Answer:
The usually speed of the bus is 50 miles/h.
Step-by-step explanation:
Let the usual speed of the bus be x mile/hour.
We know that
[tex]speed=\frac{distance}{time}[/tex]
[tex]\Rightarrow time = \frac{distance}{speed}[/tex]
The bus travels 200 miles.
To reach its destination it takes time [tex]=\frac{200}{x}[/tex] h
This week however the bus leaves at 5:40.
The bus late 40 minutes [tex]=\frac{40}{60} h[/tex] [tex]= \frac{2}{3}h[/tex]
Now the speed of the bus is = (x+10) miles/h
The new time to reach the destination is [tex]=\frac{200}{x+10}[/tex] h
According to the problem,
[tex]\frac{200}{x}-\frac{200}{x+10}=\frac{2}{3}[/tex]
[tex]\Rightarrow 200[\frac{x+10-x}{x(x+10)}]=\frac{2}{3}[/tex]
[tex]\Rightarrow 200[\frac{10}{x^2+10x}]=\frac{2}{3}[/tex]
⇒2(x²+10x)=200×10×3
⇒x²+10x = 3000
⇒x²+10x -3000=0
⇒x²+60x-50x-3000=0
⇒x(x+60)-50(x+60)=0
⇒(x+60)(x-50)=0
⇒x= -60,50
∴x=50 [since speed does not negative]
The usually speed of the bus is 50 miles/h.
The bus's usual speed is 60 mph.
To find the bus's usual speed, we can set up an equation based on the given information. Let the usual speed be x mph. Then, the time taken to travel 200 miles at the usual speed is 200/x. The time taken to travel the same distance at the increased speed (x+10) mph is 200/(x+10). Since the bus left late, these times should be equal, leading to the equation 200/x = 200/(x+10). Solving this equation, we find that x = 60 mph, which is the usual speed of the bus.
Look at the proof. Name the postulate you would use to prove the two triangles are congruent.
A. AAA Postulate
B. SSS Postulate SAS
C. SAS Postulate
Answer:
Option C, SAS Postulate
Step-by-step explanation:
I think that it is option C because it does not give you 3 angles or 3 sides, it gives you 2 angles and 1 side.
Answer: Option C, SAS Postulate
Brainliest & 15 pts to whoever helps pls!!
You are comparing the heights of contemporary males and eighteenth-century males. The sample mean for a sample of 30 contemporary males is 70.1 inches with a sample standard deviation of 2.52 inches. The sample mean for eighteenth century males was 65.2 inches with a sample standard deviation of 3.51 inches. Is there sufficient data to conclude that contemporary males are taller than eighteenth-century males?
a. The P-value is less than 0.00001. There is insufficient data to reject the null hypothesis.
b. The P-value is greater than 0.00001. There is sufficient data to reject the null hypothesis.
c. The P-value is greater than 0.00001. There is insufficient data to reject the null hypothesis.
d. The P-value is less than 0.00001. There is sufficient data to reject the null hypothesis.
Answer:
D
Step-by-step explanation:
If Naomi were to paint her living room alone, it would take 5 hours. Her sister Jackie could do the job in 8 hours. How many hours would it take them working together? Express your answer as a fraction reduced to lowest terms, if needed.
Answer:
40/13
The decimal form is going to be 3.076
PLEASE HELP!!!!
ERGF is inscribed in a circle.
Find the measure of angle E.
In a cyclic quadrilateral ( a quadrilateral that is inscribed in a circle),
opposite angles add up to 180 degrees. So you can form an equation and solve for x, and thus angle E.
Therefore:
(-2 + 6x) + (7x - 13) = 180
13x - 15 = 180
13x = 195
x = 15
So angle E = 5x
= 5 (15)
= 75 degrees
dont skip just help plz
Answer:
(1,-3)
Step-by-step explanation:
the x-axis for A is positive and the y-axis is negative. point A's X value is 1 because it is 1 point away from the origin and the value of the Y is 3 units away from the origin and it has to be negative.
Find a degree 3 polynomial with real coefficients having zeros 3 and 3−3i and a lead coefficient of 1. Write P in expanded form.
Answer:
P = x³ − 9x² + 36x − 54
Step-by-step explanation:
Complex roots come in conjugate pairs. So if 3−3i is a zero, then 3+3i is also a zero.
P = (x − 3) (x − (3−3i)) (x − (3+3i))
P = (x − 3) (x − 3 + 3i) (x − 3 − 3i)
P = (x − 3) ((x − 3)² − (3i)²)
P = (x − 3) ((x − 3)² + 9)
P = (x − 3)³ + 9 (x − 3)
P = x³ − 9x² + 27x − 27 + 9x − 27
P = x³ − 9x² + 36x − 54
The paraboloid z = 6 − x − x2 − 5y2 intersects the plane x = 2 in a parabola. Find parametric equations in terms of t for the tangent line to this parabola at the point (2, 2, −20).
Answer:
x = 2
y = 2 + t
z = -20 -20t
Step-by-step explanation:
First, we are going to find the equation for this parabola. We replace x = 2 in the equation of the paraboloid, thus:
[tex]z = 6-x-x^{2} -5y^{2}[/tex]
if x = 2, then
[tex]z = 6-(2)-2^{2}-5y^{2}[/tex]
[tex]z = -5y^{2}[/tex]
Now, we calculate the tangent line to this parabola at the point (2,2,-20)
The parametrization of the parabola is:
x = 2
y = t
[tex]z = -5t^{2}[/tex] since [tex]z = -5y^{2}[/tex]
We calculate the derivative
[tex]\frac{dx}{dt}= 0[/tex]
[tex]\frac{dy}{dt}= 1[/tex]
[tex]\frac{dz}{dt}= -10t[/tex]
we evaluate the derivative in t=2, since at the point (2,2,-20) y = 2 and y = t
Thus:
[tex]\frac{dx}{dt}= 0[/tex]
[tex]\frac{dy}{dt}= 1[/tex]
[tex]\frac{dz}{dt}= -10(2)= -20[/tex]
Then, the director vector for the tangent line is (0,1,-20)
and the parametric equation for this line is:
x = 2
y = 2 + t
z = -20 -20t
The parametric equation of the tangent line is [tex]L(t)=(2,2+t,-20-20t)[/tex]
Parabola :The equation of Paraboloid is,
[tex]z =6-x-x^{2} -5y^{2}[/tex]
Equation of parabola when [tex]x = 2[/tex] is,
[tex]z=6-2-2^{2} -5y^{2} \\\\z=-5y^{2}[/tex]
The parametric equation of parabola will be,
[tex]r(t)=(2,t,-5t^{2} )[/tex]
Now, we have to find Tangent vector to this parabola is,
[tex]T(t)=\frac{dr(t)}{dt}=(0,1,-10t)[/tex]
We get, the point [tex](2, 2, -20)[/tex] when [tex]t=2[/tex]
The tangent vector will be,
[tex]T(2)=(0,1,-20)[/tex]
The tangent line to this parabola at the point (2, 2, −20) will be,
[tex]L(t)=(2,2,-20)+t(0,1,-20)\\\\L(t)=(2,2+t,-20-20t)[/tex]
Learn more about the Parametric equation here:
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Nanette earns $14 per hour. Last week, she worked 2 hours on Monday, 10 hours on Tuesday, and 9 hours on Wednesday. She had Thursday off, and then she worked 8 hours on Friday. How much money did Nanette earn in all last week?
Answer: $406
Step-by-step explanation:
Answer: she earned $406 last week.
Step-by-step explanation:
Last week, she worked 2 hours on Monday, 10 hours on Tuesday, and 9 hours on Wednesday. This means that the number of hours that she worked for the first three days is
2 + 10 + 9 = 21 hours
She had Thursday off, and then she worked 8 hours on Friday. Therefore, the total number of hours that she worked for the week is 21 + 8 = 29 hours.
If Nanette earns $14 per hour, then the total amount of money that Nanette earned in all last week is
29 × 14 = $406
Select the correct answer. Solve -9 2/7 -(-10 3/7) . A. -1 1/7 B. 1 1/7 C. 19 1/7 D. 19 5/7
Answer:
B. 1 1/7
Step-by-step explanation:
-9 2/7-(-10 3/7)
=-9 2/7+10 3/7
=1 1/7
Therefore, B. 1 1/7
Answer:
The answer is B
Step-by-step explanation:
B. 1 1/7
The average number of field mice per acre in a 5-acre wheat field is estimated to be 14. (a) Find the probability that fewer than 12 field mice are found on a given acre. (b) Find the probability that fewer than 12 field mice are found on 2 of the next 3 acres inspected.
Answer:
(a) [tex]P(X < 12)=0.26[/tex]
(b) [tex]P(X=2)=0.15[/tex]
Step-by-step explanation:
Question a
This is a Poisson distribution. The average/mean, μ = 14
So, probability that fewer than 12 field mice are found on a given acre is:
[tex]P(X < 12) = e^{-14}(\frac{14^{0}}{0!} +\frac{14^{1}}{1!} + \frac{14^{2}}{2!} + \frac{14^{3}}{3!} +\frac{14^{4}}{4!} + \frac{14^{5}}{5!} +\frac{14^{6}}{6!}+\frac{14^{7}}{7!}+\frac{14^{8}}{8!} +\frac{14^{9}}{9!}+\frac{14^{10}}{10!}+\frac{14^{11}}{11!})\\ \\P(X < 12) = e^{-14}(1+14+98+457.33+1600.67+4481.87+10457.69+20915.38+36601.91+56936.31+79710.83+101450.15)\\\\P(X < 12) = 8.315*10^{-7}(312725.1248)=0.26 \\\\P(X < 12)=0.26[/tex]
Question b
This is a Binomial distribution with:
Probability of success, p = 0.26
n = 3
[tex]P(X=2)= (3C2)p^{2}(1-p)=\frac{3!}{2!(3-2)!}*(0.26^{2})*(1-0.26)\\ \\P(X=2)=3(0.0676)(0.74)=0.15\\\\P(X=2)=0.15[/tex]
Final answer:
To find the probability that fewer than 12 field mice are found on a given acre and on 2 of the next 3 acres inspected, use the cumulative distribution function (CDF) of the Poisson distribution and the binomial distribution.
Explanation:
To find the probability that fewer than 12 field mice are found on a given acre, we need to use the cumulative distribution function (CDF) of the Poisson distribution. The average number of field mice per acre is 14, so the parameter of the Poisson distribution is also 14.
(a) To find the probability that fewer than 12 field mice are found on a given acre, we calculate P(X < 12) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 11), where X is the number of field mice found on a given acre
(b) To find the probability that fewer than 12 field mice are found on 2 of the next 3 acres inspected, we calculate P(X < 12) for each acre and use the binomial distribution to determine the probability of 2 successes out of 3 trials.
My Notes Determine the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution. Do not attempt to find the solution. (Enter your answer using interval notation.)t(t−4)y"+3ty'+4y=2,y(3)=0,y'(3)=−1
Answer:
The answer to the question is
The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is (-∞, 4)
Step-by-step explanation:
To apply look for the interval, we divide the ordinary differential equation by (t-4) to
y'' + [tex]\frac{3t}{t-4}[/tex] y' + [tex]\frac{4}{t-4}[/tex]y = [tex]\frac{2}{t-4}[/tex]
Using theorem 3.2.1 we have p(t) = [tex]\frac{3t}{t-4}[/tex], q(t) = [tex]\frac{4}{t-4}[/tex], g(t) = [tex]\frac{2}{t-4}[/tex]
Which are undefined at 4. Therefore the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution, that is where p, q and g are continuous and defined is (-∞, 4) whereby theorem 3.2.1 guarantees unique solution satisfying the initial value problem in this interval.
The existence and uniqueness theorems for ODEs determine that the longest interval where the initial value problem has a unique and twice-differentiable solution is (0, 4), avoiding discontinuities at t=0 and t=4.
Explanation:The initial value problem provided is a second-order linear ordinary differential equation (ODE) of the form:
t(t-4)y"+3ty'+4y=2, with initial conditions y(3)=0 and y'(3)=-1.
To determine the longest interval in which the solution is guaranteed to be unique and twice-differentiable, we need to consider the existence and uniqueness theorems for ODE's, which are predicated on the functions of the equation being continuous over the interval considered. Here, the coefficients of y" and y' are t(t-4) and 3t respectively. The problematic points occur where the coefficient of y" is zero because it will make the equation not well-defined, which occurs at t=0 and t=4. Therefore, the longest interval around the initial condition t=3 that avoids these points is (0, 4). Within this interval, the coefficients are continuous, and hence, the conditions for the existence and uniqueness of the solution are satisfied.
The Houston Astros fan population is 1,450,000 and is decreasing at an annual rate of 0.99% per year .Write an exponential equation to represent this situation after x years.
Answer:
Step-by-step explanation:
We would apply the formula for
exponential decay which is expressed as
A = P(1 - r)^t
Where
A represents the population after t years.
t represents the number of years.
P represents the initial population.
r represents rate of growth.
From the information given,
P = 1,450,000
r = 0.99% = 0.99/100 = 0.0099
t = x years
Therefore, an exponential equation to represent this situation after x years is
A = 1450000(1 - 0.0099)^t
A = 1450000(0.9901)^t
A right cylindrical solid is cut in half to form the figure shown. If the length is 20 cm and the diameter is 8 cm, what is the surface area?
(80π + 160) cm2
(96π + 160) cm2
320π cm2
(320π + 160) cm2
Answer:
(96π + 160) cm2
Step-by-step explanation:
HELP HOW DO I FIND THE B VALUE OF THIS
Answer:
b = [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
period = [tex]\frac{2\pi }{b}[/tex], that is
b = [tex]\frac{2\pi }{period}[/tex] = [tex]\frac{2\pi }{\frac{3\pi }{4} }[/tex] = 2π × [tex]\frac{4}{3\pi }[/tex] = [tex]\frac{8}{3}[/tex]
Answer:
f(x) = 4cos(8/3)x - 3.
The missing space is 8/3.
Step-by-step explanation:
The general form is f(x) = Acosfx + B where A = the amplitude, f = frequency and B is the vertical shift..
Here A is given as 4, B is - 3 and the frequency f = 2 π / period =
2π / (3π/4)
= 8/3.
So the answer is f(x) = 4cos(8/3)x - 3.
Power (denoted by PPP) can be defined as a function of work (denoted by WWW) and time (denoted by ttt) using this formula: P=\dfrac{W}{t}P= t W P, equals, start fraction, W, divided by, t, end fraction Work is measured in \dfrac{\text{kg}\cdot\text{m}^2}{\text{s}^2} s 2 kg⋅m 2 start fraction, start text, k, g, end text, dot, start text, m, end text, squared, divided by, start text, s, end text, squared, end fraction, and time is measured in \text{s}sstart text, s, end text.
Answer: kg*m^2 / s^3
Answer:
Answer: kg*m^2 / s^3
Step-by-step explanation:
You and your friend are skiing down a hill, your friend is almost at the finish line, and you want to catch up with him, how many seconds will it take you to reach him?
Answer:It depends
Step-by-step explanation:
A pure acid measuring x liters is added to 300 liters of a 20% acidic solution. The concentration of acid, f(x), in the new substance is equal to the liters of pure acid divided by the liters of the new substance, or . Which statement describes the meaning of the horizontal asymptote? The greater the amount of acid added to the new substance, the more rapid the increase in acid concentration. The greater the amount of acid added to the new substance, the closer the acid concentration is to one-fifth. As more pure acid is added, the concentration of acid approaches 0. As more pure acid is added, the concentration of acid approaches 1.
Answer:
the answer is d
Step-by-step explanation:
Canaries provide more food to their babies when the babies beg more intensely. Researchers wondered if begging was the main factor determining how much food baby canaries receive, or if parents also take into account whether the babies are theirs or not. To investigate, researchers conducted an experiment allowing canary parents to raise two broods: one of their own and one fostered from a different pair of parents. If begging determines how much food babies receive, then differences in the " begging intensities" of the broods should be strongly associated with differences in the amount of food the broods receive. The researchers decided to use the relative growth rates ( the growth rate of the foster babies relative to that of the natural babies, with values greater than 1 indicating that the foster babies grew more rapidly than the natural babies) as a measure of the difference in the amount of food received. They recorded the difference in begging intensities ( the begging intensity of the foster babies minus that of the natural babies) and relative growth rates. Here are data from the experiment:Difference in begging intensity -14 -12.5 -12 -8 -8 - 6.5 -5.5 -3.5 -3 -2 -1.5Relative growth rate 0.85 1 1.33 0.85 0.9 1.15 1 1.3 1.33 1.03 0.95Difference in begging intensit -1.5 0 0 2 2 3 4.5 7 8 8.5 Relative growth rate 1.15 1.13 1 1.07 1.14 1 0.83 1.15 0.93 0.7 Make a scatterplot that shows how relative growth rate responds to the difference in begging intensity.The scatterplot suggests that the relationship between relative growth rate and difference in begging intensityLinear or Not Linear ?
Answer:
The required scatterplot is given in attached file.
Step-by-step explanation:
From the scatterplot we see that two study variables are not linearly related. There may be some non-linear relation between the two variables.
The question asks about the relationship between canary chick begging intensity and their relative growth rate. This can be determined by creating and interpreting a scatterplot of the provided data. The relationship would be considered linear if there's a consistent rate of change between begging intensity and growth rate, and non-linear if the rate of change varies.
Explanation:The question is asking if the relationship between the relative growth rate of canary chicks and the difference in begging intensity is linear or not. By plotting the data on a scatterplot, we would visualize whether there is a consistent, straight-line relationship (linear) or not (non-linear) between these two variables.
Without the actual scatterplot, I cannot definitively say if the relationship is linear or not. However, linear relationships typically involve variables moving in the same direction at a constant rate, while non-linear relationships involve variables moving at different rates or directions. Therefore, if the increase in begging intensity is consistently associated with an increase in relative growth rate (and vice versa), the relationship could be considered linear. On the other hand, if increases or decreases in begging intensity inconsistently affect the relative growth rate, the relationship would likely be non-linear.
An important part of this research is the ability to interpret scatterplots and understand the concepts of linear and non-linear relationships in biological data. Interpreting such relationships is integral in the study of animal behavior and understanding how different factors, such as parental care and chick begging, affect survival and growth in bird species like canaries.
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Tierra rode in a bike-a-thon. Her sponsors donated $7 for every 5 miles she biked. At the end of the bike-a-thon, Tierra had raised $147. How many miles did she ride?
Answer:
105 miles
Step-by-step explanation:
The question seeks to know the number of miles traveled by Tiera given that she received a certain amount of money in payment.
The total amount of money she received is $147. She receives $7 for every 5 miles traveled. The number of 5 miles traveled is calculated as 147/7 = 21
This means she traveled 5 miles 21 times.
Thus, the total number of miles she had traveled would be 21 * 5 = 105 miles in total
(04.01)
Which of the following shows the correct steps to find the value of 16 to the power of 1 over 4 ? (1 point)
Group of answer choices
16 to the power of 1 over 4 equals 2 to the power of 4 to the power of 1 over 4 equals 2 to the power of 4 multiplied by 1 over 4 equals 2
16 to the power of 1 over 4 equals 4 to the power of 4 to the power of 1 over 4 equals 4 to the power of 4 multiplied by 1 over 4 equals 4
16 to the power of 1 over 4 equals 2 to the power of 8 to the power of 1 over 4 equals 8 to the power of 8 multiplied by 1 over 4 equals 4
16 to the power of 1 over 4 equals 8 to the power of 2 to the power of 1 over 4 equals 2 to the power of 2 multiplied by 1 over 4 equals 8
Answer:
16 to the power of 1 over 4 equals 2 to the power of 4 to the power of 1 over 4 equals 2 to the power of 4 multiplied by 1 over 4 equals 2
Step-by-step explanation:
16 to the power of 1 over 4 equals 2 to the power of 4 to the power of 1 over 4 equals 2 to the power of 4 multiplied by 1 over 4 equals 2
(16)^1/4 = (2^4)^1/4
4 cancels 4
2^1 = 2
Answer:
Step-by-step explanation:
The answer is the first one.
[tex]16^{\frac{1}{4}}[/tex] simplifies down to
[tex](2^4)^{\frac{1}{4}}[/tex] The power to power rule is that you multiply the exponents together:
[tex]2^{\frac{4}{4}}[/tex] which is [tex]2^1[/tex] which is 2
I'm assuming that you are also working with radicals (since radicals and exponents are inverses of each other). The way to write this is as a radical and simplify it is:
[tex]16^{\frac{1}{4}[/tex] as a radical is
[tex]\sqrt[4]{16^1}[/tex]
To simplify, try to write the radicand (the number under the square root) so it's a number with a power that matches the index (the number in the "arm" of the radical sign. Our index is a 4).
16 is the same as 2⁴:
[tex]\sqrt[4]{2^4}[/tex]
The power on the 2 is a 4, which is the same as the index. When the power matches the index, you pull out the base as a single number:
[tex]\sqrt[4]{2^4}=2[/tex]
Which inequality can Josh use to determine x, the minimum number of visits he needs to earn his first free movie ticket?
Answer:
3.5x + 15 ≥ 55
Step-by-step explanation:
I think the question below contains the missing information.
Josh has a rewards card for a movie theater. - He receives 15 points for becoming a rewards card holder. - He earns 3.5 points for each visit to the movie theatre. - He needs at least 55 points to earn a free movie ticket. Which inequality can Josh use to determine x, the minimum number of visits he needs to earn his firs free movie ticket?
My answer:
Becoming a member = 15 pointsVisiting the moving theater = 3.5 pointsTotal points needed for a free movie ticket = 55Let x is the number of times he visits = 3.5x
Total points = Points received on becoming a member + Points received on x visits
So,
Total Points = 15 + 3.5x
We know the total points must be at least 55 for a free movie ticket. This can be expressed as:
3.5x + 15 ≥ 55
What are the solutions to the system of equations?
{y=2x2−8x+5
{y=x−2
Final answer:
To find the solutions to the system of equations, use the substitution method. The solutions are (1/2, -3/2) and (7, 5).
Explanation:
To find the solutions to the system of equations, we can use the substitution method. First, solve one of the equations for y in terms of x. Let's solve the second equation for y:
y = x - 2
Now substitute this expression for y into the first equation:
x - 2 = 2x^2 - 8x + 5
Now we have a quadratic equation. Rearrange it into standard form:
2x^2 - 9x + 7 = 0
Next, factor the quadratic equation:
(2x - 1)(x - 7) = 0
Set each factor equal to zero and solve for x:
2x - 1 = 0, x - 7 = 0
x = 1/2, x = 7
Now substitute these values of x back into either of the original equations to find the corresponding values of y:
For x = 1/2: y = 1/2 - 2 = -3/2
For x = 7: y = 7 - 2 = 5
So the solutions to the system of equations are (1/2, -3/2) and (7, 5).
Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
C(x)= 9000x +72,000
R(x)= 15,000x
Answer:
12
Step-by-step explanation:
15000x = 9000x +72000
6000x = 72000
x = 12
Answer: the number of units that must be sold to break even is 12
Step-by-step explanation:
The cost function is expressed as
C(x)= 9000x +72000
The revenue function is expressed as
R(x) = 15000x
Profit = Revenue - cost
At the point of break even, the total revenue is equal to the total cost. This means that profit is zero. The expression becomes
Revenue - cost = 0
Revenue = cost
R(x) = C(x)
Therefore,
15000x = 9000x +72000
15000x - 9000x = 72000
6000x = 72000
x = 72000/6000
x = 12
Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. Which of the following statements must be true?
I. At least one of the homes was sold for more than $165,000.
II. At least one of the homes was sold for more than $130,0000 and less than $150,000
III. At least one of the homes was sold for less than $130,000.
A. I only
B. II only
C. III only
D. I and II
E. I and III
Answer:
A. I Only.
Step-by-step explanation:
To begin, we must first be clear that it is the median and that it is the arithmetic mean:
Median is the middle value of a sequence of ordered numbers, for example:
{4,4,4,4,4}, the median is 4 despite being the same numbers.
Now the arithmetic mean is the average value of the samples and is independent of the amplitudes of the intervals.
Then let's analyze each of our options:
I. At least one of the homes was sold for more than $ 165,000.
We know through the flushed:
X1 + X2 +. . . + X7 + (X8 = $130,000) + X9 +. . . + X15 = 15 ∗ 150,000 = $ 2,250,000
Now we will assume the lowest possible value from X1 to X8 = $ 130,000 and from X9 to X15 = X, which is what we want to calculate. That is to say:
X1 = X2 = X3 = X4 = X5 = X6 = X7 = X8 = 130 and X9 = X10 = X11 = X12 = X13 = X14 = X15 = X,
knowing that the total value must be the average of 15, which is equal to $ 2250000 , we have the following equation:
8 ∗ $ 130,000 + 7X = $ 2,250,000
Rearranging:
X = ($ 2,250,000 $ - $ 1,040,000) / 7
X = $ 172,857
Therefore the first statement is true, because at least one house was sold at $ 172,857 which is more than $ 165,000
Evaluating the second option
II. At least one of the homes was sold for more than $ 130,0000 and less than $ 150,000
As the example of the median in the previous case you could have 8 houses that were sold for $ 130,000 or less, therefore here it loses validity, statement II is false.
Evaluating the third option
III. At least one of the homes was sold for less than $ 130,000.
We know that the eighth house sold for $ 130,000, but houses 1 to 7 may also have been sold for that same price. The statement III is false.
Therefore the answer is A. I Only.
A scoop of ice cream has a 3 inch radius. How tall should the ice cream cone of the same radius be in order to contain all of the ice cream inside the cone?
Answer:
12cm
Step-by-step explanation:
The scoop of Ice Cream is in the shape of a circular solid which is a Sphere.
For the ice cream to fit into the cone, the volume of the cone must be equal to that of the sphere.
Radius of the Sphere=3cm
Volume of a Sphere = [tex]\frac{4}{3}\pi r^3[/tex]
Volume of a Cone=[tex]\frac{1}{3}\pi r^2h[/tex]
[tex]\frac{1}{3}\pi X 3^2h=\frac{4}{3}\pi X 3^3\\\frac{1}{3}h=\frac{4}{3} X 3\\\frac{1}{3}h=4\\h=4 X 3=12cm[/tex]
The Cone of same radius must be 12cm tall.
(1 point) A rock is thrown into a still pond and causes a circular ripple. If the radius of the ripple is increasing at a rate of 4 feet per second, how fast is the circumference changing when the radius is 18 feet?
Answer:
8pi feet per second
Or, 25.1 feet per second (3 sf)
Step-by-step explanation:
C = 2pi×r
dC/dr = 2pi
dC/dt = dC/dr × dr/dt
= 2pi × 4 = 8pi feet per second
dC/dt = 25.1327412287
Suppose that an ordinary deck of 52 cards (which contains 4 aces) is randomly divided into 4 hands of 13 cards each. We are interested in determining p, the probability that each hand has an ace. Let
Ei
be the event that the ith hand has exactly one ace. Determine
p=P(E1E2E3E4)
by using the multiplication rule.
Answer:
P ( E_1*E_2*E_3*E_4 ) = 0.1055
Step-by-step explanation:
Given:
- 52 cards are dealt in 1 , 2 , 3 , 4 hands.
- Events:
E_1 Hand 1 has exactly 1 ace
E_2 Hand 2 has exactly 1 ace
E_3 Hand 3 has exactly 1 ace
E_4 Hand 4 has exactly 1 ace
Find:
p =P ( E_1*E_2*E_3*E_4 )
Solution:
Multiplication rule.
- For n ε N and events E_1 , E_2 , ... , E_n:
P ( E_1*E_2*......*E_n ) = P (E_1)*P(E_2|E_1)*P(E_3|E_2*E_1)*......*(E_n|E_1*E_2...E_n-1 )
- So for these events calculate 4 probabilities:-
- For E_1, is to choose an ace multiplied by the number of ways to choose remaining 12 cards out of 48 non-aces:
P ( E_1 ) = 4C1 * 48C12 / 52C13
- For E_2 | E_1 , one ace and 12 other cards have already been chosen. there are 39C13 equally likely hands. The number of different one ace hand 2 is the number of ways to choose an ace from 3 remaining multiplied by the number of ways to choose the remaining 12 from 36, we have:
P ( E_2 | E_1 ) = 3C1 * 36C12 / 39C13
P ( E_3| E_2*E_1 ) = 2C1 * 24C12 / 26C13
P ( E_4 | E_3*E_2*E_1 ) = 1C1*12C12 / 13C13 = 1
- So the multiplication rule for n = 4 is as follows:
P ( E_1*E_2*E_3*E_4 ) = P (E_1)*P(E_2|E_1)*P(E_3|E_2*E_1)*P ( E_4 | E_3*E_2*E_1 ) = [ 4C1 * 48C12 / 52C13 ] * [ 3C1 * 36C12 / 39C13 ] * [ 2C1 * 24C12 / 26C13 ]
P ( E_1*E_2*E_3*E_4 ) = [ 4!*48! / (12!)^4 ] / [ 52! / (13!)^4 ]
P ( E_1*E_2*E_3*E_4 ) = [ 4!*13^4 / (52*51*50*49) ]
P ( E_1*E_2*E_3*E_4 ) = 0.1055
The probability that each hand in a deck of 52 cards gets exactly one ace is approximately 10.5%.
To determine the probability that each hand in a randomly divided deck of 52 cards has exactly one ace, we use the concept of conditional probability.
Let's find it step by step
Step 1 : consider the event E1 that the first hand has exactly one ace:
There are 4 aces and 52 total cards. The probabilities for drawing an ace for the first hand are affected by the decreasing number of both aces and cards.
The probability of the first hand receiving one ace is calculated as:
P(E1) = (4/52) * (48/51) * (47/50) * ... * (36/39)
Step 2 : consider the event E2 that the second hand receives exactly one ace, given that the first hand already has one:
With one ace already given to the first hand, there are 3 aces remaining and 39 cards left for the second hand.
The probability is calculated as:
P(E2|E1) = (3/39) * (35/38) * ... * (25/26)
Step 3 : Proceed similarly for the third and fourth hands:
P(E3|E1E2) = (2/26) * ... * (12/13)
P(E4|E1E2E3) = 1 (since only one ace remains for the last hand)
Step 4 : Using the multiplication rule, the overall probability P(E1E2E3E4) is calculated by multiplying the individual probabilities:
P(E1E2E3E4) = P(E1) * P(E2|E1) * P(E3|E1E2) * P(E4|E1E2E3)
Step 5 : After performing the calculations, we find:
The combined probability P(E1E2E3E4) = (4/52)*(3/39)*(2/26)(1/13) after simplifying is approximately 0.105 or 10.5%.
100 pyramid shaped chocolate candies with a square base of 12 mm size and height of 15 mm are melted in a cylinder coil pot if the part has a radius of 75 mm what is the height of the melted candies in the pot.
Answer: the height of the melted candies in the pot is 12.2 mm
Step-by-step explanation:
The formula for determining the volume of a square base pyramid is expressed as
Volume = area of base × height
Area of the square base = 12² = 144 mm²
Volume of each pyramid = 15 × 144 = 2160 mm³
The volume of 100 pyramid shaped chocolate candies is
2160 × 100 = 216000 mm³
The formula for determining the volume of a cylinder is expressed as
Volume = πr²h
Since the pyramids was melted in the cylindrical pot whose radius is 75 mm, it means that
216000 = 3.14 × 75² × h
17662.5h = 216000
h = 216000/17662.5
h = 12.2 mm
Answer:
The height of the melted candies in the pot is 4.07mm
Step-by-step explanation:
H= 100*1/3(12)^2(15)/π(75)^2=64/5π=4.07
What is the volume of a cylinder, in cubic m, with a height of 5m and a base diameter of 20m? Round to the nearest tenths place
What is the volume of a cylinder, in cubic m, with a height of 5m and a base diameter of 20m? Round to the nearest tenths place.
Answer: 1570.8
The volume of a cylinder with a height of 5m and a base diameter of 20m is approximately 1,570.8 cubic meters when rounded to the nearest tenths place.
To find the volume of a cylinder with a height of 5m and a base diameter of 20m, we will use the formula for the volume of a cylinder: V = πr²h , where V is volume, r is the radius of the base, and h is the height of the cylinder. The radius is half of the diameter, so for a diameter of 20m, the radius is 10m. Substituting these values into the formula gives us V = (π × 10² × 5), which we can calculate as V = 3.1416 × 100 × 5 = 1,570.8 cubic meters, rounded to the nearest tenths place.
a bag contains 6 red jelly beans 4 green jelly beans 4 blue jelly beans
Answer:
12/91Explanation:
The question is incomplete. The complete question is:
A bag contains 6 red jelly beans, 4 green jelly beans, and 4 blue jelly beans.
If we choose a jelly bean, then another jelly bean without putting the first one back in the bag, what is the probability that the first jelly bean will be green and the second will be red?
Solution
The probability that the first jelly bean will be green is the number of green jelly beans divided by the total number of jelly beans:
4/14After chosing the first green jelly bean, there will be 13 jelly beans, from which 6 are red. Thus, the probability that the second jelly bean will be red is:
6/13The probability of the joint events is the product of the two consecutive events:
(4/14) × (6/13) =12/91 ← answer
The probability that the first jelly bean will be green and the second will be red is 12/91.
We start by determining the total number of jelly beans in the bag, which is:
6 red + 4 green + 4 blue = 14 jelly beans.
Step 1: Probability of the first jelly bean being green
The probability of drawing a green jelly bean first is the number of green jelly beans divided by the total number of jelly beans:
P(Green first) = 4/14 = 2/7.
Step 2: Probability of the second jelly bean being red
Once the first green jelly bean is chosen, there are now 13 jelly beans left in the bag, with 6 being red:
P(Red second | Green first) = 6/13.
Step 3: Combined probability
The combined probability of both events happening (first green, then red) is given by multiplying their individual probabilities:
P(Green first and Red second) = (2/7) * (6/13) = 12/91.
Thus, the combined probability is 12/91.
Complete question: A bag contains 6 red jelly beans, 4 green jelly beans, and 4 blue jelly beans. If we choose a jelly bean, then another jelly bean without putting the first one back in the bag, what is the probability that the first jelly bean will be green and the second will be red?