graph the linear equation. Find three points that solve the equation, then plot on the graph. -3y=-x-6
Answers
Answer:
hope u get it.......!!
Related Questions
Which value of x makes 7+5(x-3)=227+5(x−3)=227, plus, 5, left parenthesis, x, minus, 3, right parenthesis, equals, 22 a true statement? Choose 1 answer:
Answers
Answer:
7 + 5(x - 3) = 22
5(x - 3) = 15
x - 3 = 3
x = 6
Answer:
x = 6
Step-by-step explanation:
Step 1: Distribute 5
7 + 5x - 15 = 22
Step 2: Combine like terms
5x - 8 = 22
Step 3: Add 8 to both sides
5x = 30
Step 4: Divide both sides by 5
x = 6
compute the missing data in the table for the following exponential function f(x)={1/4}
Answers
Answer:
1/256
Step-by-step explanation:
The table shows a chain of fractions for f(x), x1 is 1/4, x2 is 1/16 and x3 is 1/64. All you need to do is multiply the denominator by 4 and put 1 over it. 64*4 = 256, adding the 1 as the numerator gives us the answer of 1/256 as x4.
Alexandra has $15 to buy drinks for her friends at the baseball game. Soda
costs $2.75 and bottled water costs $2.00. This relationship can be
represented by the inequality 2758+2w $ 15. Three of Alexandra's friends
asked for water. Which inequality represents the number of sodas she can
buy?
A. OS 85 3.27
B. 85 3.27
C. OSSS3
D. 853
Answers
Answer:
C
Step-by-step explanation:
write an equation for the costs:
if x is the number of sodas
and y is the number of waters
2.75x + 2y <= 15
(<= is less than or equal to)
if we substitute 3 for y
we get 2.75x + 2(3) <= 15
2.75x + 6 <= 15
2.75x <= 9
9 / 2.75 = 3.2727
however, you cannot buy part of a soda
so, round to 3
you also cannot buy negative sodas
so, the answer is C
The dimensions of a closed rectangular box are measured as 96 cm, 58 cm, and 48 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box.
Answers
Answer:
161.6 cm²Step-by-step explanation:
Surface Area of the rectangular box = 2(LW+LH+WH)
L is the length of the box
W is the width of the box
H is the height of the box
let dL, dW and dH be the possible error in the dimensions L, W and H respectively.
Since there is a possible error of 0.2cm in each dimension, then dL = dW = dH = 0.2cm
The surface Area of the rectangular box using the differentials is expressed as shown;
S = 2{(LdW+WdL)+(LdH+HdL)+(WdH+HdW)]
Also given L = 96cm W = 58cm and H = 48cm, on substituting this given values and the differential error, we will have;
S = 2{(96*0.2+58*0.2) + (96*0.2+48*0.2)+(58*0.2+48*0.2)}
S = 2{19.2+11.6+19.2+9.6+11.6+9.6}
S = 2(80.8)
S = 161.6 cm²
Hence, the surface area of the box is 161.6 cm²
In a particular year, the mean score on the ACT test was 19.6 and the standard deviation was 5.2. The mean score on the SAT mathematics test was 546 and the standard deviation was 126. The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal placesFind the z-score for an ACT score of 26. The Z-score for an ACT score of 26 is ______ .
Answers
Answer:
0.11
Step-by-step explanation:
Let the random variable score, X = 26; mean, ∪ = 19.6; standard deviation, α = 5.2
By comparing P(0≤ Z ≤ 26)
P(Z ≤ X - ∪/α) = P(Z ≤ 26 - 19.6/5.2)
= P(Z ≤ 1.231)
Using Table: P(0 ≤ Z ≤ 1) = 0.39
P(Z > 1) = (0.5 - 0.39) = 0.11
∴ P(Z > 26) = 0.11
Suppose you just purchased a digital music player and have put 12 tracks on it. After listening to them you decide that you like 2 of the songs. With the random feature on your player, each of the 12 songs is played once in random order. Find the probability that among the first two songs played (a) You like both of them. Would this be unusual? (b) You like neither of them. (c) You like exactly one of them. (d) Redo (a)-(c) if a song can be replayed before all 12 songs are played.
Answers
Answer:
The answer is below
Step-by-step explanation:
We have the following information:
Number of songs you like = 2
Total number of songs = 12
a) P(you like both of them) = 2/12 x 1/11 = 0.015
This is unusual because the probability of the event is less than 0.05
b) P(you like neither of them) = 10/12 x 9/11 = 0.68
c) P(you like exactly one of them) = 2 x 2/12 x 10/11 = 0.30
d) If a song can be replayed before all 12,
P(you like both of them) = 2/12 x 2/12 =0.027
This is unusual because the probability of the event is less than 0.05
P(you like neither of them) = 9/12 x 9/12 = 0.5625
P(you like exactly one of them) = 2 x 2/12 x 9/12 = 0.25
Two balls are drawn in succession out of a box containing 2 red and 5 white balls. Find the probability that at least 1 ball was red, given that the first ball was (Upper A )Replaced before the second draw. (Upper B )Not replaced before the second draw.
Answers
Answer:
With replacement = 14/49without replacement = 3/7Step-by-step explanation:
Since there are 2 red and 5 white balls in the box, the total number of balls in the bag = 2+5 = 7balls.
Probability that at least 1 ball was red, given that the first ball was replaced before the second can be calculated as shown;
Since at least 1 ball picked at random, was red, this means the selection can either be a red ball first then a white ball or two red balls.
Probability of selecting a red ball first then a white ball with replacement = (2/7*5/7) = 10/49
Probability of selecting two red balls with replacement = 2/7*2/7 = 4/49
The probability that at least 1 ball was red given that the first ball was replaced before the second draw= 10/49+4/49 = 14/49
If the balls were not replaced before the second draw
Probability of selecting a red ball first then a white ball without replacement = (2/7*5/6) = 10/42 = 5/21
Probability of selecting two red balls without replacement = 2/7*2/6 = 4/42 = 2/21
The probability that at least 1 ball was red given that the first ball was not replaced before the second draw = 5/21+4/21 = 9/21 = 3/7
The probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.
Since two balls are drawn in succession out of a box containing 2 red and 5 white balls, to find the probability that at least 1 ball was red, given that the first ball was A) replaced before the second draw; and B) not replaced before the second draw; the following calculations must be performed:
2 + 5 = X7 = X
(2/7 + 2/7) / 2 = X (0.285 + 0.285) / 2 = X 0.285 = X
(2/7 + 1/6) / 2 = X (0.28 + 0.16) / 2 = X 0.451 / 2 = X 0.225 = X
Therefore, the probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.
Learn more about probability in https://brainly.com/question/14393430
In a study of 205 adults, the average heart rate was 75 beats per minute. Assume the population of heart rates is known to be approximately normal, with a standard deviation of 8 beats per minute. What does a margin of error of 1.1 for the 95% confidence interval of the average beats per minute mean? There is a 95% chance that the population mean is between 67 and 83 beats per minute. There is a 95% chance that the population mean is between 73.9 and 76.1 beats per minute. There is a 5% chance that the population mean is less than 75 beats per minute. There is a 5% chance that the population mean is more than 75 beats per minute.
Answers
Answer:
There is a 95% chance that the population mean is between 73.9 and 76.1 beats per minute.
Step-by-step explanation:
i have the test
There is a 95% chance that the population mean is between 73.9 and 76.1 beats per minute.
Calculation of margin of error:Since
The average heart rate was 75 beats per minute.
The standard deviation is 8 beats per minute
And, there is the study of 205 adults
Now the following formula is to be used
Since
[tex]x \pm z \frac{\sigma}{\sqrt{n} }[/tex]
Here
z = 1.96 at 95% confidence interval
So,
[tex]= 75 \pm 1.96 \frac{8}{\sqrt{205} } \\\\= 75 - 1.96 \frac{8}{\sqrt{205} } , 75 + 1.96 \frac{8}{\sqrt{205} }[/tex]
= 73.9 ,76.1
Hence, the above statement should be true.
Learn more about standard deviation here: https://brainly.com/question/20529928
Use the Laplace transform to solve the given initial-value problem.
y' + 3y = f(t), y(0) = 0
where f(t) = t, 0 ≤ t < 1 0, t ≥ 1
Answers
Answer:
The solution to the given Initial - Value - Problem is [tex]y(t) = \frac{-1}{9} + \frac{1}{3}t + \frac{1}{9}e^{-3t} - [\frac{-1}{9} + \frac{1}{3}t - \frac{2}{9}e^{-3(t-1)}]u(t-1)[/tex]
Step-by-step explanation:
y' + 3y = f(t).................(1)
f(t) = t when 0 ≤ t < 1
f(t) = 0 when t ≥ 1
Step 1: Take the Laplace transform of the LHS of equation (1)
That is L(y' + 3y) = sY(s) + 3Y(s) = Y(s)[s + 3]..............(*)
Step 2: Get an expression for f(t)
For f(t) = t when 0 ≤ t < 1
f₁(t) = t (1 - u(t - 1)) ( there is a time shift of the unit step)
For f(t) = 0 when t ≥ 1
f₂(t) = 0(u(t-1))
f(t) = f₁(t) + f₂(t)
f(t) = t - t u(t-1)................(2)
Step 3: Taking the Laplace transform of equation (2)
[tex]F(s) = \frac{1}{s^2} - e^{-s} ( \frac{1}{s^2} + \frac{1}{s})[/tex]...............(**)
Step 4: Equating * and **
[tex]Y(s) [s + 3]=\frac{1}{s^2} - e^{-s} ( \frac{1}{s^2} + \frac{1}{s}) \\Y(s) = \frac{1}{s^2(s+3)} - e^{-s} ( \frac{1}{s^2(s+3)} + \frac{1}{s(s+3)})[/tex].......................(3)
Since y(t) is the solution we are looking for we need to find the Inverse Laplace Transform of equation (3) by first breaking every fraction into partial fraction:
[tex]\frac{1}{s^2 (s+3)} = \frac{-1}{9s} + \frac{1}{3s^2} + \frac{1}{9(s+3)}[/tex]
[tex]\frac{1}{s (s+3)} = \frac{1}{3s} + \frac{1}{3(s+3)}[/tex]
We can rewrite equation (3) by representing the fractions by their partial fractions.
[tex]Y(s) = \frac{-1}{9s} + \frac{1}{3s^2} + \frac{1}{9(s+3)} - e^{-s} [\frac{-1}{9s} + \frac{1}{3s^2} + \frac{1}{9(s+3)} + \frac{1}{3s} + \frac{1}{3(s+3)}]\\Y(s) = \frac{-1}{9s} + \frac{1}{3s^2} + \frac{1}{9(s+3)} - e^{-s}[\frac{2}{9s} + \frac{1}{3s^2} - \frac{2}{9(s+3)}][/tex]................(4)
step 5: Take the inverse Laplace transform of equation (4)
[tex]y(t) = \frac{-1}{9} + \frac{1}{3}t + \frac{1}{9}e^{-3t} - u(t-1)[\frac{2}{9} + \frac{1}{3}(t-1) - \frac{2}{9}e^{-3(t-1)}][/tex]
Simplifying the above equation:
[tex]y(t) = \frac{-1}{9} + \frac{1}{3}t + \frac{1}{9}e^{-3t} - [\frac{-1}{9} + \frac{1}{3}t - \frac{2}{9}e^{-3(t-1)}]u(t-1)[/tex]
The Laplace transform is use to solve the differential equation problem.
The solution for the given initial-value problem is,
[tex]y(t)=\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{1}{9}e^-3t-\left[\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{2}{9}e^{-3(t-1)}\right]u(t-1)[/tex]
Given:
The given initial value problem is [tex]y' + 3y = f(t)[/tex].
Consider the left hand side of the given equation.
[tex]y'+3y[/tex]
Take the Laplace transform.
[tex]L(y' + 3y) = sY(s) + 3Y(s) \\L(y' + 3y) = Y(s)[s + 3][/tex]
Consider the right hand side and get the expression for [tex]f(t)[/tex].
[tex]f(t) = t[/tex] when 0 ≤ t < 1
From time shift of the unit step
[tex]f_1(t) = t (1 - u(t - 1))[/tex]
For f(t) = 0 when t ≥ 1
Now,
[tex]f_2(t) = 0(u(t-1))f(t) = f_1(t) + f_2(t)f(t) = t - t u(t-1)[/tex]
Take the Laplace for above expression.
[tex]F(s)=\dfrac{1}{s^2}-e^{-s}\left(\dfrac{1}{s^2}+\dfrac{1}{s}\right)[/tex]
Now, the equate the above two equation.
[tex]Y(s)\left[s+3\right ]=\dfrac{1}{s^2}-e^{-s}\left(\dfrac{1}{s^2}+\dfrac{1}{s}\right)\\Y(s)=\dfrac {1}{(s^2(s+3))}-e^{-s}\left(\dfrac{1}{(s^2(s+3))}+\dfrac{1}{s(s+3)\right)}[/tex]
Find the inverse Laplace for the above equation.
[tex]\dfrac{1}{(s^2(s+3))}=\dfrac{-1}{9s}+\dfrac{1}{3s^2}+\dfrac{1}{9(s+3)}\\\dfrac{1}{(s(s+3))}=\dfrac{1}{3s}+\dfrac{1}{3(s+3)}[/tex]
Calculate the partial fraction of above equation.
[tex]Y(s)=\dfrac{-1}{9s}+\dfrac{1}{3s^2}+\dfrac{1}{9(s+3)}-e^{-s}\left[\dfrac{-1}{9s}+\dfrac{1}{3s^2}+\dfrac{1}{9(s+3)}+\dfrac{1}{3s}+\dfrac{1}{3(s+3)}\right]\\Y(s)=\dfrac{2}{9s}+\dfrac{1}{3s^2}+\dfrac{1}{9(s+3)}-e^{-s}\left[\dfrac{2}{9s}+\dfrac{1}{3s^2}-\dfrac{2}{9(s+3)}\right][/tex]
Take the inverse Laplace of the above equation.
[tex]y(t)=\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{1}{9}e^-3t-\left[\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{2}{9}e^{-3(t-1)}\right]u(t-1)[/tex]
Thus, the solution for the given initial-value problem is,
[tex]y(t)=\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{1}{9}e^-3t-\left[\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{2}{9}e^{-3(t-1)}\right]u(t-1)[/tex]
Learn more about what Laplace transformation is here:
https://brainly.com/question/14487937
The following chart represents the record low temperatures recorded in Phoenix for April-November. Select the answer below that best describes the mean and the median of the data set (round answers to the nearest tenth). A graph titled Phoenix Low Temperatures has month on the x-axis and temperature (degrees Fahrenheit) on the y-axis. April, 32; May, 40; June, 50; July, 61; August, 60; September, 47; October, 34; November, 25. a. The mean is 43.5°F, and the median is 43.6°F. b. The mean is 60.5°F, and the median is 60.5°F. c. The mean is 60°F, and the median is 61°F. d. The mean is 43.6°F, and the median is 43.5°F.
Answers
Answer:
d. The mean is 43.6°F, and the median is 43.5°F.
Step-by-step explanation:
Hello!
The data corresponds to the low temperatures in Phoenix recorded for April to November.
April: 32ºF
May: 40ºF
June: 50ºF
July: 61ºF
August: 60ºF
September: 47ºF
October: 34ºF
November: 25ºF
Sample size: n= 8 months
The mean or average temperature of the low temperatures in Phoenix can be calculated as:
[tex]\frac{}{X}[/tex]= ∑X/n= (32+40+50+61+60+47+34+25)/8= 43.625ºF (≅ 43.6ºF)
The Median (Me) is the value that separates the data set in two halves, first you have to calculate its position:
PosMe= (n+1)/2= (8+1)/2= 4.5
The value that separates the sample in halves is between the 4th and the 5th observations, so first you have to order the data from least to greatest:
25; 32; 34; 40; 47; 50; 60; 61
The Median is between 40 and 47 ºF, so you have to calculate the average between these two values:
[tex]Me= \frac{(40+47)}{2} = 43.5[/tex] ºF
The correct option is D.
I hope this helps!
Answer:
it is d
Step-by-step explanation:
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 58 cells. (a) Find the relative growth rate. (Assume t is measured in hours.) k = (b) Find an expression for the number of cells after t hours. P(t) = (c) Find the number of cells after 8 hours. cells (d) Find the rate of growth after 8 hours. (Round your answer to three decimal places.) billion cells per hour (e) When will the population reach 20,000 cells? (Round your answer to two decimal places.) hr
Answers
Answer:
a) k=2.08 1/hour
b) The exponential growth model can be written as:
[tex]P(t)=Ce^{kt}[/tex]
c) 977,435,644 cells
d) 2.033 billions cells per hour.
e) 2.81 hours.
Step-by-step explanation:
We have a model of exponential growth.
We know that the population duplicates every 20 minutes (t=0.33).
The initial population is P(t=0)=58.
The exponential growth model can be written as:
[tex]P(t)=Ce^{kt}[/tex]
For t=0, we have:
[tex]P(0)=Ce^0=C=58[/tex]
If we use the duplication time, we have:
[tex]P(t+0.33)=2P(t)\\\\58e^{k(t+0.33)}=2\cdot58e^{kt}\\\\e^{0.33k}=2\\\\0.33k=ln(2)\\\\k=ln(2)/0.33=2.08[/tex]
Then, we have the model as:
[tex]P(t)=58e^{2.08t}[/tex]
The relative growth rate (RGR) is defined, if P is the population and t the time, as:
[tex]RGR=\dfrac{1}{P}\dfrac{dP}{dt}=k[/tex]
In this case, the RGR is k=2.08 1/h.
After 8 hours, we will have:
[tex]P(8)=58e^{2.08\cdot8}=58e^{16.64}=58\cdot 16,852,338= 977,435,644[/tex]
The rate of growth can be calculated as dP/dt and is:
[tex]dP/dt=58[2.08\cdot e^{2.08t}]=120.64e^2.08t=2.08P(t)[/tex]
For t=8, the rate of growth is:
[tex]dP/dt(8)=2.08P(8)=2.08\cdot 977,435,644 = 2,033,066,140[/tex]
(2.033 billions cells per hour).
We can calculate when the population will reach 20,000 cells as:
[tex]P(t)=20,000\\\\58e^{2.08t}=20,000\\\\e^{2.08t}=20,000/58\approx344.827\\\\2.08t=ln(344.827)\approx5.843\\\\t=5.843/2.08\approx2.81[/tex]
which equation represents the graph function?
Answers
Answer:
[tex]\displaystyle y=-\frac{1}{3}x+3[/tex]
Step-by-step explanation:
First, notice that since the graph of the function is a line, we have a linear function.
To find the equations for linear functions, we need the slope and the y-intercept. Recall the slope-intercept form:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
We are given the point (0,3) which is the y-intercept. Thus, b = 3.
To find the slope, we can use the slope formula:
[tex]\displaystyle m=\frac{\Delta y}{\Delta x} =\frac{2-3}{3-0}=-1/3[/tex]
Therefore, our equation is:
[tex]\displaystyle y=-\frac{1}{3}x+3[/tex]
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 418 gram setting. It is believed that the machine is underfilling the bags. A 9 bag sample had a mean of 413 grams with a standard deviation of 20. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?
Answers
Answer:
No. At a significance level of 0.1, there is not enough evidence to support the claim that the bags are underfilled (population mean significantly less than 418 g.)
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the bags are underfilled (population mean significantly less than 418 g.)
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=418\\\\H_a:\mu< 418[/tex]
The significance level is 0.1.
The sample has a size n=9.
The sample mean is M=413.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=20.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{20}{\sqrt{9}}=6.6667[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{413-418}{6.6667}=\dfrac{-5}{6.6667}=-0.75[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=9-1=8[/tex]
This test is a left-tailed test, with 8 degrees of freedom and t=-0.75, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-0.75)=0.237[/tex]
As the P-value (0.237) is bigger than the significance level (0.1), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.1, there is not enough evidence to support the claim that the bags are underfilled (population mean significantly less than 418 g.)
objective: Solve applications involving problem-s...
1 of 21 (0
1.1.A-4
Cookies are sold singly or in packages of 8 or 24. With this packaging, how many
ways can you buy 48 cookies?
Answers
Step-by-step explanation:
With the packaging of 8
48 cookies = 48 ÷ 8 = 6 boxes
With the packaging of 24
48 cookies = 48 ÷ 24 = 2 boxes
An industrial psychologist conducted an experiment in which 40 employees that were identified as "chronically tardy" by their managers were divided into two groups of size 20. Group 1 participated in the new "It's Great to be Awake!" program, while Group 2 had their pay docked. The following data represent the number of minutes that employees in Group 1 were late for work after participating in the program.
Does the probability plot suggest that the sample was obtained from a population that is normally distributed? Provide TWO reasons for your classification.
Answers
Answer:
The probability plot of this distribution shows that it is approximately normally distributed..
Check explanation for the reasons.
Step-by-step explanation:
The complete question is attached to this solution provided.
From the cumulative probability plot for this question, we can see that the plot is almost linear with no points outside the band (the fat pencil test).
The cumulative probability plot for a normal distribution isn't normally linear. It's usually fairly S shaped. But, when the probability plot satisfies the fat pencil test, we can conclude that the distribution is approximately linear. This is the first proof that this distribution is approximately normal.
Also, the p-value for the plot was obtained to be 0.541.
For this question, we are trying to check the notmality of the distribution, hence, the null hypothesis would be that the distribution is normal and the alternative hypothesis would be that the distribution isn't normal.
The interpretation of p-valies is that
When the p-value is greater than the significance level, we fail to reject the null hypothesis (normal hypothesis) and but if the p-value is less than the significance level, we reject the null hypothesis (normal hypothesis).
For this distribution,
p-value = 0.541
Significance level = 0.05 (Evident from the plot)
Hence,
p-value > significance level
So, we fail to reject the null or normality hypothesis. Hence, we can conclude that this distribution is approximately normal.
Hope this Helps!!!
Which expressions are equivalent to -3(2w+6)-4
Answers
Answer:
B is the answer
Step-by-step explanation:
-3(2w+6)-4
-6w-18-4
-6w-22
Answer:
B = 2(−3w + (−11)) is the answer.Step-by-step explanation:
-3(2w + 6) - 4
1. Distribute
= -3*2w = -6w
= -3 * 6 = -18
= -6w -18
2. Simplify like terms
= -18 - 4
= -22
3. Place variables and numbers together
= -6w - 22
-6w -22 is the answer.So, B is the answer.Explanation:
2 * -3w = -6w
2*-11 = -22
Place them together and you get the answer!
¿Cuál serie numérica tiene como regla general Xn = 2n +1?
a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5
Answers
Answer:
The series of numbers that correspond to the general rule of [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.
Step-by-step explanation:
We are given with the following series options below;
a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5
And we have to identify what number series has a general rule as [tex]X_n=2n+1[/tex].
For this, we will put the values of n in the above expression and then will see which series is obtained as a result.
So, the given expression is ; [tex]X_n=2n+1[/tex]
If we put n = 1, then;
[tex]X_1=(2\times 1)+1[/tex]
[tex]X_1 = 2+1 = 3[/tex]
If we put n = 2, then;
[tex]X_2=(2\times 2)+1[/tex]
[tex]X_2 = 4+1 = 5[/tex]
If we put n = 3, then;
[tex]X_3=(2\times 3)+1[/tex]
[tex]X_3 = 6+1 = 7[/tex]
If we put n = 4, then;
[tex]X_4=(2\times 4)+1[/tex]
[tex]X_4 = 8+1 = 9[/tex]
Hence, the series of numbers that correspond to the general rule of [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.
PLEASE HELP!
Fill in the reason for statement 3 in proof below:
SAS
AA
SSS
Answers
Answer:
SAS
Step-by-step explanation:
ΔABD ~ ΔECD is similar through:
S - because ED = CD (Given)
A - same angle ∠D (Statement 2)
S - because AD = BD (Given)
Cheers!
Answer:
SAS
Step-by-step explanation:
You can notice that you have ED/AB = CD/BD You have one common angleWill anyone help me with geometry ASAP!? Please!? In desperate help!!!
Answers
Answer:
14. C 41
15. k = 72
Step-by-step explanation:
14.
For parallel lines, alternate exterior angles must be congruent.
3x - 43 = 80
3x = 123
x = 41
15.
The sum of the measures of the angles of a triangle is 180 deg.
k + 33 + 75 = 180
k + 108 = 180
k = 72
Answer:
1. 32
2. 41
3. 72
Step-by-step explanation:
Which of the following graphs is described by the function given below?
y = 2x^2 + 8x + 3
Answers
Answer:
Option A
Step-by-step explanation:
Equation of the given quadratic function is,
y = 2x² + 8x + 3
y = 2(x² + 4x) + 3
= 2(x² + 4x + 4 - 4) + 3
= 2(x + 2)² - 8 + 3
= 2(x + 2)² - 5
By comparing this equation with the equation of a quadratic function in vertex form,
y = a(x - h)² + k
Here (h, k) is the vertex of the parabola
Vertex of the given equation will be (-2, -5) and coefficient 'a' is positive (a > 0)
Therefore, vertex will lie in the 3rd quadrant and the parabola will open upwards.
Option (A). Graph A will be the answer.
The length of a rectangle is 5M more than twice the width and the area of the rectangle is 63M to find the dimension of the rectangle
Answers
Answer:
width = 4.5 m
length = 14 m
Step-by-step explanation:
okay so first you right down that L = 5 + 2w
then as you know that Area = length * width so you replace the length with 5 + 2w
so it's A = (5 +2w) * w = 63
then 2 w^2 + 5w - 63 =0
so we solve for w which equals 4.5 after that you solve for length : 5+ 2*4.5 = 14
At her favorite sneakers store Nyeema saved $48 because of a
sale.
If the sneakers normally cost $120. How much did she save?
Answers
Answer:
40%
Step-by-step explanation:
We can find what percent 48 is of 120 by dividing:
48/120 = 0.4 or 40%
So, she saved 40% from the original price.
Which set of numbers can represent the lengths of the sides of a triangle? A. {1,2,3} B. {3,5,7} C. {3,9,14} D. {4,4,8}
Answers
To form a triangle, the sum of any 2 sides of a triangle must be greater than the measure of the third side. For B, 3+5>7 works.
The set of numbers that can represent the lengths of the sides of a triangle are 3,5,7. That is option B.
What is a triangle?Triangle is defined as a type of polygon that has three sides in which the sum of both sides is greater than the third side.
That is to say, 3+5 = 8 is greater than the third side which is 7.
Therefore, the set of numbers the would represent a triangle are 3,5,7.
Learn more about triangle here:
https://brainly.com/question/17335144
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how many types of progression in mathematics?
Answers
Explain
In math , there are three different type , they are arithmetic progression ( Ap) , Geometric progression and Harmonic
Arithmetic Progression - When a fix constant is added to each number except the first number.
For example : 2,4,6,8,10..... Here 2 is added each time to get the next number.
2. Geometric Progression - When a fix constant is multiplied to each number except the first number.
For example : 2,6,18,54.... Here 3 is multiplies each time to get first number.
3. Harmonic - a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression.
For example : 1/2 , 1/4 , 1/6, 1/8 ....
Fake Question: Should Sekkrit be a moderator? (answer if you can) Real Question: Solve for x. [tex]x^2+3x=-2[/tex]
Answers
Answer:
x = -2 , -1
Step-by-step explanation:
Set the equation equal to 0. Add 2 to both sides:
x² + 3x = -2
x² + 3x (+2) = - 2 (+2)
x² + 3x + 2 = 0
Simplify. Find factors of x² and 2 that will give 3x when combined:
x² + 3x + 2 = 0
x 2
x 1
(x + 2)(x + 1) = 0
Set each parenthesis equal to 0. Isolate the variable, x. Note that what you do to one side of the equation, you do to the other.
(x + 2) = 0
x + 2 (-2) = 0 (-2)
x = 0 - 2
x = -2
(x + 1) = 0
x + 1 (-1) = 0 (-1)
x = 0 - 1
x = -1
x = -2 , -1
~
Answer:
x = -2 OR x = -1
Step-by-step explanation:
=> [tex]x^2+3x = -2[/tex]
Adding 2 to both sides
=> [tex]x^2+3x+2 = 0[/tex]
Using mid-term break formula
=> [tex]x^2+x+2x+2 = 0[/tex]
=> x(x+1)+2(x+1) = 0
=> (x+2)(x+1) = 0
Either:
x+2 = 0 OR x+1 = 0
x = -2 OR x = -1
P.S. Ummmm maybe...... Because he usually reports absurd answers! So, Won't it be better that he could directly delete it. And one more thing! He's Online 24/7!!!!!
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Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
0.25 = 1/4 because 25/100 = 1/4
▹ Step-by-Step Explanation
0.25 to a fraction → 25/100
25/100 = 1/4
Therefore, this statement is true. (0.25 = 1/4 because 25/100 = 1/4)
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Find the remainder when f(x)=2x3−x2+x+1 is divided by 2x+1.
Answers
Step-by-step explanation:
it can be simply done by using remainder theorem.
15% as a fraction in its lowest terms is:
-3/20
-5/100
-1/15
-3/100
Answers
Answer:
3/20
Step-by-step explanation:
15%
15/100
/5 /5
3/20
Suppose 150 students are randomly sampled from a population of college students. Among sampled students, the average IQ score is 115 with a standard deviation of 10. What is the 99% confidence interval for the average IQ of college students? Possible Answers: 1) A) E =1.21 B) E = 1.25 C) E =2.52 D) E = 2.11 2) A) 112.48 < μ < 117.52 B) 113.79 < μ < 116.21 C) 112.9 < μ < 117.10 D) 113.75 < μ < 116.3
Answers
Answer:
99% confidence interval for the mean of college students
A) 112.48 < μ < 117.52
Step-by-step explanation:
step(i):-
Given sample size 'n' =150
mean of the sample = 115
Standard deviation of the sample = 10
99% confidence interval for the mean of college students are determined by
[tex](x^{-} -t_{0.01} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01} \frac{S}{\sqrt{n} } )[/tex]
Step(ii):-
Degrees of freedom
ν = n-1 = 150-1 =149
t₁₄₉,₀.₀₁ = 2.8494
99% confidence interval for the mean of college students are determined by
[tex](115 -2.8494 \frac{10}{\sqrt{150} } , 115 + 2.8494\frac{10}{\sqrt{150} } )[/tex]
on calculation , we get
(115 - 2.326 , 115 +2.326 )
(112.67 , 117.326)
Select the correct answer.
If two angles of a triangle have equal measures and the third angle measures 90º, what are the angle measures of the triangle?
ОА.
60°, 60°, 60°
OB.
459,909, 90°
Ос.
30°, 30°, 90°
OD.
45°, 45°, 90°
Answers
Answer:
OD. 45,45,90
Step-by-step explanation: