Answer:
The probability that a student arriving at the ATM will have to wait is 67%.
Step-by-step explanation:
This can be solved using the queueing theory models.
We have a mean rate of arrival of:
[tex]\lambda=1/3\,min^{-1}[/tex]
We have a service rate of:
[tex]\mu=1/2\,min^{-1}[/tex]
The probability that a student arriving at the ATM will have to wait is equal to 1 minus the probability of having 0 students in the ATM (idle ATM).
Then, the probability that a student arriving at the ATM will have to wait is equal to the utilization rate of the ATM.
The last can be calculated as:
[tex]P_{n>0}=\rho=\dfrac{\lambda}{\mu}=\dfrac{1/3}{1/2}=\dfrac{2}{3}=0.67[/tex]
Then, the probability that a student arriving at the ATM will have to wait is 67%.
Need help ASAP!! thank you sorry if u can’t see it good :(
Answer/Step-by-step explanation:
==>Given:
=>Rectangular Pyramid:
L = 5mm
W = 3mm
H = 4mm
=>Rectangular prism:
L = 5mm
W = 3mm
H = 4mm
==>Required:
a. Volume of pyramid:
Formula for calculating volume of a rectangular pyramid us given as L*W*H
V = 5*3*4
V = 60 mm³
b. Volume of prism = ⅓*L*W*H
thus,
Volume of rectangular prism given = ⅓*5*3*4
= ⅓*60
= 20mm³
c. Volume of the prism = ⅓ x volume of the pyramid
Thus, 20 = ⅓ × 60
As we can observe from our calculation of the solid shapes given, the equation written above is true for all rectangular prism and rectangular pyramid of the same length, width and height.
Solve the system of equations. \begin{aligned} & -5y-10x = 45 \\\\ &-3y+10x=-5 \end{aligned} −5y−10x=45 −3y+10x=−5
Answer:
x = -2
y = -5
Step-by-step explanation:
We can solve this algebraically (substitution or elimination) or graphically. I will be using elimination:
Step 1: Add the 2 equations together
-8y = 40
y = -5
Step 2: Plug y into an original equation to find x
-3(-5) + 10x = -5
15 + 10x = -5
10x = -20
x = -2
And we have our final answers!
Answer:
[tex]\boxed{\sf \ \ \ x=-2 \ \ \ and \ \ \ y=-5 \ \ \ }[/tex]
Step-by-step explanation:
let s solve the following system
(1) -5y-10x=45
(2) -3y+10x=-5
let s do (1) + (2) it comes
-5y-10x-3y+10x=45-5=40
<=>
-8y=40
<=>
y = -40/8=-20/4=-5
so y = -5
let s replace y in (1)
25-10x=45
<=>
10x=25-45=-20
<=>
x = -20/10=-2
so x = -2
The figure shows a square floor plan with a smaller square area that will accommodate a combination fountain and pool.The floor with the fountain pool area removed has an area of 33 Square meters and a perimeter of 36 meters. Find the dimensions of the floor and the dimensions of the square that will accommodate the fountain and pool.
Answer:
(x, y) = (7, 4) meters
Step-by-step explanation:
The area of the floor without the removal is x^2, so with the smaller square removed, it is x^2 -y^2.
The perimeter of the floor is the sum of all side lengths, so is 4x +2y.
The given dimensions tell us ...
x^2 -y^2 = 33
4x +2y = 36
From the latter equation, we can write an expression for y:
y = 18 -2x
Substituting this into the first equation gives ...
x^2 -(18 -2x)^2 = 33
x^2 -(324 -72x +4x^2) = 33
3x^2 -72x + 357 = 0 . . . . write in standard form
3(x -7)(x -17) = 0 . . . . . factor
Solutions to this equation are x=7 and x=17. However, for y > 0, we must have x < 9.
y = 18 -2(7) = 4
The floor dimension x is 7 meters; the inset dimension y is 4 meters.
Which of the following is a polynomial with roots: − square root of 3 , square root of 3, and −2? (6 points) Question 7 options: 1) x3 − 2x2 − 3x + 6 2) x3 − 3x2 − 5x + 15 3) x3 + 2x2 − 3x − 6 4) x3 + 3x2 − 5x − 15
Answer:
The polynomial is [tex]x^{3} - 1.46x^{2} - 3.93x + 6[/tex]
Step-by-step explanation:
A nth order polynomial f(x) has roots [tex]x_{1}, x_{2}, ..., x_{n}[/tex] such that [tex]f(x) = (x - x_{1})*(x - x_{2})*...*(x - x_{n}}[/tex],
Which of the following is a polynomial with roots: − square root of 3 , square root of 3, and −2?
So
[tex]x_{1} = x_{2} = \sqrt{3}[/tex]
[tex]x_{3} = -2[/tex]
Then
[tex](x - \sqrt{3})^{2}*(x - (-2)) = (x - \sqrt{3})^{2}*(x + 2) = (x^{2} -2x\sqrt{3} + 3)*(x + 2) = x^{3} + 2x^{2} - 2x^{2}\sqrt{3} - 4x\sqrt{3} + 3x + 6[/tex]
Since [tex]\sqrt{3} = 1.73[/tex]
[tex]x^{3} + 2x^{2} - 3.46x^{2} - 6.93x + 3x + 6 = x^{3} - 1.46x^{2} - 3.93x + 6[/tex]
The polynomial is [tex]x^{3} - 1.46x^{2} - 3.93x + 6[/tex]
Find the volume of the cone.
Diameter: 20 m, Slant Height: 26 m
Round to the nearest whole number.
Volume
=
[?] m3
Answer:
2513the step-by-step explanation for height first :
[tex]h=\sqrt{h^{2} } +r^{2} =26[/tex]
[tex]h=\sqrt{h^{2} } +10^{2} =676[/tex]
[tex]h=\sqrt{h^{2} } + 100 = 676[/tex]
[tex]100-100 = 0[/tex]
[tex]676-100=576[/tex]
[tex]\sqrt{576}[/tex]
[tex]height =[/tex] 24 m
________________
step-by-step explanation for the problem :
FORMULA : [tex]v = \frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]r^{2}[/tex] · [tex]h[/tex]
v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]10^{2}[/tex] · [tex]24[/tex] = [tex]800\pi[/tex] = [tex]2513.27412[/tex] = 2513
Consider the set of sequences of seven letters chosen from W and L. We may think of these sequences as representing the outcomes of a match of seven games, where W means the first team wins the game and L means the second team wins the game. The match is won by the first team to win four games (thus, some games may never get played, but we need to include their hypothetical outcomes in the points in order that we have a probability space of equally likely points).A. What is the probability that a team will win the match, given that it has won the first game?B. What is the probability that a team will win the match, given that it has won the first two games? C. What is the probability that a team will win the match, given that it has won two out of the first three games?
Answer:
a) Probability that a team will win the match given that it has won the first game = 0.66
b) Probability that a team will win the match given that it has won the first two games= 0.81
c) Probability that a team will win the match, given that it has won two out of the first three games = 0.69
Step-by-step explanation:
There are a total of seven games to be played. Therefore, W and L consists of 2⁷ equi-probable sample points
a) Since one game has already been won by the team, there are 2⁶ = 64 sample points left. If the team wins three or more matches, it has won.
Number of ways of winning the three or more matches left = [tex]6C3 + 6C4 + 6C5 + 6C6[/tex]
= 20 + 15 + 6 + 1 = 42
P( a team will win the match given that it has won the first game) = 42/64 = 0.66
b) Since two games have already been won by the team, there are 2⁵ = 32 sample points left. If the team wins two or more matches, it has won.
Number of ways of winning the three or more matches left = [tex]5C2 + 5C3 + 5C4 + 5C5[/tex] = 10 + 10 + 5 +1 = 26
P( a team will win the match given that it has won the first two games) = 26/32 = 0.81
c) Probability that a team will win the match, given that it has won two out of the first three games
They have played 3 games out of 7, this means that there are 4 more games to play. The sample points remain 2⁴ = 16
They have won 2 games already, it means they have two or more games to win.
Number of ways of winning the three or more matches left = [tex]4C2 + 4C3 + 4C4[/tex] = 6 + 4 + 1 = 11
Probability that a team will win the match, given that it has won two out of the first three games = 11/16
Probability that a team will win the match, given that it has won two out of the first three games = 0.69
Points a, b, and c are midpoints of the sides of right triangle def. Which statements are true select three options. A B C D E
Answer : The correct statements are,
AC = 5 cm
BA = 4 cm
The perimeter of triangle ABC is 12 cm.
Step-by-step explanation :
As we know that a, b, and c are midpoints of the sides of right triangle that means midpoint divide the side in equal parts.
Now we have to calculate the sides of triangle ABC by using Pythagoras theorem.
Using Pythagoras theorem in ΔACF :
[tex](AC)^2=(FA)^2+(CF)^2[/tex]
Now put all the values in the above expression, we get the value of side AC.
[tex](AC)^2=(3)^2+(4)^2[/tex]
[tex]AC=\sqrt{(9)^2+(16)^2}[/tex]
[tex]AC=5cm[/tex]
Using Pythagoras theorem in ΔDAB :
[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]
[tex](BD)^2=(AD)^2+(BA)^2[/tex]
Now put all the values in the above expression, we get the value of side BA.
[tex](5)^2=(3)^2+(BA)^2[/tex]
[tex]BA=\sqrt{(5)^2-(3)^2}[/tex]
[tex]BA=4cm[/tex]
Using Pythagoras theorem in ΔBEC :
[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]
[tex](BE)^2=(CE)^2+(CB)^2[/tex]
Now put all the values in the above expression, we get the value of side CB.
[tex](5)^2=(4)^2+(CB)^2[/tex]
[tex]CB=\sqrt{(5)^2-(4)^2}[/tex]
[tex]CB=3cm[/tex]
Now we have to calculate the perimeter of ΔABC.
Perimeter of ΔABC = Side AB + Side CB+ Side AC
Perimeter of ΔABC = 4 + 3 + 5
Perimeter of ΔABC = 12 cm
Now we have to calculate the area of ΔABC.
Area of ΔABC = [tex]\frac{1}{2}\times 4\times 3=6cm^2[/tex]
Now we have to calculate the area of ΔDEF.
Area of ΔDEF = [tex]\frac{1}{2}\times 8\times 6=24cm^2[/tex]
Area of ΔABC = [tex]\frac{6}{24}\times[/tex] Area of ΔDEF
Area of ΔABC = [tex]\frac{1}{4}[/tex] Area of ΔDEF
Find the LCM of the set of algebraic expressions.
28x2,49xy, 28y
Answer
Answer:
196x^2y
Step-by-step explanation: The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.
Marie plants 12 packages of vegetable seeds in a community garden. Each package costs $1.97. What is the total cost of the seeds?
Answer:
$23.64
Step-by-step explanation:
12 * $1.97 = $23.64
Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. AIB Insurance randomly sampled 100 recently paid policies and determined the average age of clients in this sample to be 77.7 years with a standard deviation of 3.6. The 90% confidence interval for the true mean age of its life insurance policy holders is
A. (76.87, 80.33)
B. (72.5, 82.9)
C. (77.1, 78.3)
D. (74.1, 81.3)
E. (74.5, 80)
Answer:
[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.102[/tex]
[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]
And the best option would be:
C. (77.1, 78.3)
Step-by-step explanation:
Information given
[tex]\bar X=77.7[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=3.6 represent the sample standard deviation
n=100 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=100-1=99[/tex]
Since the Confidence is 0.90 or 90%, the significance would be [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value for this case would be [tex]t_{\alpha/2}=1.66[/tex]
And replacing we got:
[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.10[/tex]
[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]
And the best option would be:
C. (77.1, 78.3)
State whether the data described below are discrete or continuous, and explain why.
The exact lengths (in kilometers) of the ocean coastlines of different countries.
a. The data are continuous because the data can only take on specific values.
b. The data are discrete because the data can only take on specific values.
c. The data are continuous because the data can take on any value in an interval.
d. The data are discrete because the data can take on any value in an interval.
Answer:
c. The data are continuous because the data can take on any value in an interval.
Step-by-step explanation:
A variable is said to be continuous if it can take on any value in an interval. Examples are lengths, temperature, etc
A discrete variable, on the other hand, can only take on specific values. Examples of discrete variables are the number of students and age.
The exact lengths (in kilometers) of the ocean coastlines of different countries is a continuous variable because it can take on any value in an interval.
A stated earlier, Lengths are in general, continuous variables.
Find the general solution to 3y′′+12y=0. Give your answer as y=... . In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter c1 as c1 and c2 as c2.
Answer:
[tex]y(x)=c_1e^{2ix}+c_2e^{-2ix}[/tex]
Step-by-step explanation:
You have the following differential equation:
[tex]3y''+12y=0[/tex] (1)
In order to find the solution to the equation, you can use the method of the characteristic polynomial.
The characteristic polynomial of the given differential equation is:
[tex]3m^2+12=0\\\\m^2=-\frac{12}{3}=-4\\\\m_{1,2}=\pm2\sqrt{-1}=\pm2i[/tex]
The solution of the differential equation is:
[tex]y(x)=c_1e^{m_1x}+c_2e^{m_2x}[/tex] (2)
where m1 and m2 are the roots of the characteristic polynomial.
You replace the values obtained for m1 and m2 in the equation (2). Then, the solution to the differential equation is:
[tex]y(x)=c_1e^{2ix}+c_2e^{-2ix}[/tex]
$5.60 is what perecentage of $17.50?
Answer:
To find it's percentage divide $5.60 by
$17.50 and multiply it by 100%
That is
5.60/ 17.50 × 100%
= 32%
Hope this helps you
Please answer this correctly
Answer:
13 students
Step-by-step explanation:
At least 30 and fewer than 67 makes it 30-66
So,
30-66 => 13 students
Answer:
16
Step-by-step explanation:
There are two columns in the diagram.
The column headed stem represents tens while the column headed leaf represents units. e.g. 2 3 = 23
So we just have to count how many of the numbers are less than 8 in the 6th Stem column and all the numbers below it, which are:
20, 23, 28, 31, 31, 34, 38, 40, 44, 50, 51, 53, 54, 65, 65, 66
i need help on this. anyone ?
Answer:
Read below
Step-by-step explanation:
To copy a segment, you have to open your compass to the length of the given segment. The instructions say to have an endpoint at R, so, with the compass open to the length of the given line segment, place one end of the compass at R and draw an arc that intersects the line that R lies on. This new segment is congruent to the given segment.
I hope this helps!
Can someone please help
Use the In key on your calculator to estimate
the logarithm.
In 44
Round your answer to the nearest thousandth.
Answer:
3.784
Step-by-step explanation:
What is the product? (3x-b)(2x^2-7x+1) A. -12x^2+42x-6 B. -12x^2+21x+6 C. 6x^3-33x^2+45x-6 D. 6x^3-27x^2-39x+6
Answer:
C.6x³-33x² + 45x-6
Step-by-step explanation:
(3x-6)(2x^2-7x+1)
= 3x(2x² - 21x +1) -6(2x² - 7x+1)
= (6x³ - 21x² + 3x) - (12x² - 42x+6)
= 6x³ - 21x² + 3x -12x² + 42x -6
= 6x³-33x² + 45x-6
Pls Help!
Given the polynomial function below, find F(3).
F(x) = 2x3 - 7x + 1
A. 34
B. -8
C. 26
D. -2
Answer:
34
Step-by-step explanation:
F(x) = 2x^3 - 7x + 1
Let x= 3
F(3) = 2* 3^3 - 7*3 + 1
= 2 * 27 -21+1
= 54 -21 + 1
= 34
Answer: 34
Step-by-step explanation:
Identify the Type II error if the null hypothesis, H0, is: The capacity of Anna's car gas tank is 10 gallons. And, the alternative hypothesis, Ha, is: Anna believes the capacity of her car's gas tank is not 10 gallons.
Answer:
20gallons
Step-by-step explanation:
2x^2+8x = x^2-16
Solve for x
Answer:
x=-4
Step-by-step explanation:
[tex]2x^2+8x=x^2-16[/tex]
Move everything to one side:
[tex]x^2+8x+16=0[/tex]
Factor:
[tex](x+4)^2=0[/tex]
By the zero product rule, x=-4. Hope this helps!
Answer:
x=-4
Step-by-step explanation:
Move everything to one side and combine like-terms
x²+8x+16
Factor
(x+4)²
x=-4
PLEASE answer pic provided
Answer:
50 to 60 seconds is the answer
1/5divided by (-5/7)
Answer:
-0.28
Step-by-step explanation:
(1/5) : (-5/7)=(1*5)/(5*(-5))=-(7/25)=-0.28
Answer:
[tex]-7/25[/tex]
Step-by-step explanation:
[tex]1/5 \div -5/7[/tex]
Do the reciprocal of the second fraction.
[tex]1/5 \times 7/-5[/tex]
Multiply the first fraction by the reciprocal of the second fraction.
[tex]7/-25=-0.28[/tex]
The answer in decimal form is -0.28.
Tamar is measuring the sides and angles of Triangle T U V to determine whether it is congruent to the triangle below. For triangle K L M, side K M is 27 millimeters, side L M is 20 millimeters, and side K L is 12 millimeters. Angle K is 45 degrees, angle M is 25 degrees, angle L is 110 degrees. Which pair of measurements would eliminate the possibility that the triangles are congruent? Measure of angle T = 25 degrees and Measure of angle U = 45 degrees Measure of angle T = 110 degrees and Measure of angle V = 25 degrees Measure of angle T = 25 degrees and TU = 12 Measure of angle T = 110 degrees and UV = 27
Answer: Measure of angle T = 25 degrees and Measure of angle U = 45 degrees
Step-by-step explanation:
Measure of angle T = 25 degrees and TU = 12 is the pair of measurements would eliminate the possibility that the triangles are congruent.
What are congruent triangles?
" Triangles are said to be congruent if the corresponding sides and angles of the one triangle are equals to the other triangles."
According to the question,
In triangle KLM,
KM =27millimeters
LM = 20millimeters
KL = 12 millimeters
∠K= 45degrees
∠M= 25 degrees
∠L = 110degrees
From the given measurements of the triangle we have,
side with measure 27millimeters is opposite to angle 110° .
side with measure 12millimeters is opposite to angle 25° .
side with measure 20millimeters is opposite to angle 45°.
From the conditions in triangle TUV to be congruent to triangle KLM ,
Measure of angle T = 25 degrees and TU = 12 is against the given condition of congruent triangle.
As angle T and side TU are adjacent to each other, which is against the correspondence of the given triangle.
Hence, measure of angle T = 25 degrees and TU = 12 is the pair of measurements would eliminate the possibility that the triangles are congruent.
Learn more about congruent triangle here
https://brainly.com/question/12413243
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If the statement shown is rewritten as a conditional statement in if-then form, which best describes the conclusion?
When a number is divisible by 9, the number is divisible by 3.
then the number is divisible by 3
then the number is divisible by 9
O if a number is divisible by 3
O if a number is divisible by 9
Answer:
Correct statement: "the number is divisible by 3".
Step-by-step explanation:
The statement provided is:
When a number is divisible by 9, the number is divisible by 3.
The general form of a conditional statement in if-then form is:
[tex]p\rightarrow q[/tex]
This implies that if p, then q.
The part after the "if" is known as the hypothesis and the part after the "then" is known as the conclusion.
The if-then form of the provided statement is:
If a number is divisible by 9, then the number is divisible by 3.
So, the conclusion is:
"the number is divisible by 3"
Answer:
a
Step-by-step explanation:
How can you use an equilateral triangle to find the lengths of the sides in a 30-60-90 triangle?
Answer:
Step-by-step explanation:
1) divide equilateral tri from the middle you will get two 30-60-90 triangles
2) by using pythagorean law & trigimintory, you will get two unknowns (height and side length) and two functions
Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation. Do not solve the equation Can the method of undetermined coefficients together with superposition be applied to find a particular solution of the given equation?
A. No, because the right side of the given equation is not the correct type of function
B, Yes °
C. No, because the differential equation is not linear.
D. No, because the differential equation does not have constant coefficients.
Answer:
D. No, because the differential equation does not have constant coefficients.
Step-by-step explanation:
The undetermined coefficient method cannot be applied to non homogeneous variables. The differential equation does not have constant variables therefore the method of undetermined superposition can not be applied. To complete a solution of non homogeneous equation the particular solution must be added to the homogeneous equation.
What is the slope of a line that is perpendicular to the line 2y – 3x = 8?
Answer:
[tex] = \frac{3}{2} [/tex]
Step-by-step explanation:
[tex]y = mx + c[/tex]
Here,
m => slopec => interceptIn this equation ,
[tex]2y - 3x = 8[/tex]
to find the value of m or the value of slope we have to solve for y
Let's solve,
[tex]2y - 3x = 8 \\ 2y = 8 + 3x \\ \frac{2y}{2} = \frac{8 + 3x}{2} \\ y = 4 + \frac{3x}{2} \\ y = \frac{3x}{2} + 4[/tex]
So, the slope is,
[tex] = \frac{3}{2}[/tex]
LA=
Round your answer to the nearest hundredth.
A
5
B
3
Answer:
You didn't state it but you need to find Angle A.
From the Pythagorean Theorem, we calculate side ac
side ac^2 = 5^2 - 3^2 =25 -9 = 16 Side AC = 4
arc tangent angle A = 3 / 4 = .75
angle A = 36.87 Degrees
Step-by-step explanation:
Which of the following is the equation of the function below?
Answer:
Step-by-step explanation:
its B
Answer:
the answer is B
Step-by-step explanation:
someone pls help me! ❤️❤️❤️
Answer:
(x-1) ( x -i) (x+i)
Step-by-step explanation:
x^3 -2x^2 +x-2
Factor by grouping
x^3 -2x^2 +x-2
x^2(x-2) +1(x-2)
Factor out (x-2)
(x-2) (x^2+1)
Rewriting
(x-1) ( x^2 - (-1)^2)
(x-1) ( x -i) (x+i)
Answer:
Should be b
Step-by-step explanation:
Since it's a multiple choice question you know that -2 or 2 has to be a root for the cubic.
You can test both -2 and 2 and see that replacing x for 2 has the expression evaluate to 0.
Then, since you know the imaginary roots have to be conjugates, you get B.