Answer:
0.2333 = 23.33% probability that both of them have the secret decoder ring
Step-by-step explanation:
The cereals are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
45 boxes, which means that [tex]N = 45[/tex]
22 have the secret decoder ring, which means that [tex]k = 22[/tex]
Two boxes, which means that [tex]n = 2[/tex]
What is the probability that both of them have the secret decoder ring?
This is P(X = 2). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,45,2,22) = \frac{C_{22,2}*C_{23,0}}{C_{45,2}} = 0.2333[/tex]
0.2333 = 23.33% probability that both of them have the secret decoder ring
henry who is 3 years younger than sandra is 14 write an equation to represent sandras age
of the marbles in a bag, 5 are red, 5 are yellow, and 3 are white. Sandra will randomly choose one marble from the bag. Fill in the blanks in parts a and b. a.
The probability that Sandra will choose a white marble from the bag is __ out of__ or ?/? (fraction)
b. It is _____ that Sandra will choose a white marble from the bag.
B.
If m ZACB = 180°, and mZACD = 55°, then
mZDCB = [?]
Enter
Answer:
125
Step-by-step explanation:
/_ ACB = 180
/_ ACD = 55
/_ ACB is made up of /_ACD and
/_ DCB
Hence, /_ ACB = /_ ACD + /_ DCB
*We then plug in the known values*
180 = 55 + /_ DCB
We now solve for the missing angle
Subtract 55 from both sides
125 = /_ DCB
If h(x) = 4x - 3, what is an equation for h-1(x)?
Answer:
h(x-1)=4x-7
Step-by-step explanation:
Given :
h(x)=4x-3
Now,
putting the value of x =x-1
h(x-1)=(4(x-1)-3)
h(x-1)=4x-4-3
h(x-1)=4x-7
Answer will be h(x-1)=4x-7
Given the linear equation 5x+3y-9=0. Write another linear equation in two variables such that the geometrical representation of the pair so formed are parallel lines
Answer:[tex]5x+3y+1=0[/tex]
Step-by-step explanation:
Given
The linear equation is [tex]5x+3y-9=0[/tex]
The other linear equation parallel to the given line can be represented by
[tex]5x+3y+c=0[/tex]
Here, c can take any value . for example c=1, line becomes
[tex]\Rightarrow 5x+3y+1=0[/tex]
please answer and explain the link below
Answer:
2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFunctionsFunction NotationCalculus
Limits
Limit Rule [Constant]: [tex]\displaystyle \lim_{x \to c} b = b[/tex]
Definition of a Derivative: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
f(x) = 2x - 5
Step 2: Differentiate
[Limit] Substitute in x [Function f(x)]: [tex]\displaystyle \lim_{\triangle x \to 0} \frac{[2(x + \triangle x) + 5] - f(x)}{\triangle x}[/tex][Limit] Substitute in function: [tex]\displaystyle \lim_{\triangle x \to 0} \frac{[2(x + \triangle x) + 5] - (2x + 5)}{\triangle x}[/tex][Distributive Property] Distribute 2: [tex]\displaystyle \lim_{\triangle x \to 0} \frac{[2x + 2\triangle x + 5] - (2x + 5)}{\triangle x}[/tex][Distributive Property] Distribute negative: [tex]\displaystyle \lim_{\triangle x \to 0} \frac{2x + 2\triangle x + 5 - 2x - 5}{\triangle x}[/tex][Subtraction] Combine like terms: [tex]\displaystyle \lim_{\triangle x \to 0} \frac{2\triangle x}{\triangle x}[/tex][Division] Simplify: [tex]\displaystyle \lim_{\triangle x \to 0} 2[/tex]Evaluate limit [Limit Rule - Constant]: [tex]\displaystyle 2[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
How many solutions does the system have?
4x−6y=−24
2x−3y=−6
Answer:
none
Step-by-step explanation:
if we plot it, it's clear, but you might also spot that the plotted lines will be parallel in the equation
because x and y in line two are the same multiple of these in line one (both values are just the half)
plotted with desmoes
Each student gets a bag with 6 celery sticks in it. Dwayne eats 4 of his celery sticks. Write the fraction of celery sticks Dwayne eats. Dwayne thinks he ate 2 3 of his celery sticks. Is he correct?
help me solve for m<4 and m<5 and x
Answer:
x = 18
Angle 4 = 31 degree
Angle 5 = 59 degree
Step-by-step explanation:
According to the question, angle 3 is 90 degree and the sum of angle 4 and 5 is equal to the angle 3 as they are vertically opposite angles.
Angle 4 + angle 5 = 90 degree
Angle 4 = 2 x - 5
angle 5 = 4 x - 13
So, according to the question,
2 x - 5 + 4 x - 13 = 90
6 x - 18 = 90
6 x = 108
x = 18
So, angle 4 = 2 (18) - 5 = 31 degree
So, angle 5 = 4 (18) - 13 = 59 degree
I NEED HELP ASAP IM STRESSJNG OUT
Answer:
A
Step-by-step explanation:
Using the Sine rule in Δ ABC
∠ B = 180° - (30 + 50)° = 180° - 80° = 100° ( sum of angles in triangle ) , then
[tex]\frac{13}{sin100}[/tex] = [tex]\frac{BC}{sin30}[/tex] ( cross- multiply )
BC × sin100° = 13 × sin30° ( divide both sides by sin100° )
BC = [tex]\frac{13sin30}{sin100}[/tex] ≈ 6.6 ( to the nearest tenth )
Please help
this is important (is a activity )
Answer:
y = 5
Step-by-step explanation:
This is a horizontal line. The value of y does not change
The equation is of the form y = constant
y = 5
Answer:
y = 5
Step-by-step explanation:
Share $150 among John, Mary, and Sarah so that each of the two girls receives twice as much as John. Calculate the amount of money Jon received.
(please help) Find m
Answer:
[tex]m\angle MLK=78^{\circ}[/tex]
Step-by-step explanation:
The Base Angle Theorem states that the base angles of the two equal legs of an isosceles triangle are equal. Since there are 180 degrees in a triangle, we have:
[tex]m\angle MLK+51+51=180,\\m\angle MLK +102=180,\\m\angle MLK=\boxed{78^{\circ}}[/tex]
what is the slope that passes through the points : (-2,9) and (4,-7)
Use the slope formula below:
[tex] \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]
The m-term represents the slope.
The formula is the changes of two y-points over the changes of two x-points. We are given two points. Substitute both points in the formula.
[tex] \large{m = \frac{9 - ( - 7)}{ - 2 - 4} } \\ \large{m = \frac{9 + 7}{ - 6} \longrightarrow \frac{16}{ - 6} } \\ \large{m = \frac{8}{ -3 } \longrightarrow - \frac{8}{3} }[/tex]
Therefore the slope is -8/3
Answer
the slope is -8/3Hope this helps! Let me know if you have any doubts.
Answer:
y = -8 / 3x + 11/3
Step-by-step explanation:
Using the slope formula:
[tex]slope = y = \frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}[/tex]
1. Select one point to be [tex](x_{1} ,y_{1} )[/tex] and the other [tex](x_{2} ,y_{2} )[/tex]
I chose (-2, 9) to be [tex](x_{1} ,y_{1} )[/tex] and (4, -7) to be [tex](x_{2} ,y_{2} )[/tex]
2. Plug the values into the formula:
[tex]y = \frac{-7-9}{4-(-2)} \\\\y= \frac{-16}{6} \\\\y = \frac{-8}{3}[/tex]
3. Finding the c-value by plugging in one of the points into the equation
y = mx + c
9 = -8/3 (-2) + c
9 = 16/3 + c
c = 11/3
4. y = -8/3x + 11/3
Not sure what it means pls help
I need this answer asap omg it’s the last question on my final lord
Answer:
oh lord may we put our head down and pray this manz aces his test or whatever it is amen.
Help
I tried solving it but I can’t
Step-by-step explanation:
tanN= perpendicular/base= 15/8
Answer:
tanN = 15/8
Step-by-step explanation:
Draw a picture!
tan = opp/adj
tanN =MO/ON
tanN = 15/8
The drama teacher wants to determine whether more students at the school would attend a comedy or a musical performance. Select all the following that would NOT help the drama teacher draw conclusions about which performance more students would attend.
A. Students who do not act.
B. Every 4th student selected from an alphabetical list of all students at the school.
C. Students who are in drama club.
D. Students who are in theater class.
E. The same number of students from each grade whose names are randomly selected from a hat.
Answer:
Option C and D
Step-by-step explanation:
The teacher wants to evaluate how many students will attends the comedy class and how many will attend the musical performance. Hence, He must be able to determine the number of students attending the drama club and theatre club as this will help him in determining the approximately correct number of students attending comedy or music class.
Hence, option C and D are correct
On Saturday, the fruit and juice bar was selling 27 glasses of fruit punch an hour. By 7 p.m., they had sold 243 glasses. If their goal was to sell more than 324 glasses of fruit punch, find the number of hours, h, they must stay open past 7 p.m. to make their goal.
Answer: 3 hours
Step-by-step explanation:
the answer this can be solved by the function:
324 = 27x + 243
-243 -243
27x = 81
/27 /27
x = 3 hours past 7.
Stella earned $72 working 9 hours. How much will she earn in 23 hours?
Answer: Stella would earn $184 in 23 hours.
Step-by-step explanation: First we need to find the unit rate so start by dividing by 9
[tex]\frac{72}{9} =8\\\frac{9}{9}=1[/tex]
Now we know every hour Stella will earn $8. We can now multiply the amount for 1 hour by 23 to get the amount for 23 hours.
8x23=184
1*23=23
Now we can see that Stella would earn $184 for working 23 hours.
Find the volume of a rectangular prism with a length of 5 cm, a width of 5 cm and a
height of 20 cm, to the nearest tenth of a cubic centimeter.
Answer:
500 cubic centimetres
Step-by-step explanation:
a cone with base circumference 6 pi and
a height equal to half the radius
A cone with a base circumference of 6 pi and a height equal to half the radius. The volume of the cone is 42.39.
What is the volume of a cone?The volume of the cone is the product of one-third of the height, pie, and square of the radius.
The volume of the cone = 1/3 [tex]\pi r^{2} h[/tex]
A cone with a base circumference of 6 pi and a height equal to half the radius.
The circumference of the circular base = 2πr
6π = 2πr
r = 3
The radius of the circular base of a cone is 3 unit.
A height equal to half the radius. Thus, the height is 1.5
The volume of the cone = 1/3 [tex]\pi r^{2} h[/tex]
= 1/3 (3.14) (9)(1.5)
= 42.39
Learn more about volume;
https://brainly.com/question/1578538
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Identify the slope and y-intercept for the line y = -2x -3.
Answer:
The slope is -2 and the y intercept is -3
Step-by-step explanation:
y = -2x -3
This equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is -2 and the y intercept is -3
Help me to do exercise no 5
Answer:
Step-by-step explanation:
a) x + 20 = 70 Vertically opposite angles are congruent
b) 2x - 50 = x + 20 Vertically opposite angles are congruent
c) 3x - 10 + 140 = 180 Linear pair
Answer:
(a) 70= x+20 (vertical angles are equal)
70 - 20=x
50=x
(b) x +20 = 2x -50 (vertical angles are equal)
20 + 50 = 2x - x
70 = x
(c) 140 +3x -10=180 (angles on the straight line)
130 +3x = 180
3x = 180 - 130
3x = 50
x= 50/3
PLEASE HELP. !!!!!!!!!!
Answer:
the last one bottom right
Step-by-step explanation:
well, did it in my head, but the idea is to calculate it out
(x-8)*(x-8)=50
is just
x²-16x+64=50
to get the 64 down to just 5, we need to subtract 59, on both sides, leaving us with -9 on the righthand side
find hcf and LCM of 40 ,60 and 80
hear here is your answer in attachment attach
Answer:
Step-by-step explanation:
40 = 2*2*2*5
60 = 2 * 2 * 3 * 5
80= 2 * 2 * 2 * 2 * 5
LCM = 2 * 2 * 2 * 2 * 5 * 3 = 240
HCF = 2*2*5= 20
Correct description of (2x+5)^2
Under any given transformation, an image is an original image while the pre-image is the new image.
A. True
B. False
Answer:
This has some fact to it. Its sorta tricky but I'd say False.
Step-by-step explanation:
The boys and girls soccer clubs are fundraising for new uniforms. The boys soccer club is selling candy bars for $2 a piece. The girls soccer club is selling candles for $4. They must raise more than $800. The girls expect to sell at least 100 candles. Write a system of inequalities to represent the situation
Inequality 1:
Inequality 2:
Answer:
2b + 4c = 800
c > 100
Step-by-step explanation:
The two linear inequalities are 2S+4C>800
and C[tex]\geq[/tex]100
It is given that The boys soccer club is selling candy bars for $2 a piece. The girls soccer club is selling candles for $4.They must raise more than $800. The girls expect to sell at least 100 candles. We have to write this situation in system of linear equality
What is system of linear inequalities?
A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables.
The soccer ball is denoted by S and Candles by C
Therefore 2S+4C>800 (We use > symbol for More than)
and C[tex]\geq[/tex]100
To learn more about linear inequalities:
https://brainly.ph/question/11773421
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The polygons are similar, but not necessarily drawn to scale.
