a) P(X = x₀, Y = 2x₀) = 1/36
P(X = x₀, Y = k) = 1/18 for k between x₀+1 and 2x₀-1 inclusive
Every other event has probability 0. x₀ is any number between 1 and 6 inclusive.
b) P(X = x₀, Y = x₀) = x₀/36
P(X = x₀, Y = k) = 1/36 for k between x₀+1 and 6 inclusive.
x₀ is between 1 and 6 inclusive. Every other event has probability 0.
c) P(X = x₀, Y = x₀) = 1/36
P(X = x₀, Y = k) = 1/18 with k between x₀+1 and 6 inclusive
x₀ between 1 and 6 inclusive. Any other event has probability 0.
What is a joint probability?Joint probability is the probability of two events happening simultaneously.
Let P(A) = probability that event A takes place and P(B) = probability that event B takes place. Then, probability of event A and B happening together i.e. P(A and B) is called joint probability.
What is the Calculation of joint probability?(1) When A and B are independent events: When event A has no impact on event B or vice versa, the two events are said to be independent. For independent events, formula for joint probability is:
P(A and B) = P(A) × P(B)
Example: I am performing two acts at a time (i) tossing a coin and (ii) throwing a dice. What is the probability that the coin shows up “head” and the dice shows up “3”?
There is no doubt that getting “head” on coin and getting “3” on dice are independent events.
Probability of the coin showing up “head” = 1/2
Probability of the dice showing up “3” = 1/6
Therefore, probability of getting “head” on coin and “3” on dice = (1/2)×(1/6) = 1/12
(2) When A and B are dependent events: If event A and event B cannot be considered independent, calculation of joint probability requires knowledge of conditional probability. For dependent events, formula for joint probability is:
P(A and B) = P(A) × P(B, given A) = P(B) × P(A, given B).
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If the logarithm of 5832 is 6, what is the base?
[tex] logx(5832) = 6[/tex]
Answer:
The base is 4.2426.
Step-by-step explanation:
Logarithm definition:
Suppose we have that:
[tex]\log_{a}{b} = c[/tex]
It means that;
[tex]b = a^c[/tex]
In this question:
[tex]\log_{x}{(5832)} = 6[/tex]
It means that:
[tex]x^6 = 5832[/tex]
[tex]x = \sqrt[6]{5832}[/tex]
[tex]x = (5832)^{\frac{1}{6}}[/tex]
[tex]x = 4.2626[/tex]
The base is 4.2426.
34 in.
16 in.
22 in.
Lateral Surface Area =
in squared
Total Surface Area =
in squared
Volume =
in cubed
Answer:
Step-by-step explanation:
Lateral surface area of the triangular prism = Perimeter of the triangular base × Height
By applying Pythagoras theorem in ΔABC,
AC² = AB² + BC²
(34)² = (16)² + BC²
BC = [tex]\sqrt{1156-256}[/tex]
= [tex]\sqrt{900}[/tex]
= 30 in.
Perimeter of the triangular base = AB + BC + AC
= 16 + 30 + 34
= 80 in
Lateral surface area = 80 × 22
= 1760 in²
Total Surface area = Lateral surface area + 2(Surface area of the triangular base)
Surface area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(30)(16)[/tex]
= 240 in²
Total surface area = 1760 + 2(240)
= 1760 + 480
= 2240 in²
Volume = Area of the triangular base × Height
= 240 × 20
= 4800 in³
complete the table below to show the differences bettween algebraic expression and equation
Complete the table below to show the differences between algebraic
expression and equation.
Describe each to show their differences.
Give 3 examples of each.
Answer:
Explained below with examples
Step-by-step explanation:
1. Algebraic expression in mathematics are basically expressions that are formed from variables, integer constants, and also algebraic operations.
Examples include;
>> 2x² − xy
>> 3ab + 2b²
>> x² + y²
2. An algebraic equation is a phrase where the two sides of the equation which are the left and right hand sides are connected by the equal to sign (=).
Examples are;
>> 3y - y² = 2y² + 2
>> 3x - 4y = x + 2
>> 5a + 3b = 2b - 1
Find the side length of a square with an area of 1521 m².
Answer:
39
Step-by-step explanation:
a=A=1521=39
The tenants in an apartment building voted on whether to places couches in the lobby of the building. The number of votes for placing couches in the lobby was 765. The number of votes against placing couches in the lobby was 1,785. What percent of the voters were in favor of placing couches in the lobby of the building.REEEEE
A.20%
B.25%
C.30%
D.35%
does anyone else play woozworld? if so, add me SummerRae0
A book costs $1.49 and is sold in a retail store for $8.99. What is the percentage in mark up? *
Answer:
603.35%
Step-by-step explanation:
Given that a book costs $ 1.49 and is sold in a retail store for $ 8.99, to determine what is the percentage in mark up, the following calculation must be performed:
1.49 = 100
8.99 = X
8.99 x 100 / 1.49 = X
899 / 1.49 = X
603.35 = X
Thus, the mark up percentage of the book is 603.35%, which implies an increase of more than 6 times its initial value.
A small bar of gold measures 20 mm by 250 mm by 2 mm. One cubic millimeter of gold weighs about
0.0005 ounces. Find the volume in cubic millimeters and the welght in ounces of this small bar of gold.
cubic millimeters and the weight of the bar is
The volume of the bar is
ounce(s).
Answer: 5 ounces
Step-by-step explanation:
volume is 20*250*2=10000 cubic mm
10,000*0.0005=5
Jim caught 15 fish over course of 3 days. After 4 days how many total fish will Jim have caught?
Answer:
20
Step-by-step explanation:
15 divided by 3 is 5
15 over 4 days = 20
Mr. Thorbes bought a new journal for his poetry. If the journal normally cost $22 but was on sale for 20% off, how much did Mr. Thorbes save?
Answer:
He would save $4.40
Step-by-step explanation:
And in total he would pay 17.60
5x≥25 help th bewbsanks
Calcular el valor de la fuerza que se debe aplicar para dezlisar un bloque de la siguiente figura a velocidad constante, si tiene un peso de 150 N y al coeficiente de friccian dinamico es de 0.3
Answer:
azsdfghjkljhgfdsasdfghjm,.
Step-by-step explanation:
4x + y = 23
3x - y = 11
Answer:
Step-by-step explanation:
4x + y = 23
3x - y = 11
I got x = 34/7
Answer:it will be x= 34/7 and y= 25/7
Step-by-step explanation:4x+y=23for y:
4x+y=23
4x+y+−4x=23+−4x(Add -4x to both sides)
y=−4x+23
−4x+23foryin3x−y=11:
3x−y=11
3x−(−4x+23)=11
7x−23=11(Simplify both sides of the equation)
7x−23+23=11+23(Add 23 to both sides)
7x=34
7x
7
=
34
7
(Divide both sides by 7)
x=
34
7
Step: Substitute
34
7
forxiny=−4x+23:
y=−4x+23
y=−4(
34
7
)+23
y=
25
7
(Simplify both sides of the equation)
Answer:
x=
34
7
and y=
25
7
What is the ratio in simplest form between the length of a side in ABCD and the length of its corresponding side in WXYZ?
a.2\3
b.1\2
c.3\4
d.6\5
Answer:
The Answer would be C) 3/4
Step-by-step explanation:
If you subtract a quarter of the number presented on right left hand on the picture you get the numbers presented on the left hand side of the picture shown. There fore the ratio is 3/4 or three quarters of the already existing number.
d. Cloe has 84 packs of potato chips and 86 juice boxes.
He wants to share them equally with all his friends. How
A many friend does Cloe have
? How many packs of chips
and juice boxes will each friend receive? is it LCM or GCF?
Answer:
I was trying to look up the answer to help out but I think I accidently found the answer key ill put it in the explanation
Step-by-step explanation:
https://www.louisianabelieves.com/docs/default-source/assessment/grade-7-answer-key.pdf?sfvrsn=e005981f_2
Write 108 in exponential form using only prime numbers as a base
A manufacturer of band saws wants to estimate the average repair cost per month for the saws he has sold to certain industries. He cannot obtain a repair cost for each saw, but he can obtain the total amount spent for saw repairs and the number of saws owned by each industry. Thus, he decides to use cluster sampling, with each industry as a cluster. The manufacturer selects a simple random sample of n = 20 from the N = 96 industries he services. The data on total cost of repairs per industry and number of saws per industry are as given in the accompanying table. Estimate the average repair cost per saw for the past month and place a bound on the error of estimation.
Industry No.of saws Total repair cost for past month
1 3 50
2 7 110
3 11 230
4 9 140
5 2 60
6 12 280
7 14 240
8 3 45
9 5 60
10 9 230
11 8 140
12 6 130
13 3 70
14 2 50
15 1 10
16 4 60
17 12 280
18 6 150
19 5 110
20 8 120
Answer:
The average repair cost per saw for the past month is 20.
The bound of error of estimation is ±10.
Step-by-step explanation:
a) Data and Calculations:
Industry No.of saws Total repair cost Average
for past month
1 3 50 16.67
2 7 110 15.71
3 11 230 20.91
4 9 140 15.56
5 2 60 30
6 12 280 23.33
7 14 240 17.14
8 3 45 15
9 5 60 12
10 9 230 25.56
11 8 140 17.50
12 6 130 21.67
13 3 70 23.33
14 2 50 25
15 1 10 10
16 4 60 15
17 12 280 23.33
18 6 150 25
19 5 110 22
20 8 120 15
Total 130 2,565 19.73
Average = Sum of the total repair cost for past month divided by the number of saws repaired
= 19.73 (2,565/130)
= 20
The bound on error of estimation = the difference between the upper bound of the interval and the calculated mean
= 30 - 20
= 10
The lower bound = 10
The bound of error is also = (30 -10)/2 = 10
PLEASE HELP!
The equation of a parabola is y=1/2x^2+6x+23.
What is the equation of the directrix?
y = 5.5
y = 4.5
y = 2
y = 0.5
Answer:
Step-by-step explanation:
y = ½x² + 6x + 23
= ½(x² + 12x) + 23
= ½(x² + 12x + 6²) - ½(6²) + 23
= ½(x+6)² + 5
vertex (-6,5)
focal length = 1/(4∙½) = ½
directrix: y = 5-½ = 4.5
Answer: y=4.5 Just confirming
Step-by-step explanation:
Just a test good luck
Solve for x and show work please!
Answer:
Every quadrilateral's 4 angles add up to 360 degrees.
The four angles would be 100° + 7x +37 + 100° + 7x +37 = 360°
200° + 14x + 74° = 360°
14x = 360° - 274
14x = 86
x = 6.1428571429
Step-by-step explanation:
Answer: x=43/7
Step-by-step explanation:
One of the properties of the inner angle of a parallelogram is that the two angles on the same side add up to 180°
100+(7x+37)=180
100+7x+37=180
137+7x=180
137+7x-137=180-137
7x=43
x=43/7≈6.14
Hope this helps!! :)
Please let me know if you have any questions
Un círculo tiene una circunferencia de 18.4 m. Determina el valor del radio. (Utiliza el valor de π = 3.14)
Answer: 2.92
Step-by-step explanation:
De la circunferencia del círculo, se encuentra que su radio es de 2.93m.
El circunferencia de un círculo de radio r es dada por:
[tex]C = 2\pi r = 2(3.14)r = 6.28r[/tex]
En este problema, la circunferencia es de 18.4. Así, es posible aplicar la fórmula de la cincumference para encontrar su radio, puesto que [tex]C = 18.4[/tex].
[tex]C = 6.28r[/tex]
[tex]6.28r = 18.4[/tex]
[tex]r = \frac{18.4}{6.28}[/tex]
[tex]r = 2.93[/tex]
El radio es de 2.93m.
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The radius of a cylindrical water tank is 4 ft, and its height is 10 ft. What is the volume of the tank?
Answer:
502 cubic feet
Step-by-step explanation:
The Volume of the tank is 502 cubic feet.
Apples weighing 30 pounds are placed in a crate that weighs p pounds. Which equation can
be used to find t, the total weight of both the crate and the apples in pounds?
A. t=30p
B. t=p+30
C. t=p-30
D. t=30-p
A survey conducted by the U.S. department of Labor found the 48 out of 500 heads of households were unemployed. Compute a 99% confidence interval for the proportion of unemployed heads of households in the population. Round to three decimal places. (make sure to type a zero in front of the decimal place ie. 0.1 vs .1 otherwise your answer will be marked incorrect) Lower limit
Answer:
99% Confidence interval is given as;
Lower Limit = 0.062
Upper Limit = 0.130
Step-by-step explanation:
Given the data in the question;
x = 48
n = 500
sample proportion p = x/n = 48/500 = 0.096
with 99% confidence
significance level ∝ = 1 - 99% = 1 - 0.99 = 0.01
∝/2 = 0.01 / 2 = 0.005
Critical Z-value = [tex]Z_{\alpha /2[/tex] = [tex]Z_{0.005[/tex] = 2.576
Now,
Standard error of p : SE = √[ (p × ( 1 - p) / n ) ]
we substitute
SE = √[ (0.096 × ( 1 - 0.096) / 500 ) ]
SE = √[ (0.096 × 0.904) / 500 ]
SE = √[ 0.086784 / 500 ) ]
SE = 0.0131745
so
Margin of Error E = [tex]Z_{\alpha /2[/tex] × SE
E = 2.576 × 0.0131745
E = 0.0339
Now 99% confidence interval will be
⇒ 0.096 ± 0.0339
⇒ (0.096 - 0.0339, 0.096 + 0.0339 )
⇒ ( 0.062, 0.130 )
Lower Limit = 0.062
Upper Limit = 0.130
How many times greater is 6,680 than 668
Answer:
10
Step-by-step explanation:
668 x 10 = 6,680
Determine whether the given equation has one solution, no solution, or infinitely many solutions. 2 - 3(x+ 4) = 3(3 - x) cannot be determined one solution Ono solution infinitely many solutions.
Answer:
no solution
Step-by-step explanation:
The given equation is :
2 - 3(x+ 4) = 3(3 - x)
We need to solve the equation. It can be done as follows :
2-3x-12 = 9-3x
As -3x gets canceled from both sides. It means the given equation has no solution.
Find the measurements of the numbered angles in each kite
Answer:
∠1 = 23°
∠2 = 23°
Step-by-step explanation:
Tina constructed triangle XYZ.
Which two words describe triangle XYZ?
A. equilateral and right
B. equilateral and isosceles
C. isosceles and scalene
D. isosceles and right
Answer:
It's D... Isosceles and right
Step-by-step explanation:
got it right on the quiz.
the area of a rectangle with a height of 2 and a width of 5x^2-2x+3
Answer:
Area is 10x^2 - 4x + 6
Step-by-step explanation:
To find this area, multiply the width and height together:
(5x^2 - 2x + 3)(2) = 10x^2 - 4x + 6
x2 + 16x – 2 = 11
1) Rewrite the equation by completing the square.
Your equation should look like (x + c)2 = d or (x - c)2 = d.
I
+
utan
pls help
Answer:
(x+8)^2=77 and x=negative 8±√77
Step-by-step explanation:
After watching a video, I got it right on Khan
The equation with completing the squares is (x + 8)² = 77.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
x² + 16x - 2 = 11
We can make complete squares.
x² + 16x - 2 - 11 = 0
x² + 16x - 13 = 0
x² + 2 x 8 x (x) -8² + 8² - 13 = 0
(x² + 16x + 8²) - 64 - 13 = 0
(x + 8)² - 77 = 0
(x + 8)² = 77
Thus,
The equation is (x + 8)² = 77.
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If an object travels at 2 feet per second, how many feet does it travel in 3 hours?
Object will cover 21600 feet in 3 hours.
What is distance?
Distance is defined as the product of the speed and time.
The distance an object travelled is measured in distance per second here.
So, let us convert the hours into seconds to arrive at our answer.
One hour = 60 minutes = (60×60) seconds = 3600 seconds.
The object travels 2 feet for every second.
Then, total distance covered in 3 hours is
2×3×3600 = 21600 feet.
Hence, object will cover 21600 feet in 3 hours.
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