Write a recursive formula for the sequence 7, 13, 19, 25, 31, ... Then find the next term.
Answers
Answer:
see explanation
Step-by-step explanation:
there is a common difference between consecutive terms , that is
d = 13 - 7 = 19 - 13 = 25 - 19 = 31 - 25 = 6
this indicates the sequence is arithmetic
the recursive formula lets us find any term in the sequence by adding the common difference to the previous term , that is
\(a_{n}\) = \(a_{n-1}\) + 6 ; a₁ = 7
the next term in the sequence is
31 + 6 = 37
Related Questions
please help! provide step by step, clear explaination! algebra 1 work. thanks
Answers
B) 201=3H+1.5C
C) 28=C and 53=H
Consider the function f(x)=x3−3x2+cx+d, where c and d are real numbers. (a) The coordinates of the turning points on the graph y=f(x) are (−1,5) and (u,v) Show that in this case c=−9,d=0,v=−27 and determine the value of u. (b) For what values of d does the graph of y=x3−3x2−9x+d cross the x−ax is at three distinct points? (c) For what values of c and d does the graph of y=x3−3x2+cx+d have two distinct turning points? (d) If the graph of y=f(x) is translated p units to the left away from the y-axis, it becomes the graph of y=x3. Find the values of p,c, and d in this case.
Answers
The Values of p, c, and d are -1, 3, and -1, respectively.
(a) We are given that the coordinates of the turning points on the graph of \(y=f(x)\) are (-1, 5) and (u, v). Let's start by substituting the given values into the equation \(f(x) = x^3 - 3x^2 + cx + d\) to find the values of c, d, and v.
For the turning point (-1, 5), we have:
\[f(-1) = (-1)^3 - 3(-1)^2 + c(-1) + d = -1 + 3 + (-c) + d = 5\]
Simplifying, we get:
\[4 - c + d = 5 \Rightarrow -c + d = 1 \quad \text{(1)}\]
For the turning point (u, v), we have:
\[f(u) = u^3 - 3u^2 + cu + d = v\]
Substituting the values of u and v, we get:
\[u^3 - 3u^2 + cu + d = v\]
Now, let's substitute the values of c, d, and v from equation (1) into the above equation:
\[u^3 - 3u^2 - u + 1 = 0\]
We can observe that this equation is satisfied when u = 1. Therefore, we have found that c = -9, d = 0, and v = -27. Also, the value of u is 1.
(b) To find the values of d for which the graph of \(y = x^3 - 3x^2 - 9x + d\) crosses the x-axis at three distinct points, we need to determine the conditions for the cubic equation to have three real roots. For a cubic equation in the form \(ax^3 + bx^2 + cx + d = 0\), if the discriminant \(\Delta = 18abcd - 4b^3d + b^2c^2 - 4ac^3 - 27a^2d^2\) is positive, then the equation has three distinct real roots.
In this case, we have \(a = 1\), \(b = -3\), \(c = -9\), and the discriminant \(\Delta = -2916d + 108c^3 + 4b^3d - 27a^2d^2 + b^2c^2\).
By substituting the values of c = -9 and b = -3 into the discriminant expression, we have:
\[\Delta = -2916d + 108(-9)^3 + 4(-3)^3d - 27(1)^2d^2 + (-3)^2(-9)^2\]
Simplifying further:
\[\Delta = -2916d - 8748 + 108d - 27d^2 + 243\]
\[\Delta = -27d^2 - 2812d - 8505\]
For the equation to have three distinct real roots, \(\Delta\) must be positive. So we solve the inequality:
\[-27d^2 - 2812d - 8505 > 0\]
Using quadratic techniques, we can find the range of values for d that satisfy the inequality.
(c) To find the values of c and d for which the graph of \(y = x^3 - 3x^2 + cx + d\) has two distinct turning points, we need to determine the conditions for the cubic equation to have two real roots. For a cubic equation in the
form \(ax^3 + bx^2 + cx + d = 0\), if the discriminant \(\Delta = 18abcd - 4b^3d + b^2c^2 - 4ac^3 - 27a^2d^2\) is positive and the sign of \(f''(x)\) changes, then the equation has two distinct turning points.
In this case, we have \(a = 1\), \(b = -3\), and the discriminant \(\Delta = 18abcd - 4b^3d + b^2c^2 - 4ac^3 - 27a^2d^2\).
By substituting the values of a = 1 and b = -3 into the discriminant expression, we have:
\[\Delta = 18cd - 4(-3)^3d + (-3)^2c^2 - 4c^3 - 27d^2\]
Simplifying further:
\[\Delta = 18cd + 36d - 9c^2 - 4c^3 - 27d^2\]
To determine the values of c and d for which \(\Delta\) is positive and the sign of \(f''(x)\) changes, we need to analyze the nature of the graph and the second derivative of the cubic function \(f(x)\). However, without specific information about the behavior of the function, we cannot determine the precise values of c and d that satisfy these conditions.
(d) If the graph of \(y = f(x)\) is translated p units to the left away from the y-axis, it becomes the graph of \(y = x^3\). To determine the values of p, c, and d in this case, we need to compare the equations of the two functions and observe the effect of the translation.
Comparing the equations, we have:
\[f(x) = x^3 - 3x^2 + cx + d\]
\[y = x^3\]
To translate the graph of \(f(x)\) p units to the left, we replace \(x\) with \(x + p\) in the equation. So we have:
\[y = (x + p)^3\]
Comparing this equation with the original equation, we can equate the terms to find the values of p, c, and d:
\[x^3 - 3x^2 + cx + d = (x + p)^3\]
Expanding the right side using binomial expansion, we get:
\[x^3 - 3x^2 + cx + d = x^3 + 3px^2 + 3p^2x + p^3\]
Comparing the coefficients of like terms, we have:
\[3p = -3 \quad \Rightarrow \quad p = -1\]
\[3p^2 = c \quad \Rightarrow \quad c = 3\]
\[p^3 = d \quad \Rightarrow \quad d = -1\]
Therefore, in this case, the values of p, c, and d are -1, 3, and -1, respectively.
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Which of the following is NOT a type of fat?
Saturated
Unsaturated
Trans-Fats
Fiber
Answers
Answer:
Fiber
Step-by-step explanation:
Fiber is a carbohydrate and not a fat ------ it is all the polysaccharides that humans can't digest.
Answer:
fiber is not a type of fat
if my avg is a 96 and my final exam is a 75 which is 25% of my whole grade what will my final grade be
Answers
Step-by-step explanation:
That means the 96 is 75% of your grade
96 (.75) + 75 (.25) = 90.75 final grade
explain what precision and confidence are and how they influence
sample size.
Discuss what is meant by this statement; "There is a trade-off
between precision and confidence under certain
conditions".
Answers
Precision and confidence are statistical concepts that influence sample size in research studies. Precision refers to the level of variability or margin of error in the measurements or estimates obtained from a sample. Confidence, on the other hand, refers to the degree of certainty or reliability associated with the results obtained from the sample.
Precision refers to the level of accuracy or consistency in the measurements or estimates obtained from a sample. It reflects the degree of variability or margin of error in the data. A high precision indicates low variability and a small margin of error, while low precision indicates high variability and a larger margin of error. Confidence, on the other hand, relates to the level of certainty or reliability in the results obtained from the sample. It represents the degree to which the sample results can be generalized to the population.
In statistical analysis, increasing precision often requires a larger sample size. A larger sample reduces the margin of error and increases the accuracy of the estimates. However, increasing the sample size also requires more resources, time, and effort. Therefore, there is a trade-off between precision and sample size.
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help please
Based on a your normal distribution curve, 68% of a sample pack of M&M's would have
at LEAST how many orange M&M's out of a pack of 56 total M&M's
Answers
Based on your normal distribution curve, 68% of the sample pack of M&M's will have 38 orange M&M's
Data obtained from the questionTotal pack = 56Percentage = 68%Amount of M&M's =?How to determine the amount of M&M'sThe amount of M&M's that will be obtained from the pack of 56 can be obtained as follow:
Amount = percentage × total
Amount of M&M's = 68% × 56
Amount of M&M's = 0.68 × 56
Amount of M&M's = 38
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To study the effect of mindfulness meditation on mental health, an experimental investigation was done by comparing serum cortisol (as an indicator of stress level) between 2 groups of medical students who volunteered to participate in the study. Group 1 took a 4- day meditation program, while Group 2 did not. Volunteers from both groups then had a blood test and their serum cortisol was measured in nmol/L. Results were as follows: Group 1: 267 245 263 316 246 282 379 300 291 306 425 190 346 150 344 Group 2 470 222 443 506 455 518 360 408 375 246 189 368 Do the results support the hypothesis that meditation helps reduce stress level, with 95% confidence? You must properly identify and follow all the necessary steps for this investigation (Hint: for comparing variances, you can use 98% confidence.)
Answers
The results of the study suggest that the 4-day meditation program had a significant effect in reducing the stress levels of the medical students compared to the group that did not participate in the meditation program.
To determine if the results support the hypothesis that meditation helps reduce stress levels, we need to perform the necessary statistical analysis. Here are the steps involved:
Step 1: Define the hypothesis:
The null hypothesis (H₀) is that there is no significant difference in stress levels between the two groups.
The alternative hypothesis (Hₐ) is that there is a significant difference in stress levels between the two groups, with meditation reducing stress.
Step 2: Identify the appropriate statistical test:
Since we are comparing the means of two independent groups and want to test if there is a significant difference, we can use an independent samples t-test.
Step 3: Set the significance level:
The significance level (α) is the probability of rejecting the null hypothesis when it is true. In this case, we will use a significance level of 0.05, corresponding to a 95% confidence level.
Step 4: Calculate the sample statistics:
Calculate the means, standard deviations, and sample sizes for both groups.
Group 1:
Mean (x1) = (267 + 245 + 263 + 316 + 246 + 282 + 379 + 300 + 291 + 306 + 425 + 190 + 346 + 150 + 344) / 15 = 290.2
Standard deviation (s1) = 70.764
Sample size (n1) = 15
Group 2:
Mean (x2) = (470 + 222 + 443 + 506 + 455 + 518 + 360 + 408 + 375 + 246 + 189 + 368) / 12 = 377.5
Standard deviation (s2) = 109.057
Sample size (n2) = 12
Step 5: Conduct the statistical test:
We can now perform an independent samples t-test using the sample statistics.
Step 5a: Test for equal variances:
Before conducting the t-test, we need to check if the variances of the two groups are equal. We can use a F-test to compare the variances.
Null hypothesis (H₀): The variances of the two groups are equal.
Alternative hypothesis (Hₐ): The variances of the two groups are not equal.
Using a significance level of 0.02 (98% confidence), we can calculate the F-statistic and compare it to the critical F-value from the F-distribution table.
F = s1² / s2² = 70.764² / 109.057² = 0.428 (approximately)
The critical F-value for a 98% confidence level with (n1-1) = 14 and (n2-1) = 11 degrees of freedom is 3.72.
Since our calculated F-value is smaller than the critical F-value, we fail to reject the null hypothesis. Thus, we can assume equal variances.
Step 5b: Conduct the t-test:
Since the variances are assumed to be equal, we can perform the independent samples t-test using the sample means and pooled standard deviation.
Pooled standard deviation (sp) = √(((n1 - 1) × s1² + (n2 - 1) × s2²) / (n1 + n2 - 2)) = √(((15 - 1) × 70.764² + (12 - 1) × 109.057²) / (15 + 12 - 2)) = 90.362
t = (x1 - x2) / (sp × √(1/n1 + 1/n2)) = (290.2 - 377.5) / (90.362 × √(1/15 + 1/12)) = -2.227
Degrees of freedom (df) = n1 + n2 - 2 = 15 + 12 - 2 = 25
Using the t-distribution table or a statistical software, we can find the critical t-value for a two-tailed test at a significance level of 0.05 with 25 degrees of freedom. The critical t-value is approximately ±2.060.
Since our calculated t-value (-2.227) is smaller than the critical t-value (-2.060), we reject the null hypothesis and accept the alternative hypothesis. Therefore, there is evidence to support the claim that mindfulness meditation helps reduce stress levels, with a 95% confidence level.
In conclusion, the results of the study suggest that the 4-day meditation program had a significant effect in reducing the stress levels of the medical students compared to the group that did not participate in the meditation program.
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A pair of walkie-talkies has a 35-meter range. Anand's apartment is 18 meters
east and 19 meters north of Isaac's apartment. Isaac's apartment is at sea
level, while Anand's apartment is 7 meters above sea level. Can they use the
walkie-talkies to talk to each other from their apartments?
, because the distance between their apartments is square root meters, or to the nearest tenth, meters.
Answers
Yes, they can use the walkie-talkies to talk to each other.
The distance between them is given as 28.2 meters.
How to solve for the distance?The horizontal and vertical distances should be considered when calculating the distance between their apartments using the three-dimensional form of the Pythagorean theorem.
This comes out as \(\sqrt((18^2 + 19^2 + 7^2))\), which equals \(\sqrt(798)\) square root meters, or, to the nearest tenth, 28.2 meters.
Since this distance is less than the 35-meter range of the walkie-talkies, communication should be possible between the two apartments.
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The graph shows a driver’s distance versus time.
Which statements are true? Check all that apply.
The average speed for the first 3 hours is 40 miles per hour.
The graph shows a proportional relationship for the full 8 hours.
The average speed for the last 3 hours is 40 miles per hour.
The total distance driven is 180 miles.
The distance always increases as time increases.
Answers
Answer:
it's a and c
Step-by-step explanation:
I guessed and it gave me the answers
In triangle ABC, AC=13, BC=84, and AB=85. Find the measure of angle C
Answers
Answer:
90degrees
Step-by-step explanation:
To get the measure of angle C, we will use the cosine rule as shown;
AB² = AC²+ BC² - 2(AC)(BC)cos C
85² = 13²+ 84² - 2(13)(84)cos C
7225 = 169 + 7056 - 2184cosC
7225 - 7225 = -2184cosC
0 = -2184cosC
cosC = -0/2184
cosC = 0
C = arccos0
C = 90degrees
Hence the measure of angle C is 90degrees
The supermarket has 48 aisles. 12 of the aisles are empty. What percentage of the aisles are empty
Answers
Answer:
25% of the isles are empty
Step-by-step explanation:
48/12 is 25%
Answer:
25%
Step-by-step explanation:
12 + 12 + 12 + 12= 48
if 12 isles are empty, then that is 1/4 of 48 aka 25%
20 points! pls helppppp it's almost recognition day for me!!
I'm sorry but i'm bad at math ;-;
using the given figures, find the values of the unknown variables
(PROVING ISOSCELES TRAPEZOID)
Answers
2. x = 32, y = 52
3. x = 4, y = 5
assuming that all the shapes are regular
Please help this is due in a few Brainliest will be rewarded!!!!!
Answers
Step-by-step explanation:
the middle one has to be the same for both part ratios.
the best here is to bring the ratio element of B in the first part ratio to 10. we need to double the B element there
for that (as a ratio is a fraction) we also have to adapt the A element in the same way.
so, we get
4×2 : 5×2 : 9 =
= 8 : 10 : 9
and that is also shown in the graphic.
Answer:
X:Y:Z= 8:10:9
Step-by-step explanation:
Let x be the number of students in class A
Let y be the number of students in class B
Let z be the number of students in class C
x:y = 4:5
y:z= 10: 9
x:y:z = ?
Find the LCM of the y terms (5 and 10 ) which is 10
Divide 10 by the first y term (5) = 2
Divide 10 by the second y term(10) = 1
X: y = (4 x 2) :(5 x 2)= 8:10
y:z =(10 x 1) : (9:1)= 10:9
x:y:z= 8:10:9
solve for x -
\(x {}^{2} - 6x + 5= 0\)
ty! ~
Answers
Answer:
x = 5, x = 1
Step-by-step explanation:
Hello!
We can solve this quadratic by factoring.
Solve\(x^2 - 6x + 5 = 0\)\(x^2 - 5x - x + 5 = 0\)\(x(x - 5) - 1(x - 5) = 0\)\((x - 5)(x - 1) = 0\)Use the zero product property:
x - 5 = 0x = 5x - 1 = 0
x = 1
x = 5, or x = 1
what is the answer........
Answers
C - -3,-2
D - -3,-5
suppose that you are attempting to estimate the weight of 600 parts. in order to use the infinite standard deviation formula, what sample size, n, should you use?
Answers
The sample size should be n ≤ 30
What is standard deviation?The standard deviation of a set indicates how accurate and near the set's measurements are. The square root of the variance of a random variable, sample, statistical population, data collection, or probability distribution represents its standard deviation. The average absolute deviation is more robust in theory but less so in practice. The standard deviation's useful virtue is that, unlike the variance, it is expressed in the same unit as the data.
The precision increases as the standard deviation decreases.
N=600
for infinite standard deviation (σ) = 1
corelation factor (f) = n/N
f ≤ 0.05
n/N ≤ 0.05
n ≤ 0.05*600
n ≤ 30
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a triangular parcel of land has sides of lengths 590 feet, 980 feet and 1423 feet. a) what is the area of the parcel of land? area
Answers
The area of the parcel of land is 226934.799 square feet.
Given:
a triangular parcel of land has sides of lengths 590 feet, 980 feet and 1423 feet.
a).
Let a = 590 , b = 980, c = 1423 lengths
s = semi-perimeter
= 1/2(a+b+c)
= 1/2(590+980+1423)
= 1496.5
s-a = 1496.5-590
= 906.5
s-b = 1496.5-980
=516.5
s-c = 1496.5-1423
= 73.5
Heron's formula for area:
A = \(\sqrt{(s(s-a)(s-b)(s-c))}\)
= √1496.5(906.5)(516.5)(73.5)
= √51499402997.4
≈ 226934.799
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The LIGO experiment, which historically detected gravita- tional waves for the first time in September 2015, uses a pair of highly sensitive Michelson interferometers. These have arms that are 4.00 km long and use powerful Nd:Yag lasers with 1064 nm wavelength. The beams traverse the arms both ways 280 times before recombining, which effectively lengthens the arm length to 1120 km. The devices are tuned so that the beams destructively interfere when they recom- bine if no gravitational wave is present. (a) The beam has a power of 100 kW, concentrated into an area of a square centimeter. Calculate the amplitude of the electric field in the beam. (b) LIGO can detect a gravitational wave that temporarily lengthens one arm by the minus- cule amount of 10-18 m! When this happens, the beams combine with a phase difference of p d. Estimate the shift d in radians. Note that the phase difference accumulates during both traversals of each round trip. (c) Use Eq. (35.7) to estimate the sensitivity of the photodetector in terms of the minimal electric field strength needed to detect a gravi- tational wave.
Answers
To calculate the amplitude of the electric field in the LIGO beam, we divide the power of 100 kW by the area of a square centimeter.
(a) The amplitude of the electric field in the LIGO beam can be calculated using the formula:
Amplitude of electric field = √(Power / Area)
Converting the power of 100 kW to 100,000 W and the area of a square centimeter to square meters:
Amplitude of electric field = √(100,000 / 0.0001) = √(10^9) = 10^4 V/m
Therefore, the amplitude of the electric field in the LIGO beam is 10,000 V/m.
(b) The phase shift caused by a gravitational wave temporarily lengthening one arm by 10^-18 m can be estimated using the formula:
Phase shift = (2π * d) / λ
Where d is the change in arm length and λ is the wavelength of the laser. In this case, the effective arm length is 1120 km, which is equivalent to 1.12 x 10^6 m, and the laser wavelength is 1064 nm, or\(1.064 x 10^-6 m.\)
Phase shift =\((2π * 10^-18) / (1.064 x 10^-6) = 2π * 10^-12 radians\)
Therefore, the estimated phase shift caused by the gravitational wave is approximately\(6.28 x 10^-12\) radians.
(c) Using Eq. (35.7), the sensitivity of the photodetector can be estimated by relating the minimal electric field strength required to detect a gravitational wave to the phase shift:
Minimal electric field strength = (λ * Amplitude of electric field) / (4π * d)
Substituting the values obtained:
Minimal electric field strength = \((1.064 x 10^-6 * 10^4) / (4π * 10^-12)\)
Simplifying the equation:
Minimal electric field strength = 8.49 x \(10^7\) V/m
Therefore, the estimated sensitivity of the photodetector is approximately 8.49 x \(10^7\) V/m, indicating the minimal electric field strength needed to detect a gravitational wave.
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Question 2 of 10
For which sample size (n) and sample proportion () can a normal curve be
used to approximate the sampling distribution?
A. n = 65; p = 0.9
O B. n = 35; p = 0.9
C. n = 35; p = 0.8
O D. n = 65; 6 = 0.8
Answers
Answer:
n = 65; p = 0.8
Step-by-step explanation:
The sample size (n) and sample proportion () can a normal curve be
used to approximate the sampling distribution is n = 65, p = 0.8.
The correct option is D.
According to the Central Limit Theorem, the shape of sample distribution of sample proportions with a population proportion, 'p' is normal
If n·p ≥ 10 and n·(1 - p) ≥ 10.
n = 65, p = 0.8
∴ n·p = 65 x 0.8 = 52 > 10
n·(1 - p) = 65 × (1 - 0.8) = 13 > 10
For n = 90, p = 0.9, n·(1 - p) = 18 > 10, a normal distribution can be used to approximate the sampling distribution.
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You must decide whether to buy new machinery to produce product X or to modify existing machinery. You believe the probability of a prosperous economy next year is 0.7. Prepare a decision tree and use it to calculate the expected value of the buy new option. The payoff table is provided below (+ for profits and - for losses).
When entering the answer, do not use the $ symbol. Do not enter the thousand separator. Enter up to 2 decimal places after the decimal point. For example, $6,525.35 must be entered as 6525.35
N1: Prosperity ($) N2: Recession ($)
A1 (Buy New) $1,035,332 $-150,000
A2(Modify) $823,625 $293,648
Answers
The expected value of the "Buy New" option is 724732.60.
Decision Tree:
To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:
Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:
Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)
Substituting the given values in the above formula, we get:
Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60
Therefore, the expected value of the "Buy New" option is 724,732.60.
Conclusion:
To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.
The expected value of the "Buy New" option is 724,732.60.
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What is a simpler form of the radical expression sqrt 36g^6.
Answers
Answer:6|g4
Step-by-step explanation:
Felicity will always drink wither fruit juice or coffee with her breakfast. She will eat either cereal or a yoghurt. What is the probability of her having coffee and a yoghurt expressed as a decimal
Answers
The probability of her having coffee and a yoghurt is 0.25
We can approach this problem using the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.
Let's denote the event of Felicity having coffee as C and the event of her having a yoghurt as Y. Then, according to the problem statement, we know:
P(C) = probability of Felicity having coffee = 0.5 (since she always drinks either fruit juice or coffee, and there are only two options)
P(Y) = probability of Felicity having a yoghurt = 0.5 (since she will eat either cereal or a yoghurt, and there are only two options)
To find the probability of Felicity having both coffee and a yoghurt, we need to calculate
P(C and Y) = probability of Felicity having coffee and a yoghurt
If we assume that the events of having coffee and having a yoghurt are independent (i.e., having coffee does not affect the probability of having a yoghurt, and vice versa), then we can use the multiplication rule to find:
P(C and Y) = P(C) x P(Y) = 0.5 x 0.5 = 0.25
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you draw a single card from a normal deck of cards. what is the probability that it will be a 7?
Answers
The probability of drawing a 7 from a normal deck of cards is 1/13 or approximately 0.0769 (rounded to four decimal places).
A normal deck of cards contains 52 cards, which includes 13 cards in each of the four suits: clubs, diamonds, hearts, and spades. Within each suit, there are cards numbered 2 through 10, plus face cards (jack, queen, king) and an ace.
Since there are four 7's in a deck of cards (one in each suit), the probability of drawing a 7 from a normal deck of cards is simply the ratio of the number of 7's to the total number of cards:
P(7) = 4/52
Simplifying, we get:
P(7) = 1/13
P(7) = 0.0769
It is important to note that the probability of drawing a 7 is independent of any previous draws, assuming the deck is shuffled thoroughly before each draw. That is, the probability of drawing a 7 remains the same whether it is the first card drawn or the tenth card drawn.
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Calculate the geometric mean return of the following data set: (Negative value should be indicated by a minus sign. Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
Answers
The geometric mean return of the given data set is 0.02.
The geometric mean return measures the compound rate of return over a period of time. It is calculated by taking the product of all the returns and then taking the nth root of the product, where n is the number of returns.
Formula: GMR = ((1+r1)(1+r2)…(1+rn))^1/n – 1
In this case, the data set is as follows:
r1 = 0.05
r2 = 0.03
r3 = -0.02
Using the formula above, the geometric mean return is calculated as:
GMR = ((1+0.05)(1+0.03)(1-0.02))^1/3 - 1
GMR = ((1.05)(1.03)(0.98))^1/3 - 1
GMR = (1.1394)^1/3 - 1
GMR = 0.0204
Therefore, the geometric mean return of the given data set is 0.02.
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Find x. Pleaseee I need to pass this or I fail the class!!!!
Answers
x = 8sin60 = 6.93
Find the precent of each number.
A. 59% of 640
B. 0.20% of 3,542
C. 195% of 568
D. 74% of 920
PLEASE HELP +10 points!
Answers
Answer:
A.)377.6
B.)7.084
C.)1107.6
D.)680.8
Step-by-step explanation:
What’s the answer to this if u know this!! APPREICATED heavily!
Answers
Step-by-step explanation:
75° and (3x + 15)° are supplementary (add up to 180°).
Therefore 75 + 3x + 15 = 180, 3x = 90 and x = 30.
Answer:
x = 30
Step-by-step explanation:
3x + 15 and 75 are adjacent angles and are supplementary, then
3x + 15 + 75 = 180
3x + 90 = 180 ( subtract 90 from both sides )
3x = 90 ( divide both sides by 3 )
x = 30
Jun has two less than three times as many books as Harriet. If June has 13 books, how many books does Harriet have?
Write the equation out in mathematical terms, and then find the answer.
Answers
Answer:
Look below
Step-by-step explanation:
Harriet- x books
June=3x-2
Substitute x for 13
(13x3)-2
39-2=37
June has 37 books
what is the equation of y=x^3 with the given transformations
Answers
Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.
1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.
2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.
3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.
4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.
5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.
6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.
Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.
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The urface area of a cylinder i 24π m². The ditance around the bae of the cylinder i 3π meter and the diameter of a bae of the cylinder i 4 meter. What i the height of the cylinder? Enter your anwer, a a implified fraction, in the box
Answers
After solving, the height of the cylinder is 6 meters.
The surface area of a cylinder is 24π m².
The distance around the base of the cylinder is 3π meter.
The diameter of a base of the cylinder is 4 meter.
Now the radius of the cylinder = diameter/2
The radius of the cylinder = 4/2
The radius of the cylinder = 2 meter.
The formula of surface area of cylinder:
S = 2πrh
From the question:
2πrh = 24π
Now putting the value of r
2π × 2 × h = 24π
4πh = 24π
Divide by 4π on both side, we get
h = 6
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The complete question is:
The surface area of a cylinder is 24π m². The distance around the base of the cylinder is 3π meter and the diameter of a base of the cylinder is 4 meter. What is the height of the cylinder? Enter your answer, in a simplified fraction, in the box.