Answer:
P = 0.1764
The events are dependent
Step-by-step explanation:
We have a total of 9 + 6 + 3 = 18 stuffed animals.
The probability of the first animal pulled being a bear is:
P(bear) = N(bear) / N(total)
P(bear) = 9 / 18 = 0.5
Then, for the second animal, we now have only 17 stuffed animals in total.
So the probability of the second animal pulled being a lion, given the first animal was a bear, is:
P(lion | bear) = N(lion) / N(total)
P(lion | bear) = 6 / 17 = 0.3529
So the final probability is the product of these probabilities:
P = P(bear) * P(lion | bear) = 0.5 * 0.3529 = 0.1764
To find if the events are dependent or independent, let's find the probability of the first pick being a lion:
P(lion) = N(lion) / N(total)
P(lion) = 6 / 18 = 0.3333
The probability of picking a lion is different from the probability of picking a lion given we already picked a bear, so the events are dependent.
The top of a lighthouse is 100 m above sea level. The angle of elevation from the
deck of the sailboat to the top of the lighthouse is 28°. Calculate the distance
between the sailboat and the lighthouse.
Answer:
188 m
Step-by-step explanation:
The tangent of the angle is the ratio of the side opposite (height of the lighthouse) to the side adjacent (distance to the lighthouse):
tan(28°) = (100 m)/distance
distance = (100 m)/tan(28°) ≈ 188 m
The distance between the sailboat and the lighthouse is about 188 m.
HELP PLEASE SIMPLIFY !!!
Answer:
[tex]=x^{\frac{5}{6}}+2x^{\frac{7}{3}}[/tex]
Step-by-step explanation:
[tex]x^{\frac{1}{3}}\left(x^{\frac{1}{2}}+2x^2\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=x^{\frac{1}{3}},\:b=x^{\frac{1}{2}},\:c=2x^2\\=x^{\frac{1}{3}}x^{\frac{1}{2}}+x^{\frac{1}{3}}\cdot \:2x^2\\=x^{\frac{1}{3}}x^{\frac{1}{2}}+2x^2x^{\frac{1}{3}}\\\mathrm{Simplify}\:x^{\frac{1}{3}}x^{\frac{1}{2}}+2x^2x^{\frac{1}{3}}:\quad x^{\frac{5}{6}}+2x^{\frac{7}{3}}\\x^{\frac{1}{3}}x^{\frac{1}{2}}+2x^2x^{\frac{1}{3}}\\x^{\frac{1}{3}}x^{\frac{1}{2}}=x^{\frac{5}{6}}[/tex]
[tex]x^{\frac{1}{3}}x^{\frac{1}{2}}\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\x^{\frac{1}{3}}x^{\frac{1}{2}}=\:x^{\frac{1}{3}+\frac{1}{2}}\\=x^{\frac{1}{3}+\frac{1}{2}}\\\mathrm{Join}\:\frac{1}{3}+\frac{1}{2}:\quad \frac{5}{6}\\\frac{1}{3}+\frac{1}{2}\\\mathrm{Least\:Common\:Multiplier\:of\:}3,\:2:\quad 6\\Adjust\:Fractions\:based\:on\:the\:LCM\\=\frac{2}{6}+\frac{3}{6}[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{2+3}{6}\\\mathrm{Add\:the\:numbers:}\:2+3=5\\=\frac{5}{6}\\=x^{\frac{5}{6}}\\2x^2x^{\frac{1}{3}}=2x^{\frac{7}{3}}\\=x^{\frac{5}{6}}+2x^{\frac{7}{3}}[/tex]
Please answer this correctly without making mistakes
Answer:
589
Step-by-step explanation:
l x w
19x11
5x31
5x45
589
Answer:
589 is the answer
How many tons is 22,000 pounds?
Answer:
1 ton = 2,000 pounds
Step-by-step explanation:
With that said, 22,000 pounds is 11 tons because 2,000 x 11 = 22,000.
So 22,000 pounds is 11 tons.
Hope it helps and pls mark me brainliest if it did! :)
Calculating a correlation can help describe a relation between two quantitative variables' ___ and ___ . However, it is not sufficient to use a correlation coefficient to describe two variables. The addition of ___ can provide other helpful details such as __ _."
Answer:
direction
shape
scatter plots
shape and outliers
Step-by-step explanation:
Correlation is defined as the degree of correspondence between two variables.
When the values increase together, correlation is positive and when one value decreases as the other increases, correlation is negative .
Calculating a correlation can help describe a relation between two quantitative variables' direction and shape. However, it is not sufficient to use a correlation coefficient to describe two variables. The addition of scatter plots can provide other helpful details such as shape and outliers
Answer the inequality
Answer:
A.
Step-by-step explanation:
Add 4:
-5x ≤ 10
Divide by -5:
x ≥ -2
The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than 1% of her customers. What number of minutes should the advertisement use? Step 1 We need to find a so that P(X ≥ a) =
Answer:
The number of minutes advertisement should use is found.
x ≅ 12 mins
Step-by-step explanation:
(MISSING PART OF THE QUESTION: AVERAGE WAITING TIME = 2.5 MINUTES)
Step 1For such problems, we can use probability density function, in which probability is found out by taking integral of a function across an interval.
Probability Density Function is given by:
[tex]f(t)=\left \{ {{0 ,\-t<0 }\atop {\frac{e^{-t/\mu}}{\mu}},t\geq0} \right. \\[/tex]
Consider the second function:
[tex]f(t)=\frac{e^{-t/\mu}}{\mu}\\[/tex]
Where Average waiting time = μ = 2.5
The function f(t) becomes
[tex]f(t)=0.4e^{-0.4t}[/tex]
Step 2The manager wants to give free hamburgers to only 1% of her costumers, which means that probability of a costumer getting a free hamburger is 0.01
The probability that a costumer has to wait for more than x minutes is:
[tex]\int\limits^\infty_x {f(t)} \, dt= \int\limits^\infty_x {}0.4e^{-0.4t}dt[/tex]
which is equal to 0.01
Step 3Solve the equation for x
[tex]\int\limits^{\infty}_x {0.4e^{-0.4t}} \, dt =0.01\\\\\frac{0.4e^{-0.4t}}{-0.4}=0.01\\\\-e^{-0.4t} |^\infty_x =0.01\\\\e^{-0.4x}=0.01[/tex]
Take natural log on both sides
[tex]ln (e^{-0.4x})=ln(0.01)\\-0.4x=ln(0.01)\\-0.4x=-4.61\\x= 11.53[/tex]
ResultsThe costumer has to wait x = 11.53 mins ≅ 12 mins to get a free hamburger
Is 3/5 A.irrational, B.rational, C.natural and whole, or D.natural, whole integer and rational
Answer:
B
Step-by-step explanation:
3/5 is a fraction, meaning it isn't irrational, natural, whole or an integer, therefore the answer is rational (B).
Answer:
B.rational
Step-by-step explanation:
3/5 is written as a fraction so it is a rational number
It is not a whole number since it is a reduced fraction that is less than 1
The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is between 50.1 and 51.1 min. P(50.1 < X < 51.1) =
Answer:
P(50.1 < X < 51.1) = 0.5
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X between c and d is given by the following formula:
[tex]P(c < X < d) = \frac{d - c}{b - a}[/tex]
The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min.
This means that [tex]a = 50, b = 52[/tex]
So
[tex]P(50.1 < X < 51.1) = \frac{51.1 - 50.1}{52 - 50} = 0.5[/tex]
Could someone please help me with the steps for this problem? Factor by grouping: w²+3w+w+3
Answer:
Please see steps below
Step-by-step explanation:
In order to factor by grouping, we divide the four terms given into two groups, and extract on each group any common factor we can.
In our example, we can select the terms: [tex]w^2[/tex] and [tex]w[/tex] as one of our groups, and [tex]3w[/tex] and 3 in the other group. Then we re-organize the expression as:
[tex](w^2+w)+(3x+3)[/tex]
Now we extract from the first binomial group, the factor [tex]w[/tex] as a common factor of both terms, and from the second group we extract the factor "3" as common factor of those two terms:
[tex](w^2+w)+(3x+3)\\w(w+1)+3(w+1)[/tex]
We notice now that after the extraction, we are left with two exactly equal binomial factors [tex](w+1)[/tex] that appeared in the first group and in the second group. We proceed then to extract it as common factor for the two groups:
[tex]w(w+1)+3(w+1)\\(w+1)(w+3)[/tex]
this last product of two binomials ([tex](w+1)\,(w+3)[/tex] is the result of factoring the original expression.
Mr. Hobbs took out a loan of $12,000 for 4 years at a simple annual
interest rate of 7%. How much interest did he pay?
Answer:
Step-by-step explanation:
I= P*r*t
I = 12000* 7% *4
Total interest paid was $3360.
Answer: $3,360
Step-by-step explanation:
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are Normally distributed with a mean of 6.5 inches and a standard deviation of 1.2 inches. According to the 68-95-99.7 rule, we expect 95% of head breadths to be:___________.
Answer:
"According to the 68-95-99.7 rule, we expect 95% [95.45%] of head breadths to be" between 4.1 inches and 8.9 inches.
Step-by-step explanation:
According to the 68-95-99.7 rule, approximately:
68% (more precisely, 68.27%) of the data from the normal distribution lie one standard deviation, [tex] \\ \sigma[/tex], above and below the population mean, [tex] \\ \mu[/tex].95% (more precisely, 95.45%) of the data lie two standard deviations, [tex] \\ 2\sigma[/tex], above and below the population mean, [tex] \\ \mu[/tex], and finally,99.7 (or more precisely, 99.73%) of the data lie three standard deviations, [tex] \\ 3\sigma[/tex], above and below the population mean, [tex] \\ \mu[/tex].Then, if we have--from the question--that:
The random variable is head breadths.This variable follows a normal distribution.The population's mean for this distribution is [tex] \\ \mu = 6.5[/tex] inches.The population's standard deviation is [tex] \\ \sigma =1.2[/tex] inches.We have to remember that two parameters characterize a normal distribution: the population's mean and the population's standard deviation. So, mathematically, the distribution we have from question is [tex] \\ N(6.5, 1.2)[/tex].
For 95% (95.45%) of the head breadths, we expect that they are two standard deviations below and above the population's mean.
For solving this, we need to use the cumulative standard normal distribution (in case we need to find probabilities) and also use standardized values or z-scores:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
A z-score "tells us" the distance from the mean in standard deviations units. If the z-score is positive, it is above the mean. If it is negative, it is below the mean.
Since 95% (95.45%) of the head breadths are two standard deviations (above and below the mean), we have (using [1]):
[tex] \\ \pm2 = \frac{x - \mu}{\sigma}[/tex]
But we already know that [tex] \\ \mu=6.5[/tex] inches and [tex] \\ \sigma=1.2[/tex] inches.
Thus (without using units) for values above the population's mean:
[tex] \\ 2 = \frac{x - 6.5}{1.2}[/tex]
Solving the equation for x, we multiply by 1.2 at each side of [1] :
[tex] \\ 2 * 1.2 = \frac{x - 6.5}{1.2} * 1.2[/tex]
[tex] \\ 2 * 1.2 = (x - 6.5)\frac{1.2}{1.2}[/tex]
[tex] \\ 2 * 1.2 = (x - 6.5)\frac{1.2}{1.2}[/tex]
[tex] \\ 2 * 1.2 = (x - 6.5)*1[/tex]
[tex] \\ 2 * 1.2 = x - 6.5[/tex]
Adding 6.5 at each side of the previous equation:
[tex] \\ (2 * 1.2) + 6.5 = x - 6.5 + 6.5[/tex]
[tex] \\ (2 * 1.2) + 6.5 = x + 0[/tex]
[tex] \\ (2 * 1.2) + 6.5 = x[/tex]
Therefore, the raw value, x, in the distribution that is two standard deviations above the population's mean is:
[tex] \\ x = (2 * 1.2) + 6.5[/tex]
[tex] \\ x = 2.4 + 6.5[/tex]
[tex] \\ x = 8.9[/tex] inches.
For two standard deviations below the mean, we proceed in the same way:
[tex] \\ -2 = \frac{x - 6.5}{1.2}[/tex]
[tex] \\ -2*1.2 = x - 6.5[/tex]
[tex] \\ (-2*1.2) + 6.5 = x[/tex]
[tex] \\ x = (-2*1.2) + 6.5[/tex]
[tex] \\ x = -2.4 + 6.5[/tex]
[tex] \\ x = 4.1[/tex] inches
Therefore, "according to the 68-95-99.7 rule, we expect 95% [95.45%] of head breadths to be" between 4.1 inches and 8.9 inches.
The graph below shows these values, and the shaded area represents 95% of the data, or, to be more precise, 95.45% (0.954499).
Please help!! Which of the following is equal to the rational expression when x ≠ 2 or -4? 5(x-2)/(x-2)(x+4)
Answer:
5 / (x+4) x ≠2 x≠-4
Step-by-step explanation:
5(x-2)/(x-2)(x+4)
The denominator cannot be zero so x ≠2 x≠-4
Cancel like terms in the numerator and denominator
5 / (x+4) x ≠2 x≠-4
One third of the sum of 15
and thrice a certain number is
equal to twice the number. Find
the number
Answer:
x=-1/39
Step-by-step explanation:
A car travelled 80km in 48minutes. find the speed of the car in km/hr
80km / 48 min = 1 2/3 km per minute.
1 2/3 km per minute x 60 minutes(1 hour) = 100 km per hour
ACB = DCE
A = 3x-10, C = 45°, D = 2x+10
Please help confused
Answer:
x = 20
Step-by-step explanation:
The congruence statement tells you that angle A is congruent to angle D. (Both are listed first in the triangle names.) This means ...
∠A = ∠D
3x -10 = 2x +10
x = 20 . . . . . . . . . . add 10-2x to both sides
Name the x-axis of symmetry for the parabola sketched below
Answer:
x=-3
Step-by-step explanation:
The vertex is at x = -3
The axis of symmetry is along the vertex
x=-3
Answer:
x=-3
Step-by-step explanation:
To find the axis of symmetry, you just need to find the x-coordinate of the vertex using this formula: -b/2a=x
*Only when provided a three variable quadratic equation.
For looking at a graph, you find the center of the parabola in which when you reflect it over itself, it will be symmetrical.
According to the graph, x=-3 is the line which you can draw to fold over to the other side and it can fit perfectly.
The value of m compared to the standard is
1/1000
1000
1/100
10
The Tennessean, an online newspaper located in Nashville, Tennessee, conducts a daily poll to obtain reader opinions on a variety of current issues. In a recent poll, readers responded to the following question: "If a constitutional amendment to ban a state income tax is placed on the ballot in Tennessee, would you want it to pass?
Required:
a. What was the sample size for this poll?
b. Are the data categorical or quantitative?
c. Would it make more sense to use averages or percentages as a summary of the data for this question?
d. Of the respondents, 67% said Yes, they would want it to pass. How many individuals provided this response?
Answer:
Answers below
Step-by-step explanation:
a. What was the sample size for this poll?
b. Are the data categorical or quantitative?
c. Would it make more sense to use averages or percentages as a summary of the data for this question?
d. Of the respondents, 67% said Yes, they would want it to pass. How many individuals provided this response?
Triangles E F G and K L M are shown. Angles E F G and K L M are congruent. The length of side K L is 6, the length of side M L is 5, and the length of K M is 8. The length of E G is 24, the length of G F is 15, and the length of E F is 18. Can the triangles be proven similar using the SSS or SAS similarity theorems? Yes, △EFG ~ △KLM only by SSS. Yes, △EFG ~ △KLM only by SAS. Yes, △EFG ~ △KLM by SSS or SAS. No, they cannot be proven similar by SSS or SAS.?
Answer:
The Answer is C: Yes, △EFG~ △KLM by SSS or SAS
Step-by-step explanation:
SSS is for side-side-side
Both triangles have all three sides given, so the SSS similarity theorem is one way to prove these triangles are similar.
SAS is for side-angle-side
Both triangles have one angle measurement given, and two side lengths given, therefore we can also use the SAS similarity theorem to prove the two triangles are similar.
Since both SSS and SAS work to prove the triangles are similar, the correct answer is C: Yes, △EFG~ △KLM by SSS or SAS
(I also just answered this question on the assignment and got it correct)
Answer:
Answer is C
Step-by-step explanation:
Took it on Edg
Every product manufactured by a company goes through 6 different tests before being shipped out. It is known that the probability that a product passes any single test is 0.9 and the tests are independent. Only those products that pass the first three tests and also pass at least one of the three remaining tests are shipped out. Find the probability that a manufactured product is shipped out.
Answer:
The Probability that the product is shipped out is 0.7283
Step-by-step explanation:
Here, we are given that, a product passes through 6 tests before it is shipped out and a product is shipped out only if it passes all the first 3 tests and at least 1 of the remaining 3 tests.
We have P(pass)= 0.9, is the Probability of passing any test.
Which implies, P(fail)= 1- 0.9= 0.1
We have to find the Probability that the product is shipped out.
P(product is shipped out) = P(it passes first 3 tests )*P(passes at least 1 of the remaining 3 tests) •••••••••••(i)
We can take the product as the tests are Independent.
Now, let us obtain
P(it passes first 3 tests ) = P(pass)*P(pass)*P(pass)
=P(pass)]^3 = (0.9)^3 = 0.729
Hence, P( it passes first 3 tests)= 0.729 •••••••(ii)
Now,
P(passes at least 1 of the remaining 3 tests)
= 1-P(fails all the 3 remaining tests)
= 1-(0.1)^3 = 1 - 0.001 = 0.999
Hence,
P(passes atleast 1 of the remaining 3 tests)=0.999 ••••••••(iii)
Now, substituting the 2nd and 3rd equations in the first equation, we have;
P(product is shipped out) = P(it passes first 3 tests )*P(passes at least 1 of the remaining 3 tests)
= (0.729)*(0.999)
= 0.728271
= 0.7283
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
The correct answer would be A
(I am not guessing I had the same quiz before)
Use Newton's method with initial approximation x1 = 1 to find x2, the second approximation to the root of the equation x4 − x − 3 = 0. (Round your answer to four decimal places.) x2 =?
Answer:
[tex]x_{2} = 0.0000[/tex]
Step-by-step explanation:
The formula for the Newton's method is:
[tex]x_{i+1} = x_{i} + \frac{f(x_{i})}{f'(x_{i})}[/tex]
Where [tex]f' (x_{i})[/tex] is the first derivative of the function evaluated in [tex]x_{i}[/tex].
[tex]x_{i+1} = x_{i} + \frac{x_{i}^{4}-x_{i}-3}{4\cdot x_{i}^{3}-1}[/tex]
Lastly, the value of [tex]x_{2}[/tex] is determined by replacing [tex]x_{1}[/tex] with its numerical value:
[tex]x_{2} = x_{1} + \frac{x_{1}^{4}-x_{1}-3}{4\cdot x_{1}^{3}-1}[/tex]
[tex]x_{2} = 1.0000 + \frac{1.0000^{4}-1.0000-3}{4\cdot (1.0000)^{3}-1}[/tex]
[tex]x_{2} = 0.0000[/tex]
What’s the correct answer for this question?
Answer:
the radius
Step-by-step explanation:
the correct answer is the radius
Find lim x→3 sqrt 2x+3-sqrt 3x/ x^2-3x. you must show your work or explain your work in words plsss I need help
I'm assuming the limit is supposed to be
[tex]\displaystyle\lim_{x\to3}\frac{\sqrt{2x+3}-\sqrt{3x}}{x^2-3x}[/tex]
Multiply the numerator by its conjugate, and do the same with the denominator:
[tex]\left(\sqrt{2x+3}-\sqrt{3x}\right)\left(\sqrt{2x+3}+\sqrt{3x}\right)=\left(\sqrt{2x+3}\right)^2-\left(\sqrt{3x}\right)^2=-(x-3)[/tex]
so that in the limit, we have
[tex]\displaystyle\lim_{x\to3}\frac{-(x-3)}{(x^2-3x)\left(\sqrt{2x+3}+\sqrt{3x}\right)}[/tex]
Factorize the first term in the denominator as
[tex]x^2-3x=x(x-3)[/tex]
The [tex]x-3[/tex] terms cancel, leaving you with
[tex]\displaystyle\lim_{x\to3}\frac{-1}{x\left(\sqrt{2x+3}+\sqrt{3x}\right)}[/tex]
and the limand is continuous at [tex]x=3[/tex], so we can substitute it to find the limit has a value of -1/18.
What’s the correct answer for this question?
Answer:
A and B
Step-by-step explanation:
1) Distance to the focus
From (x,y) to the focus(2,-4) {using distance formula}
=√(x-2)²+(y+4)²
2) Distance to the directrix
Is, y+p where P here is (-6)
So
d2 = y+p
= y+(-6)
= y-6
What’s the correct answer for this question?
Answer:
Height = 12 inches
Step-by-step explanation:
Volume = Area × Height
1080 = 90 × H
H = 1080/90
H = 12 inches
A tree grows three feet per year. What happens to the growth of the
When the number of years increases, the number of feet decrea
When the number of years decreases, the number of feet stays
When the number of years increases, the number of feet increas
When the number of years decreases, the number of feet increa
Answer:
The answer is C :,)
Step-by-step explanation:
Answer:
The answer to your question is c
Step-by-step explanation:
Because the years have to increase for it to grow.
85 points!! | All of the following expressions have the same value, when x= -2 and y= 4, except
-2xy
0-4x2
0x²y
0 (-2) ²y
Answer:
They have two sets of equal answers...
Step-by-step explanation:
-2 * 2 * 4 = -16
0 - 4 * -2 * -2 = -16
0 * -2 * -2 * 4 = 0
0 * 4 * 4 = 0
If 9: x= x-4, then x=
0 36
18
0 24
6
Answer:
2±√13
Step-by-step explanation:
9/x=x-4
x² -4x - 9=0
x² -4x +4- 13=0
(x -2)²=13
x-2= ±√13
x= 2±√13
