Answer:
0.735 = 73.5% probability of getting at least 4 calls between eight and nine in the morning.
Step-by-step explanation:
We have the mean during a time interval, which means that the Poisson distribution is used to solve this question.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 5.
This means that [tex]\mu = 5[/tex]
Calculate the probability of getting at least 4 calls between eight and nine in the morning.
This is:
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-5}*5^{0}}{(0)!} = 0.0067[/tex]
[tex]P(X = 1) = \frac{e^{-5}*5^{1}}{(1)!} = 0.0337[/tex]
[tex]P(X = 2) = \frac{e^{-5}*5^{2}}{(2)!} = 0.0842[/tex]
[tex]P(X = 3) = \frac{e^{-5}*5^{3}}{(3)!} = 0.1404[/tex]
Then
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0067 + 0.0337 + 0.0842 + 0.1404 = 0.265[/tex]
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.265 = 0.735[/tex]
0.735 = 73.5% probability of getting at least 4 calls between eight and nine in the morning.
Henry wants to buy a new table saw for his carpentry shop. he saved $360 which is 2/3 of the price of the saw.how much does the table saw cost?
Answer:
Step-by-step explana
540
What are the solutions to the equation?
x3 – 6x2 – 9x + 54 = 0
Answer:
x = -3 or x = 3 or x = 6
Step-by-step explanation:
x3 – 6x2 – 9x + 54 = 0
There is no common factor to factor out. There are 4 terms. We try factoring by grouping. Factor a common factor out of the first two terms. Factor a common factor out of the last two terms.
x^2(x - 6) - 9(x - 6) = 0
x - 6 is a common factor, so we factor it out.
(x^2 - 9)(x - 6) = 0
x^2 - 9 is the difference of 2 squares, so we factor it.
(x + 3)(x - 3)(x - 6) = 0
x + 3 = 0 or x - 3 = 0 or x - 6 = 0
x = -3 or x = 3 or x = 6
Answer:
x=6 x=3 x=-3
Step-by-step explanation:
x^3 – 6x^2 – 9x + 54 = 0
Factor by grouping
x^3 – 6x^2 – 9x + 54 = 0
x^2(x-6) -9(x-6 ) =0
Factor out x-6
(x-6)(x^2 -9) =0
Notice x^2 -9 is the difference of squares
(x-6)(x-3)(x+3) = 0
Using the zero product property
x-6 =0 x-3 =0 x+3 =0
x=6 x=3 x=-3
What is the difference between the temperature - 7 Celsius and - 12 Celsius on a scatter diagram
Answer:
I have to go get my car from the doctor office today
If the integer $152AB1$ is a perfect square, what is the sum of the digits of its square root?
9514 1404 393
Answer:
13
Step-by-step explanation:
152AB1 is not a square in hexadecimal, so we assume A and B are supposed to represent single digits in decimal.
If A=B=0, √152001 ≈ 389.9
If A=B=9, √152991 ≈ 391.1
The least significant digit of 152AB1 being non-zero, we know it is not the square of 390. Hence, it must be the square of 391.
For 152AB1 to be a perfect square, we must have ...
152AB1 = 391² = 152881
The sum of the digits of the square root is 3+9+1 = 13.
Suppose $1,000 was deposited into an account compounded quarterly that grew to $1,490 at rate of 6%. How long did it take for this to occur?
Answer:
A (1 + i)^n = 1490 time for amount to reach 1490
(1 + i)^n = 1.49 since A = $1000
n log (1 + .06/4) = log 1.49 take log of both sides at 1.5% per quarter
n = log (1.49) / log 1.015 = 26.78 periods or 6.695 years
(compare to 6.843 years compounded annually)
[tex]t = ln(A/P) / n[ln(1 + r/n)]\\t = ln(1,490.00/1,000.00) / ( 4 * [ln(1 + 0.06/4)] )\\t = ln(1,490.00/1,000.00) / ( 4 * [ln(1 + 0.015)] )\\t = 6.7 years[/tex]
It would take around 6 years 8 months to get $1,490 from $1,000 at 6%.
I hope I've helped! :)
Evaluating linear piecewise functions
Perform the following series of rigid transformations on ∆ABC: Translate ∆ABC by moving it 5 units to the right and 2 units up. Draw the line y = -x, and reflect ∆A'B'C' across the line. Rotate ∆A''B''C'' counterclockwise about the origin by 270°.
Answer:
The answer is below
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point A(x, y) is translated a units right and b units up, the new point is at A'(x + a, y + b).
If a point A(x, y) is reflected across the line y = -x, the new point is at A'(-y, -x).
If a point A(x, y) is rotated counterclockwise by 270 degrees, the new point is at A'(y, -x).
Let us assume that triangle ABC has vertices at A(-6, -1), B(-3, -3) and C(-1, -2).
If it is moved 5 units to the right and 2 units up, the new point is at A'(-1, 1), B'(1, -1) and C'(3, 0). If it is reflected across the line y = -x, the vertices are at A"(-1, 1), B"(1, -1) and C"(0, -3). If it is then rotated counterclockwise about the origin by 270°, the new point is at A'"(-1, -1), B"'(1, 1), C"'(3, 0)
Need help due tomorrow
Answer:
[tex]Given:[/tex] Δ ABC ≈ ΔDEF
[tex]therefor:[/tex] A(ΔABC)/A(ΔDEF)=(BC)²/(EF)²
⇒ 34/A(ΔDEF)=9²/(13.5)²
⇒34/A(ΔDEF)=81/182.25
⇒A(ΔDEF)=34×182.25/81
⇒Area of ΔDEF=76.5 cm²
----------------------------------
Hope it helps...
Have a great day!!!
What is
the solution to the system of equations graphed below?
What is 10 + 15k equivalent
Plz hurry
Answer:
if you mean 15k as is 15 thousand then the answer would be 15,010
Solve 2x2 - 9x - 5 = 0 by factoring.
AS IN THE PICTURE...........
The probability I take a nap today is 4/5. The probability I will take a nap and a bubble bath today
is 1/5. What is the probability I will take a bubble bath today, given that I took a nap?
Use Bayes Theorem to compute that probability. I will denote bath as [tex]B[/tex] and nap as [tex]N[/tex], the probability will be denoted as [tex]P(B)[/tex] or [tex]P(N)[/tex].
By Bayes Theorem
[tex]P(B\mid N)=\frac{P(N\mid B)\cdot P(B)}{P(N)}[/tex]
Which reads,
"What is the probability of [tex]B[/tex] given [tex]N[/tex]".
We know that [tex]P(N\mid B)[/tex] is 1 because we already took a bath. So the formula simplifies to,
[tex]P(B\mid N)=\frac{P(B)}{P(N)}[/tex]
Now insert the data,
[tex]P(B\mid N)=\frac{1/5}{4/5}=\boxed{\frac{1}{4}}[/tex]
So the probability that you will take a bath is [tex]0.25[/tex] after you have taken a nap.
Hope this helps. :)
In the diagram attached, ΔABC has coordinates A(1,1), B(4,1), and C(4,5).
Given the function rule
f(x, y) → (x − 5, −y − 2)
Describe the transformation as completely as possible.
The diagram is attached-- Thanks in advance!
(No this is not homework, I was using a study guide I found online to study for a test.)
Answer:
Step-by-step explanation:
ΔABC has the vertices as A(1, 1), B(4, 1) and C(4, 5).
Rule for the transformation has been given as,
f(x, y) → (x - 5, -y - 2)
By this rule vertices of the transformed image will be,
A(1, 1) → A'(1 - 5, -1 - 2)
→ A'(-4, -3)
B(4, 1) → B'(4 - 5, -1 - 2)
→ B'(-1, -3)
C(4, 5) → C'(4 - 5, -5 - 2)
→ C'(-1, -7)
What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long?
9514 1404 393
Answer:
opposite: 4.88adjacent: 14.18Step-by-step explanation:
SOH CAH TOA is a mnemonic intended to remind you of the relevant trig relations.
Sin = Opposite/Hypotenuse ⇒ opposite = 15×sin(19°) ≈ 4.88 units
Cos = Adjacent/Hypotenuse ⇒ adjacent = 15×cos(19°) ≈ 14.18 units
Answer:
For plato users the correct option is D.
Step-by-step explanation:
D. 4.9 units, 14.2 units
3|3x+4|-7=5 please help
Answer:
[tex]x = 0[/tex]
Step-by-step explanation:
[tex]3 |3x + 4| - 7 = 5[/tex]
Add 7[tex]3 |3x + 4 | = 12[/tex]
Divide by 3.[tex] |3x + 4| = 4[/tex]
Remove the absolute value signs and left with:[tex]3x + 4 = 4[/tex]
Subtract[tex]3x = 0[/tex]
[tex]x = 0[/tex]
Expand -11(5-p) can someone answer that please
Answer:
-55 +11p
Step-by-step explanation:
-11(5-p)
Distribute
-11*5 -11*(-p)
-55 +11p
A test is divided into 4 sets of problems with the same number pf problems in each set. Alice correctly solves 35 problems. How many problems are on the test if Alice solved more than 60 percent of all the problems, but less than 65 percent of all problems? Give all possible answers.
Answer:
54, 55, 56, 57, 58
Step-by-step explanation:
Answer:
56 problems
Step-by-step explanation:
Set up an equation.
[tex]\frac{3}{5}x<35<\frac{13}{20}x[/tex]
Why do we do this? We are told that she solved MORE than 60%, or [tex]\frac{3}{5}[/tex], and LESS than 65%, or [tex]\frac{13}{20}[/tex]. Therefore, if we set the TOTAL number of problems to x, we have an equation we can solve.
[tex]\frac{3}{5}x<35<\frac{13}{20}x\\[/tex]
Multiply all parts of the inequality by 20 to get rid of the denominators.
[tex]20*\frac{3}{5}x<20*35<20*\frac{13}{20}x\\ \\12x<700<13x[/tex]
Now we can solve TWO individual inequalities to isolate the x variable.
[tex]12x<700\\x<\frac{700}{12}\\x < 175/3\\x<58[/tex]
We can approximate 175/3 to about 58 (rounding down). We will sometimes round down when we have to deal with whole numbers.
The second inequality is as follows.
[tex]13x>700\\x>700/13\\x>53[/tex]
Therefore, we can combine the two inequalities.
[tex]53<x<58[/tex]
There were in between 53 and 58 questions. Since the number of questions must be a whole number, there can be 54, 55, 56, 57, OR 58. Why does 58 also work? When you plug 58 back into the original equation, you get that it STILL works. This is due to the fact that inaccuracies in computations allow you to round UP.
However, the last thing to keep in mind is that there are four sections with an equal number of questions. Meaning, the final answer has to be a multiple of four. The only multiple of 4 is 56; therefore, the final answer is 56.
uppose cattle in a large herd have a mean weight of 1158lbs and a standard deviation of 92lbs. What is the probability that the mean weight of the sample of cows would differ from the population mean by less than 12lbs if 55 cows are sampled at random from the herd
Answer:
Hence the probability that the mean weight of the sample of 55 cows would differ from the population mean by less than 12 lbs is 0.66545.
Step-by-step explanation:
2. The two equal sides of an isosceles triangle each have a length of 4x + y - 5. The perimeter of the triangle is
10x + 4y - 18. Determine the length of the third side. Explain how you found your answer. (4 marks)
9514 1404 393
Answer:
2x +2y -8
Step-by-step explanation:
If the equal sides are 'a' and the third side is 'b', then the perimeter is ...
P = a +a +b = 2a +b
The length of the third side is then ...
b = P -2a . . . . . . subtract 2a from both sides
Substituting the given expressions, we find ...
b = (10x +4y -18) -2(4x +y -5)
b = 10x +4y -18 -8x -2y +10
b = 2x +2y -8 . . . . the length of the third side
Nicole was shopping at a local department store and had a budget of $60. She was
buying shorts (s) priced at $10 and t-shirts (t) priced at $8. She was heading to the
checkout stand when she saw a sign that said all t-shirts are 40% off. Write and simplify
an equation that Nicole could use to find the possible combinations of shorts and t-shirts
she could buy for $60.
Answe YEAH BOIIIIII!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
For a certain company, the cost for producing x items is 40x+300 and the revenue for selling x items is 80x−0.5x2. The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!
Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)
Part b: Find two values of x that will create a profit of $300.
The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1). The order of the list does not matter. To enter a−−√, type sqrt(a).
Part c: Is it possible for the company to make a profit of $15,000?
Answer:
The profit is maximum when x = 40.
Step-by-step explanation:
Cost function, C = 40 x + 300
Revenue function, R = 80 x - 0.5 x^2
The profit function is
[tex]P = R - C\\\\P = 80 x - 0.5 x^2 - 40 x - 300\\\\P = - 0.5 x^2 + 40 x - 300\\\\\frac{dP}{dx} = - x + 40\\\\So, \frac{dP}{dx} = 0\\\\-x + 40 = 0 \\\\x = 40[/tex]
So, the profit is maximum when x = 40 .
Work out the length x. 14 cm 7 cm Х
Answer:
If you want the area of something with the sides 14cm and 7cm then it would be 98 cm.
Step-by-step explanation:
Area = length * width
Area = 14 cm * 7 cm
Area = 98 cm
A study by researchers at a university addressed the question of whether the mean body temperature of an animal is 98 6°F Among other data, the researchers obtained the body temperatures of 109 healthy animals. Suppose you want to use those data to decide whether the mean body temperature of healthy animals is less than 98.6°F.
Required:
a. Determine the null hypothesis
b. Determine the alternative hypothesis
Answer:
H0 : μ ≥ 98.6
H1 : μ < 98.6
Step-by-step explanation:
The population mean temperature, μ = 98.6
The null hypothesis takes up the value of the population mean temperature as the initial truth ;
The alternative hypothesis on the other hand is aimed at using a sample size of 109 to establish if the mean temperature is less than the population mean temperature.
The hypothesis ;
Null hypothesis, H0 : μ ≥ 98.6
Alternative hypothesis ; H1 : μ < 98.6
Dodi bicycles 14mph with no wind. Against the wind, Dodi bikes 10mi in the same time it takes to bike 20mi with the wind. What is the speed of the wind?
Answer:
4.67 mph
Step-by-step explanation:
Speed with no wind = 14 mph
Let wind speed = w mph
Thus;
Speed with wind = 14 + w
Speed against the wind = 14 - w
Now, we are told that against the wind he bikes 10 miles.
Thus, from; time = distance/speed, we have;
Time = 10/(14 - w)
Also, we are told he biked 20 miles with the wind. Thus;
Time = 20/(14 + w)
We are told the times he used in both cases are the same.
Thus;
10/(14 - w) = 20/(14 + w)
Divide both sides by 10 to get;
1/(14 - w) = 2/(14 + w)
Cross multiply to get:
1(14 + w) = 2(14 - w)
14 + w = 28 - 2w
w + 2w = 28 - 14
3w = 14
w = 14/3
w = 4.67 mph
Leo is running in a 5-kilometer race along a straight path. If he is at the midpoint of the path, how many kilometers does he have left to run?
Answer:
2.5 km left
The midpoint is half of 5, which is 2.5, so he'll still have 2.5 km left to complete
Verify if : (-30) x ( 13.+ (-3)] =[(-30) x 13] + [(-30) (-3)]
a. A contest entrant has a 0.002 probability of winning $12,165. If this is the only prize and the fee is $35, then find the expected value of winning the contest. b. The probability of winning a lottery is 0.125. What is the probability of winning AT LEAST ONCE in twelve trials?
Answer:
The right answer is:
(a) -10.67
(b) 0.7986
Step-by-step explanation:
(a)
According to the question,
X P(X) X.P(X) X2.P(X)
12130 0.002 24.26 294274
-35 0.998 -34.93 1222.55
Now,
[tex]\Sigma x.P(x) = -10.67[/tex]
or,
[tex]\Sigma x^2.P(x) = 295496.35[/tex]
hence,
The mean will be:
[tex]\Sigma x.P(x) = -10.67[/tex]
(b)
According to the question,
n = 12
p = 0.125
q = 1 - p
= 0.875
Now,
⇒ [tex]P(X=x) = \binom{n}{x} p^x q^{n-x}[/tex]
By substituting the values, we get
⇒ [tex]P(X \geq 1)=1-(\binom{12}{0} 0.125^0. 0.875^{12-0})[/tex]
⇒ [tex]=1-(1 (0.125^0) (0.875^{12}))[/tex]
⇒ [tex]=1-(1(1.0)(0.2014))[/tex]
⇒ [tex]=1-(0.2014)[/tex]
⇒ [tex]=0.7986[/tex]
Find the length of AC
A. 377.19
B. 378.63
C. 2.89
D. 33.13
Answer:
AC = 377.19
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 5 = 33/AC
AC tan 5 = 33
AC = 33/ tan 5
AC = 377.19
michael has an average of 68% in his 3 papers but that is below the pass mark of 70%. what must be his least score in the fouth paper to enable him pass?
Answer:
His least score for him in the fourth paper has to be 76.
Step-by-step explanation:
Given that Michael has an average of 68% in his 3 papers but that is below the pass mark of 70%, to determine what must be his least score in the fouth paper to enable him pass the following calculation must be performed:
(70 x 4) - (68 x 3) = X
280 - 204 = X
76 = X
Therefore, his least score for him in the fourth paper has to be 76.
Work out giving ur answer as a mixed number
Answer:
6 11/12
Step-by-step explanation:
4 1/6 + 2 3/4
Get a common denominator of 12
4 1/6 *2/2 + 2 3/4 *3/3
4 2/12 + 2 9/12
6 11/12
