Answer:
(x+5)^2+(y+7)^2=74
Step-by-step explanation:
So we are given this (x+5)^2+(y+7)^2=r^2
We need to find r so just plug in your point (0,0) for (x,y) and solve for r :)
(0+5)^2+(0+7)^2=r^2
25+49=r^2
74=r^2
So the answer is (x+5)^2+(y+7)^2=74
Answer:
(x+5)^2+(y+7)^2=74
Step-by-step explanation:
What's the square root of 25, 100, 36, 84, and 4.
Step-by-step explanation:
[tex] \sqrt{25} = \pm \: 5 \\ \\ \sqrt{100} = \pm \: 10 \\ \\ \sqrt{36} = \pm \: 6 \\ \\ \sqrt{84} = \pm \: 9.165\\ \\ \sqrt{4} = \pm \: 2 \\ \\ [/tex]
A survey showed that 84% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 17 adults are randomly selected, find the probability that at least 16 of them need correction for their eyesight. Is 16 a significantly high number of adults requiring eyesight correction?
Final answer:
The probability of at least 16 adults requiring eyesight correction out of 17 is found by summing up individual probabilities of exactly 16 and exactly 17 adults in need, calculated using the binomial probability formula. A comparison of this probability to a typical significance threshold will determine if 16 is a significantly high number.
Explanation:
The probability that at least 16 out of 17 randomly selected adults need correction for their eyesight, given that 84% of adults need such correction, is calculated using the binomial probability formula. The binomial probability of exactly k successes in n trials, where p is the probability of success on a single trial, is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Here, we calculate the probability for exactly 16 adults and exactly 17 adults needing vision correction and then sum these to get at least 16:
Calculate P(X = 16), where n = 17, k = 16, and p = 0.84.
Calculate P(X = 17), where n = 17, k = 17, and p = 0.84.
Sum P(X = 16) and P(X = 17) for the total probability.
To answer if 16 is a significantly high number requiring correction, it is important to compare the probability with a threshold of significance, such as 0.05 commonly used in statistics. If the probability is less than this threshold, then 16 can be considered a significantly high number.
The mean salary of 5 employees is $33700. The median is $34600. The mode is $35600. If the median paid employee gets a $3500 raise, then ...
Hint: It will help to write down what salaries you know of the five and think about how you normally calculate mean,median, and mode.
a) What is the new mean? (3 point)
New Mean = $
b) What is the new median?
New Median = $
c) What is the new mode?
New Mode = $
Step-by-step explanation:
Given:
Mean = 33700
Median = 34600
Mode = 35600
The mean is the average, the median is the middle number, and the mode is the most common number.
a)
First, we need to find the new mean (average) if one of the employees gets a 3500 raise. The average is the total salary divided by number of employees:
(5 × 33700 + 3500) / 5 = 34400
b)
The mode is the most common number in a set. Since there are only five employees, and the mode is different than the median, then the two highest earners must have the same salary. The salaries from smallest to largest is therefore:
?, ?, 34600, 35600, 35600
When the median gets the 3500 raise, the set becomes:
?, ?, 35600, 35600, 38100
So the new median is 35600.
c)
The most common number is still 35600. So the mode hasn't changed: 35600.
A hypothesis is: a The average squared deviations about the mean of a distribution of values b) An empirically testable statement that is an unproven supposition developed in order to explain phenomena A statement that asserts the status quo; that is, any change from what has been c) thought to be true is due to random sampling order dA statement that is the opposite of the null hypothesis e) The error made by rejecting the null hypothesis when it is true
Answer:
b) An empirically testable statement that is an unproven supposition developed in order to explain phenomena.
Step-by-step explanation:
b) An empirically testable statement that is an unproven supposition developed in order to explain phenomena.
A hypothesis is an unproven supposition.This may be derived from previous research or theory and is developed prior to data collection.
Note:
Variance is the average squared deviations about the mean of a distribution of values.
PLEASE ANSWER
factor the polynomial using the pattern
x^2+9x+8
x^2(a+b)x+ab=(x+a)(x+b)
Answer:
x² + 9x + 8 = (x + 1)(x + 8)
x² + 9x + 8 = (x + 8)(x + 1)
Step-by-step explanation:
* Lets explain how to factorize the polynomial using the pattern
- The form of the quadratic polynomial is x² + px + q, where p is the
coefficient of x and q is the numerical term
∵ x² + (a + b)x + (ab) = (x + a)(x + b)
- From the formula above the coefficient of x is the sum of the two
factors a and b
∴ p = a + b and q = ab
- That means p is the sum of two numbers and q is the product of
the same numbers
* Lets solve the problem
∵ x² + 9x + 8 is a quadratic polynomial
∵ x² + px + q is the form of quadratic polynomial
∴ p = 9 and q = 8
∵ p = a + b and q = ab
∴ a + b = 9 ⇒ (1)
∴ ab = 8 ⇒ (2)
- We must to find two numbers their product is 8 and their sum is 9
∵ The possibility of 8 as a product of two numbers is:
2 × 4 OR 1 × 8
∵ The sum of 1 + 8 = 9
∴ The value of a and b are 1 and 8
- It does't matter which of them = 1 or which of them = 8
∴ x² + (a + b)x + ab = x² + (1 + 8)x + (1)(9)
∵ x² + (a + b)x + (ab) = (x + a)(x + b)
∴ x² + (1 + 8)x + (1)(9) = (x + 1)(x + 8)
∴ x² + 9x + 8 = (x + 1)(x + 8)
- OR
∴ x² + 9x + 8 = (x + 8)(x + 1)
Tangent lines-someone please help explain
The angle between radius and tangent to circle is 90 degrees.
The quadrilateral formed by the two tangents and the two rays has two angles of 90 degrees, an angle of 40 degrees and an unknown angle.
The sum of the angles of a quadrilateral is 360 degrees.
⇒ x = 360° - 90 - 90 - 40 = 140°
x = 140°
The ratio of the areas of two similar polygons is 49:36. If the perimeter of the first polygon is 15 cm, what is the perimeter of the second polygon? Round to the nearest hundredth. 11.76 cm 11.02 cm 13.25 cm 12.85 cm
Answer:
12.85 cm
Step-by-step explanation:
Area ratio of 49:36 means a side length ration of 7:6.
7/6 = 15/x
7x = 90
x = 90/7
= 12.85
Answer: 12.85 cm
Step-by-step explanation:
(a) Suppose you borrowed $400,000 for a home mortgage on January 1, 2010 with an annual interest rate of 3.5% per year compounded monthly. If you didn't make any payments and were only charged the interest (and no late fees), how much would you owe on the mortgage on January 1, 2030?
Answer:
$804,680.814 ( approx )
Step-by-step explanation:
The amount formula in compound interest is,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where, P is the principal amount,
r is the annual rate of interest,
n is the compounding periods in a year,
t is the time in years,
Given, P = $ 400,000,
r = 3.5 %=0.035,
n = 12, ( 1 year = 12 months )
t = 20 years,
Thus, the amount would be,
[tex]A=400000(1+\frac{0.035}{12})^{240}[/tex]
[tex]=400000(\frac{12.035}{12})^{240}[/tex]
[tex]=\$ 804680.813963[/tex]
[tex]\approx \$ 804680.814[/tex]
The amount owed on the mortgage on January 1, 2030, would be approximately [tex]\$765,320.99.[/tex]
To solve this problem, we need to calculate the compound interest on the mortgage over a period of 20 years (from January 1, 2010, to January 1, 2030). The formula for compound interest is given by:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
Given:
- [tex]\( P = \$400,000 \)[/tex]
-[tex]\( r = 3.5\% = 0.035 \)[/tex] (as a decimal)
- n = 12 (since the interest is compounded monthly)
- t = 20 years
Plugging these values into the compound interest formula, we get:
[tex]\[ A = 400,000 \left(1 + \frac{0.035}{12}\right)^{12 \times 20} \][/tex]
[tex]\[ A = 400,000 \left(1 + \frac{0.035}{12}\right)^{240} \][/tex]
[tex]\[ A = 400,000 \left(1 + 0.002916667\right)^{240} \][/tex]
[tex]\[ A = 400,000 \left(1.002916667\right)^{240} \][/tex]
Now, we calculate the value inside the parentheses:
[tex]\[ 1.002916667^{240} \ = 1.913209802 \][/tex]
Finally, we multiply this by the principal amount to find out how much would be owed:
[tex]\[ A \ = 400,000 \times 1.913209802 \][/tex]
[tex]\[ A \ = \$765,320.99 \][/tex]
Consider the following matrix A={{1,-1,0,0},{2,-1,0,0},{0,0,1,0},{-1,-1,0,1}}Which of the following statements is true? Check the correct answer(s) below.A. The homogeneous system Ax=0 has infinitely many solutionsB. The matrix A has determinant −1C. The matrix A is not invertibleD. The matrix A is singular.E. None of the above
The correct answer is:
Option: E
E. None of the above
Step-by-step explanation:We know that a system of equation i.e.[tex]Ax=0[/tex] has infinite many solutions if det(A)=0
Also, the matrix is singular if det(A)=0and is non-singular or invertible otherwise i.e. when det(A)≠0
We know that when a homogeneous system has i.e. [tex]Ax=0[/tex] is such that: |A|≠0 then the system has a unique solution.The matrix that will be formed by the given set of vectors is:
[tex]A=\begin{bmatrix}-1 &2 &0 &-1 \\ -1&-1 &0 &-1 \\ 0 &0 &1 &0 \\ 0 &0 &0 &1 \end{bmatrix}[/tex]
Also, determinant i.e. det of matrix A is calculated by:
[tex]\begin{vmatrix}-1 &-2 &0 &-1 \\ -1&-1 &0 &-1 \\ 0 &0 &1 &0 \\ 0 &0 &0 &1 \end{vmatrix}=1(1(1+2))=3[/tex]
Hence, determinant is not equal to zero.
This means that the matrix is invertible and non-singular.
A drawer contains 2 red socks, 4 white socks, and 8 blue socks. Without looking, you draw out a sock, return it, and draw out a second sock. What is the probability that the first sock is red and the second sock is blue?
[tex]|\Omega|=14^2=196\\|A|=2\cdot8=16\\\\P(A)=\dfrac{16}{196}=\dfrac{4}{49}\approx8.2\%[/tex]
There are 20 multiple-choice questions on an exam, each having responses a, b, c, or d. Each question is worth 5 points, and only one response per question is correct. Suppose a student guesses the answer to each question, and her guesses from question to question are independent. If the student needs at least 40 points to pass the test, the probability the student passes is closest to
Ok, the student needs 40 points and each question is worth 5, so 40/5 = 8 questions are needed.
Each question has 4 possibilities, 1 is right, so the chances to guess it correctly is one in 4, or 1/4, or 25%.
[tex]\frac{8}{20} = \frac{2}{5}[/tex]
To know the probability to pass the exam we can do:
[tex]\frac{25}{100}*\frac{2}{5} = 10%[/tex]
Answer: 0.102 or 10.2%.
Step-by-step explanation:
Given : Number of multiple-choice questions = 20
Number of options in any question=4
Each question is worth 5 points and only one response per question is correct.
Probability of getting a correct answer = [tex]\dfrac{1}{4}=0.25[/tex]
If the student needs at least 40 points to pass the test, that mean he needs at-least [tex]\dfrac{40}{5}=8[/tex] questions correct.
Let x denotes the number of correct questions .
By using binomial distribution , we find
[tex]P(x\geq8)=1-P(x<8)\\\\ =1-P(x\leq7)\\\\=1-0.898\ \ \text{[By using binomial table for n= 20 , p=0.25 and x=7]}\\\\=0.102[/tex]
[Binomial table gives the probability [tex]P(X\leq x)=\sum_{x=0}^c^nC_xp^x(1-p)^{n-x}[/tex] ]
Hence, the probability the student passes is closest to 0.102 or 10.2%.
The Thomas Supply Company Inc. is a distributor of gas-powered generators. As with any business, the length of time customers take to pay their invoices is important. Listed below, arranged from smallest to largest, is the time, in days, for a sample of The Thomas Supply Company Inc. invoices. 13 13 13 20 26 27 31 34 34 34 35 35 36 37 38 41 41 41 45 46 47 47 48 52 53 56 56 62 67 82
Determine the first and third quartiles, determine the seconds decile and the eighth decile,determine the 67th percentile.
Final answer:
Explanation of quartiles, deciles, and percentiles in a dataset of gas-powered generator invoice payment times. Lastly, the 67th percentile in the data set is approximately 46 days.
Explanation:
The first quartile (Q1) is found by locating the median of the lower half of the data set, which results in a value of 34 days. The third quartile (Q3) is the median of the upper half of the data set, yielding a value of 47 days. The second decile corresponds to the 20th percentile, which is approximately 31 days. The eighth decile corresponds to the 80th percentile, which is approximately 47 days. Lastly, the 67th percentile in the data set is approximately 46 days.
In a particular course, it was determined that only 70% of the students attend class on Fridays. From past data it was noted that 95% of those who went to class on Fridays pass the course, while only 10% of those who did not go to class on Fridays passed the course. If a student passes the course, what is the probability that they did not attend on Fridays?
Answer: Probability that students who did not attend the class on Fridays given that they passed the course is 0.043.
Step-by-step explanation:
Since we have given that
Probability that students attend class on Fridays = 70% = 0.7
Probability that who went to class on Fridays would pass the course = 95% = 0.95
Probability that who did not go to class on Fridays would passed the course = 10% = 0.10
Let A be the event students passed the course.
Let E be the event that students attend the class on Fridays.
Let F be the event that students who did not attend the class on Fridays.
Here, P(E) = 0.70 and P(F) = 1-0.70 = 0.30
P(A|E) = 0.95, P(A|F) = 0.10
We need to find the probability that they did not attend on Fridays.
We would use "Bayes theorem":
[tex]P(F\mid A)=\dfrac{P(F).P(A\mid F)}{P(E).P(A\mid E)+P(F).P(A\mid F)}\\\\P(F\mid A)=\dfrac{0.30\times 0.10}{0.70\times 0.95+0.30\times 0.10}\\\\P(F\mid A)=\dfrac{0.03}{0.695}=0.043[/tex]
Hence, probability that students who did not attend the class on Fridays given that they passed the course is 0.043.
A red car is driving along the road in the direction of the police car and is 100 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 85 feet per second. How fast is the red car actually traveling along the road?
I think to solve this question, subtract the rate of feet per second disappearing from the distance of feet between the 2 cars.
100-85=15fps
The car is traveling at 15 feet per second.
Hope this helps!
The partial fraction decomposition of LaTeX: \frac{x-9}{x^2-3x-18} x − 9 x 2 − 3 x − 18 is LaTeX: \frac{A}{x-6}+\frac{B}{x+3} A x − 6 + B x + 3 . Find the numbers LaTeX: A\: A and LaTeX: B B . Then, find the sum LaTeX: A+B A + B , which is a whole number. Enter that whole number as your answer.
Not entirely sure what the question is supposed to say, so here's my best guess.
First, find the partial fraction decomposition of
[tex]\dfrac{x-9}{x^2-3x-18}[/tex]
This is equal to
[tex]\dfrac{x-9}{(x-6)(x+3)}=\dfrac a{x-6}+\dfrac b{x+3}[/tex]
Multiply both sides by [tex](x-6)(x+3)[/tex], so that
[tex]x-9=a(x+3)+b(x-6)[/tex]
Notice that if [tex]x=6[/tex], the term involving [tex]b[/tex] vanishes, so that
[tex]6-9=a(6+3)\implies a=-\dfrac13[/tex]
Then if [tex]x=-3[/tex], the term with [tex]a[/tex] vanishes and we get
[tex]-3-9=b(-3-6)\implies b=\dfrac43[/tex]
So we have
[tex]\dfrac{x-9}{x^2-3x-18}=-\dfrac1{3(x-6)}+\dfrac4{3(x+3)}[/tex]
I think the final answer is supposed to be [tex]a+b[/tex], so you end up with 1.
George was given 11 grams of medicine, but the full dose is supposed to be 25 grams. What percent of his full dose did George receive? Solve with percent table and equivalent fractions
Answer: George receive 44 % of his full dose .
Step-by-step explanation:
Given : The amount for full dose : 25 grams
The amount received by George = 11 grams
Now, the percent of his full dose received by George :-
[tex]\dfrac{\text{Dose taken by George}}{\text{Full dose}}\times100[/tex]
[tex]=\dfrac{11}{25}\times100=44\%[/tex]
Hence, George receive 44 % of his full dose .
The half-life of a certain radioactive element is 200 years. How will it take for a 100 pound chunk of this element to decay to a chunk that is 50 pounds?
It would take 200 years (by definition of half-life). 50 is 1/2 of 100.
.......Help Please......
Answer:
largest: Rsmallest: KStep-by-step explanation:
The slope of the graph at x=0 is related to the value of b. It is also proportional to the value of a, which is the same for all but curve B. The red curve R has the largest slope at x=0, (much larger than 3/4 the slope of curve B), so curve R has the greatest value of b.
Similarly, the smallest value of b will correspond to the curve with the smallest (most negative) slope. That would be curve K. Curve K has the smallest value of b.
A radio station claims that the amount of advertising per hour of broadcast time has an average of 10 minutes and a standard deviation equal to 5 minutes. You listen to the radio station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 8.2 minutes. Calculate the z-score for this amount of advertising time. Round your answer to 2 decimal places.
Answer: -0.36
Step-by-step explanation:
Given: Mean : [tex]\mu=10\text{ minutes}[/tex]
Standard deviation : [tex]\sigma=5\text{ minutes}[/tex]
We know that the formula to calculate the z-score is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x=8.2 minutes, we have
[tex]z=\dfrac{8.2-10}{5}=0.36[/tex]
Hence, the z-score for this amount of advertising time = -0.36
Final answer:
The z-score for the observed amount of advertising time (8.2 minutes) compared to the radio station's average of 10 minutes with a standard deviation of 5 minutes is -0.36, when rounded to two decimal places.
Explanation:
To calculate the z-score for the amount of advertising time observed on the radio station (8.2 minutes), we use the formula: Z = (X - μ) / σ, where X is the value to calculate the z-score for, μ is the mean of the data, and σ is the standard deviation. Plugging in the given values: X = 8.2 minutes (amount of advertising time observed), μ = 10 minutes (average advertising time), σ = 5 minutes (standard deviation).
So, the z-score is calculated as follows:
Z = (8.2 - 10) / 5 = -1.8 / 5 = -0.36.
Thus, the z-score of the amount of advertising time (8.2 minutes) is -0.36, rounded to two decimal places.
A Membership to the Gym Costs $ 25 Per Person in 1995 .The Membership Cost has Increased by an average of $ 6 per Person for each Year Since 1995 .Write a Linear Equation for the Cost of a GYM Membership For One Person Since 1995. So , What is the Cost of A GYM Membership in 2009 ????
Step-by-step explanation:
Let n = number of years since 1995
Let C = cost of gym membership in any particular year
Initial cost in 1995 = $25
Additional cost each year = $6
We can say the following:
Cost at any given year = cost in 1995 + ($6 x number of years after 1995)
Or expressed as the following : C = 25 + 6n (Ans)
In 2009, the number of years since 1995,
= 2009 - 1995
= 14 years
Hence, cost in 2009,
= $25 + ($6 x 14 years)
= $109 (Ans)
$109 is the Cost of A GYM Membership in 2009.
What does "cost" mean to you?
The cost is the sum of money that a business spends on the development or manufacturing of goods or services. It excludes the profit margin markup. The sum of money spent to create a good or product, as seen from the seller's perspective, is the cost.given,
Let n = number of years since 1995
Let C = cost of gym membership in any particular year
Initial cost in 1995 = $25
Additional cost each year = $6
formula ,
Cost at any given year = cost in 1995 + ($6 x number of years after 1995)
put value in formula
C = 25 + 6n
now,
In 2009, the no of member in years since 1995,
= 2009 - 1995
= 14 years
Hence, cost of gym membership in 2009,
= $25 + ($6 x 14 years)
= $109
Therefore, cost of gym membership in 2009 = $109
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Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = ∞ e−stf(t) dt 0 is said to be the Laplace transform of f, provided that the integral converges. Find ℒ{f(t)}. (Write your answer as a function of s.)
The Laplace Transform of a function f(t) is a tool used to solve differential equations by converting them into simpler algebraic equations. The transform itself is given by the integral ℒ{f(t)} = ∫∞₀ e−stf(t) dt, but without knowing the specific form of f(t), the exact transformation cannot be computed.
Explanation:The Laplace Transform, as defined by Definition 7.1.1, is a mathematical tool often used to handle differential equations, especially in the fields of Physics and Engineering. The main idea behind the transform is to convert the differential equations, which are difficult to solve, into simple algebraic equations. These simple equations are relatively easy to solve. Once solved, the inverse Laplace Transform is employed to obtain the solution to the original differential equation.
The question asks to compute the Laplace Transform ℒ{f(t)} of a function. By definition, the Laplace transform of a function f(t), defined for t ≥ 0 is given by the integral ℒ{f(t)} = ∫∞₀ e−stf(t) dt. The question doesn't give an explicit form of the function f(t). In general, if f(t) = e^(-αt), where α is a constant, then its Laplace Transform is given by ℒ{e^(-αt)} = 1/(s + α) for s > α.
If you could kindly provide me with the specific function f(t), I can better determine the Laplace Transform ℒ{f(t)}
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g. How many different 6-letter arrangements can be formed using the letters in the word ABSENT, if each letter is used only once? a. 6 b. 36 c. 720 d. 46,656
Answer:
720
Step-by-step explanation:
Given : The word ABSENT
To Find: How many different 6-letter arrangements can be formed using the letters in the word ABSENT, if each letter is used only once?
Solution:
Number of letters in ABSENT = 6
So, No. of arrangements can be formed using the letters in the word ABSENT, if each letter is used only once = 6!
= [tex]6 \times 5 \times 4\times 3 \times 2 \times 1[/tex]
= [tex]720[/tex]
So, Option C is true
Hence there are 720 different 6-letter arrangements can be formed using the letters in the word ABSENT.
Final answer:
There are 720 different 6-letter arrangements that can be formed from the word ABSENT, by applying the permutation formula 6! = 720. The correct option is c.
Explanation:
The question asks: How many different 6-letter arrangements can be formed using the letters in the word ABSENT, if each letter is used only once? To answer this, we need to calculate the number of permutations of 6 letters taken from 6. This is a simple permutation problem where we use the formula for permutations which is n!, where n is the total number of items to choose from and ! denotes a factorial, meaning the product of all positive integers up to n.
Given that the word ABSENT has 6 letters and we are arranging all 6, we have 6! = 6×5×4×3×2×1 = 720. Therefore, there are 720 different 6-letter arrangements that can be formed using the letters in ABSENT, with each letter used only once.
What is the square root of m6?
Answer:
[tex]\large\boxed{\text{if}\ m\geq0,\ \text{then}\ \sqrt{m^6}=m^3}\\\\\boxed{\text{if}\ m<0,\ \text{then}\ \sqrt{m^6}=-m^3}[/tex]
Step-by-step explanation:
[tex]\sqrt{m^6}=\sqrt{m^{3\cdot2}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt{(m^3)^2}\qquad\text{use}\ \sqrt{a^2}=|a|\\\\=|m^3|\\\\\text{if}\ m\geq0,\ \text{then}\ \sqrt{m^6}=m^3\\\\\text{if}\ m<0,\ \text{then}\ \sqrt{m^6}=-m^3[/tex]
Answer:M^3 is the square root of m6
Step-by-step explanation:
good luck!!!
3 balls are randomly drawn from a box containing 4 yellow 2 blue and 5 red balls. Youwin a prize if all three are yellow. What is the probability of winning?
Answer: [tex]\dfrac{4}{165}[/tex]
Step-by-step explanation:
Given : The number of yellow balls in the box = 4
The total number of balls = [tex]4+2+5=11[/tex]
Since the given situation has dependent events.
Then, the probability of that all three balls are yellow is given by :-
[tex]\text{P(YYY)}==\dfrac{^4P_3}{^{11}P_3}=\dfrac{4\times3\times2}{11\times10\times9}\\\\\Rightarrow\ \text{P(YYY)}=\dfrac{4}{165}[/tex]
Hence, the probability of winning =[tex]\dfrac{4}{165}[/tex]
A runner runs around a circular track. He completes one lap at a time of t = 269 s at a constant speed of v = 4.6 m/s. What is the radius, r in meters, of the track?
Answer:
[tex]\boxed{\text{197 m}}[/tex]
Step-by-step explanation:
The formula relating distance (d), speed (s), and time (t) is
d = st
1. Calculate the distance
d = 269 s × 4.6 m·s⁻¹ = 1240 m
2.Calculate the track radius
The distance travelled is the circumference of a circle
[tex]\begin{array}{rcl}C & = & 2 \pi r\\1240 & = & 2 \pi r\\\\r & = & \dfrac{1240}{2 \pi }\\\\& = & 197\\\end{array}\\\text{The radius of the track is }\boxed{\textbf{197 m}}[/tex]
The radius in meters is 196.9 meters.
The runner ran around the track in 269 seconds at a speed of 4.6 m/s. This will enable us to find the distance around the track which is the circumference of the track.
Distance = Speed × time
= 4.6 × 269
= 1,237.4 meters
The distance here is the circumference which can also be found by the formula:
Circumference = π × diameter
1,237.4 = 22/7 × Diameter
Diameter = 1,237.4 ÷ 22/7
= 393.7 meters
Now that we have the diameter, the radius is:
= Diameter / 2
= 196.9 meters
In conclusion, the radius is 196.3 meters
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A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 lower than in the first. The tax in the first city was 6.5% and the tax in the second city was 4.5% The total hotel tax paid for the two cities was $582.50
. How much was the hotel charge in each city before tax?
Answer:
First city: $5,500
Second city: $5,000
Step-by-step explanation:
Let's define x as the hotel price in the first city and y the hotel price in the second city. We can start with this equation:
y = x - 500 (The hotel before tax in the 2nd city was $500 lower than in the 1st.)
Then we can say
0.065x + 0.045y = 582.50 (the sum of the tax amounts were $582.50)
We place the value of y from the first equation in the second equation:
0.065x + 0.045 (x - 500) = 582.50
0.065x + 0.045x - 22.50 = 582.50 (simplifying and adding 22.5 on each side)...
0.11x = 605
x = 5,500
The cost of the first hotel was $5,500
Thus, the cost of the second hotel was $5,000 (x - 500)
A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 42 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 6000 aspirin tablets actually has a 5% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
Answer: Hence, the probability that the whole shipment would be accepted is 0.371.
Many would be rejected.
Step-by-step explanation:
Since we have given that
Number of tablets to be tested = 42
Probability of getting a defect = 5% = 0.05
We need to find the probability that this whole shipment will be accepted.
As we have mentioned that if there is only one or none defect, then the whole shipment would be accepted.
P(accepted) = P(either none or one defect) = P(X=0)+P(X=1)
[tex]P(X=0)=(1-0.05)^{42}=(0.95)^{42}=0.115\\\\and\\\\P(X=1)=42\times (0.05)(0.95)^{41}=0.006\times 42=0.256[/tex]
So, P(Accepted) = 0.115+0.256=0.371
Hence, the probability that the whole shipment would be accepted is 0.371.
Many would be rejected.
Factor out the GCF (greatest common factor)
8m^2 n^3 - 24m^2 n^2 + 4m^3 n +
Answer:
4m²n
Step-by-step explanation:
The GCF is the factor by which all the terms among the given can be divided.
In the expression 8m²n³-24m²n²+4m³n,
The GCF between 8,24 and 4 is 4
The greatest common factor between m²,m² and m³ is m²
The greatest common factor between n³, n² and n is n
Thus multiplying the three we get:
4×m²×n
=4m²n
Graph the line that passes through the given point and has the given slope m. (3,10); m=-(5)/(2)
Step-by-step explanation:
given a slope and a point that the line passes through you have 2 options
Option 1: Solve for the equation of the line so you can just use that to graph the line. In this scenario it would be y=(-5/2)x - (20/13)
Option 2: plot the given point and, based on the slope, plot the next point that it crosses. In this case the next point would be (5, 7). Then you can just draw a line using these 2 points.
When Jill Thompson received a large settlement from an automobile accident, she chose to invest $115,000 in the Vanguard 500 Index Fund. This fund has an expense ratio of 0.17 percent. What is the amount of the fees that Jill will pay this year? (Round your answer to 2 decimal places.) Annual fee
Answer:
$195.50
Step-by-step explanation:
0.17% × $115,000 = $195.50
Jill's account will be charged $195.50 in expense fees.
Answer:
Jill will have to pay $195.5 in fees this year.
Step-by-step explanation:
This question may be solved by a simple rule of three.
This fund has an expense ratio of 0.17 percent. This means that for each investment in this fund, there is a fee of 17% percent of the value.
$115,000 is 100%, that is, decimal 1. How much is 0.17%, that is, 0.0017 of this value. So
1 - $115,000
0.0017 - $x
[tex]x = 115000*0.0017 = 195.5[/tex]
Jill will have to pay $195.5 in fees this year.