a) The probabilities are given as follows:
i) Exactly 2 green: 0.0479 = 4.79%.
ii) At most 3 blue: 0.2174 = 21.74%.
iii) Between 8 and 12 red: 0.6926 = 69.26%.
b) The binomial distribution is not used as there is not a fixed number of trials, and also the trials are not independent, as there is no replacement.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter n is dependent of the sample size of 25, hence:
n = 25.
For item i, the probability is of P(X = 2) with p = 88/400 = 0.22, hence, using the binomial distribution, it is of:
0.0479 = 4.79%.
For item ii, the probability is of P(X <= 3) with p = 60/400 = 0.15, hence, using the binomial distribution, it is of:
0.2174 = 21.74%.
For item iii, the probability is of P(8 <= X <= 12), with p = 160/400 = 0.4, hence the probability is of:
0.6926 = 69.26%.
For problem b, the binomial distribution cannot be used, as:
It can take 5, 6, ..., 400 trials to take 5 yellow erasers, there is not a fixed number of trials.There is no replacement, hence the probability of a success on differential trials are different.More can be learned about the binomial distribution at https://brainly.com/question/24756209
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Which of the following is an equation of a line that is parallel to y = 6x - 2 and has a y-intercept of (0, 3)
A-y = 3x + 6
B-y = 6x - 3
C-y = 3x - 6
D-y = 6x + 3
The equation of a line which is parallel to the given line; y = 6x - 2 as required in the task content is; Choice D-y = 6x + 3.
Equation of parallel lines.It follows from the task content that the equation of a line which is parallel to the given equation; y = 6x - 2 is to be determined.
First, by comparison the given equation with the slope-intercept model of a linear equation; y = mx + c. where m is slope and c is y-intercept.
Slope, m = 6.
Hence, since parallel lines are lines which have equal slopes.
The slope of the required line is therefore; 6 and it's y-intercept (0, 3) has a y-coordinate of; 3.
The required equation of the line is therefore; y = 6x + 3.
The correct answer choice among the answer choices is; Choice D; y = 6x + 3.
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Solve the equation without using a calculator
[tex]\bf\log_x\big(2+\sqrt{3} \big)=log_{\big(x+6\big)}\big(1+2\sqrt{3} \big).[/tex]
Answer:
[tex]x=7+4\sqrt{3}[/tex]=====================
Given[tex]log_x(2+\sqrt{3})=log_{x+6}(1+2\sqrt{3})[/tex]Solve it in below steps[tex]2log_x(2+\sqrt{3})=2log_{x+6}(1+2\sqrt{3)}[/tex][tex]log_x(2+\sqrt{3})^2=log_{x+6}(1+2\sqrt{3})^2[/tex][tex]log_x(7+4\sqrt{3})=log_{x+6}(13+4\sqrt{3})[/tex][tex]log_x(7+4\sqrt{3})=log_{x+6}(7+4\sqrt{3}+6)[/tex]Let 7 + 4√3 = t, then[tex]log_xt = log_{x+6}(t+6)[/tex][tex]logt/logx=log(t+6)/log(x+6)[/tex][tex]logx/log(x+6)=logt/log(t+6)[/tex][tex]log_{x+6}x=log_{t+6}t[/tex][tex]x = t[/tex]The value of x is[tex]x=7+4\sqrt{3}[/tex]For rectangles with the same area, the length varies inversely to the width. Henry is trying to decide how to plan the dimensions of his new rectangular swimming pool. He is planning on his pool being 200 square feet. One option would be to have a length of 20 ft and a width of 10ft. Write an equation to model this scenario.
PLEASE HELP WILLMARK BRAINLIEST
A: 10=a/20
B: 20=a/10
C: 10=20/a
D: 20= 10/a
Answer:
It would be c.................
A scuba diver descends in the water at a rate of 23.5 feet per minute for 2.6 minutes. He immediately changes course when he sees a large fish and ascends at a rate of 28 feet per minute for 2 minutes. What is the scuba diver's position relative to sea level after the 4.6 minutes? Enter your answer as a decimal in the box.
Answer:
Step-by-step explanation:
t is given that a scuba driver descends in water for 2.8 minutes at a rate of feet per minute.
Let's assume the descending position as negative.
The position at which the scuba driver will be after 2.8 minutes is :
= - feet per minute × 2.8 minutes
= - 57.4 feet
Now , he sees a large fish and changes his direction and starts diving ascending at a rate of 25 feet per minute for 2 minutes.
Let's assume the ascending position as positive.
So , The position at which the scuba driver will be after 2 minutes after seeing large fish is :
= 25 × 2
= 50 feet
So , the scuba diver's position relative to sea level after the 4.8 minutes will be :
= -57.4 + 50
= -7.4 feet
This meant Scuba driver is 7.4 feet below sea level.
i need help asap with this question
Answer: B
Step-by-step explanation:
The width = 23/4
The length = 2 × the width = 2 × 23/4 = 23/2
The perimeter of the rectangle = 2 ( length + width)
= 2 (23/2 + 23/4 )
= 2 ( 69/4)
= 69/2
= 34 .1/2
2. Раскройте скобки.
a) (6 + a) * 7;
6) 5 (10-x)
Answer:
a) 7a + 42 b) -5x + 50Step-by-step explanation:
a) (6 + a) × 7 = ?
→ (6 + a) × 7
→ (6 × 7) + (a × 7)
→ 42 + 7a
→ 7a + 42
The answer is 7a + 42.
b) 5(10 - x) = ?
→ 5(10 - x)
→ (5 × 10) - (5 × x)
→ 50 - 5x
→ -5x + 50
The answer is -5x + 50.
13. Critique Reasoning In math class, you are checking how a friend balanced an equation. His work is at the right. What error did your friend make? Explain.
The error in balancing the equation is that the although the number terms on both sides of the equation are the same, the operation on the 1 on the left is an addition while the operation on the number 1 on the Right Hand Side of the equation is a subtraction
What is a balanced equation?A balanced equation is one in which the values or amounts on both sides of the equation are the same.
The unbalanced equation is presented as follows;
16 ÷ 8 = 16 ÷ 8 - 1
The form balanced equation in the question is; 16 ÷ 8 + 1 = 16 ÷ 8 - 1
The error is that in the balanced equation a 1 was added to the Left Side of the equation, while in the unbalanced equation, the difference between the left and right side of the equation is a subtraction of a 1 from the Right Hand Side of the equation.
The step to correctly balance the unbalanced equation involves the subtraction of a 1 from the Left Hand Side as follows;
16 ÷ 8 - 1 = 16 ÷ 8 - 1 (Balanced equation)The unbalanced equation 16 ÷ 8 = 16 ÷ 8 - 1 can be balanced by applying the addition (or subtraction) property of equality, which states that the when the same quantity is added (or subtracted) from two quantities that are initially equal, the resulting quantities that have a different amount following the addition (or subtraction) will remain equal.
The expression, 16 ÷ 8 and 16 ÷ 8 are the same.
Subtracting the same amount of 1 from both sides will result in two new expressions that are also equal in amount as follows;
16 ÷ 8 = 16 ÷ 8
16 ÷ 8 - 1 = 16 ÷ 8 - 1
The error is therefore in adding rather than subtracting a 1 from the Left Hand Side of the equation to balance the equations.
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- 9 + 5z - 12z = 15 help please
Answer: z=24/7
Step-by-step explanation:
Each element in the domain of a function corresponds to______
element in the range.
Each element in the domain of a function corresponds to exactly one
element in the range.
What is an element ?
A pure substance made entirely of one species of atoms, or a chemical element, is a species of atoms with a specific number of protons in their nuclei. Chemical elements, in contrast to chemical compounds, cannot be converted through any chemical reaction into simpler substances.
The items in a set are its elements. A property that all the objects share may serve to define a set. Consider the set E, which consists of all positive even integers. E is equivalent to 2, 4, 6, 8, or 10 dots. E={2,4,6,8,10…}.
A function is a relation in which each element of the domain corresponds to exactly one element of the range.
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a divided by 4 is equal to For a= 7
Answer:
no no lose me das las respuestas
Jason bought 10 of the 30 raffle tickets for a drawing. Assuming that he chooses the winning ticket each time, what is the probability that Jason will win all 3 of the prizes if once a raffle ticket wins a prize, the ticket is thrown away?
The needed probability that Jason will take home all three awards is 2.96%.
Jason purchased 10 of the 30 tickets for the raffle, which was a drawing.
If a raffle ticket wins a prize and is then discarded, we must calculate the likelihood that Jason will win all three of the prizes.
Let A stand for the scenario in which Jason wins all 3 prizes, and let S stand for the sample area for the experiment in which 3 tickets are drawn at random from 30 raffle tickets.
Since a lottery ticket is discarded after winning a prize,
[tex]n(S) = ^{30} P_{3} = \frac{30!}{(30-3)!} =\frac{30!}{27!} = 24360\\\\n(A) = ^{10} P_{3} = \frac{10!}{(10-3)!} =\frac{10!}{7!} = 720\\[/tex]
Therefore, the probability of event A is given by
P(A) = [tex]\frac{n(A)}{n(S)} = \frac{720}{24360} =0.029955 = 2.96[/tex]%
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How can a polynomial expression be factored completely?
Answer:
Step-by-step explanation:
To factor the GCF out of a polynomial, we do the following:
Find the GCF of all the terms in the polynomial. Express each term as a product of the GCF and another factor. Use the distributive property to factor out the GCF.
hope it helps!
AR 14 What value of x makes this equation true?
12x-15=6-3x. F 7./3. G. 3/7. H5/7. J. 7/5
Answer: 7/5
Step-by-step explanation:
[tex]12x-15=6-3x\\\\15x-15=6\\\\15x=21\\\\\boxed{x=21/15 \ or\ 7/5}[/tex]
You deposit $2100 in an account earning 3.6% interest compounded monthly. How much will you have in the account in 7 years?
The compound interest after 7 years is $2701.
What is compound interest?
The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.
When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:
A = P (1 + r/12)[tex].^{n/12}[/tex]
A = 2100(1+3.6/12)[tex].^{7/12}[/tex]
A=2701
Hence the compound interest after 7 years will be $2701.
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Amit sold 3 shells last week for $5 each
and 2 more shells this week for $5 each.
Show two ways to determine how much
money Amit made in the two weeks.
The two ways to determine how much money Amit made in the two weeks are,
$5(3 + 2) = $25 and $5(3) + $5(2) = $25.
What is shell?
A hard, protective outer layer is typically produced by an animal that lives in the sea and is referred to as a shell, seashell, or simply a shell. The animal's body includes the shell. Beachcombers regularly discover empty seashells washed up on beaches.
Given: Amit sold 3 shells last week for $5 each.
And 2 more shells this week for $5 each.
So, the equation which represent the total money is,
$5(3) + $5(2) = $15 + $10 = $25.
Also we can express this equation as,
$5(3 + 2) = $5(5) = $25
Therefore, the two ways to determine how much money Amit made in the two weeks are,
$5(3 + 2) = $25 and $5(3) + $5(2) = $25
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Option 2: Summarizing Data with a Measure of Center
A high school basketball player is creating a scout summary of their sophomore season. Here are the points scored during their 12 game season listed out. 29, 24, 32, 20, 0, 22, 28, 29 33, 34, 30, and 27. What measure of center would give the player the best picture of their points scored per game average? Explain how data can be skewed or how measures of center (mean, median, or mode) can be used in favor or against different scenarios in this essay. This is a essay please help!
Because it is more robust, or unaffected by the specific numerical values of those outliers, the median is typically a better indicator of the center when there are extreme values or outliers.
What is mean, median and mode?
The sum of the numbers is added, and the result is divided by the total number of numbers in the list to determine the arithmetic mean. An average usually refers to anything like this. In a list with values ranging from smallest to largest, the median is the middle value. On the list, the mode appears the most frequently.
As given, a high school basketball player is creating a scout summary of their sophomore season.
The points are, 29, 24, 32, 20, 0, 22, 28, 29 33, 34, 30, and 27.
Arrange these numbers in ascending order,
0, 20, 22, 24, 27, 28, 29, 29, 30, 32, 33, 34.
So,
Mean = (0 + 20 + 22 + 24 + 27 + 28 + 29 + 29 + 30 + 32 + 33 + 34) / 12
Mean = 308 / 12
Mean = 28
Median = 29
Mode = 29 (2 times repeating)
Because it is more robust, or unaffected by the specific numerical values of those outliers, the median is typically a better indicator of the center when there are extreme values or outliers.
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Devaughn is 13 years younger than Sydney. The sum of their ages is 43 . What is Sydney's age?
Answer:
30 years
Step-by-step explanation:
subtract devaughn's age from the sum of ages
Your cross country team ran at a pace of 6 mph for 90 minutes. How far did your team run?
Answer:
9 miles
Step-by-step explanation:
90 min = 1hr and 30 min
6(miles)*1(hr) = 6
6(miles)*0.5(hr) = 3
[ remember we multiply by 0.5 because half of 1 hour is 30 min. ]
Answer: 9 miles
Step-by-step explanation:
convert 90 minutes into hours: 90 mins/60 mins in an hour = 1.5 hours
find how far the team ran: 6mph * 1.5 hours = 9 miles
answer: the team ran 9 miles in 90 minutes
Jason can wax the family car in 30minutes, while his brother Kevin can wax the car in 120minutes. How long would it take Jason and Kevin to wax the car together?
____ minutes
This is a proportions math problem.
Using ratios and proportions, the time it takes for both of them to wash both cars is 24 minutes
ProportionsProportion is explained majorly based on ratio and fractions. A fraction, represented in the form of a/b, while ratio a:b, then a proportion states that two ratios are equal. The ratio is a way of comparing two quantities of the same kind by using division. The ratio formula for two numbers a and b is given by a:b or a/b. Multiply and dividing each term of a ratio by the same number (non-zero), doesn’t affect the ratio.
When two or more such ratios are equal, they are said to be in proportion.
The time it takes for Jason to wax the car in 1 minute = 1/30 minutes
The time it takes for Kevin to wax the car in 1 minute = 1/120
The time it takes for both of them to do it will be in 1 minute = 1/30 + 1/120 = 1/24.
The time it takes for both of them to wax the car = 24 minutes
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Scarlett and Kamila are throwing a pizza party. They invited 436 students from school. Each pizza was cut into 6 pieces. How many pizza should they order?
Answer:
73 pizzas
Step-by-step explanation:
Scarlett and Kamila are throwing a pizza party. They invited 436 students from school. Each pizza was cut into 6 pieces. How many pizza should they order?
pizzas are cut into 6 slices so:
436/6 = 72.66 pizzas
Because you cannot order a partial pizza round up to:
73 pizzas
One positive number is 5 more than twice another. If their product is 738, find the numbers.
Answer:
the numbers are 53 and 24.
Step-by-step explanation:
let x be the positive number (x>0) and y the other number
one positive number is 5 more than twice another number x = 5 + 2y
their product is 1272
x*y = 1272
plug x = 5 + 2y into the last equation (5 + 2y)y = 1272 by solving we find y= 24 x = 5 + 2*24
x = 53
the numbers are 53 and 24.
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A truck can be rented from Company A for $100 a day plus $0.30 per mile. Company B charges $50 a day plus $0.80 per mile to rent the same truck. Find the number of miles in a day at which the
rental costs for Company A and Company B are the same.
Atmiles, the rental costs are the same from either company.
Answer:
100 miles
Step-by-step explanation:
Let m be the number of miles.
[tex]100 + .30m = 50 + .80m[/tex]
[tex]100 = 50 + .50m[/tex]
[tex].50m = 50[/tex]
[tex]m = 100[/tex]
Answer:
100
Step-by-step explanation:
You can put into a graph such as desmos and see where the lines intersect. the x value of the intersection is the answer you want.
27. Given: BC || AD, Prove: AB = CD
In this congruent of the triangle its proven that AB = CD.
What is congruent of the triangle?
The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.
Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."
Given BC || AD
Both triangles are congruent.
We know the distance between parallel lines always remains the same. So As it is given that BC || AD, AB, and CD both are just distances og the parallel lines
So we can say that both are equal AB = CD
Hence the side AB = CD, in this given figure,
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*
Hamburger meat is priced at $5.98
for 1.3 pounds of meat. What is the
the price per pound?
Your answer
The price per pound of meat is $4.60.
How to calculate the price of meat?Given that hamburger meat is priced at $5.98 for 1.3 pounds of meat.
It should be noted that to find the cost per pound of meat, we will need to divide the value given.
This will be:
= Cost of meat / Pound of meat
= $5.98 / 1.3
= $4.6
The price is $4.60.
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Find the distance between the points (2,3) and (5,-2)
The distance between points (2,3) and (5, -2) is [tex]\sqrt{34}[/tex] units.
The given points are (2,3) and (5, -2)
The distance (D) between two points [tex](x_{1} ,y_{1} )[/tex] [tex](x_{2} ,y_{2} )[/tex] is
D = [tex]\sqrt{(x_{1} -x_{2} )^{2} +(y_{1} -y_{2} )^{2} }[/tex]
For evaluating the distance between the points (2,3) and (5, -2)
The distance (D) = [tex]\sqrt{(2 - 5)^{2} +(3 -(-2) )^{2} } = \sqrt{(-3)^{2} +5^{2} } = \sqrt{9+25} = \sqrt{34}[/tex]
Hence, the distance between points (2,3) and (5, -2) is [tex]\sqrt{34}[/tex] units.
Distance is a numerical or occasionally qualitative dimension of how a ways apart objects or points are.
In normal utilization, distance may additionally discuss with a bodily duration or an estimation primarily based on different standards.
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I need help on question 5
4. In triangle ΔABC, AB≅BC An altitude is drawn from B to AC and intersects always true?
1) ∠ABD≅∠CBD
2) ∠BDA≅∠BDC
3) AD≅BD
4) AD≅DC
5. In ΔEFG, IF is a median, GE=3 x+5 and I E=x+6. Find x.
Answer:
4. 1), 2), 4) are true
5. x = 7
Step-by-step explanation:
In question 4.
1), 2), and 4) are true
Triangles ABD and CBD are congruent by AAS. Then by CPCTC, 1) and 4) are true. 2) is true by definition of altitude and all right angles are congruent.
5.
Your drawing is good.
Since IF is a median, then IE = IG = (1/2)GE
IE = (1/2)GE
x + 6 = (1/2)(3x + 5)
2x + 12 = 3x + 5
-x = -7
x = 7
need some help please
The values are given below,
Left Hand Limit i.e. [tex]\lim_{x \to 1^-} f(x)[/tex] = 3 ,
Right Hand Limit i.e. [tex]\lim_{x \to 1^+} f(x)[/tex] = 1 ,
Function value at x = 1 [tex]f(1)[/tex] = 1 ,
Left Hand Derivative [tex]\lim_{x \to 1^-} f'(x)[/tex] = -6 and
Right Hand Derivative [tex]\lim_{x \to 1^+} f'(x)[/tex] = -6.
So, the function f(x) is neither continuous nor differentiable at x = 1.
Given, a piecewise function
3㏑(3 - 2x) + 3 for x < 1
f(x) =
-3x² + 4 for x ≥ 1
Now, for [tex]\lim_{x \to 1^-} f(x)[/tex] we will consider the function 3㏑(3 - 2x) + 3, as we have to find the Left Hand Limit of the function, at x = 1.
[tex]\lim_{x \to 1}[/tex] 3㏑(3 - 2x) + 3 = 3㏑(3 - 2(1)) + 3
= 3 ㏑(1) + 3
= 0 + 3
= 3
Now, for [tex]\lim_{x \to 1^+} f(x)[/tex] we will consider the function -3x² + 4, as we have to find the Right Hand Limit of the function, at x = 1.
[tex]\lim_{x \to 1}[/tex] -3x² + 4 = -3(1)² + 4
= -3 + 4
= 1
Now, for [tex]f(1)[/tex] we will consider the function -3x² + 4,
[tex]f(1)[/tex] = -3(1)² + 4
= -3 + 4
= 1
Now, for [tex]\lim_{x \to 1^-} f'(x)[/tex] we will consider the derivative of the function
3㏑(3 - 2x) + 3,
[tex]\lim_{x \to 1}[/tex] -6/(3 - 2x) = -6/(3 - 2(1))
= -6
Now, for [tex]\lim_{x \to 1^+} f'(x)[/tex] we will consider the derivative of the function
-3x² + 4,
[tex]\lim_{x \to 1}[/tex] -6x = -6(1)
= -6
So, the function f(x) is neither continuous nor differentiable at x = 1.
Hence, [tex]\lim_{x \to 1^-} f(x)[/tex] = 3 , [tex]\lim_{x \to 1^+} f(x)[/tex] = 1 , [tex]f(1)[/tex] = 1 , [tex]\lim_{x \to 1^-} f'(x)[/tex] = -6 and [tex]\lim_{x \to 1^+} f'(x)[/tex] = -6
The function is neither continuous nor differentiable at x = 1.
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What mixed number is represented on the number line shown here?
Answer:
The mixed number is 1 and 2/5. If it is split into 5 parts.
Step-by-step explanation:
No explanation sorry!
Answer:
Step-by-step explanation:
We already know how to represent whole numbers on the number line. Let us consider the image shown, here, the digits 0 and 1 are represented on the number line.
Representation of 0 and 1 on The Number Line
If we divide the number line into two equal parts, as shown in the figure below, what value does that mid-point hold? Half of what the graduation between 0 and 1 holds.
So, the point represents (1-0)/2 = ½
Fraction - Representation Of Fraction On The Number Line
Thus we saw, to represent a fraction on the number line, we need to divide the line segment between two whole numbers into n equal parts where n represents the denominator of the fraction. For example, if we have to represent the fraction 1/5 on the number line, hence, we need to divide the line segment between 0 and 1 into five equal parts, where the first point as shown in the figure represents the fraction 1/5, the second represents 2/5 and so on.
Fraction Representation
We must note that, 0/5 = 0 here and 5/5 = 1.
Here you have seen the representation of proper fraction on the number line. To represent improper fractions, you first convert them into mixed fractions. The same procedure, as shown above, is used with the whole number as the starting point.
In the general multiple regression equation, which of the following variables represents the Y-intercept? Select one: O a. b1 O b. X1 c. d. a
Answer:
it is a since using the pythagoras theorium the brainly bahahaha
Use synthetic division to find the quotient if polynomial P(x) = x³ - 7 x + 6 is divided by x - 2
A) x²+2 x+3
B) x²-2 x-3
C) x²-2 x+3
D) x²+2 x-3
The polynomial function p(x) = x³ - 7x + 6 divided by x - 2 = x² + 2x - 3
Synthetic Division of PolynomialsSynthetic division is a method used to perform the division operation on polynomials when the divisor is a linear factor. One of the advantages of using this method over the traditional long method is that the synthetic division allows one to calculate without writing variables while performing the polynomial division, which also makes it an easier method in comparison to the long division.
We can represent the division of two polynomials in the form:
p(x)/q(x) = Q(x) + R/(q(x))
where,
p(x) is the dividendq(x) is the linear divisorQ(x) is quotientR is remainderThe polynomial function p(x) = x³ - 7x + 6 is divided by x - 2
x³ - 7x + 6 ÷ x - 2 = (x - 1)(x + 3)
x² + 3x - x - 3 = x² + 2x - 3
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