The probability of Celia being first and Felicity last in a line is found by multiplying the probabilities of each independent event. For a line of n people, it would be [tex](1/n) \(*\) (1/(n-1))[/tex]. For 10 people, this probability would be 1/90.
The scenario implies that there's a line of people, and we are interested in the probability of Celia being the first and Felicity being the last in this line. This is a combinatorial probability problem. To calculate the probability, we must first acknowledge that each person in the line is equally likely to be in any position. If we assume there are n people in total, the probability that Celia is first is 1/n, and once Celia is in place, assuming Felicity is not first, the probability that Felicity is last is 1/(n-1). Since these two events are independent (Celia being first does not affect the probability of Felicity being last), we multiply these probabilities together to find the combined probability.
Using the formula for independent events:
P(Celia first and Felicity last) = P(Celia first) * P(Felicity last given that Celia is first)P(Celia first and Felicity last) = (1/n) * (1/(n-1))If there are 10 people in the line, for example, the probability would be (1/10) * (1/9) = 1/90.
a(3x-8)=b-18x
what is a value?
what is b value?
Amy volunteers at an animal shelter. She worked 10 hours in March, 12 hours in April, 14 hours in May, and 16 hours in June. If the pattern continues, how many hours will she work in December?
By continuing the pattern of Amy increasing her volunteer hours by 2 each month, she will work for 30 hours in December.
Explanation:To find out how many hours Amy will work in December, we must first identify the number of terms between June and December.
Counting inclusively, we see that there are seven months between June and December (June, July, August, September, October, November, December), which means we should look for the 7th term after June to find the number of hours Amy will work in December.
Since we have established an increase of 2 hours each month, we can calculate this by adding 7 terms of an arithmetic progression to Amy's last known volunteering hours.
To do this, we use the explicit formula for an arithmetic sequence:
Tn = a + (n - 1) * d,
where Tn is the term we wish to find, a is the first term in the sequence, n is the position of the term in the sequence, and d is the common difference between terms. Amy's last known volunteering hours in June (the 4th term in the sequence) were 16, with a common difference of 2.
Adding 7 intervals of 2 hours each gives us 14 additional hours by December.
Therefore, we add this to the 16 hours she worked in June: 16 + 14 = 30 hours.
Amy is expected to volunteer for 30 hours in December.
Determine whether the two figures are similar. If so, give the similarity ratio of the smaller figure to the larger figure. The figures are not drawn to scale
A. yes; 1:1:2
B. yes; 1:1:4
C. yes; 1:2:4
D. no
In the diagram, the base of the tower is at point H, and the top of the tower is at point F. If the distance from the base of the tower to point G is 7x feet and the distance from the base of the tower to point E is 6x + 12 feet, find GE, the distance across the lake.
A. 84 feet
B.
94 feet
C. 168 feet
D. 186 feet
Please help confused
19. # Q Find the missing side length
determine the domain of the function h(x)= 9x/x(x^2-36)
Final answer:
The domain of the function h(x)=9x/x(x²-36) is all real numbers except 0, 6, and -6, because the function is undefined at these points.
In conclusion, the domain of h(x) is x ∈ ℝ, x ≠ 0, x ≠ 6, x ≠ -6.
Explanation:
The question asks to determine the domain of the function h(x) = 9x / x(x² - 36).
The domain of a function consists of all the real numbers x for which the function is defined. In this case, the function will be undefined when the denominator is zero because division by zero is not defined in mathematics.
To find these values, we set the denominator equal to zero and solve the resulting equation:
x(x² - 36) = 0.This can be factored further as x(x - 6)(x + 6) = 0, which gives us the zero points of x = 0, x = 6, and x = -6.
Therefore, the domain of h(x) is all real numbers except 0, 6, and -6.
In conclusion, the domain of h(x) is x ∈ ℝ, x ≠ 0, x ≠ 6, x ≠ -6.
Blue cassests hold 45 min. Of music
Green cassets hold 55 min. Of music
If Niko has 16 cassets containing 830 min. Of music
How many are blue? And how many are green?
When the sum of 5 and three times a positive number is subtracted from the square of the number, 0 results. Find the number.
To solve for the positive number when the sum of 5 and three times the number is subtracted from the square of the number to yield zero, set up and solve the quadratic equation x^2 - 3x - 5 = 0 using the quadratic formula.
Explanation:The student has asked for help in finding a positive number when the sum of 5 and three times the number is subtracted from the square of the number, and the result is 0. This involves setting up a quadratic equation and solving for the number.
Let's denote this positive number as 'x'. According to the problem statement, the equation can be written as:
x2 - (5 + 3x) = 0.
We can then expand and simplify this equation:
x2 - 5 - 3x = 0
And, rearrange it into standard quadratic form:
x2 - 3x - 5 = 0
Next, we can either factorize this equation, if possible, or use the quadratic formula to find the value of 'x' that satisfies the equation. Since this equation does not factor neatly, we use the quadratic formula:
x = ∛2 - 4ac) / 2a
In this case, a = 1, b = -3, and c = -5. Plugging these into the quadratic formula, we find the two possible solutions for x. Only the positive solution is relevant since the problem states that the number is positive.
Factor 4x^2-20x-144
Which expression has a value closest to 1? (Use 3.14 as the value of .)
Answer:
C)square 37 - square root 26
Step-by-step explanation:
Monica is shopping for candy for her wedding and needs lollipops and gummy bears for a display she is making for the reception. Lollipops are $1 per pound and gummy bears are $0.75 per pound. She knows she wants to spend exactly $15 on candy. If she spent $9 on lollipops, which of the following is the number of pounds of gummy bears she purchased?
6 8 9 12
We have been given that she wants to spend exactly $15 on candy.
Also, she spent $9 on lollipops. It means she spent [tex]15-9= $6[/tex] on gummy bears.
Also, we have been given that the cost of gummy bears are $0.75 per pound.
Thus, in 1$ she can purchase [tex]\frac{0.75}{6}[/tex] pounds of gummy bears.
Hence, in $6, she can purchase
[tex]\frac{1}{0.75} \times 6\\ \\ =8[/tex]
Therefore, she purchased 8 pounds of gummy bears.
simplify the expression
find any points of discontinuity for each rational function. Sketch a graph. Describe any verticals or horizontal asympyoyes and any holes
(X^2-4)/(X+2)(X^2-49)
To find the points of discontinuity and sketch the graph of the rational function (x^2-4)/(x+2)(x^2-49), we need to determine the values of x that make the denominator equal to zero. We find that x = -2, x = 7, and x = -7 are the points of discontinuity. We can then sketch the graph by plotting the vertical asymptotes at x = -2, x = 7, and x = -7, and determining the behavior of the function on each side of those points.
Explanation:To find the points of discontinuity for the rational function (x^2-4)/(x+2)(x^2-49), we need to determine where the denominator is equal to zero. The denominator has two factors, (x+2) and (x^2-49). Setting each factor equal to zero, we find that x = -2, x = 7, and x = -7. These are the points where the function has vertical asymptotes or holes.
To sketch the graph, we can start by plotting the vertical asymptotes at x = -2, x = 7, and x = -7. Next, we can examine the sign of the function on each side of the vertical asymptotes to determine the behavior of the graph. Finally, we can plot any holes in the graph at the corresponding x-values.
Additionally, we should determine if there are any horizontal asymptotes. For rational functions, horizontal asymptotes occur when the degree of the numerator is less than or equal to the degree of the denominator. In this case, the degree of the numerator is 2 and the degree of the denominator is 3, so there is no horizontal asymptote.
Graph 12x-9y=36 please???
Answer:
The graph for 12x-9y=36 is given below
Step-by-step explanation:
The graph for 12x-9y=36 is given below.
[tex]12x-9y=36\\\frac{12x}{36}+\frac{9y}{-36}=1\\\frac{x}{3}+\frac{y}{-4}=1[/tex]
So x intercept is 3 and y intercept is -4.
The required graph is shown below which represents the equation 12x - 9y = 36.
To graph the equation 12x-9y=36, we can rearrange it to slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.
First, solve for y by subtracting 12x from both sides and then dividing by -9. This gives us y=-4/3x+4.
Now we can see that the slope is -4/3 and the y-intercept is 4.
To graph this line, we can start at the y-intercept of (0,4) and then use the slope to find another point.
Since the slope is negative, we can move down 4 units (which is the denominator of the slope) and then move to the right 3 units (which is the numerator of the slope) to get another point at (3,0).
We can then draw a straight line through these two points to graph the equation.
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Express this equation in word form:
5 + ( 2 x 6 )
Using the law of cosines, a=2.2
Use your answer above to find m<B, to the nearest degree. m<B=__
Answer:
81
Step-by-step explanation:
Kendrick travel 2/3 mile to his friend’s house.He cycles 3/4 of his distance and walks the rest of the way.What fraction of a mile did he cycle?
ABC has coordinates of A(–5, –7), B(6, –3), and C(2, 7). Find the coordinates of its image after a dilation centered at the origin with a scale factor of 2.
The coordinates of the image after dilation with a scale factor of 2 are A'(-10, -14), B'(12, -6), C'(4, 14).
Explanation:Your question involves geometry and specifically, dilation transformations. A dilation is a transformation that moves each point along the ray from the center of dilation to the point. The number given as the scale factor tells you how much to move. In this case, we are asked to dilate the given points with a scale factor of 2 centered at the origin (0,0).
So, each coordinate of the original triangle should be multiplied by 2. Let's find each coordinate after dilation:
A: -5*2, -7*2 = A'(-10, -14)B: 6*2, -3*2 = B'(12, -6)C: 2*2, 7*2 = C'(4, 14)So, the coordinates of the image after a dilation with a scale factor of 2 are A'(-10, -14), B'(12, -6), and C'(4, 14).
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15 points!!! GEOMETRY help please!!
Questions attached!
A person whose eye level is 1.5 meters above the ground is standing 75 meters from the base of the jin mao building in shanghai, china. the person estimates the angle of elevation to the top of the building is about 80º. what is the approximate height of the building
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The height of the building from the ground is 426.85 meters.
What is Tangent (Tanθ)?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
As it is given that the angle of elevation from the person's view is 80°, while the distance between the person and the base of the building is 75 meters, therefore, using the trigonometric function the height of the building top from the person eye level is,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}\\\\\\Tan(80^o) = \dfrac{\text{Height of the building}}{75\ meters}\\\\\\\text{Height of the building} = 75 \times tan(80^o) = 425.35\ meters[/tex]
Now, we know the height of the building top from a person's eye level, and we also know the person's eye level as well, therefore, the height of the building can be written as,
[tex]\text{Height of the building} = 425.35 + 1.5 = 426.85\rm\ meters[/tex]
Hence, the height of the building from the ground is 426.85 meters.
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which values of x are solutions of the equation x^3+ x^2-2x=0
ABCD and DECF are both squares. If AC = 28 millimeters, what is the perimeter of DECF?
Adam charges 20$ to mow his neighbor's lawn every 2 weeks for the 18 weeks of grass growing season. he wants to but a new
Since Adam's expenses exceed his earnings, he will have a negative net earnings. Therefore, Adam will not earn any money this season. In fact, he will have a net loss of $7.50.
To calculate how much Adam will earn this season, subtract his expenses from his total earnings.
Earnings per mowing session: $20
Number of mowing sessions in the grass-growing season: 18 weeks / 2 weeks = 9 sessions
Total earnings: $20 per session * 9 sessions = $180
Expenses:
Cost of the lawn mower: $165
Cost of gasoline per session: $2.50 per session * 9 sessions = $22.50
Total expenses: $165 + $22.50 = $187.50
To find Adam's net earnings, subtract his expenses from his total earnings:
Net earnings = Total earnings - Total expenses
Net earnings = $180 - $187.50
Net earnings = -$7.50
Since Adam's expenses exceed his earnings, he will have a negative net earnings. Therefore, Adam will not earn any money this season. In fact, he will have a net loss of $7.50.
Adam charges $20 to mow his neighbors lawn every 2 weeks for the 18 weeks of grass-growing season. He wants to buy a nice lawn mower for $165 and gasoline costs $2.50 every 2 weeks. How much will Adam earn this season?
Use the X method to find the solutions of 6x2 + 2x – 20 = 0. x = x =
The solutions of the given quadratic equations is 5/3 and -2
Given the quadratic function expressed as:
6x^2 + 2x – 20 = 0Factorizing the function we will have:
6x^2 + 2x – 20 = 0
3x^2 + x - 10 = 0
3x^2 +6x - 5x - 10 = 0
3x(x+2) 5(x+2) = 0
Group the function;
(3x-5)(x+2) = 0
Find the factors
3x- 5 = 0 and x + 2 = 0
x = 5/3 and -2
The solutions of the given quadratic equations is 5/3 and -2
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solve by substitution 3x+2y=-5, 2x-5y=-16
The solution to the system of equations is [tex]\(x = -3\)[/tex] and [tex]\(y = 2\).[/tex]
let's solve the system of equations using the substitution method.
Given:
1. [tex]\(3x + 2y = -5\)[/tex]
2.[tex]\(2x - 5y = -16\)[/tex]
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve equation 1 for [tex]\(x\):[/tex]
[tex]\[3x = -2y - 5\][/tex]
[tex]\[x = \frac{-2y - 5}{3}\][/tex]
Step 2: Substitute the expression for [tex]\(x\)[/tex]from step 1 into the other equation.
Substitute [tex]\(x = \frac{-2y - 5}{3}\)[/tex] into equation 2:
[tex]\[2\left(\frac{-2y - 5}{3}\right) - 5y = -16\][/tex]
Step 3: Solve for [tex]\(y\).[/tex]
[tex]\[ \frac{-4y - 10}{3} - 5y = -16 \][/tex]
[tex]\[ -4y - 10 - 15y = -48 \][/tex]
[tex]\[ -19y - 10 = -48 \][/tex]
[tex]\[ -19y = -38 \][/tex]
[tex]\[ y = 2 \][/tex]
Step 4: Substitute the value of [tex]\(y\)[/tex] into one of the original equations to solve for [tex]\(x\).[/tex]
Let's use equation 1:
[tex]\[3x + 2(2) = -5\][/tex]
[tex]\[3x + 4 = -5\][/tex]
[tex]\[3x = -9\][/tex]
[tex]\[x = -3\][/tex]
So, the solution to the system of equations is [tex]\(x = -3\)[/tex] and [tex]\(y = 2\).[/tex]
Complete question:
solve by substitution 3x+2y=-5, 2x-5y=-16
Please answer this question I need it fast:
Together, Mary Sue and Betty have 603 necklaces. Mary Sue has 115 more necklaces than Betty. How many necklaces does Betty have?
Answer:
mary sue: 359, betty; 244
Step-by-step explanation:
⇔↓⊕㏒㏑∞
1.
The balance on Brent Tyson’s Discover card on December 1 is $205.84.
In December, he charges an additional $98.42 of purchases, has returns of $18.63, and makes a payment of $25.
If the finance charges are calculated at 1.5% per month on the unpaid balance, find the new balance on January 1.
To find the new balance on January 1, we need to calculate the total balance after considering purchases, returns, payments, and finance charges.
Calculate the total charges:
Total charges = Previous balance + New purchases − Returns
Total charges = $205.84 + $98.42 − $18.63
Total charges = $285.63
After the payment, ascertain the extra amount due:
Unpaid balance = Total charges − Payment
Unpaid balance = $285.63 − $25
Unpaid balance = $260.63
Calculate the finance charges:
Finance charges=Unpaid balance×Monthly interest rate
Monthly interest rate = 1.5% = 0.015
Finance charges = $260.63 × 0.015
Finance charges ≈ $3.91
Calculate the new balance:
New balance = Unpaid balance + Finance charges
New balance = $260.63 + $3.91
New balance = $264.54
So, the new balance on January 1 is approximately $264.54.
To calculate Brent Tyson's new balance on January 1, we first determine the total charges by adding new purchases and subtracting returns from the previous balance.
Then, we deduct his payment to find the unpaid balance.
Next, we calculate finance charges at a rate of 1.5% per month on the unpaid balance.
Finally, we add the finance charges to the unpaid balance to get the new balance.
After these steps, Brent Tyson's new balance on January 1 is $264.54.
This process ensures we account for all transactions and interest charges to accurately determine the updated balance on his Discover card.
Complete Question:
The balance on Brent Tyson’s Discover card on December 1 is $205.84.
In December, he charges an additional $98.42 of purchases, has returns of $18.63, and makes a payment of $25.
If the finance charges are calculated at 1.5% per month on the unpaid balance, find the new balance on January 1.
Alice collected donations of $50, $125, $10, $210, $50, $24, and $175 for charity. What is the mean of her collections?
Answer:92
Step-by-step explanation:
92
Use a change of variables to find the indefinite integral xe^(x^2) dx