The probability that both are red marbles = [tex]\bold{\frac{17}{147} }[/tex]
What is probability?"It is finding out the possibilities of the occurrence of an event."
Formula to find the probability of an event:"P(A) = n(A) / n(S)
where, n(A) is the number of favorable outcomes of an event A
n(S) is the total number of outcomes for an experiment"
For given example,
A jar contains 17 red marbles and 32 blue marbles.
If we pull out 2 marbles at random, we need to find the probability that both are red.
The number of possible outcomes,
[tex]\Rightarrow n(S)=^{49}C_2\\\\ \Rightarrow n(S)=\frac{49!}{2!(49-2)!}\\\\ \Rightarrow n(S)=1176[/tex]
The number of possible outcomes of selecting both the red marbles.
[tex]\Rightarrow n(A)=^{17}C_2\\\\ \Rightarrow n(A)=\frac{17!}{2!(17-2)!}\\\\ \Rightarrow n(A)=136[/tex]
The probability that both the marbles are red,
[tex]\Rightarrow P(A)=\frac{n(A)}{n(S)}\\\\ \Rightarrow P(A)=\frac{136}{1176}\\\\ \Rightarrow P(A)=\frac{17}{147}[/tex]
Therefore, the probability that both are red marbles = [tex]\bold{\frac{17}{147} }[/tex]
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A Penguin walks 6 feet in 15 seconds. At this speed How far does the penguin walk in 6 seconds?
Answer:
The penguin will walk 75.15 feet in 45 sec
Step-by-step explanation:
Two trains leave towns 474 kilometers apart at the same time and travel toward each other. One train travels13 km/m faster than the other. If they meet in 2 hours, what is the rate of each train?
Answer:
112 km/h
125 km/hr
Step-by-step explanation:
Distance = time * speed
Distance = distance train 1 + distance train 2
474 = 2(s) + 2(s + 13)
Distribute
474 = 2s + 2s + 26
Combine like terms
474 = 4s + 26
Subtract 26 from both sides
448 = 4s
Divide both sides by 4
112 = s
s = 112 km/h
s + 13 = 125 km/hr
please help me with -6 - (1 - 2 x) in Distributive Property this question
Answer:
-7 + 2x
Step-by-step explanation:
Why would a number line be divided into 20 parts?
Answer:
_ _
1 2 all the way to twenty
Step-by-step explanation:
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.23.
How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 98% confidence level with an error of at most 0.03? Round your answer up to the next integer.
Using the z-distribution, it is found that a sample size of 1066 is required.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of .
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
From the previous study, the estimate is of 0.23, hence [tex]\pi = 0.23[/tex].
98% confidence level, hence[tex]\alpha = 0.98[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.98}{2} = 0.99[/tex], so [tex]z = 2.327[/tex].
The sample size is n for which M = 0.03, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 2.327\sqrt{\frac{0.23(0.77)}{n}}[/tex]
[tex]0.03\sqrt{n} = 2.327\sqrt{0.23(0.77)}[/tex]
[tex]\sqrt{n} = \left(\frac{2.327\sqrt{0.23(0.77)}}{0.03}\right)[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.327\sqrt{0.23(0.77)}}{0.03}\right)^2[/tex]
[tex]n = 1065.5[/tex]
Rounding up, a sample size of 1066 is required.
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Guys I really need some help with this one!
If anybody could help me out here I would be incredibly grateful! (Simple algebra problem involving functions)
Answer:
f( 1 ) = 3
Step-by-step explanation:
Given the linear function, f(x) = -4x + 7, we could easily find f( 1 ) by substituting the value of the input, x = 1, into the function.
f(x) = -4x + 7
f( 1 ) = -4( 1 ) + 7
f( 1 ) = -4 + 7
f( 1 ) = 3
Therefore, the output value is f( 1 ) = 3.
answer this question fast
Answer:
corona virus sjuwiwiwoe
Step-by-step explanation:
iaisowowow
What is the length of side YZ to the nearest tenth please show your work!
Length of side YZ to the nearest tenth is 16 ft
To solve this question we would use the sine rule. The sine rule states that
A/sin a = B/sin b
if we take our angle a to be XZY, and b to be ZXY.
Going by angles in a triangle, ZXY = 180 - 90 - 35 = 55. This means that our angle b is 55º
applying the sine rule, we have
11/sin 35 = B/sin 55
11/0.5736 = B/0.8192, if we cross multiply, we have
B = (11 * 0.8192)/0.5736
B = 9.0112/0.5736
B = 15.7 ft
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Answer:
15.7
Step-by-step explanation:
a student required to 40% marks to pass in exam he got 190 marks and fail with 10 marks. find total marks?
Answer:
500
Step-by-step explanation:
40%=190+10
40%=200
10%=50
100%=500
A coach divided his team into two groups of equal size.
.
of the first group drinks at least 2 glasses of water a day
• 75% of the second group drinks at least 2 glasses of water a day.
What fraction of the team drinks at least 2 glasses of water a day?
Applying the percentages, and considering that 70% of the first group drinks at least 2 glasses of water a day, it is found that 0.725 = 72.5% of the team drinks at least 2 glasses of water a day.
The team is divided into two equal groups, hence, each represents 50%.
The percentages associated with drinking at least 2 glasses of water a day is:
70% of 50%(first group)75% of 50%(second group)Hence, applying the weighed percentage, the total percentage is:
[tex]T = 0.7(0.5) + 0.75(0.5) = 0.725[/tex]
0.725 = 72.5% of the team drinks at least 2 glasses of water a day.
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Write the following sentence as an equation. Use x to represent "a number."
The product of 2 and the sum of
6 and a number is -40.
The equation is a
(Do not simplify.)
Answer:
Step-by-step explanation:
5×(-2+x)=-20
-10+5x=-20
5x=-20+10
5x=-10
x=-10/5
x=-2
Round off the decimal 55.345 to 2 decimal places.
Answer:
Step-by-step explanation:
55.345 is rounded off two places therefore, the hundreths place
the number next to 4 is 5 in the thousandths place. 5 is high and therefore 4 is changed to 5 and makes it 53.35
Which graph represents the function y = 2x - 4?
ТУ
2
2
.
4
X +
x
-4 -3 -2 -1
X
TO
O
-3 -2 -1
2.34
Answer:
the third graph.
the one where x intercept with 2
Step-by-step explanation:
2x-4=0
2x=4
x=2
therefore the graph should have a line that have a x-intercept of 2
a
In a math class with 25 students, a test was given the same day
that an assignment was due. There were 15 students who passed
the test and 20 students who completed the assignment. There
were 13 students who passed the test and also completed the
assignment. What is the probability that a student passed the test
given that they did not complete the homework?
a
Using it's concept, it is found that there is a 0.4 = 40% probability that a student passed the test given that they did not complete the homework.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, of the 25 - 20 = 5 students that did not complete the homework, 15 - 13 = 2 passed the test, hence the probability is given by:
p = 2/5 = 0.4 = 40%.
0.4 = 40% probability that a student passed the test given that they did not complete the homework.
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Help ASAP Homework Due Tomorrow
Answer:
Its definitely D
Step-by-step explanation:
Your welcome ♀️
y=7x+7 convert in standard form
Answer:
y/7=x+1
hope this helps you!!
WARM UP ACTIVITY (5 MIN) Ms. Chantel's car can go 228 miles on 6 gallons of gas. During a drive last week Ms. Chantel used 7 gallons of gas. a.) How far did she drive? b).Explain how the problem changes if you were given the distance Ms. Chantel drove last week instead of how much gas she used.
How does the problem change????
Answer:
a. 266
b. if you were given the distance you can just do, the distance divided by 38
Step-by-step explanation:
A. 228/6=38
228+38=266
-3/5 > -4/5 in a number line
Answer:correct
Step-by-step explanation: >
Help help help help help help help
Here is ur perfect answer
Answer:
second one
Step-by-step explanation:
show how the work is done and help and have to be fast with math
Answer:
Answer is 14
Step-by-step explanation:
By understanding the concept of math
Answer: you mom
Step-by-step explanation:
Is this a function or not a function?
Answer:
This is indeed a function
At Arnold's Arcade, a child can buy 21 tokens for $6. At this rate, how many tokens would $20 get someone?
Based on the information given, the number of tokens that will be bought if a child has $20 will be 70.
Since a child can buy 21 tokens for $6, the cost of one token will be:
= $6 / 21 = $0.2857143
Therefore, if a child has $20, the number of tokens that will be gotten will be:
= $20 / $0.2857143
= 70
Therefore, 70 tokens will be bought.
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Max has 345 fiction books and 179 nonfiction books. He wants to give 205 books
to his local library for a donation. How many books does Max have left after
making his donation?
Answer:
319 books
Step-by-step explanation:
345+179=524
524-205 = 319
The graph of f(x) = x² is transformed to create the graph of g(x) = f(x + 6). Which
statement is true?
A The graph of g(x) reflects the graph of f(x) across the x-axis.
B The graph of g(x) reflects the graph of f(x) across the y-axis.
CThe vertex of the graph of g(x) is 6 units to the left of the vertex of the graph of f(x).
DThe y-intercept of the graph of g(x) is 6 units above the y-intercept of the graph of f(x).
Answer:
Given a function \displaystyle f\left(x\right)f(x), a new function \displaystyle g\left(x\right)=-f\left(x\right)g(x)=−f(x) is a vertical reflection of the function \displaystyle f\left(x\right)f(x), sometimes called a reflection about (or over, or through) the x-axis.
Given a function \displaystyle f\left(x\right)f(x), a new function \displaystyle g\left(x\right)=f\left(-x\right)g(x)=f(−x) is a horizontal reflection of the function \displaystyle f\left(x\right)f(x), sometimes called a reflection about the y-axis.
Step-by-step explanation:
A rectangular field is 350 meters long and 200 meters wide. What is the area of the field in square kilometers? Do not round your answer. Be sure to include
the correct unit in your answer.
0
km
km2
km
The area of the rectangular field is 0.07 square kilometers (km²).To find the area of the rectangular field in square kilometers, we need to convert the given dimensions from meters to kilometers.
To find the area of the rectangular field in square kilometers, we need to convert the given dimensions from meters to kilometers and then calculate the area.
Given:
Length of the field = 350 meters
Width of the field = 200 meters
To convert from meters to kilometers, we divide the measurements by 1000, since there are 1000 meters in a kilometer.
Length in kilometers = 350 meters / 1000 = 0.35 kilometers
Width in kilometers = 200 meters / 1000 = 0.2 kilometers
Now that we have the dimensions of the field in kilometers, we can calculate the area.
Area of the field = Length in kilometers * Width in kilometers
Area of the field = 0.35 kilometers * 0.2 kilometers
Multiplying the values, we get:
Area of the field = 0.07 square kilometers
Therefore, the area of the rectangular field is 0.07 square kilometers.
It's important to include the correct unit in the answer, which is "square kilometers" (km²). This represents the unit for measuring the two-dimensional area. In this case, the area of the field is 0.07 km².
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need help now please i will give 25 points
Answer:
Answer is letter B
if im wrong i'm sorry that my opinion
Answer:
B) y = -x + 2
Step-by-step explanation:
First, we pick 2 points that are on the line:
(0, 2) and (1, 1)
Next, we find the slope (m):
m = (y2 - y1)/(x2 - x1)
m = (1 - 2)/(1 - 0)
m = (-1)/1
m = -1
Then, we do point-slope formula to create the equation:
y - y1 = m(x - x1)
y - 2 = -1(x - 0)
y - 2 = -x
y = -x + 2
c¹⁰ ÷ c⁵ please help me asap thank you
Answer:
c^5
Step-by-step explanation:
All you have to do is take away the powers because of the law of indeces when dividing number with indices
Hope this helps :) im really bad at the explanations part :D
...........................................................
Select the best description for the slope of Line a.
Positive Slope
Negative Slope
Zero Slope
Undefined Slope
what is the surface area of the regular pyramid below?
A. 1512 units^2
B. 952 units^2
C. 1316 units^2
D. 756 units^2
D. 756 units^2
Step-by-step explanation:
there ya go :)
The surface area of the regular pyramid is 960 square units, the correct answer is B.
How to find the volume and base's area of a right rectangular pyramid?Suppose the base of the pyramid has length = l units, and width = w units.
Suppose that the height of the pyramid is of h units, then:
[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]
is the volume of that pyramid.
The base is a rectangle with length = L units, and width = W units, so its area is:
[tex]b = l \times w\: \rm unit^2[/tex]
We are given that;
Base of square pyramid is 20, the height is 14
Now,
Perimeter = 4 x 20 = 80 units
Base area = 20 x 20 = 400 square units
Surface area = (1/2) x 80 x 14 + 400
Surface area = 560 + 400
Surface area = 960 square units
Therefore, the surface area pyramid will be 960 square units.
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Kelly worked on a straight 8 % commission. Her friend worked on a salary of $850 plus a 6% commission. In a particular month, they both sold $21,700 worth of
merchandise
Step 1 of 2: How much did Kelly earn for this month? Follow the problem-solving process and round your answer to the nearest cent, if necessary.
The total amount of money Kelly earned for the month is $1,736
Commission refers to a sum of money paid to a salesperson for every sale that he or she makes. It is usually a percentage of the total sales.Given:
Kelly
Worth of goods sold = $21,700
commission = 8%
Total earned = 8% of $21,700
= 8/100 × 21,700
= 0.08 × 21,700
= $1,736
Approximately, $1,736.00
Therefore, the amount of money Kelly earned for this month is $1,736
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