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Brainliest Awarded
See attachment
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It is the bottom left.
Exhibit 4-3 x: 10, 12, 6, 8, 9, 11, 13, 13, 5, 0, 1 refer to exhibit 4-3. what is the mean?
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During a laboratory experiment, the average number of radioactive particles passing through a counter in 1 millisecond is 4. what is the probability that 6 particles enter the counter in a given millisecond?
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This question uses poisson distribution, not binominals
X~possions(λ = 4)
P (X=6) = 4-^λ λ^k/k! = e⁻⁴(4)⁶/6!
(0.018316) * (4096) / 720 = ≈0.10419678888≈0.1042 miliseconds
The probability of exactly 6 radioactive particles passing through a counter in 1 millisecond, with an average rate of 4, is approximately 0.1041 or 10.41%.
To find the probability of a specific number of events occurring in a Poisson distribution, use the formula:
P(X = k) = [tex](e^{(-\lambda)} \times \lambda^k) / k![/tex]
Where:
P(X = k) is the probability of observing k events.
e is the base of the natural logarithm, approximately equal to 2.71828.
λ (lambda) is the average rate of events occurring in a given time period.
k is the number of events you want to find the probability for.
k! is the factorial of k.
λ is the average number of radioactive particles passing through the counter in 1 millisecond, which is 4.
So, to find the probability of 6 particles entering the counter in a given millisecond:
P(X = 6) = (e⁻⁴) × 4⁶) / 6!
Let's calculate it step by step:
Calculate 6! (6 factorial):
6! = 6 x 5 x 4 x 3 x 2 x 1
= 720
Calculate e⁻⁴:
e⁻⁴ ≈ 0.01832 (rounded to five decimal places)
Calculate 4⁶:
4⁶ = 4 x 4 x 4 x 4 x 4 x 4
= 4,096
Now, plug these values into the formula:
P(X = 6) = (0.01832 × 4,096) / 720
P(X = 6) ≈ 0.1041
Therefore, the probability that exactly 6 radioactive particles enter the counter in a given millisecond is approximately 0.1041, or about 10.41%.
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Call a household prosperous if its income exceeds $100,000. call the household educated if the householder completed college. select an american household at random, and let a be the event that the selected household is prosperous and b the event that it is educated. according to a survey, p(a) = 0.132, p(b) = 0.227, and the probability that a household is both prosperous and educated is p(a and
b.= 0.082. what is the conditional probability that a household is prosperous, given that it is educated? (round your answer to four decimal places.) .3612 explain why your result shows that events a and b are not independent. if a and b were independent, then p(a|b) would equal p(a), and p(a and
b.would equal the product p(a)p(b). if a and b were independent, then p(a|b) would equal p(a), and p(a and
b.would equal the sum p(a) + p(b). if a and b were independent, then p(a|b) would equal p(a and b), and p(a and
b.would equal the product p(a)p(b). if a and b were independent, then p(a|b) would equal p(b), and p(a and
b.would equal the product p(a)p(b). if a and b were independent, then p(a|b) would equal p(b), and p(a and
b.would equal the sum p(a) + p(b). submit answer save progress
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.. = 0.082/0.227
.. ≈ 0.3612
If these events were independent, p(a|b) = p(a) and p(a&b) = p(a)*p(b). (Looks like your 1st selection.)
Tommy has a coupon for an additional 25% off the price of any sale item at a store. The store has put a Art Kit on sale for 15% off the original price of $40. What is the price of the Art Kit after BOTH discounts?
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Each runner in a relay race runs one leg, or 1/8 kilometer. How many runners will it take to cover the 3/4 kilometer? Show your work.
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can someone help me with factoring by grouping
x^3 + x^2 - 25x - 25
please show work
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Factor x3+x2−25x−25x3+x2−25x−25=(x+1)(x+5)(x−5)
adding fractions with denominators of 10 and 100
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Make a common denominator
100 is a common denominator.
When you multiply a number to the denominator, you MUST multiply the same number to the numerator
x/10 (10/10) = 10x/100
10x/100 + y/100 is your answer
* x and y being the numerators
hope this helps
Ms. Romero is buying a scrapbook and sheets of designer paper. She has $30 and needs at least $15.75 to buy the scrapbook. Each sheet of paper costs $0.29. 30−0.29x≥15.75 to find the number of sheets of paper, x, she can buy. How many sheets of paper can she buy?
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solving inequalities is similar to solving unknowns in an equation, the same set of steps are followed, except that x could be equal to the final answer or more or less than that value depending on the sign .
30−0.29x ≥ 15.75
-0.29x ≥ -14.25
when dividing by a negative number (-0.29) the inequality side should change its direction
In this case ≥ changes to ≤
x ≤ -14.25/-0.29
x ≤ 49.13
since they are asking for number of sheets of paper it should be the nearest whole number that is less than or equal to 49.13
since 49.13 is not a whole number we should round it off to the nearest whole number that is less than that.
x ≤ 49
she can buy maximum 49 sheets of paper and have enough money to buy the scrapbook.
49 x $ 0.29 + 15.75 = 14.21 + 15.75 = $29.96
Ms. Romero can buy up to 49 sheets of paper.
To determine the number of sheets of paper \( x \) that Ms. Romero can buy, we start with the inequality:
[tex]\[ 30 - 0.29x \geq 15.75 \][/tex]
First, isolate the term involving \( x \) by subtracting 15.75 from both sides:
[tex]\[ 30 - 15.75 \geq 0.29x \][/tex]
Simplify the left side:
[tex]\[ 14.25 \geq 0.29x \][/tex]
Next, solve for \( x \) by dividing both sides by 0.29:
[tex]\[ \frac{14.25}{0.29} \geq x \][/tex]
Calculate the value:
[tex]\[ x \leq \frac{14.25}{0.29} \]\[ x \leq 49.13793103448276 \][/tex]
Since \( x \) must be a whole number, we take the greatest integer less than or equal to 49.13793103448276, which is 49. Therefore, the maximum number of sheets of paper she can buy is:
[tex]\[ x = 49 \][/tex]
Thus, Ms. Romero can buy up to 49 sheets of paper.
A calculus student takes a 20-question, multiple choice test with 5 answer choices for each question. find the mean and standard deviation of the number of questions that he/she gets correct
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The number of questions is n=20 questions.
The mean of binomial distribution is
mean=n*p= 20*1/5=4
b] The standard deviation of a binomial distribution is given by:
σ=√(n*p*(1-p))
=√(20*0.2*0.8)
=1.79~1.8
Answer:
μ=4 ; σ=1.8
the city is planning to build a new park by enlarging the current park by a scale factor of 4. The current park has an area of 37,625 yd squared. what is the area of the new park
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When you enlarge a shape (or a park) by a factor, you are multiplying the length of its sides by that factor. In this case, we are multiplying its length and width by 4.
Let l be the old length and w be the new length. The old area would be given by A=lw.
Enlarging this by a factor of 4 would make the new length 4l and the new width 4w. The new area would be 4l(4w)=16lw. The new area is 16 times larger than the old area, so:
37,625(16)=602,000.
find the unknown in the equation. Blake ×1/6=1/6+1/6+1/6
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Find the value of x so that line m is parallel to line n.
A. 57
B. 51
C. 50
D. 49
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3x + 11 = 161
3x = 150
x = 50
Answer:
,C) x =50
Step-by-step explanation:
Given : Parallel line m and n in figure.
To find : Find the value of x
Solution : We have given
Two parallel line with traversal line
Alternate interior angle property : The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles are equal.
3x + 11 and angle 161 are alternate angle .
3x + 11 =161.
On subtracting both sides by 11
3x = 161 -11
3x = 150
On dividng both sides by 3
x =50
Therefore,C) x =50
the perimeter of a quarter circle is 14.28 KM. What is the quarter circle's radius?
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Circumference= perimeter
14.28km= 2(3.14)r
14.28= 6.2831853072r
divide both sides by 6.2831853072
2.27= r
ANSWER: The radius is 2.27km
Hope this helps! :)
The height of a triangle is increasing at a rate of 2 cm/min while the area of the triangle is increasing at a rate of 12 square cm/min. at what rate is the base of the triangle changing when the height is 4 centimeters and the area is 12 square centimeters?
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- Rate of height = 2 cm/min
- Rate of area = 12 cm^2/min
- Initial height = 4 cm
- Initial area = 12 cm^2
Calculation:
- Find Initial base using initial height and area:
Since A = 1/2 * b * h; Therefore, 12 = 1/2 * b * 4
Solve for b: 12 = 2b; Therefore, b = 6
- Find rate of base:
after 1 minute: height increased 2 cm, area increased 12 cm^2
which is: height = 6, area = 24 <-- (using these, find base)
24 = 1/2 * b * 6; 24 = 3b; b = 8 (after 1 min)
Therefore, since base changed from 6 to 8 the rate is 2 cm/min
Answer: 2 cm/min
When the height of a triangle is 4 cm and the area is 12 square cm, with the height increasing at 2 cm/min and the area increasing at 12 square cm/min, then the base of the triangle is changing at a rate of 5 cm/min.
Explanation:The subject of this question is Mathematics and is at the High School level. This question deals with the concept of related rates in calculus. First and foremost, remember the formula for the area of a triangle, which is A = 1/2bh, where A is the area, b is the base, and h is the height. Since we're given the rate of change of the height (dh/dt=2 cm/min) and the area (dA/dt=12 square cm/min), we can use this information in combination with the formula for the area of a triangle to derive an implicit function representing the rate of change of the base. By differentiating with respect to time t, we get dA/dt = 1/2b dh/dt + 1/2h db/dt. Plugging in the given values and solving for db/dt (the rate of change of the base length), we get db/dt = (2*dA/dt/h) - dh/dt. Then input the specific values at the given point, h = 4 cm and dA/dt = 12 square cm/min, dh/dt = 2 cm/min. The calculation results in db/dt = 5 cm/min. Therefore, the base of the triangle changes at a rate of 5 cm/min when the height is 4 cm and the area is 12 square cm.
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Use the information below to find EF such that triangle ABC is congruent to triangle DEF
AB=36 BC=24 DE=48 m<B=110 m<E=110 EF=?
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notice, the green numbers are the given ones, and the red ones are the implicit ones.
since we know both triangles are congruent, then all their sides as well as angles are congruent as well.
so if triangle ABC has sides of 24 and 36, so does triangle DEF, and if triangle DEF has a side of 48, so does triangle ABC.
Jake needs to put gas in the delivery van. Regular gasoline is $3.20 per gallon. He only had a $ 20 bill on him. How many gallons can he buy
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The answer is "6 gallons".
Reason:
Just divide 20 by 3.20.....
20/3.20=6.25
Round to the nearest whole number will be 6.
If you need anymore help feel free to ask me!
Hope this helps!
~Nonportrit
Which ordered pair represents the x-intercept for the linear equation, 3y + 4x = 8?
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To find the x-intercept means to find the place where the line intersects the x-axis. If the line is intersecting the x-axis, then the point where it intersects the x-axis must be a place where y = 0. If y didn't equal 0, then that point wouldn't be on the x-axis.
So, to find the x-intercept, we set y in the given equation to 0, like this:
[tex]3y + 4x = 8 [/tex]
[tex]3(0) + 4x = 8[/tex]
[tex]4x = 8[/tex]
[tex]x = \frac{8}{4}[/tex]
[tex]x=2[/tex]
So, [tex]x=2[/tex]. We assumed that [tex]y=0[/tex] to find the x-intercept at the beginning. Then, our ordered pair in the usual order [tex](x,y)[/tex] is [tex](0,2)[/tex]. You can see this is correct by looking at the attached graph.
Final answer:
To find the x-intercept for the equation 3y + 4x = 8, set y to 0 and solve for x, which results in x = 2. Thus, the ordered pair for the x-intercept is (2, 0).
Explanation:
The question is asking to determine the x-intercept of the linear equation 3y + 4x = 8. The x-intercept occurs where the graph of the equation crosses the x-axis, which is when y is equal to 0. To find the x-intercept, you set y to 0 and solve for x:
3(0) + 4x = 8
4x = 8
x = 8/4
x = 2
Therefore, the ordered pair that represents the x-intercept is (2, 0). This is the point on the graph where the line crosses the x-axis.
Which is a true statement about the diagram? m∠5 + m∠6 = m∠1 m∠3 + m∠4 + m∠5 = 180° m∠1 + m∠2 = 180° m∠2 + m∠3 = m∠5
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m<1 +m<2 = 180° is the answer
Answer:
Third option is the right choice.
Step by step explanation:
We have been given an diagram and we are asked to choose the true statement about the diagram.
Let us see our all choices one by one.
1. [tex]m\angle5+m\angle6=m\angle1[/tex]
We can see that [tex]\angle5[/tex] and [tex]\angle6[/tex] are supplementary and there measure should be equal to 180 degrees. [tex]\angle1[/tex] is exterior angle of our triangle and its measure must be equal to sum of measures of [tex]\angle5[/tex] and [tex]\angle3[/tex].
Therefore, 1st option is incorrect.
2. [tex]m\angle3+m\angle4+m\angle5=180^{o}[/tex]
We can see that [tex]\angle3[/tex] and [tex]\angle4[/tex] are supplementary and they must be equal to 180 degrees. Therefore, 2nd option is also incorrect.
3. [tex]m\angle1+m\angle2=180^{o}[/tex]
We can see from our diagram that [tex]\angle1[/tex] and [tex]\angle2[/tex] are supplementary. Therefore, 3rd option is the correct choice.
4. [tex]m\angle2+m\angle3=m\angle5[/tex]
We can see that [tex]\angle2[/tex], [tex]\angle3[/tex] and [tex]\angle5[/tex] are interior angles of our triangle and their measure should be equal to 180 degrees. By exterior angle theorem sum of measures of [tex]\angle2[/tex] and [tex]\angle3[/tex] will be equal to measure of [tex]\angle6[/tex] instead of [tex]\angle5[/tex].
Therefore, our 4th option is also incorrect.
carla travels on a high speed train for 30 minutes. If she travels 160 km, how many kilometers will she travel in one hour
plz help
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160 x 2 = 320 km in 1 hour
We do 30x2= 1 hour. ; And if she were to travel only 160 in 30 minutes, then we would also multiply this by 2 also.
160x2=320.
SHe traveled 320 kilometers in 1 hour.
The bookstore marked some notepads down from ???$ 3.00 but still kept the price over ???$ 2.00. It sold all of them. The total amount of money from the sale of the pads was ???$ 27.95. How many notepads were??? sold? What was the price of each??? notepad?
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I tried numbers greater than 10 using a trial and error strategy until I got to 13 notebooks sold and found that it $27.95 was divisible by 13 to get an answer between $2 and $3 ($2.15 exactly).
Hi! can someone please answer this question
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360 m - 160 m = 200 m
The width of the garden is 200 meters.
_____
Of course, you know that 1 km = 1000 m, so 0.72 km = 720 m.
In order to find the answer to the question, we can begin by converting the measurements into one common unit. In this case, we can convert 0.72km to 720 meters, which will make the final calculation a bit easier.
The formula to find the perimeter of the garden is L2+W2.
The length is 160 meters, so we can multiply this by two to find a portion of the rectangle.
160 x 2 = 320
Now, we can subtract 320 from the total number: 720
720 - 320 = 400
To find the width, we simply now need to divide 400 by 2.
[tex] \frac{400}{2} [/tex] = 200
The width of the garden is 200 meters.
I hope this helps you! Have a wonderful day!
-MMMski
Nolan bought 26 yards of rope, the rope costs 2 dollars per foot, how much did Nolan play for the rope?
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Multiply x^2-8x+15/3x * 8x/x-3
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1. First, you should apply the dstributive property:
=(x²-8x+15/3x)(8x/x-3)
=(8x³-64x²+120x)/3x(x-3)
2. As you can see, the common factor in the numerator is: "8x". So, you have:
=8x(x²-8x+15)/3x(x-3)
3. Then, when you simplify, you obtain:
=8(x²-8x+15)/3(x-3)
Therefore, the solution is: 8(x²-8x+15)/3(x-3)
4x + 3y =4 2x - y =7 in substitution
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What is the value of X to the nearest 10th? The figure is not drawn to scale.
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11.2 * 5.4 = 60.48
60.48/6.3 = 9.6
Answer is C. x = 9.6
Answer: C: 9.26
Step-by-step explanation:
Find the general solution of the differential equation y'' +4y = 3sin2t
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Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.
A; an = 2 • 3n - 1
B; an = 2 • (-3)n - 1
C; an = 2 • 3n
D; an = 2 • (-3)n + 1
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r^3 = 162/-6 = -27
so r = -3
a1 * r-3 = -6 so first term = 2
an = 2. (-3)^(n-1) Answer
Its B
The answer is B, I have just confirmed it.
Rhono has a part-time job at the local supermarket working 3 hours after school each night and 5 hours on saturdays. His gross hourly pay is $8.75. Estimate and then calculate his next wages for the month, after 20% tax is deducted. Each month his expenses are: Entertainment $35.00, health and beauty $21.00, transport $18.00, clothing $24.00, hire purhases payments $15.75. Calculate the amount Rhono has left over at the end of each month, and how much he would have saved at the end of 12 months.
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.. 4*20*8.75*(1 -0.20) = $560
The listed expenses add to
.. 35 +21 +18 +24 +15.75 = 113.75
The amount left over at the end of each 4-week period is
.. $560 -113.75 = $446.25
If he saves the remainder, after 12 months, he will have saved
.. 12*$446.25 = $5,355.00
___
* There are 13 periods of 4 weeks in a year. If Rhono takes no vacation, his savings balance may be $560 more than the above amount, that is, $5,915.00.
Rhono earns a net monthly pay of $560.00 after taxes, with monthly expenses totaling $113.75. This leaves him with $446.25 per month, resulting in a total savings of $5,355.00 at the end of 12 months.
Let's calculate Rhono's monthly wages first.Rhono works:
- 3 hours each night after school
- 5 hours on Saturdays
His gross hourly pay is $8.75.
To calculate his monthly wages, we need to find his total hours worked per month.In a week, he works 3 hours × 5 days from Monday to Friday and 5 hours on Saturday,
which totals 15 hours + 5 hours
= 20 hours per week.
In a month (considering approximately 4 weeks per month), he works 20 hours × 4 weeks
= 80 hours per month.
Now, let's calculate his gross monthly income before tax deductions:Gross monthly income = hourly wage × total hours worked per month
Gross monthly income = 8.75 × 80
Gross monthly income = $700
Now, let's calculate the amount of tax that will be deducted.Rhono's gross monthly income is $700, and 20% of this will be deducted.
Tax deduction = 0.20 × 700
Tax deduction = 140
Now, let's calculate his total monthly expenses:Total monthly expenses = 35.00 + 21.00 + 18.00 + 24.00 + 15.75
Total monthly expenses = $113.75
Now, let's calculate the amount Rhono has left over after tax and expenses:Net monthly income = Gross monthly income - Tax deduction - Total monthly expenses
Net monthly income = 700 - 140 - 113.75
Net monthly income = $446.25
This is the amount Rhono has left over at the end of each month.
To calculate how much he would have saved at the end of 12 months, we multiply this amount by 12:Total savings after 12 months = 446.25 × 12
Total savings after 12 months = $5,355
So, Rhono would have saved $5,355 at the end of 12 months.
Joan and Ernie are earning money for summer camp. Joan receives a $7 weekly allowance plus $6 for each hour she helps her father paint. Ernie writes the equation y = 5x + 7 to represent the relationship between the number of hours he helps his father with yard work and his weekly allowance. Which statement best describes the graphs of their earnings for one week?
Answers
The Correct statement are:
Joan has more money in 10 weeks
Their y-intercepts are the same
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Joan:
Joan receives a $7 weekly allowance plus $6 for each hour
so, the Equation for Joan Earning, y= 6x+ 7
Ernie Earning y = 5x + 7
So, the slope for Joan is 7 and Ernie's slope is 7.
Then, the Correct statement is:
Joan has more money in 10 weeks
Their y-intercepts are the same
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