The probabilities are solved and:
(a) A and B are independent.
(b) C and D are not independent.
(c) E and F are independent.
Given data:
To determine if two events are independent or not, determine if the probability of their intersection is equal to the product of their individual probabilities.
(a)
A = {X is even}, B = {X is divisible by 5}
The probability of event A is P(A) = 50/100 = 1/2, as there are 50 even numbers from 1 to 100.
The probability of event B is P(B) = 20/100 = 1/5, as there are 20 numbers divisible by 5 from 1 to 100.
To determine if A and B are independent, compare P(A ∩ B) with P(A) * P(B).
The probability of the intersection A ∩ B is the probability of choosing a number that is both even and divisible by 5. From 1 to 100, there are 10 such numbers: 10, 20, 30, ..., 90. Therefore, P(A ∩ B) = 10/100 = 1/10.
P(A) * P(B) = (1/2) * (1/5) = 1/10.
Since P(A ∩ B) = P(A) * P(B), A and B are independent events.
(b)
C = {X has two digits}, D = {X is divisible by 3}
The probability of event C is P(C) = 90/100 = 9/10, as there are 90 two-digit numbers from 1 to 100.
The probability of event D is P(D) = 33/100, as there are 33 numbers divisible by 3 from 1 to 100.
To determine if C and D are independent, compare P(C ∩ D) with P(C) * P(D).
The probability of the intersection C ∩ D is the probability of choosing a number that is both two digits and divisible by 3. From 1 to 100, there are 30 such numbers: 12, 15, 18, ..., 99. Therefore, P(C ∩ D) = 30/100 = 3/10.
P(C) * P(D) = (9/10) * (33/100) = 297/1000.
Since P(C ∩ D) ≠ P(C) * P(D), C and D are not independent events.
(c)
E = {X is a prime}, F = {X has a digit 5 prime number}
The probability of event E is P(E) = π(x)/100 = π(100)/100 = 25/100 = 1/4, as there are 25 primes from 1 to 100.
The probability of event F is P(F) = 4/100 = 1/25, as there are 4 prime numbers (5, 25, 55, and 75) that have the digit 5.
To determine if E and F are independent, compare P(E ∩ F) with P(E) * P(F).
The probability of the intersection E ∩ F is the probability of choosing a prime number that has the digit 5. From 1 to 100, there is only one such number: 5. Therefore, P(E ∩ F) = 1/100.
P(E) * P(F) = (1/4) * (1/25) = 1/100.
Since P(E ∩ F) = P(E) * P(F), E and F are independent events.
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Select two ratios that are equivalent to 7:6
Two ratios that are equal to 7:6 are 14:12 and 21:18, as they are the same, but 7 and 6 are multiplied by the same number (2 in the first, and 3 in the second.)
Translate the following argument in a standard form categorial syllogims then use venn diagram or rules for syllogim to determine whether each is valid or invalid.
All of the movies except the romantic comedies were exciting. Hence, the action films were exciting,because none of them is a romantic comedies.
Answer:
couldnt tell you
Step-by-step explanation:
jkj
A study of the amount of time it takes a mechanic to rebuild the transmission for a 2010 Chevrolet Colorado shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 8.9 hours.
Answer:
96.08% probability that their mean rebuild time is less than 8.9 hours.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 8.4, \sigma = 1.8, n = 40, s = \frac{1.8}{\sqrt{40}} = 0.2846[/tex]
Find the probability that their mean rebuild time is less than 8.9 hours.
This is the pvalue of Z when X = 2.9.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2.9 - 2.4}{0.2846}[/tex]
[tex]Z = 1.76[/tex]
[tex]Z = 1.76[/tex] has a pvalue of 0.9608
96.08% probability that their mean rebuild time is less than 8.9 hours.
Andrew plans to retire in 36 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal.
(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 36 years will exceed 11%?
(b) What is the probability that the mean return will be less than 5%?
Answer:
a) 24.82% probability that the mean annual return on common stocks over the next 36 years will exceed 11%
b) 13.57% probability that the mean return will be less than 5%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 8.7, \sigma = 20.2, n = 36, s = \frac{20.2}{\sqrt{36}} = 3.3667[/tex]
(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 36 years will exceed 11%?
This is 1 subtracted by the pvalue of Z when X = 11.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{11 - 8.7}{3.3667}[/tex]
[tex]Z = 0.68[/tex]
[tex]Z = 0.68[/tex] has a pvalue of 0.7518
1 - 0.7518 = 0.2482
24.82% probability that the mean annual return on common stocks over the next 36 years will exceed 11%
(b) What is the probability that the mean return will be less than 5%?
This is the pvalue of Z when X = 5.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5 - 8.7}{3.3667}[/tex]
[tex]Z = -1.1[/tex]
[tex]Z = -1.1[/tex] has a pvalue of 0.1357
13.57% probability that the mean return will be less than 5%
solve the exponential function 3 to the x-5 = 9
Answer:
x = 7
Step-by-step explanation:
[tex] 3^{x - 5} = 9 [/tex]
[tex] 3^{x - 5} = 3^2 [/tex]
[tex] x - 5 = 2 [/tex]
[tex] x = 7 [/tex]
how many are 4 x 4 ?
4 times 4 is 16, think of it like 4 + 4 + 4 + 4.
4 times 4 is 16, think of it like 4 + 4 + 4 + 4.
student throws 3 coins in the air. Find the probability that exactly 2 landed on heads, given that at least 2 landed on heads.
Step-by-step explanation:
Head(H) Tails(T)
Sample space is S (HHH,HHT,HTH,THH)
Event(HHT,HTH,THH)
so the probability is 3/4
Answer:
3/4
Step-by-step explanation:
WHY CAN'T ANYONE HELP ME? In 2001 there were 6680 electric-powered vehicles in use in the United States. In 1998 only 4760 electric vehicles were being used. Assume that the relationship between time, x, and number of electric-powered vehicles, y, is linear. Write an equation in slope-intercept form describing this relationship. Use ordered pairs of the form (years past 1998, number of vehicles).
Answer:
y = 640x +4760
Step-by-step explanation:
Given:
(x, y) = (years past 1998, number of vehicles) = (0, 4760), (3, 6680)
Find:
a slope-intercept form linear equation through these points
Solution:
The 2-point form of the equation of a line is a useful place to start:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (6680 -4760)/(3 -0)(x -0) +4760
y = 1920/3x +4760
y = 640x +4760 . . . . . the desired equation
What is the difference between the estimated and real value of 55-21?
Answer: The difference between the estimated and real value of 55-21 is about 4 or 5
Step-by-step explanation:
Answer:
The difference between the estimate and the real value of 55-21 is that when you estimate you're giving an educated guess and the real value is when you're actually doing the work to prove your answer and not just guess.
Step-by-step explanation:
Real Value
55-21=34
55
- 21
34
Estimated
55-21=32
A postal service will accept a package if its length plus its girth is not more than 96 inches. Find the dimensions and volume of the largest package with a square end that can be mailed.
Answer:
Dimension - 16in by 16in by 32inVolume - 8,192in³Step-by-step explanation:
Let the length and width of the rectangular package be x and y respectively. Since end of the package is a square, the perimeter of the package will be expressed as P = 4x+y and the volume will be expressed as V = x²y
If a postal service will accept a package if its length plus its girth is not more than 96 inches, then the perimeter is equivalent to 96 inches.
96 = 4x+y
y = 96-4x
Substituting the value of x into the formula for calculating the volume, we will have;
V(x) = x²(96-4x)
V(x) = 96x²-4x³
To get the dimensions and volume of the largest package, we will find V'(x) and equate it to zero.
V'(x) = 192x-12x²
192x-12x² = 0
Factoring out x;
x(192-12x) = 0
x = 0 and 192-12x = 0
12x = 192
x = 192/12
x = 16
This shows that we have a maximum value at x = 16 and minimum at x = 0
To get y, we will substitute x = 16 into the expression y = 96-4x
y = 96-4(16)
y = 96-64
y = 32
- The dimensions of the largest package is therefore 16in by 16in by 32in
- Volume of largest package = x²y = 16²*18 = 8,192in³
5c + 16.5 = 13.5 + 10c
Answer:
Hello!
________________________
5c + 16.5 = 13.5 + 10c
Exact Form: c = 3/5
Decimal Form: c = 0.6
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
Hope this helped you!
Answer:
3000+3d=noods
Step-by-step explanation:
Solve the quadratic equation x2 + 14x = 51 by completing the square.
Question 3 options:
A)
x = –17, x = –3
B)
x = –17, x = 3
C)
x = 3, x = 17
D)
x = –3, x = 17
Answer:
B
Step-by-step explanation:
Given
x² + 14x = 51
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(7)x + 49 = 51 + 49 , that is
(x + 7)² = 100 ( take the square root of both sides )
x + 7 = ± [tex]\sqrt{100}[/tex] = ± 10 ( subtract 7 from both sides )
x = - 7 ± 10
Thus
x = - 7 - 10 = - 17
x = - 7 + 10 = 3
I don't know what to do.
Answer:
True.
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
We can simply plug in the 3 variables to see if it forms a Pythagorean Triple:
6² + 13² = 14.32²
36 + 169 = 205.062
205 = 205 (rounded), so True.
According to Advertising Age, the average base salary for women working as copywriters in advertising firms is higher than the average base salary for men. The average base salary for women is $67,000 and the average base salary for men is $65,500 (Working Woman, July/August 2000). Assume salaries are normally distributed and that the standard deviation is $7000 for both men and women.
Required:
a. What is the probability of a woman receiving a salary in excess of $75,000 (to 4 decimals)?
b. What is the probability of a man receiving a salary in excess of $75,000 (to 4 decimals)?
c. What is the probability of a woman receiving a salary below $50,000 (to 4 decimals)?
d. How much would a woman have to make to have a higher salary than 99% of her male counterparts (0 decimals)?
Answer:
(a) The probability of a woman receiving a salary in excess of $75,000 is 0.1271.
(b) The probability of a man receiving a salary in excess of $75,000 is 0.0870.
(c) The probability of a woman receiving a salary below $50,000 is 0.9925.
(d) A woman would have to make a higher salary of $81,810 than 99% of her male counterparts.
Step-by-step explanation:
Let the random variable X represent the salary for women and Y represent the salary for men.
It is provided that:
[tex]X\sim N(67000, 7000^{2})\\\\Y\sim N(65500, 7000^{2})[/tex]
(a)
Compute the probability of a woman receiving a salary in excess of $75,000 as follows:
[tex]P(X>75000)=P(\frac{X-\mu_{x}}{\sigma_{x}}>\frac{75000-67000}{7000})[/tex]
[tex]=P(Z>1.14)\\\\=1-P(Z<1.14)\\\\=1-0.87286\\\\=0.12714\\\\\approx 0.1271[/tex]
Thus, the probability of a woman receiving a salary in excess of $75,000 is 0.1271.
(b)
Compute the probability of a man receiving a salary in excess of $75,000 as follows:
[tex]P(Y>75000)=P(\frac{Y-\mu_{y}}{\sigma_{y}}>\frac{75000-65500}{7000})[/tex]
[tex]=P(Z>1.36)\\\\=1-P(Z<1.36)\\\\=1-0.91309\\\\=0.08691\\\\\approx 0.0870[/tex]
Thus, the probability of a man receiving a salary in excess of $75,000 is 0.0870.
(c)
Compute the probability of a woman receiving a salary below $50,000 as follows:
[tex]P(X<50000)=P(\frac{X-\mu_{x}}{\sigma_{x}}<\frac{50000-67000}{7000})[/tex]
[tex]=P(Z>-2.43)\\\\=P(Z<2.43)\\\\=0.99245\\\\\approx 0.9925[/tex]
Thus, the probability of a woman receiving a salary below $50,000 is 0.9925.
(d)
Let a represent the salary a woman have to make to have a higher salary than 99% of her male counterparts.
Then,
[tex]P(Y\leq a)=0.99[/tex]
[tex]\Rightarrow P(Z<z)=0.99[/tex]
The z-score for this probability is:
z-score = 2.33
Compute the value of a as follows:
[tex]\frac{a-\mu_{y}}{\sigma_{y}}=2.33\\\\[/tex]
[tex]a=\mu_{y}+(2.33\times \sigma_{y})\\\\[/tex]
[tex]=65500+(2.33\times7000)\\\\=65500+16310\\\\=81810[/tex]
Thus, a woman would have to make a higher salary of $81,810 than 99% of her male counterparts.
Researchers studied the mean egg length (in millimeters) for a particular bird population. After a random sample of eggs, they obtained a 95% confidence interval of (45,60) in millimeters. In the context of the problem, which of the following interpretations is correct, if any?
A. We are 95% sure that an egg will be between 45 mm and 60 mm in length.
B. For this particular bird population, 95% of all birds have eggs between 45 mm and 60 mm.
C. We are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
D. We are 95% confident that the mean length of eggs in the sample is between 45 mm and 60 mm.
E. None of the above is a correct interpretation.
Answer:
C. We are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
For 95% confidence interval, it means that we are 95% confident that the mean of the population is between the given upper and lower bounds of the confidence interval.
For the case above, the interpretation of the 95% confidence interval is that we are 95% confident that the mean length of eggs for this particular bird population is between 45 mm and 60 mm.
Type 11/5 in the simplest form
Answer:
[tex]2\frac{1}{5}[/tex]
Step-by-step explanation:
11 ÷ 5 = 2 R 1 → [tex]2\frac{1}{5}[/tex]
Hope this helps! :)
What is the solution of (4x-16)1/3=36
(4x-16)/3 = 36
4x-16 = 108
4x = 108+16
4x = 124
x = 124/4
x = 31
Answer:
x = 31
Step-by-step explanation:
=> [tex](4x-16)\frac{1}{3} = 36[/tex]
Multiplying 3 to both sides
=> [tex]4x-16 = 36*3[/tex]
=> 4x-16 - 108
Adding 16 to both sides
=> 4x = 108+16
=> 4x = 124
Dividing both sides by 4
=> x = 31
The function f(x) = 2x^3 + 3x^2 is:
(a) even
(b) odd
(c) neither
(d) even and odd
Answer:
neither
Step-by-step explanation:
First we must determine if both x and -x are in the domain of the function
since it is a polynomial function our first condition is satisfied
Then we should calculate the image of -x :
2x(-x)^3 + 3*(-x)² = -2x^3+3x²
it is not equal to f(x) nor -f(x)
Maya is solving the quadratic equation by completing the square. 4x2 + 16x + 3 = 0 What should Maya do first?
Maya should Isolate the variable x² option (A) Isolate the variable x² is correct.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
The complete question is:
Maya is solving the quadratic equation by completing the What should Maya do first? square.
4x² + 16x + 3 = 0
Isolate the variable x².Subtract 16x from both sides of the equation.Isolate the constant.Factor 4 out the variable terms.We have a quadratic equation:
4x² + 16x + 3 = 0
To make the perfect square
Maya should do first:
Isolate the variable x²
To make the coefficient of x² is 1.
4(x² + 4x + 3/4) = 0
x² + 4x + 3/4 = 0
x² + 4x + 2² - 2² + 3/4 = 0
(x + 2)² - 4 + 3/4 = 0
(x + 2)² = 13/4
x + 2 = ±√(13/4)
First, take the positive and then the negative sign.
x = √(13/4) - 2
x = -√(13/4) - 2
Thus, Maya should Isolate the variable x² option (A) Isolate the variable x² is correct.
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In a study of 788 randomly selected medical malpractice lawsuits, it was found that 494 of them were dropped or dismissed. Use a 0.05 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed.
Which of the following is the hypothesis test to be conducted?
A.
Upper H 0 : p less than 0.5
Upper H 1 : p equals 0.5
B.
Upper H 0 : p greater than 0.5
Upper H 1 : p equals 0.5
C.
Upper H 0 : p equals 0.5
Upper H 1 : p not equals 0.5
D.
Upper H 0 : p equals 0.5
Upper H 1 : p less than 0.5
E.
Upper H 0 : p not equals 0.5
Upper H 1 : p equals 0.5
F.
Upper H 0 : p equals 0.5
Upper H 1 : p greater than 0.5
What is the test statistic?
Z =
(Round to two decimal places as needed.)
What is the conclusion about the null hypothesis?
A. Reject the null hypothesis because the P-value is greater than the significance level, alpha.
B. Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, alpha.
C. Fail to reject the null hypothesis because the P-value is greater than the significance level, alpha.
D. Reject the null hypothesis because the P-value is less than or equal to the significance level, alpha.
What is the final conclusion?
A.There is sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed.
B.There is not sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed.
C.There is sufficient evidence to warrant rejection of the claim that most medical malpractice lawsuits are dropped or dismissed.
D.There is not sufficient evidence to warrant rejection of the claim that most medical malpractice lawsuits are dropped or dismissed.
Answer:
Step-by-step explanation:
A. Upper H 0 : p equals 0.5
Upper H 1 : p not equals 0.5
B. Using the tests promotion formula, we have (p - P) / √P(1-P)
Where p (sample promotion) = 494/788 = 0.6269, P (population proportion) = 0.5,
(0.6269 - 0.5) / (√0.5(1-0.5))
0.1269/ √(0.5 (0.5))
0.1269/ √0.25
0.1269/0.5
Test statistics is equal to 0.2538
C. We will use the p value to determine our result, thus the p value at 0.05 level of significance is 0.79965, thus we fail to reject the null hypothesis because the P-value is greater than the significance level, alpha.
Then we conclude that There is not sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed.
Translate into an equation: The cost of V ounces at $2 per ounce equals $56.
Answer:
V = number of ounces
56 = 2V
Step-by-step explanation:
Answer:28
Step-by-step explanation:V times 2= 56
Use z scores to compare the given values. In a recent awards ceremony, the age of the winner for best actor was 34 and the age of the winner for best actress was 62. For all best actors, the mean age is 43.4 years and the standard deviation is 8.8 years. For all best actresses, the mean age is 38.2 years and the standard deviation is 12.6 years. (All ages are determined at the time of the awards ceremony.) Relative to their genders, who had the more extreme age when winning the award, the actor or the actress? Explain.
Answer:
The actress had more extreme age when winning the award.
Step-by-step explanation:
We are given that for all the best actors, the mean age is 43.4 years and the standard deviation is 8.8 years. For all best actresses, the mean age is 38.2 years and the standard deviation is 12.6 years.
To find who had the more extreme age when winning the award, the actor or the actress, we will use the z-score method.
Finding the z-score for the actor;Let X = age of the winner for best actor
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean age = 43.4 years
[tex]\sigma[/tex] = standard deviation = 8.8 years
It is stated that the age of the winner for best actor was 34, so;
z-score for 34 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{34-43.4}{8.8}[/tex] = -1.068
Finding the z-score for the actress;Let Y = age of the winner for best actress
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{Y-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean age = 38.2 years
[tex]\sigma[/tex] = standard deviation = 12.6 years
It is stated that the age of the winner for best actress was 62, so;
z-score for 62 = [tex]\frac{Y-\mu}{\sigma}[/tex]
= [tex]\frac{62-38.2}{12.6}[/tex] = 1.889
Since the z-score for the actress is more which means that the actress had more extreme age when winning the award.
What is the surface area of this regular pyramid? A. 230 in2 B. 304 in2 C. 480 in2 D. 544 in2
Answer:
B: 304in^2
Step-by-step explanation:
One triangle face: (8)(15) ÷ 2 = 60
Four triangle faces: 60 x 4 = 240
Bottom Face: (8)(8) = 64
Total Surface Area: Four triangle faces + Bottom Face
Total Surface Area: 240 + 64
Total Surface Area: 304in^2
What is the value of x in the figure above
the value of x is 115°.
hope its helpful to uh..
In her backyard, Mary is planting rows of tomatoes. To plant a row of tomatoes, mary needs 20/13 square feet. There are 40 square feet in Mary's backyard, so how many rows of tomatoes can mary plant??
Answer:
26 rows
Step-by-step explanation:
[tex]number \: of \: rows \\ = \frac{40}{ \frac{20}{13} } \\ \\ = \frac{40 \times 13}{20} \\ \\ = 2 \times 13 \\ \\ = 26 \: [/tex]
The average daily rainfall for the past week in the town of Hope Cove is normally distributed, with a mean rainfall of 2.1 inches and a standard deviation of 0.2 inches. If the distribution is normal, what percent of data lies between 1.9 inches and 2.3 inches of rainfall? a) 95% b) 99.7% c) 34% d) 68%
Answer:
D
Step-by-step explanation:
We calculate the z-score for each
Mathematically;
z-score = (x-mean)/SD
z1 = (1.9-2.1)/0.2 = -1
z2 = (2.3-2.1)/0.2 = 1
So the proportion we want to calculate is;
P(-1<x<1)
We use the standard score table for this ;
P(-1<x<1) = P(x<1) -P(x<-1) = 0.68269 which is approximately 68%
Answer:
68
Step-by-step explanation:
Question
An airplane is traveling at a constant speed of 585 miles per hour. How many feet does it travel in 6 seconds? Remember
that 1 mile is 5280 feet.
Convert the 6 seconds to hours:
5 seconds x x 1/60 ( minutes per seconds) x 1/60 (Hours per minute) = 6/3600 = 1/600 hours.
Distance = speed x time
Distance = 585 x 1/600 = 585/600 = 0.975 miles
Convert miles to feet:
0.975 x 5280 = 5,148 feet
The plane traveled 5,148 feet in 6 seconds.
An experiment consists of choosing objects without regards to order. Determine the size of the sample space when you choose the following:(a) 8 objects from 19(b) 3 objects from 25(c) 2 objects from 23
Answer:
a
[tex]n= 75, 582[/tex]
b
[tex]n= 2300[/tex]
c
[tex]n = 253[/tex]
Step-by-step explanation:
Generally the size of the sample sample space is mathematically represented as
[tex]n = \left N } \atop {}} \right. C_r[/tex]
Where N is the total number of objects available and r is the number of objects to be selected
So for a, where N = 19 and r = 8
[tex]n = \left 19 } \atop {}} \right. C_8 = \frac{19 !}{(19 - 8 )! 8!}[/tex]
[tex]= \frac{19 *18 *17 *16 *15 *14 *13 *12 *11! }{11 ! \ 8!}[/tex]
[tex]n= 75, 582[/tex]
For b Where N = 25 and r = 3
[tex]n = \left 25 } \atop {}} \right. C_3 = \frac{25 !}{(19 - 3 )! 3!}[/tex]
[tex]= \frac{25 *24 *23 *22 ! }{22 ! \ 3!}[/tex]
[tex]n= 2300[/tex]
For c Where N = 23 and r = 2
[tex]n = \left 23 } \atop {}} \right. C_2 = \frac{23 !}{(23 - 2 )! 2!}[/tex]
[tex]= \frac{23 *22 *21! }{21 ! \ 3!}[/tex]
[tex]n = 253[/tex]
The graph of y =ex is transformed as shown in the graph below. Which equation represents the transformed function?
Answer:
B. e^x+3
Step-by-step explanation:
Y=e^x
the graph is moving 3 units up
y= y+3
y=e^x+3
answer = y=e^x+3
Answer: B
Step-by-step explanation:
You wish to take out a $200,000 mortgage. The yearly interest rate on the loan is 4% compounded monthly, and the loan is for 30 years. Calculate the total interest paid on the mortgage. Give your answer in dollars to the nearest dollar. Do not include commas or the dollar sign in your answer.
Answer:
$143,739
Step-by-step explanation:
We must apply the formula for P0 and solve for d, that is,
P0=d(1−(1+rk)−Nk(rk).
We have P0=$200,000,r=0.04,k=12,N=30, so substituting in the numbers into the formula gives
$200,000=d(1−(1+0.0412)−30⋅12)(0.0412),
that is,
$200,000=209.4612d⟹d=$954.83.
So our monthly repayments are d=$954.83. To calculate the total interest paid, we find out the entire amount that's paid and subtract the principal. The total amount paid is
Total Paid=$954.83×12×30=$343,738.80
and therefore the total amount of interest paid is
Total Interest=$343,738.80−$200,000=$143,738.80,
which is $143,739 to the nearest dollar.
The interest paid is 2912683 dollars.
What is compound interest ?Compound interest is calculated for the principle taken as well as previous interest paid.
According to the given question Principle amount (P) taken from the bank is 2000000 dollars.
The yearly interest rate (r) compounded monthly is 4%.
Time in years (n) is 30.
We know, in the case of compound interest compounded yearly is
A = P(1 + r/100)ⁿ.
So, Amount compounded monthly will be
A = P[ 1 + (r/12)/100]¹²ⁿ.
A = 2000000[ 1 + (4/12)/100]¹²ˣ³⁰.
A = 2000000[ 1 + 0.003]³⁶⁰.
A = 2000000[ 1.003]³⁰⁰.
A = 2000000(2.456).
A = 4912583.
∴ The total interest paid on the mortgage is (4912683 - 2000000) = 2912683.
earn more about compound interest here :
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