Answer: The other 50%
Step-by-step explanation:
1. (1 point) Let x be a real number. Show that a (1 + x)2n > 1+ 2nx for every positive integer n.
For a real number x, by using mathematical induction it is shown that a[tex](1 + x)^{2n}[/tex] > 1 + 2nx for every positive integer n.
To prove the inequality a[tex](1 + x)^{2n}[/tex] > 1 + 2nx for every positive integer n, we will use mathematical induction.
The inequality holds true for n = 1, and we will assume it is true for some positive integer k.
We will then show that it holds for k + 1, which will complete the proof.
For n = 1, the inequality becomes a[tex](1 + x)^2[/tex] > 1 + 2x.
This can be expanded as a(1 + 2x + [tex]x^2[/tex]) > 1 + 2x, which simplifies to a + 2ax + a[tex]x^2[/tex] > 1 + 2x.
Now, let's assume the inequality holds true for some positive integer k, i.e., a[tex](1 + x)^{2k}[/tex] > 1 + 2kx.
We need to prove that it holds for k + 1, i.e., a[tex](1 + x)^{2(k+1)}[/tex] > 1 + 2(k+1)x.
Using the assumption, we have a[tex](1 + x)^{2k}[/tex] > 1 + 2kx.
Multiplying both sides by [tex](1 + x)^2[/tex], we get a[tex](1 + x)^{2k+2}[/tex] > (1 + 2kx)[tex](1 + x)^2[/tex].
Expanding the right side, we have a[tex](1 + x)^{2k+2}[/tex] > 1 + 2kx + 2x + 2k[tex]x^2[/tex] + 2[tex]x^2[/tex].
Simplifying further, we get a[tex](1 + x)^{2k+2}[/tex] > 1 + 2(k+1)x + 2k[tex]x^2[/tex] + 2[tex]x^2[/tex].
Since k and x are positive, 2k[tex]x^2[/tex] and 2[tex]x^2[/tex] are positive as well.
Therefore, we can write a[tex](1 + x)^{2k+2}[/tex] > 1 + 2(k+1)x + 2k[tex]x^2[/tex] + 2[tex]x^2[/tex] > 1 + 2(k+1)x.
This proves that if the inequality holds for some positive integer k, it also holds for k + 1.
Since it holds for n = 1, it holds for all positive integers n by mathematical induction.
Therefore, we have shown that a[tex](1 + x)^{2n}[/tex] > 1 + 2nx for every positive integer n.
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PLS HELP ILL MARK U BRAINLIEST
I DID THE FIRST 1 I NEED HELP WITH THE SECOND <3
Answer:
7m and 49 m^2
Step-by-step explanation:
i am not sure on the second answer
Children's recall of TV ads. Marketing professors at Robert Morris and Kent State Universities examined children's recall and recognition of television advertisements. (Journal of Advertising, Spring 2006.) Two groups of children were shown a 60-second commercial for Sunkist FunFruit Rockn-Roll Shapes. One group (the AN group) was shown the ad with both audio and video; the second group (the video only group) was shown only the video portion of the commercial. Following the viewing, the children were asked to recall 10 specific items from the ad. The number of items recalled correctly by each child is summarized in the accompanying table. The researchers theorized that "children who receive an audiovisual presentation will have the same level of mean recall of ad information as those who receive only the visual aspects of the ad."
Video-Only Group
n1= 20
x1_bar = 3.70
s1 = 1.98
A/V Group
n2 = 20
x2-bar = 3.30
s2 = 2.13
a. Set up the appropriate null and alternative hypotheses to test the researchers' theory.
b. Find the value of the test statistic.
c. Give the rejection region for ? = 0.10
d. Make the appropriate inference. What can you say about the researchers' theory?
e. The researchers' reported the p-value of the test as p-value = 0.62. Interpret this result.
f. What conditions are required for the inference to be valid?
a. The null hypothesis (H0) would state that the mean recall of ad information for children who receive an audiovisual presentation is equal to the mean recall.
a.The alternative hypothesis (Ha) would state that the mean recall of ad information differs between the two groups.
b. To find the test statistic, we can use the two-sample t-test formula:
t = (x1_bar - x2_bar) / sqrt((s1^2/n1) + (s2^2/n2))
Substituting the given values:
t = (3.70 - 3.30) / sqrt((1.98^2/20) + (2.13^2/20))
c. The rejection region for a significance level of α = 0.10 in a two-tailed test can be determined using a t-table or a t-distribution calculator. Since the alternative hypothesis is two-tailed, we need to split α equally between the two tails. In this case, the rejection region would be t < -1.734 or t > 1.734.
d. Based on the test statistic value calculated in part (b), we can compare it to the rejection region. If the test statistic falls within the rejection region, we reject the null hypothesis. If it falls outside the rejection region, we fail to reject the null hypothesis. In this case, we would fail to reject the null hypothesis since the test statistic does not fall within the rejection region. Therefore, we cannot conclude that the mean recall of ad information differs between the two groups, supporting the researchers' theory.
e. The p-value is a measure of the strength of evidence against the null hypothesis. In this case, the researchers reported a p-value of 0.62. Since this p-value is greater than the significance level of α = 0.10, it indicates that the observed data is likely to occur by chance alone assuming the null hypothesis is true. Therefore, we fail to reject the null hypothesis and cannot conclude that there is a significant difference in the mean recall of ad information between the two groups.
f. For the inference to be valid, certain conditions must be met. These conditions include random sampling, independence between observations, approximately normal distributions of the populations or large sample sizes, and equal variances between the groups. Without information about the sampling method and data characteristics, we cannot determine if these conditions were met. It is important to note that if the conditions for inference are not met, the validity and reliability of the test results may be compromised.
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simplify log(16x²) ± 2㏒(1÷×)
Answer: just simplify condense it then your answer will be log(16)
A 4 pack of 12-ounce bottles of water costs $4.40. What is the cost per ounce?
Answer:
5
Step-by-step explanation:
helpppppp pleaseeeeee
Answer:
50°
Step-by-step explanation:
We are to find m ∠2
And lines A and B are parallel
m ∠2 and 50° are Vertical angles. This means m ∠2 is the same as 50°
Hence,
m ∠2 = 50°
Therefore, m ∠2 = 50°
A video store has 6 new comedies, 4 new action movies, and 2 new dramas available to rent. If you choose 1 of each type of movie, how many combinations are there?
Answer:
48
Step-by-step explanation:
Number of comedy = 6
Number of action = 4
Number of drama = 2
Selecting one of each ; total Number of possible combinations ;
nCr
Comedy = 6C1
Action = 4C1
Drama = 2C1
6C1 * 4C1 * 2C1 = 6 * 4 * 2 = 48
Find the profit function if cost and revenue are given by C(x)=150+5.8x and R(x)=9x-0.01x² The profit function is P(x)
The profit function if the cost and revenue is given P(x) = -0.01x² + 3.2x - 150.
To find the profit function P(x), we subtract the cost function C(x) from the revenue function R(x). This gives us the expression for P(x) as P(x) = R(x) - C(x).
The profit function P(x) represents the difference between the revenue R(x) and the cost C(x). To find P(x), we subtract C(x) from R(x):
P(x) = R(x) - C(x)
Substituting the given expressions for R(x) and C(x), we have:
P(x) = (9x - 0.01x²) - (150 + 5.8x)
Simplifying this expression, we get:
P(x) = 9x - 0.01x² - 150 - 5.8x
Combining like terms, we have:
P(x) = -0.01x² + 3.2x - 150
Thus, the profit function is given by P(x) = -0.01x² + 3.2x - 150. This function represents the profit made as a function of the quantity of goods sold, x. It allows us to analyze the relationship between revenue, cost, and profit for different values of x.
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Solve the equation using either addition or substitution. Show all your work
Answer:
(x1, y1) = (1, 3)
(x2, y2) = (4, 12)
Step-by-step explanation:
y= x^2 - 4
y= 5x - 8
(substitute the value for y)
x^2 - 4 = 5x - 8
(solve the equation)
x = 1
x = 4
(substitute the values)
y = 5 × 1 - 8
y = 5 × 4 - 8
(solve the equations)
y = -3
y = 12
( the possible solutions are)
x1, y1 = 1, -3
x2, y2 = 4, 12
(check the solutions)
-3 = 1^2 - 4
-3 = 5 × 1 - 8
12 = 4^2 - 4
12 = 5 × 4 - 8
(simplify)
-3 = -3
-3 = -3
12 = 12
12 = 12
(the ordered pairs are the solutions)
PLEASE HELPP, DONT SCAM!! The table below represents a function. Which of the following equations could be its function rule?
Step-by-step explanation:
From the table, let's extract a set of data.
let's take x = 3, y = -9.
Let's substitute x into each of the equation to check.
A.
[tex]y = \frac{x}{ - 3} \\ y = \frac{3}{ - 3} \\ = - 1[/tex]
From here we can see the calculated y is not equal to the y in the table, therefore this cannot be the answer.
B.
[tex]y = x \\ y = - 3[/tex]
From here we also can see the calculated y is not equal to the y in the table, therefore this also cannot be the answer.
C.
[tex]y = 3x \\ = 3( - 3) \\ = - 9[/tex]
From here we can see the calculated y is equal to the y in the table , therefore this is the answer.
D.
[tex]y = - 3x \\ = - 3( - 3) \\ = 9[/tex]
From here we can see the calculated y is not equal to the y in the table, therefore this is not the answer.
Having an error of 0.01, a confidence level of 95% with a value p = 0.37 Determine: a) Z-value b) Sample size
a) The Z-value corresponding to a confidence level of 95% can be determined as 1.96.
b) To determine the required sample size, we need additional information such as the population size or an estimated proportion. Without this information, we cannot calculate the sample size.
a) The Z-value represents the number of standard deviations a data point is from the mean in a standard normal distribution. For a confidence level of 95%, which corresponds to a 5% significance level, the critical Z-value is approximately 1.96. This value can be obtained from a Z-table or using statistical software.
b) To calculate the required sample size, additional information is needed, such as the population size or an estimated proportion. The sample size formula takes into account factors such as the desired margin of error, confidence level, and variability. Without these details, it is not possible to determine the sample size accurately.
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PLSSS HELP IMMEDIATELY!!!! i’ll mark brainiest if u don’t leave a link!
Answer:
grab objects
Step-by-step explanation:
barrels and things like that would most likely grab objects so the fish can have room to swim and stuff
A photo of a beetle in a science book is increased to 655% as large as the actual size. In the
beetle is 16 millimeters, what is the size of the beetle in the photo?
The size of the beede in the photo
Answer:
104.8
Step-by-step explanation:
16 x 6.55 = 104.8
Answer:
104.8 millimeters
Step-by-step explanation:
16 x 6.55 = 104.8
As reported in Runner's World magazine, the times of the finishers in the New York City 10-km run are normally distributed with mean 60 minutes and standard deviation 9 minutes. Determine the percentage of finishers who have times between 55 and 75 minutes.
The mean of the finishers in the New York City 10-km run is 60 minutes and standard deviation is 9 minutes.
To determine the percentage of finishers who have times between 55 and 75 minutes, we need to find the Z-scores for both of these values as follows:
Z1 = (55 - 60) / 9 = -0.56Z2 = (75 - 60) / 9 = 1.67
Now, we need to find the area under the standard normal distribution curve between these two Z-scores as follows:
P(-0.56 < Z < 1.67) = P(Z < 1.67) - P(Z < -0.56) Using a standard normal distribution table,
we can find the probabilities as:
P(Z < 1.67) = 0.9525P(Z < -0.56) = 0.2881
Therefore , P(-0.56 < Z < 1.67) = P(Z < 1.67) - P(Z < -0.56)= 0.9525 - 0.2881= 0.6644Therefore, the percentage of finishers who have times between 55 and 75 minutes is 66.44%.
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Andrea reads 36 pages each night. How many pages does Andrea read in 42 nights?
A 1,502pages
B 1,512pages
C 1,552pages
D 1,582pages
Answer:
1,512
Step-by-step explanation:
36x42
The point P(2,12) lies on the curve y=x2+x+6. If Q is the point (x,x2+x+6), find the slope of the secant line PQ for the following values of x.
If x=2.1, the slope of PQ is:
and if x=2.01, the slope of PQ is:
and if x=1.9, the slope of PQ is:
and if x=1.99, the slope of PQ is:
Based on the above results, guess the slope of the tangent line to the curve at P(2,12).
Based on the results, we can observe that as x approaches 2, the slopes of PQ are getting closer to 4. Therefore, we can guess that the slope of the tangent line to the curve at P(2,12) is approximately 4.
To find the slope of the secant line PQ, we need to determine the coordinates of point Q and then calculate the slope using the formula:
slope = (change in y) / (change in x)
Given that Q is the point (x, x^2 + x + 6), we can substitute the values of x to find the corresponding slopes.
If x = 2.1:
Q = (2.1, (2.1)^2 + 2.1 + 6) = (2.1, 12.51)
Slope of PQ = (12.51 - 12) / (2.1 - 2) = 0.51 / 0.1 = 5.1
If x = 2.01:
Q = (2.01, (2.01)^2 + 2.01 + 6) = (2.01, 12.0601)
Slope of PQ = (12.0601 - 12) / (2.01 - 2) = 0.0601 / 0.01 = 6.01
If x = 1.9:
Q = (1.9, (1.9)^2 + 1.9 + 6) = (1.9, 11.61)
Slope of PQ = (11.61 - 12) / (1.9 - 2) = -0.39 / -0.1 = 3.9
If x = 1.99:
Q = (1.99, (1.99)^2 + 1.99 + 6) = (1.99, 11.9601)
Slope of PQ = (11.9601 - 12) / (1.99 - 2) = -0.0399 / -0.01 = 3.99
Based on the results, we can observe that as x approaches 2, the slopes of PQ are getting closer to 4. Therefore, we can guess that the slope of the tangent line to the curve at P(2,12) is approximately 4.
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can someone check my answer make sure it's right, if it's wrong can you please explain thanks ❤️❤️
Answer:
it is wrong
Step-by-step explanation:
the reason it is wrong is because I said so
Answer:
I am going to say no BECAUSE there are two y values, on the same point. For it to be linear it should only have one point per value. I think... good luck.
Find the missing side
Answer:
72
Step-by-step explanation:
Answer:
72 units
Step-by-step explanation:
The Pythagorean Theorem states that [tex]a^2+b^2=c^2[/tex] in a right triangle when a and b are the two legs and c is the hypotenuse (the longest side).
[tex]a^2+b^2=c^2[/tex]
In the diagram, 30 measures one of the legs and 78 measures the hypotenuse. Plug these in as a and c.
[tex]30^2+b^2=78^2\\900+b^2=6084[/tex]
Subtract 900 from both sides
[tex]900+b^2-900=6084-900\\b^2=5184[/tex]
Take the square root of both sides
[tex]900+b^2-900=6084-900\\\sqrt{b^2} =\sqrt{5184}\\b=72[/tex]
Therefore, the length of the missing side is 72 units.
I hope this helps!
The points where a graph crosses the x- and y-axis are called the __
Answer:
x-intercept
y-intercept
Step-by-step explanation:
Answer:
x-intercept y-intercept
The center of a circle is located at (4, 2). A point on the circle is located at (1, 2). What is the approximate area of the circle?
Answer: 9π≈28.26 squared units
Step-by-step explanation: The distance between the two points, 3 units, is the radius. And then we use that to find the area by squaring and multiplying by pi.
Given the angles in the diagram below what is m<2?
Answer: 98
Step-by-step explanation: According to the corresponding angles theorem m<1=82. Then according to the linear supplements theorem m<2=98. Hope this helps!
Answer:
98°
Step-by-step explanation:
Angle 1 also measures 82° because it is a corresponding angle to the given angle. Angles 1 and 2 are supplementary and therefore must add up to 180°.
please help asapppppp
Answer:
45 degree
Step-by-step explanation:
5) (3a + 1) - (4 + 2a)
Answer:
5a - 3
Step-by-step explanation:
3a + 2a = 5a
1 - 4 = -3
5a + (-3) or 5a - 3
need help with this one lol
Answer: 5 + 47 = 108
Step-by-step explanation: dont worry it works
Answer:
pythagoras thoerem
Step-by-step explanation:
y squared = 10 squared - 7 squared
y = 100 - 49= 51
y square root of 51 =7.1
Is (2, 7) the answer to the equation 5x = y?
If not, what should y be?
Answer:
[see below]
Step-by-step explanation:
[tex]5(2)=7\\\\10\neq 7[/tex]
No, (2, 7) is not the answer to the equation 5x = y.
[tex]5x=y\\\\5(2)=y\\\\\boxed{10=y}[/tex]
The value of y should be 10.
Hope this helps.
Fifty people put there name
into a two different drawings
(30 males and 20 females).
One drawing is for an iPad and
the other is for a flat screen
TV. What is the probability
that a male will win both
drawings.
Possible answers ⇒
13%
27%
36%
49%
WILL GIVE BRAINLIST
Answer:
36%
Step-by-step explanation:
30/2500 x 30/2500=
900/2500=0.36
0.36*100=36%
Always in the game and never played by the rules (rules)
Tried to let me leave (leave), fell down to my knees (knees)
Picked myself up and turned my back to the breeze, oh-oh
Spent a milli' on a milli', mama look at me (oh)
With all these diamond chokers, man, it's gettin' hard to breathe
If you made this Very good job. I like it, and its hard to make a song i like. i like about 60 songs total out of the 10000+ ik of
I WILL GIVE BRAINLIEST!!!
Answer:
F(x)=h(x)-8
I think
Step-by-step explanation:
Gary buys a 3 and 1/2 - pound bag of cat food every 3 weeks. Gary feeds his cat the same amount of food each
day. Which expression can Gary use to determine the number of pounds of cat food his cat eats each
year? (1 year = 52 weeks)
Answer:
546
Step-by-step explanation:
3 1/2 times 3 equals 10 1/2. 10 1/2 times 52 equals 546.
Andrew is saving up money for a down payment on a car. He currently has $3355, but knows he can get a loan at a lower interest rate if he can put down $4045. If he invests the $3355 in an account that earns 3.7% annually, compounded monthly, how long will it take Andrew to accumulate the $4045? Round your answer to two decimal places, if necessary.
Answer:
5.06 years or 60.75 months
Step-by-step explanation:
Compound interest formula:
[tex]AV=PV(1+\frac{i}{n})^{n*t}\\4045=3355(1+\frac{.037}{12})^{12t}\\1.025=(1.003)^{12t}\\log1.025_{1.003}=12t\\60.75=12t\\5.062[/tex]
5.06 years or 60.75 months
It will take Andrew 5 years to accumulate $4045 by investing $3355 in an account that earns 3.7% annually, compounded monthly.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We can use the formula for compound interest to solve this problem:
[tex]A = P(1 + r/n)^(^n^t^)[/tex]
where:
A is the amount of money at the end of the investment period
P is the principal amount (initial investment)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time (in years) of the investment period
In this case, we want to solve for t. We know that:
P = $3355
r = 0.037 (3.7% as a decimal)
n = 12 (compounded monthly)
A = $4045
Substituting these values into the formula, we get:
[tex]4045 = $3355(1 + 0.037/12)^(^1^2^t^)[/tex]
ln(1.206) = 12t ln(1 + 0.037/12)
ln(1.206) = 12t ln(1 + 0.0031)
ln(1.206) = 12t ln(1.0031)
0.187=12t 0.0031
0.187=0.0372t
t=5.02
Therefore, it will take Andrew approximately 5 years to accumulate $4045 by investing $3355 in an account that earns 3.7% annually, compounded monthly.
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