Answer:
-471,861
Step-by-step explanation:
The sum of 9 terms in the sequence –9, 36, –144, 576, ... is -471861.
What is a sequence?An ordered collection of objects that allows repetitions is referred to as a sequence. It has members, just like a set does. The length of the sequence is determined by the number of items.
Given:
–9, 36, –144, 576, ...
Calculate the ratio of the sequence as shown below,
ratio = 36 / -9
ratio = -4
Calculate the sum of 9 terms as shown below,
S₉ = -9 (1 - (-4)⁹) / (1 - (-4))
S₉ = -9 (1 + 262144) / 5
S₉ = -9 (262145) / 5
S₉ = -2359305 / 5
S₉ = -471861
To know more about the sequence:
https://brainly.com/question/28615767
#SPJ2
A flea jumps from the ground to a height of 30 cm and travels 15 cm horizontally from where it started. Suppose the origin is located at the point from which the flea jumped. Determine a quadratic function in vertex form to model the height of the flea compared to the horizontal distance travelled.
The quadratic function in vertex form to model the height of the flea compared to the horizontal distance travelled is h = -2/15*(d-15)² + 30 with the maximum point at (15, 30) and passing through the origin.
Explanation:The problem here can be diagnosed using concepts of
quadratic functions
and
vertex form
. In a real world scenario, the motion of a projectile like the flea jumping can be modeled using a downward opening parabola represented by a quadratic function. In this case, we are asked to find the quadratic function in vertex form, which is given by
h = a(d - h1)² + k
where (h1,k) is the vertex of the parabola. In the given scenario, the maximum height attained by the flea is 30 cm which is at a horizontal distance of 15 cm from the starting point, thus the vertex of the parabola is (15, 30). From the information given, we know that the flea starts from the ground, so at the origin, height h = 0. Substituting these values, we get the equation of the parabola as
h = -a(d-15)^2 + 30
.
To find the value of 'a'
, we can use the information that the parabola passes through the origin (0,0). Substituting these values in the equation, we get a = -30/225 = -2/15. Therefore, the quadratic function in vertex form to model the height of the flea compared to the horizontal distance travelled becomes
h = -2/15*(d-15)² + 30
.
Learn more about Quadratic Functions here:https://brainly.com/question/35505962
#SPJ3
The mean of the sampling distribution of the sample mean is: Select one: a. equal to the population mean b. greater than the population mean c. less than the population mean d. not equal to the population mean but the direction cannot be determined
Answer:
Correct option is (a) equal to the population mean.
Step-by-step explanation:
According to the Central limit theorem if a large sample is selected from an unknown population with mean μ and standard deviation σ then the sampling distribution of sample means follows a normal distribution.
The mean and standard deviation of this sampling distribution is:
[tex]\mu_{\bar x}=\mu[/tex]
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
This standard deviation of the sampling distribution of mean is known as the standard error.
Thus, the correct option is (a) equal to the population mean.
The mean of the sampling distribution of the sample mean is equal to the population mean, as stated by the Central Limit Theorem, when the sample size is sufficiently large.
Explanation:The correct answer to the student's question is: a. equal to the population mean. This principle is a key concept in statistics, known as the Central Limit Theorem. According to the theorem, if the size (n) of the sample is sufficiently large, the distribution of the sample means will be approximately normal, with the mean of these sample means equalling the population mean. Another important point to note is that the standard deviation of this distribution, called the standard error of the mean, is the population standard deviation divided by the square root of the sample size (n). Therefore, as the sample size increases, the standard deviation of the sampling distribution of the means decreases, leading to more precise estimations of the population mean.
Gerry has two different part-time jobs, and he had work 20 hours per week at each job. He earns $8 per hour at one job. Which expression represents how much Gerry earned last week if he earns d dollars per hour at this other job? A- 20+20d B- 160+ 20d C- 40+ d D- 160+ 8d PLZZZZZZ ANSWER THX!!!!!!
Answer:The answer is B. 160 + 20d
Step-by-step explanation: first find out the total for how much he makes at the first job. 20 x 8 = 160 then you just write out the equation
WILL MARK BRANLIEST! 10 POINTS!
show work for #5
Step-by-step explanation:
ok so your gonna need to set up a proportion, specifically
25 is to x as x is to 16
mathematically, it's a cross multiplying problem:
25 X
=
X 16
cross multiply and you get 400 = x²
which when solved is 20.
Have a good night dude.
The president of a college has been told that when they raised their tuition by 15 percent the previous year, total revenue from tuition remained unchanged. Assuming the change in revenue is due to the change in tuition only, the president could conclude that demand for that college, over that tuition range, must be:
Answer:
= 1
Step-by-step explanation:
The demand for that college will be equal to 1 or it can be said as unit elastic demand over the tuition range. This means that the demand for the college would move proportionately with the tuition range of that college, since the change in revenue is due to the change in tuition only.
Hope this helps.
Good luck and cheers.
Answer:
demand for the college is equal to 1
Step-by-step explanation:
- We know that the change in Total Revenue is only the function of change in tuition fee only.
- The change in tution fee is subjected to 15% last year multiplied by the corresponding change in demand for the college will lead to a change in total revenue.
- The relation can be expressed as:
ΔTR = Δ P *ΔD
Where,
ΔTR : Change in Total Revenue
Δ P : Change in tuition fee
ΔD : Change in demand.
- For TR to remain unchanged then ΔTR = 0. Hence,
ΔTR = 0 = Δ P *ΔD
- We are given a change in Δ P = 15%, so that means for ΔTR = 0, the change in demand ΔD = 0.
- ΔD = 0, also means that the elasticity of the demand curve is perfectly elastic or in other words the demand for the college is equal to 1.
Choose the correct molecular geometry of the phosphorus atom in each of these ions from the list below: A) square plane B) T-shape C) icosahedral D) seesaw E) trigonal pyramid F) bent G) octahedron H) square pyramidal I) linear J) tetrahedron K) trigonal bipyramid L) None of the above Enter two letters that correspond to PCl4+ and PCl6− in order, e.g. AB, DC, EA, etc.
Answer:
See attached picture.
Step-by-step explanation:
See attached picture.
For remaining parts resubmit question.
Suppose a firm has a net profit margin of 15%, sales of $155 million, assets of $312 million, and owner's equity of $223 million. If the dividend payout ratio is 10%, what is the firm's sustainable growth rate?
Answer:
2.7%.
Step-by-step explanation:.
Given:
Net profit margin ( profitability rate) = 15%
Total sales = $155 million
Total assets = $312 million
Total equity = $223 million.
Dividend rate = 10%
Question asked:
What is the firm's sustainable growth rate ?
First of all we will find these thing.
1. Asset utilization rate = [tex]\frac{Total \ sales}{Total \ assets}[/tex]
= [tex]\frac{155}{312} = 0.496\ million= 0.5\%[/tex]
2. Financial utilization rate = [tex]\frac{Total\ debt}{Total\ equity} \\[/tex]
Total debt = Total asset - Total equity
= $312 million - $223 million = $89 million
= [tex]\frac{89}{223} = 0.4\%[/tex]
3. Return on equity rate = Asset utilization rate [tex]\times[/tex] profitability rate
Return on equity rate = [tex]0.5\times15\times0.4=3\%[/tex]
4. Business retention rate = 100 - Dividend rate
= 100 - 10 = 90%
Now, finally we will calculate sustainable growth rate :
Sustainable growth rate = Return on equity rate [tex]\times[/tex] Business retention rate
= [tex]3\%\times90\%=2.7\%[/tex]
Therefore, firm's sustainable growth rate is 2.7%
A robot can complete 5 tasks in two thirds hour. Each task takes the same amount of time. A. How long does it take the robot to complete one task? B. How many tasks can the robot complete in one hour? A. It takes the robot nothing hour(s) to complete one task. (Simplify your answer.)
Answer:
It'll take the robot 8 minutes to complete one task
7.5 tasks will be completed in one hour
Step-by-step explanation:
Total time to complete 5 tasks is 2/3hr (40 minutes)
Time it takes to complete one task = 40 ÷ 5 = 8 minutes
Since the robot completes one task in 8 minutes, x tasks will be completed in 60 minutes.
x = 60 ÷ 8 = 7.5 tasks
Answer:
A. 8 minutes; B. 7.5 tasks in one hour; C. It takes the robot about [tex] \\ \frac{2}{15}\;hour[/tex] or about 0.1333 hour to complete one task or 13.33% of one hour.
Step-by-step explanation:
Part A
Two thirds hours is
[tex] \\ \frac{2}{3}*60 = 40\;min[/tex]
We know that each task takes the same amount of time. So, 40min can be divided by 5:
[tex] \\ \frac{40}{5} = 8\;min[/tex]
Thus, each task takes 8 min to be completed. Then, it takes the robot 8 minutes to complete one task.
Part B
The robot can complete 5 tasks in 40 minutes, how many tasks can the robot complete in 60 minutes or one hour?
There are 20 minutes ahead to complete one hour. In the next 8 minutes, the robot can complete one task. There are still 12 minutes ahead. In the next 8 minutes, the robot completes another task. There is still 4 minutes ahead to complete the hour, but in 4 minutes the robot can complete half of the task because it takes 8 minutes for a complete task. Therefore, the robot can complete 5 tasks + 2 tasks + 0.5 task = 7.5 tasks in one hour or 60 minutes.
We can obtain the same answer using proportions. That is, if 5 tasks are completed in 40 minutes, how many of them will be completed in one hour or 60 minutes.
Then
[tex] \\ \frac{5\;tasks}{40\;min} = \frac{x}{60\;min}[/tex]
[tex] \\ \frac{5\;tasks}{40\;min}*60\;min = x[/tex]
[tex] \\ x = \frac{5\;tasks*60\;min}{40\;min}[/tex]
[tex] \\ x = \frac{300\;tasks}{40} = 7.5\;tasks[/tex]
Part C (A)
From part A, we already know that the robot can complete a task in 8 minutes, which is a fraction of one hour. What is this fraction? In one hour we have 60 minutes, then
[tex] \\ 8\;min*\frac{1\;hour}{60\;min} = 1\;hour*\frac{8}{60} = 1\;hour*\frac{4}{30} = 1\;hour*\frac{2}{15} = 0.1333333....\;hours \approx 0.1333\;hours[/tex].
Therefore, it takes the robot about [tex] \\ \frac{2}{15}\;hour[/tex] or 0.1333 hour to complete one task (rounding to four decimal places) or 13.33% of one hour.
A weather balloon was filled with gas until its diameter was 5 ft. After reaching its highest altitude in the atmosphere, the balloon burst, with a diameter of 28 ft. What is the difference in volume of the balloon when it burst compared to at launch?
Answer:
Step-by-step explanation:
it is 11423 ft3
Final answer:
The difference in volume of the weather balloon from launch to burst is calculated using the formula for the volume of a sphere, considering the change in diameters from 5 ft to 28 ft. The resulting difference is approximately 11,428.89 cubic feet.
Explanation:
The question asks for the difference in volume of a weather balloon when it burst compared to at launch. To solve this, we use the formula for the volume of a sphere, which is V = \(\frac{4}{3}\)\(\pi\)r^3, where r is the radius of the sphere. Given that the diameter at launch was 5 ft and at burst was 28 ft, the radiuses would be 2.5 ft and 14 ft, respectively.
Volume at launch: V1 = \(\frac{4}{3}\)\(\pi\)(2.5)^3 \approx 65.45 cubic feet. Volume at burst: V2 = \(\frac{4}{3}\)\(\pi\)(14)^3 \approx 11,494.34 cubic feet. The difference in volume: V2 - V1 \approx 11,494.34 - 65.45 \approx 11,428.89 cubic feet.
Therefore, the difference in volume of the balloon when it burst compared to at launch is approximately 11,428.89 cubic feet.
A fire company keeps two rescue vehicles. Because of the demand on the vehicles and the chance of mechanical failure, the probability that a specific vehicle is available when needed is 90%. The availability of one vehicle is independent of the availability of the other. Find the probability that neither vehicle is available at a given time?
Step-by-step explanation:
Let us assume the two needed vehicles are A and Q.
Let P(A) be the probability of the vehicle A available when needed.
And, P(Q) be the probability of the vehicle Q available when needed.
Now, P(A) = 90 % = 0.90
⇒ P (not A) = 1 - P(A)
= 1- 0.9 = 0.1
⇒ P (not A) = 0.1
Similarly, P(Q) = 90 % = 0.90
⇒ P (not Q) = 1 - P(Q)
= 1- 0.9 = 0.1
⇒ P (not Q) = 0.1
So, the probability that both the vehicles are NOT available when needed
= P(not A) x P(not Q)
= 0.1 x 0.1 = 0.01
Hence, the probability that neither vehicle is available at a given time is 0.01
A fan of country music plans to make a custom CD with 14 of her 25 favorite songs. How many different combinations of 14 songs are possible? Is it practical to make a different CD for each possible combination?
Answer:
4457400
Step-by-step explanation:
25C14 = 4457400
Not practical, these are too many
Answer:
4,457,400 combinations.
Step-by-step explanation:
The number of combinations of 14 from 25 is a very large number :
25C14 = 25! / 14! 11!
= 4,457,400.
With so many possible combinations it would not be practical to make a Cd for all these possibilities.
The equation of a line parallel to 2x−y+4=0 that passes through the point ( -1, 5) is ___?
Answer:
y=2x+7
Step-by-step explanation:
2x−y+4=0
y=2x+4
m=2
Line are parallel, so their slope is the same.
A(-1,5)... x1 =-1,y1 =5
y-y1 =m(x-x1)
y1 - 5=2(x-(-1))
y1 - 5=2(x+1)
y1-5=2x+2
y=2x+2+5
y=2x+7
Answer: y = 2x + 7
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
c represents y intercept
m represents the slope of the line.
The equation of the given line is
2x - y + 4 = 0
y = 2x + 4
Comparing with the slope intercept form, slope = 2
If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line passing through (- 1, 5) is 2
To determine the y intercept, we would substitute m = 2, x = - 1 and y = 5 into y = mx + c. It becomes
5 = 2 × - 1 + c
5 = - 2 + c
c = 5 + 2 = 7
The equation becomes
y = 2x + 7
find the area of a rectangle that has a base of (4a) cm and a height (2a + b)
Answer:
area = 8a^2 +4ab
Step-by-step explanation:
Area = (4a)(2a + b)
= 8a^2 +4ab
Step-by-step explanation:
[tex]Area of rectangle \\ = base \times height \\ = (4a) \times (2a + b) \\ = 4a \times 2a + 4a \times b \\ = 8 {a}^{2} + 4ab \\ [/tex]
If you start at vertex A and use the "shortest route" algorithm, what would be the second path to be selected/highlighted?
Group of answer choices
AB
AC
ACF
ABE
*100% CORRECT ANSWERS
Question 1
Alan is writing out the steps using the "shortest Route Algorithm". On the second step, he just circled the route ABD as the shortest route from A to D. What should he cross out next?
AD; 6
Question 2
Beth is writing out the steps using the "Shortest Route Algorithm". She just finished writing out all the routes for the third step. What route should she circle next?
ACE; 6
Question 3
If you start at vertex A and use the "shortest route" algorithm, what would be the second path to be selected/highlighted?
ACF
(SEE ATTACHMENTS BELOW)
Answer: ACF
Step-by-step explanation: Starting at vertex A and using shortest routes algorithm the secondary route to be selected would be ACF = 1+2 = 3
The first route would be AC = 1. A vertex is a point where two straight lines meet or join, they are usually found in angles.
Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options.
y = 3/4x + 1
3x − 4y = −4
4x − 3y = −3
y – 2 = –3/4(x – 4)
y + 2 = 3/4 (x+4)
Option A: [tex]y=\frac{3}{4}x+1[/tex] is the equation of the line.
Option E: [tex]y+2=\frac{3}{4}(x+4)[/tex] is the equation of the line.
Explanation:
Given that the line is [tex]3 x-4 y=7[/tex] and passes through the point [tex](-4,-2)[/tex]
We need to determine the equation of the line.
Formula:
The equation of the line can be determined using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
Slope:
Since, the lines are parallel, from the equation [tex]3 x-4 y=7[/tex], we shall determine the slope.
Thus, we have,
[tex]-4 y=-3x+7[/tex]
[tex]y=\frac{3}{4} x+\frac{7}{4}[/tex]
Thus, the slope of the equation is [tex]m=\frac{3}{4}[/tex]
Equation of line:
Substituting [tex]m=\frac{3}{4}[/tex] and the point [tex](-4,-2)[/tex] in the formula, we get,
[tex]y+2=\frac{3}{4}(x+4)[/tex]
Hence, the equation of line is [tex]y+2=\frac{3}{4}(x+4)[/tex]
Thus, Option E is the correct answer.
Let us write the equation of line [tex]y+2=\frac{3}{4}(x+4)[/tex] in slope - intercept form.
Thus, we have,
[tex]y+2=\frac{3}{4}x+3[/tex]
[tex]y=\frac{3}{4}x+3-2[/tex]
[tex]y=\frac{3}{4}x+1[/tex]
Thus, the equation of the line is [tex]y=\frac{3}{4}x+1[/tex]
Hence, Option A is the correct answer.
Type A is 5 feet tall and grows at a rate of 9 inches per year. Type B is 8 feet tall and grows at a rate of 6 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.
Answer:
After 12 years height of both the trees would be same.
Step-by-step explanation:
Given,
Height of tree type A = 5 ft
Height of tree type B = 8 ft
We need to find after how many years both the trees will be of same height.
Solution,
Firstly we will convert the height of both plants into inches.
Since we know that 1 feet is equal to 12 inches.
So height of tree type A =[tex]5\ ft=5\times12=60\ in[/tex]
Similarly, height of tree type B =[tex]8\ ft=8\times12=96\ in[/tex]
Also given that;
Rate of growth of tree type A = 9 in/year
and rate of growth of tree type A = 6 in/year
Let the number of years be 'x'.
So according to question after 'x' years the height of both trees type A and type B will be same.
Now we can frame the equation as;
[tex]60+9x=96+6x[/tex]
Combining the like terms, we get;
[tex]9x-6x=96-60\\\\3x=36[/tex]
On dividing both side by '3' using division property, we get;
[tex]\frac{3x}{3}=\frac{36}{3}\\\\x=12[/tex]
Hence after 12 years height of both the trees would be same.
Give the coordinates of each point under the given transformation.
Answer:
see below
Step-by-step explanation:
The rotation transformations are ...
90° : (x, y) ⇒ (-y, x)
180° : (x, y) ⇒ (-x, -y)
270° : (x, y) ⇒ (y, -x)
Applying these to the given points, you get ...
9) A'(6, 9)
10) A'(15, 11)
11) A'(9, 6)
12) A'(-11, 15)
13) A'(6, -9)
14) A'(15, -11)
A light house operator is 34m above sea level. He spots a sailboat in the distance. The angle of depression of the sighting is 10. How far is the boat from the base of the lighthouse?
Answer: the distance of the boat from the base of the lighthouse is 192.9 m
Step-by-step explanation:
The scenario is represented in the right angle triangle shown in the attached photo.
Looking at triangle ABC, the height of the light house operator above sea level represents the opposite side of the right angle triangle.
Angle A = 10° because it is alternate to the angle of depression.
To determine AB, the distance of the boat from the base of the lighthouse, we would apply
the tangent trigonometric ratio which is expressed as
Tan θ, = opposite side/adjacent side. Therefore,
Tan 10 = 34/AB
AB = 34/Tan 10 = 34/0.1763
AB = 192.9 m
What is the frequency of the function f(x)?
f(x)=−sin(3x)−1
Enter your answer, in simplest fraction form, in the box.
Answer:
F=3
Step-by-step explanation:
Due to the difficulty of visualizing the graph of the function in degrees (graph 1), we will graph it in radians (graph 2)
f(x)=−sin(3x)−1 ≡ y=−sin(3x)−1
To graph y=−sin(3x)−1
y=a.sin(bx+c)+d, where
a=-1, b=3, c=0, d=-1 and the period (T) of the function is:
[tex]T=\frac{2\pi }{b}=\frac{2\pi }{3}[/tex]
On the graph 2 we place the original function y=sin(x) to compare
We watch that y=−sin(3x)−1 moves 1 down (-), but amplitud is the same (1)
Frequency is the number of repetitions (3x) of a function in a given interval, so
F=3
The frequency of the function f(x) = -sin(3x) - 1 is 3/(2π), determined by the coefficient of x inside the sine function.
The frequency of the function f(x) = -sin(3x) - 1 can be determined by examining the coefficient of x within the sine function. The standard form for a sine function is f(x) = sin(Bx), and the frequency f is given by f = B/(2π). In this case, the coefficient B is 3, so the frequency of the function is 3/(2π), which is already in simplest fraction form.
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.2, -4, and 1 3i
Answer:
[tex]f(x)=x^{4}+x^{3}-10x^{2} +8x[/tex]
Step-by-step explanation:
A number is a factor of f(x) if and only if f(x) is zero for that value/number.
For the factors of a function we write the factors as x-a where a is the zero of function i.e. value at which f(x) is zero.
To write the polynomial function of minimum degree with real coefficients whose zeros include 2, -4, and 1, 3i, we find the f(x) is the product of all factors i.e x-a where a will represent the given zeros.
[tex]f(x)=(x-2)(x-(-4))(x-1)(x-3i)\\f(x)=(x-2)(x+4))(x-1)(x-3i)\\f(x)=(x^{2} +4x-2x-8)(x^{2} -3xi-x+3i )\\f(x)=(x^{2} +2x-8)(x^{2} -x-(3x+3)i)\\[/tex]
As it is stated that polynomial should have real coefficients so skipping the terms with 'i' we get
[tex]f(x)=(x^{2} +2x-8)(x^{2} -x)\\f(x)=x^{4}-x^{3}+2x^{3}-2x^{2} -8x^{2} +8x\\f(x)=x^{4}+x^{3}-10x^{2} +8x[/tex]
Answer:
f(x) = x4 - 2x2 + 36x - 80
Step-by-step explanation:
The top five test scores in Mr. Rhodes's class were: 98, 92, 96, 97, and 97. What is
the mean absolute deviation?
plz help I'm lost!!
The mean of the top five test scores is 96. Then the mean absolute deviation is zero.
What is the mean absolute deviation?It is the average distance between each data point and the mean.
The top five test scores in Mr. Rhodes's class were: 98, 92, 96, 97, and 97.
Then the mean (μ) will be
[tex]\mu = \dfrac{98+92+96+97+97}{5}\\\\\mu = \dfrac{480}{5}\\\\\mu = 96[/tex]
Then the mean absolute deviation will be
[tex]\rm MAD = \dfrac{\Sigma (X_i - \mu)}{n}\\\\MAD = \dfrac{(98-96)+(92-96)+(96-96)+(97-96)+(97-96)}{5}\\\\MAD = \dfrac{2-4+0+1+1}{5}\\\\MAD = 0[/tex]
The mean absolute deviation is zero and the mean is 96.
More about the mean absolute deviation link is given below.
https://brainly.com/question/10258446
Final answer:
Calculating the mean absolute deviation of the top five test scores in Mr. Rhodes's class involves finding the mean score and then the average of the absolute deviations from this mean. The result is a MAD of 1.6, indicating the average dispersion of the top scores from the class mean.
Explanation:
The question involves calculating the mean absolute deviation (MAD) of the top five test scores in Mr. Rhodes's class, which are 98, 92, 96, 97, and 97. First, we find the mean (average) of these scores by adding them together and dividing by the number of scores, which gives us (98 + 92 + 96 + 97 + 97) / 5 = 96. Next, we calculate the absolute deviation of each score from the mean, which are 2, 4, 0, 1, and 1 respectively. The mean absolute deviation is then the average of these absolute deviations, calculated as (2 + 4 + 0 + 1 + 1) / 5 = 1.6.
The result of these calculations shows that the mean absolute deviation of the test scores is 1.6. This value represents how much, on average, each of the top five scores deviates from the mean score of the class, providing an understanding of the variability or dispersion within the top scores. The MAD is a useful measure in understanding how spread out the scores are from the mean.
Help ASAP Please
The following two-way frequency table shows information collected from a survey of students regarding their grade level and how they spend their screen time.
Grade vs.
Screen Time Uses the
Internet Watches
TV Plays Video
Games Total
7th Grader 6 3 6 15
8th Grader 8 3 2 13
Total 14 6 8 28
What is the probability that a student uses the Internet, given that he or she is in eighth grade?
Enter your answer rounded to two decimal places, like this: 0.42
Enter your answer as a fraction in simplest form, formatted like this: 3/14
The probability of an eighth-grade student using the Internet, based on the data provided, is approximately 0.62, or simply 8/13 as a fraction.
Explanation:To calculate the probability that a student uses the Internet given he or she is in eighth grade, we look at the eight graders' behaviors in the table. There are 13 students in total in the eighth grade, and 8 of these use the Internet.
So, the probability can be expressed as P(Internet|8th grader) = number of internet users in 8th grade / total number of 8th graders = 8 / 13.
When rounded to two decimal places, this probability would be approximately 0.62. In terms of fractions, it can simply be left as 8/13.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ12
The probability that a student uses the Internet, given that he or she is in eighth grade, is 2/3.
We are asked for the probability that a student uses the Internet, given that he or she is in eighth grade. This is the conditional probability [tex]$P({\text{Internet}} | {\text{8th Grade}})$[/tex], which can be calculated using Bayes' Theorem: \begin{align*}
[tex]P({\text{Internet}} | {\text{8th Grade}}) &= \frac{P({\text{8th Grade}} | {\text{Internet}})P({\text{Internet}})} {P({\text{8th Grade}})} \\&= \frac{\frac{8}{28} \cdot \frac{14}{28}} {\frac{13}{28}} \\&= \frac{2}{3}[/tex]
\end{align*}
Therefore, the probability that a student uses the Internet, given that he or she is in eighth grade, is [tex]$\boxed{\frac{2}{3}}$[/tex].
Here is a more detailed explanation of how we arrived at our answer:
Step 1: Calculate the probability of being in eighth grade, given that the student uses the Internet. This is the conditional probability [tex]$P({\text{8th Grade}} | {\text{Internet}})$[/tex], which can be calculated from the table as follows: [tex]$P({\text{8th Grade}} | {\text{Internet}}) = \frac{8}{14}$[/tex]
Step 2: Calculate the probability of using the Internet.** This is the marginal probability [tex]$P({\text{Internet}})$[/tex], which can be calculated from the table as follows: [tex]$P({\text{Internet}}) = \frac{14}{28}$[/tex].
Step 3: Calculate the probability of being in eighth grade.This is the marginal probability [tex]$P({\text{8th Grade}})$[/tex], which can be calculated from the table as follows: [tex]$P({\text{8th Grade}}) = \frac{13}{28}$[/tex].
Step 4: Apply Bayes' Theorem to calculate the conditional probability [tex]$P({\text{Internet}} | {\text{8th Grade}})$[/tex].
Therefore, the probability that a student uses the Internet, given that he or she is in eighth grade, is[tex]$\boxed{\frac{2}{3}}$[/tex].
For such more questions on probability
https://brainly.com/question/23417919
#SPJ6
James folds a piece of paper in half several times,each time unfolding the paper to count how many equal parts he sees. After folding the paper about six times, ti becomes too difficult to fold it again,but he is curious how many parts the paper would be broken into if he could continue to fold it. He decides to employ the modeling cycle to predict how many parts the paper would be folded into if he were able to fold it 11 times.
Answer:
There will be total 2048 parts of the given paper if James if able to fold the paper eleven times.
The needed function is [tex]y = 2 ^n[/tex]
Step-by-step explanation:
Let us assume the piece of paper James decides to fold is a SQUARE.
Now, let us assume:
n : the number of times the paper is folded.
y : The number of parts obtained after folds.
Now, if the paper if folded ONCE ⇒ n = 1
Also, when the pap er is folded once, the parts obtained are TWO equal parts.
⇒ for n = 1 , y = 2 ..... (1)
Similarly, if the paper if folded TWICE ⇒ n = 2
Also, when the paper is folded twice, the parts obtained are FOUR equal parts.
⇒ for n = 2 , y = 4 ..... (2)
⇒[tex]y = 2^2 = 2^n[/tex]
Continuing the same way, if the paper is folded SEVEN times ⇒ n = 7
So, [tex]y = 2^ n = 2^7 = 128[/tex]
⇒ There are total 128 equal parts.
Lastly, if the paper is folded ELEVEN times ⇒ n = 11
So, [tex]y = 2^ n = 2^{11} = 2048[/tex]
⇒ There are total 2048 equal parts.
Hence, there will be total 2048 parts of the given paper if James if able to fold the paper eleven times.
And the needed function is [tex]y = 2 ^n[/tex]
What is the distance between point (6, -1) and point (5, 3) rounded to the nearest tenth?
4.6 units
1.4 units
17 units
4.1 units
Answer:
4.6
Step-by-step explanation:
Use the distance formula:
d = [tex]\sqrt{(x-x)^{2}-(y-y)^{2} }[/tex]
plug in the numbers
[tex]\sqrt{(6-1)^{2} -(5-3)^{2} }\\[/tex]
PEMDAS says do parenthisee first
[tex]\sqrt{(5)^{2} -(2)^{2} }[/tex]
now square it
[tex]\sqrt{25-4}[/tex]
subtract
[tex]\sqrt{21}[/tex]
do the calculator for this part
4.582575695
round it to get
4.6
To find the depth of a well, a farmer lowers a 50-foot rope vertically into the well. If 15 feet of rope remain above the well, how deep (in feet) is the well?
The well is 35 feet deep.
Step-by-step explanation:
Given,
Length of rope = 50 feet
Length of remaining rope = 15 feet
Let,
x be the depth of well.
Total length of rope = Length of remaining + Depth of well
[tex]50=15+x\\50-15=x\\x=35[/tex]
The well is 35 feet deep.
Steve, an entrepreneur, decides to open a flower shop and looks for an appropriate location for his shop. He wants to use the center-of-gravity method for the purpose. He researches the zip codes in his area and finds the following information: Identify a true statement about the best center of gravity for the possible shop location.
A) The x-axis and the y-axis are less than 5.0.
B) The x-axis is less than 7.0 and the y-axis is more than 7.0.
C) The x-axis is more than 7.0 and the y-axis is less than 7.0.
D) The x-axis and the y-axis are more than 7.0.
Answer:
C
Step-by-step explanation:
The x-axis is more than 7.0 and the y-axis is less than 7.0.
Cheers
Find the product of 2x2(6x + 3).
A. 12x3
B. 12x3 + 3
C. 12x3 + 6x2
D. 2x2 + 6x + 3
Answer:
(option C/3) 12^3 + 6x^2
Step-by-step explanation:
Took test and got it right.
The product of 2x^2 and (6x + 3) is calculated using the distributive property of multiplication over addition, resulting in 12x^3 + 6x^2.
The question requires us to find the product of the polynomial 2x^2 with the binomial (6x + 3). We use the distributive property of multiplication over addition to multiply 2x^2 by each term in the binomial.
Step 1: Multiply 2x^2 by 6x: 2x^2 * 6x = 12x^3
Step 2: Multiply 2x^2 by 3: 2x^2 * 3 = 6x^2
Thus, the product of 2x^2(6x + 3) = 12x^3 + 6x^2. So the correct answer is D. 12x^3 + 6x^2.
Learn more about Polynomial multiplication here:
https://brainly.com/question/31961906
#SPJ2
Please help me with these rotation problem.
Answer:
see below
Step-by-step explanation:
In the attachment, the points are listed in the order given in the problem statement. (They are listed to the right of the "rotation matrix", with x-coordinates above y-coordinates.)
__
I really don't like to do repetitive calculations, so I try to use a graphing calculator or spreadsheet whenever possible. Angles are measured CCW.
As always, the rotation transformations are ...
180° — (x, y) ⇒ (-x, -y)
270° — (x, y) ⇒ (y, -x)
2. Compare and contrast East representation.
a. What are the constraints on each representation? Identify the set of x-values that make each number line true.
b. Select a value for x from your set of x-values that make each number line true.
Answer:
a) For Bella, x has to be a positive even values
For Tito, x has to be a negative even values
b) For Bella, x = 4
For Tito, x = -4
HELP I WILL MARK BRAINLIEST
Answer:
B.
Step-by-step explanation:
The line is going up 1 and over 2, making the slope 1/2 and the y-intercept is 1. Hope this helped!