample Mean 520 540
Sample Variance 38 20
Required:
a. At 95% confident level, what is the critical value?
b. State the null and alternative hypotheses to be tested.
c. Compute the test statistic.
d. Determine the p-value.
Answer:
Null hypotheses = H₀ = σ₁² ≤ σ₂²
Alternative hypotheses = Ha = σ₁² > σ₂²
Test statistic = 1.9
p-value = 0.206
Since the p-value is greater than α therefore, we cannot reject the null hypothesis.
So we can conclude that the night shift workers don't show more variability in their output levels than day workers.
Step-by-step explanation:
Let σ₁² denotes the variance of night shift-workers
Let σ₂² denotes the variance of day shift-workers
State the null and alternative hypotheses:
The null hypothesis assumes that the variance of night shift-workers is equal to or less than day-shift workers.
Null hypotheses = H₀ = σ₁² ≤ σ₂²
The alternate hypothesis assumes that the variance of night shift-workers is more than day-shift workers.
Alternative hypotheses = Ha = σ₁² > σ₂²
Test statistic:
The test statistic or also called F-value is calculated using
Test statistic = Larger sample variance/Smaller sample variance
The larger sample variance is σ₁² = 38
The smaller sample variance is σ₂² = 20
Test statistic = σ₁²/σ₂²
Test statistic = 38/20
Test statistic = 1.9
p-value:
The degree of freedom corresponding to night shift workers is given by
df₁ = n - 1
df₁ = 9 - 1
df₁ = 8
The degree of freedom corresponding to day shift workers is given by
df₂ = n - 1
df₂ = 8 - 1
df₂ = 7
We can find out the p-value using F-table or by using Excel.
Using Excel to find out the p-value,
p-value = FDIST(F-value, df₁, df₂)
p-value = FDIST(1.9, 8, 7)
p-value = 0.206
Conclusion:
p-value > α
0.206 > 0.05 ( α = 1 - 0.95 = 0.05)
Since the p-value is greater than α therefore, we cannot reject the null hypothesis corresponding to a confidence level of 95%
So we can conclude that the night shift workers don't show more variability in their output levels than day workers.
please help me explain your answer only answer if you are sure
Answer:
The answer of top prism is 262
and down prism is 478
The upper figure is triangular prism.
so, we use bh+2ls+lb formula
B=5
h=3
s=4
l=19
Now,
surface area of triangular prism = bh+2ls+lb
= 5×3+2×19×4+19×5
= 262
The down figure is rectangular prism.
so, we use 2lw+2lh+2hw
l=5
h=6
w=19
Now,
The area of rectangular prism = 2lw+2lh+2hw
= 2×5×19+2×19×6+2×5×6
= 478
You are going to sell your Samsung so you can get the new iPhone. You purchased your Samsung 2 years ago for $200. It's
value decreases at a rate of 2% each month. To the nearest dollar, how much is your Samsung worth now?
Answer:
[tex]\boxed{\ 123 \ dollars\ }[/tex]
Step-by-step explanation:
its value decreases at a rate of 2% each month
in 2 years there are 12*2=24 months
so the Samsung worth [tex]200(0.98)^{24}\\[/tex]
it gives 123 rounded to the nearest dollar
Answer:
$123
Step-by-step explanation:
initial price= $200
value decrease rate= 2% = 0.98 times a month
time = 2 years
current value= $200*0.98²⁴= $123
in four lines determine how to find a perimeter and area of garden with specific dimensions
Answer:
[tex]Perimeter\ of\ the\ Garden\ =2(l1*b1)[/tex]
[tex]Area\ of\ the\ garden\ =l1*b1[/tex]
Step-by-step explanation:
Let assume the l1 is the length of the garden and b1 is the breadth of garden then
[tex]Perimeter\ of\ the\ Garden\ = 2 ( L ength + Breadth )\\Perimeter\ of\ the\ Garden\ =2(l1*b1)[/tex]
Now,
[tex]Area\ of\ Garden\ = Length * Breadth[/tex]
[tex]Area\ of\ the\ garden\ =l1*b1[/tex]
Which flight has the fastest average speed
Answer:
Fastest wind speed ever recorded
That is, however, a patch on the top speed ever reached by an aircraft, a record held by the Lockheed Blackbird, which tickled 2,193mph in 1976
Step-by-step explanation:
The top tree broke and fell over.the remaining tree teunk is 3 feet tall.the tip of the tree rests on the ground 14 feet from the base of the trunk.what is the lenght of the broken part of the tree to the nearest tenth of a foot
Answer:
14.3 feet.
14.3 feet
Step-by-step explanation:
The problem forms a right triangle in which:
The Vertical Leg of the Right Triangle = 3 feet
The Horizontal Leg of the Right Triangle =14 feet
We are to determine the length of the broken part of the tree. This is the Hypotenuse of the Right Triangle,
Using Pythagoras Theorem
[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\Hypotenuse^2=14^2+3^2\\Hypotenuse^2=205\\Hypotenuse=\sqrt{205}\\Hypotenuse=14.32\\ \approx 14.3 feet $(to the nearest tenth of a foot).\\Therefore, the lenght of the broken part of the tree to the nearest tenth of a foot is 14.3 feet.[/tex]
Alex is planning to surround his pool ABCD with a single line of tiles. How many units of tile will he need to surround his pool? Round your answer to the nearest hundredth.
Answer:
19.82 units
Step-by-step explanation:
The number of units of tile simply refers to the perimeter.
So, we need to find all the sides of the rectangle.
Now, we have AB = 4.24 units and BD = 7.07 units.
So, we can find AD using pythagoras theorem.
So,
(AD)² + 4.24² = 7.07²
(AD)² + 17.978 = 49.985
(AD)² = 49.985 - 17.978
AD = √32.007
AD = 5.66 units
AD = BC = 5.66 units
Likewise, AB = DC = 4.24 units
Thus,
perimeter = 2(5.66) + 2(4.24) = 19.8 units
Closest answer among the options is approximately 19.82
Answer:
19.82 units
Step-by-step explanation:
just took test and got it right
Among 25- to 30-year-olds, 29% say they have used a computer while under the influence of alcohol. Suppose five 25- to 30-year-olds are selected at random. Complete parts (a) through (d) below. (a) What is the probability that all five have used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (b) What is the probability that at least one has not used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (c) What is the probability that none of the five have used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (d) What is the probability that at least one has used a computer while under the influence of alcohol? (Round to four decimal places as needed.)
Answer:
(a) The probability that all five have used a computer while under the influence of alcohol is 0.0021.
(b) The probability that at least one has not used a computer while under the influence of alcohol is 0.9979.
(c) The probability that none of the five have used a computer while under the influence of alcohol is 0.1804.
(d) The probability that at least one has used a computer while under the influence of alcohol is 0.8196.
Step-by-step explanation:
We are given that among 25- to 30-year-olds, 29% say they have used a computer while under the influence of alcohol.
Suppose five 25- to 30-year-olds are selected at random.
The above situation can be represented through the 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 = Five 25- to 30-year-olds
r = number of success
p = probability of success which in our question is probability that
people used a computer while under the influence of alcohol,
i.e. p = 29%.
Let X = Number of people who used computer while under the influence of alcohol.
So, X ~ Binom(n = 5, p = 0.29)
(a) The probability that all five have used a computer while under the influence of alcohol is given by = P(X = 5)
P(X = 5) = [tex]\binom{5}{5}\times 0.29^{5} \times (1-0.29)^{5-5}[/tex]
= [tex]1 \times 0.29^{5} \times 0.71^{0}[/tex]
= 0.0021
(b) The probability that at least one has not used a computer while under the influence of alcohol is given by = P(X [tex]\geq[/tex] 1)
Here, the probability of success (p) will change because now the success for us is that people have not used a computer while under the influence of alcohol = 1 - 0.29 = 0.71
SO, now X ~ Binom(n = 5, p = 0.71)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= [tex]1-\binom{5}{0}\times 0.71^{0} \times (1-0.71)^{5-0}[/tex]
= [tex]1 -(1 \times 1 \times 0.29^{5})[/tex]
= 1 - 0.0021 = 0.9979.
(c) The probability that none of the five have used a computer while under the influence of alcohol is given by = P(X = 0)
P(X = 0) = [tex]\binom{5}{0}\times 0.29^{0} \times (1-0.29)^{5-0}[/tex]
= [tex]1 \times 1 \times 0.71^{5}[/tex]
= 0.1804
(d) The probability that at least one has used a computer while under the influence of alcohol is given by = P(X [tex]\geq[/tex] 1)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= [tex]1-\binom{5}{0}\times 0.29^{0} \times (1-0.29)^{5-0}[/tex]
= [tex]1 -(1 \times 1 \times 0.71^{5})[/tex]
= 1 - 0.1804 = 0.8196
Help! Best Answer = brainiest!
Answer:
30 or younger
Step-by-step explanation:
Choose the inequality that could be used to solve the following problem.
Three times a number is at most negative six.
Answer:
3x ≤ -6
Step-by-step explanation:
"At most" means "less than or equal to." If x represents the number, then you have ...
(three) times (a number) (is at most) negative 6 . . . . . English
3 · x ≤ -6 . . . . . . . . . . . . . . . . Math
__
3x ≤ -6
Answer:
3x ≤ -6
Step-by-step explanation:
You received your monthly bank statement and you are reconciling your account balance using the information below. What is the true balance of your checking account? Check Register Balance $314.97 Bank Statement Balance $423.68 Outstanding Checks $123.71 Service Charge $15.00
Answer:
299.97 is the actual answer
Step-by-step explanation:
I took the test.
What is the missing number in the pattern? Please Help. Been stuck on this for hours.
Answer:
8
Step-by-step explanation:
The other patterns go with the two factors on top (2 x 3 = 6 and 3 x 3 = 9).
So, 2 x 4 = 8
Which expression would be easier to simplify if you used the associative
property to change the grouping?
A. 0.85+ (0.15 +(-3)
B. [(-3)+(-3)] +(-3)
C. (160 + 40 + 27
O D. 1+*+(-))
SUBMIT
P
Answer:
A . 0.85 + (0.15 +(-3)) = -2
B . [(-3)+(-3)]+(-3) = - 9
Step-by-step explanation:
Explanation:-
Associative property with addition
(a+(b+c)) = (a+b) + c
A)
Given 0.85 + (0.15 +(-3)) = (0.85 +0.15)+(-3)
= 1 - 3
= -2
B) Given [(-3)+(-3)]+(-3) = ( (-3)+[( -3)+(-3))]
= ( -3 +[-3-3]
= -3 -6
= -9
Final answer:-
A . 0.85 + (0.15 +(-3)) = -2
B . [(-3)+(-3)]+(-3) = - 9
A small child has 6 more quarters than nickels. If the total amount of the coins is $3.00, find the number of nickels and quarters the child has.
Answer:
nickels- 5, quarters- 11
Step-by-step explanation:
nickel= 5 p, quarter= 25 p
5x+25(x+6)= 300
30x+150=300
30x=150
x=150/30
x=5 nickels
x+6= 11 quarters
How many days are there in 12 weeks? Use the following information to convert this time to days. 1 week = 7 days
Answer:
84days
Step-by-step explanation:
1 week = 7days =>12 weeks = 12×7 = 84days
Answer:
84 days are in 12 weeks
Step-by-step explanation:
1 week = 7 days
4 weeks = 28 days
So 28 + 28 + 28 = 84 days
Which expression is equivalent to 3(x-6)+5(x-4)
Answer:
[tex]8x-38[/tex]
Step-by-step explanation:
[tex]3(x-6)+5(x-4)\\3x-18+5x-20\\3x+5x-18-20\\8x-38[/tex]
Please help I'm Timed Will Name Brainliest if Correct.
Answer:
A
Step-by-step explanation:
We can see that Function A's y coordinate doubles every time. The function A = f(x) = 5(2)^x. It is an exponential growth function, and therefore y can never be 0. This means that A does not have an x-intercept.
Function B is a rational function. x cannot be 0, since that would result in an undefined number. This also means that B does not have an x-intercept.
2. The sum of the ages of Denise and Earl is 42
years. Earl is 8 years younger than Denise.
How old is each?
d-Denis
e-Earl
d+e=42
e+8=d
e+8+e=42
2e+8=42
2e=34
e=17
d=17+8=25
Denis is 25 and Earl is 17
Answer
Earl is 17 years old.
Denis is 25 years old.
See? Easy!
Step-by-step explanation:
The first few steps in solving the quadratic equation 9x2 + 49x = 22 − 5x by completing the square are shown. 9x2 + 49x = 22 − 5x 9x2 + 54x = 22 9(x2 + 6x) = 22 Which is the best step to do next to solve the equation by completing the square? 9(x2 + 6x + 3) = 25 9(x2 + 6x + 3) = 49 9(x2 + 6x + 9) = 31 9(x2 + 6x + 9) = 103
Answer:
The Answer is : 9(x2 + 6x + 9) = 103
Step-by-step explanation:
Option D on edge2020 i got a 100 on the quiz
The resulting quadratic equation is [tex](x+3)^2-103/9=0[/tex]
Quadratic equationGiven the quadratic equation [tex]9x^2 + 49x = 22 - 5x[/tex]
Write in standard form:
[tex]9x^2 + 49x = 22 - 5x\\ 9x^2 + 49x + 5x -22= 0\\ 9x^2+54x-22=0[/tex]
Divide through by 9
[tex]x^2+6x-22/9=0\\ [/tex]
complete the square to have:
[tex]x^2+6x-22/9+3^2-3^2=0\\ x^2+6x+3^2-9-22/9 = 0\\ (x+3)^2-103/9=0[/tex]
Hence the resulting quadratic equation is [tex](x+3)^2-103/9=0[/tex]
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Write the equation of the line. Slope = -4, passing through (- 1, 5)
Answer:
y=-4x+1
Step-by-step explanation:
You want to find the equation for a line that passes through the point (-1,5) and has a slope of -4.
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
To start, you know what m is; it's just the slope, which you said was -4. So you can right away fill in the equation for a line somewhat to read:
y=-4x+b.
Now, what about b, the y-intercept?
To find b, think about what your (x,y) point means:
(-1,5). When x of the line is -1, y of the line must be 5.
Because you said the line passes through this point, right?
Now, look at our line's equation so far: . b is what we want, the -4 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (-1,5).
So, why not plug in for x the number -1 and for y the number 5? This will allow us to solve for b for the particular line that passes through the point you gave!.
(-1,5). y=mx+b or 5=-4 × -1+b, or solving for b: b=5-(-4)(-1). b=1.
The equation of line passes through the point (-1, 5) will be;
⇒ y = - 4x - 2
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line are (-1, 5).
And, The slope of line is,
⇒ m = - 4
Now,
Since, The equation of line passes through the point (- 1, 5).
And, Slope of the line is,
m = - 4
Thus, The equation of line with slope - 4 is,
⇒ y - 5 = - 4 (x - (-1))
⇒ y - 2 = - 4 (x + 1)
⇒ y - 2 = - 4x - 4
⇒ y = - 4x - 4 + 2
⇒ y = - 4x - 2
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A cereal box has a volume of 225 cubic inches. The length of the base is 9 inches and the width of the base is
2.5 inches. What is the height of the box?
Answer:
10
Step-by-step explanation:
First multiply 9 by 2.5
Then divide 225 by 22.5
What is a unit rate?
A) a rate with one in the numerator
B) a rate in which the numerator and the denominator are equal
C) a rate with one in the denominator
D) a rate in which the denominator is greater than the numerator
Hey there! Welcome to Brainly! I"m happy to help!
The unit rate is how much there is of something per one unit. The word per basically means divided or a fraction. So, if something was a, the unit rate would be a/1.
Therefore, the unit rate is C) a rate with one in the denominator.
I hope that this helps! Have a wonderful day!
which of the following are solutions to the quadratic equation check all that apply x ^ 2 + 10x + 25 = 7
Answer:
the Answers are : B and E
Step-by-step explanation:
From the given quadratic equation [tex]x^2 + 10x + 25 = 7[/tex] Thus, the solution is x = -1 and -9.
How to find the roots of a quadratic equation?Suppose that the given quadratic equation is
[tex]ax^2 + bx + c = 0[/tex]
Then its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
We have been given a quadratic equation
[tex]x^2 + 10x + 25 = 7[/tex]
[tex]x^2 + 10x + 25 - 7=0\\\\x^2 + 10x + 18[/tex]
The solution of the given equation;
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{-10 \pm \sqrt{10^2 - 4\times 18}}{2}\\\\x = \dfrac{-10 \pm \sqrt{100- 36}}{2}\\\\x = \dfrac{-10 \pm \sqrt{64}}{2}\\\\x = \dfrac{-10 \pm 8}{2}\\[/tex]
Therefore, the solution are x = -1 and -9.
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Factorizar e indicar cuántos factores primos tiene -3+3x^2+y-x^2*y-y^2+x^2*y
Given cot ø = 4/3. Find the other two reciprocal trigonometic ratios. 1) scs 2) sec
Answer:
csc ø = 5/3 ; sec ø = 5/4
Step-by-step explanation:
cot ø = adj/opp
adj = 4
opp = 3
after that, we must find the hypotenuse by using phytagoras theorem
hpy² = adj² + opp²
hpy² = 4² + 3²
hpy² = 25
hpy = 5
now let's find the other
csc ø (not scs) = hyp/opp = 5/3
sec ø = hyp/adj = 5/4
