Answer: (0.066,0.116)
Step-by-step explanation:
The confidence interval for proportion is given by :-
[tex]p_1-p_2\pm z_{\alpha/2}\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}[/tex]
Given : The proportion of men have red/green color blindness = [tex]p_1=\dfrac{89}{950}\approx0.094[/tex]
The proportion of women have red/green color blindness = [tex]p_2=\dfrac{6}{2050}\approx0.003[/tex]
Significance level : [tex]\alpha=1-0.99=0.01[/tex]
Critical value : [tex]z_{\alpha/2}=z_{0.005}=\pm2.576[/tex]
Now, the 99% confidence interval for the difference between the color blindness rates of men and women will be:-
[tex](0.094-0.003)\pm (2.576)\sqrt{\dfrac{0.094(1-0.094)}{950}+\dfrac{0.003(1-0.003)}{2050}}\approx0.091\pm 0.025\\\\=(0.09-0.025,0.09+0.025)=(0.066,\ 0.116)[/tex]
Hence, the 99% confidence interval for the difference between the color blindness rates of men and women= (0.066,0.116)
_________________ "describes a measure used to compare two different tests with the same group of participants to see how closely correlated the two sets of scores are with each other"
Answer:
The answer is Parallel-forms reliability.
Parallel-forms reliability describes a measure used to compare two different tests with the same group of participants to see how closely correlated the two sets of scores are with each other.
Test-retest reliability is a measure used to compare the results of two instances of the same test taken by the same group of participants to establish how closely correlated the two sets of scores are.
Explanation:The measure used to compare two different tests with the same group of participants to see how closely correlated the two sets of scores are with each other is called test-retest reliability.
In essence, test-retest reliability measures the consistency of results when a test is administered more than once. The higher the correlation between the two sets of scores, the higher the test’s reliability. For example, if a group of students were to take a vocabulary test one week, and then the same test a week later, a high correlation between the results would suggest that the test is reliable.
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How many solutions can a nonhomogeneous system of linear (algebraic) equations have? What if the system is homogeneous?
Answer:
Step-by-step explanation:
Infinitely many.
Infinitely many.
A non-homogeneous system of linear equations can have a unique solution, no solution, or infinitely many solutions and a homogeneous system always has at least the trivial solution, and may have infinitely many non-trivial solutions depending on the rank of A.
A non-homogeneous system of linear equations (where the vector b on the RHS is non-zero) can have three types of solutions:
Unique solution: If the matrix A is square (m=n) and its determinant is not zero, the system has exactly one unique solution.No solution: If the system is inconsistent (meaning the rows of matrix A are linearly dependent and it does not satisfy the Rouche-Capelli theorem), there is no solution.Infinitely many solutions: If the matrix A has more variables than equations (m<n) and the columns are linearly dependent, the system has infinitely many solutions.In contrast, a homogeneous system of linear equations (where the vector b on the RHS is zero) always has at least the trivial solution, where all variables equal zero. Depending on the rank of matrix A:
Trivial solution: If the rank of A is equal to the number of variables (n), the only solution is the trivial one.Non-trivial solutions: If the rank of A is less than the number of variables (m<n), there are infinitely many non-trivial solutions.These rules are concisely summarized by the Rouche-Capelli theorem.
Question 15 of 20 (1 point) View problem in a pop-up Assume that the mean systolie blood pressure of normal adults is 120 millimeters of mercury (mm Hg) and the standard deviation is 5.6. Assume the variable is normally distributed. Use a graphing calculator and round the answers to four decimal places. Part 1 If an individual is selected, find the probability that the individual's pressure will be between 120.4 and 121.9 mm Hg. P120A
Answer: 0.1052
Step-by-step explanation:
Given : Mean :[tex]\mu= 120[/tex]
Standard deviation : [tex]\sigma= 5.6[/tex]
We assume the variable is normally distributed.
The formula for z-score is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x=120.4
[tex]z=\dfrac{120.4-120}{5.6}=0.0714285714286\approx0.07[/tex]
For x=121.9
[tex]z=\dfrac{121.9-120}{5.6}=0.339285714286\approx0.34[/tex]
The p-value =[tex]P(0.07<z<0.34)=P(0.34)-P(0.07)[/tex]
[tex]=0.6330717-0.5279031=0.1051686\approx0.1052[/tex]
The probability that the individual's pressure will be between 120.4 and 121.9 mm Hg = 0.1052
Engineers want to design seats in commercial aircraft so that they are wide enough to fit 90% of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 14.9 in. and a standard deviation of 0.9 in. Find Upper P 90. That is, find the hip breadth for men that separates the smallest 90% from the largest 10%.
Answer:
16.053 inches
Step-by-step explanation:
Many such probability questions are easily answered by a suitable calculator or spreadsheet.
A bag contains three types of coins i.e. one rupee coins, 50 paisa coins and 25 paisa coins totalling 175 coins. If the total value of the coins of each kind be the same, the total amount in the bag is
a) Rs 300 b) Rs 175 c) Rs 126 d) Rs 75
one rupee coin be z
50 paisa coins=2z
25 paisa coins=4z
50/25=2 2z*2=4z
z+2x+4x=175
7z=175
7z/7=175/7
z=25
one rupee coin=25 value
50 paisa rupee coins=50 value
25 rupee coin=100 value
50/25=2 50*2=100
25+50+100=175
Answer is b) Rs 175. I think this is the answer.
[ Complex Analysis ]
Find the laurent series for 1/(1-Z2) about Z0=1.
Recall that for [tex]|z|<1[/tex], we have
[tex]\dfrac1{1-z}=\displaystyle\sum_{n\ge0}z^n[/tex]
Then
[tex]\dfrac1{1-z}=-\dfrac1z\dfrac1{1-\frac1z}=-\dfrac1z\displaystyle\sum_{n\ge0}z^{-n}=-\sum_{n\ge0}z^{-n-1}[/tex]
valid for [tex]|z|>1[/tex], so that
[tex]\dfrac1{1-z^2}=-\dfrac1{z^2}\dfrac1{1-\frac1{z^2}}=-\dfrac1{z^2}\displaystyle\sum_{n\ge0}z^{-2n}=-\sum_{n\ge0}z^{-2n-2}[/tex]
also valid for [tex]|z|>1[/tex].
4,000 students take an exam and get scores with a mean of 68 and a standard deviation of 26.
Approximately how many students scored between 16 and 120? Hint: Empirical Rule: 68%, 95%, 99.7%
Answer:
95%
Step-by-step explanation:
We have a normal distribution with a mean of 6 students and standard deviation of 26.
To solve this problem, we're going to need the help of a calculator.
P(16<z<120) = 0.9545 ≈ 95.45%
Rounding, we can say that 95% of the students scored between 16 and 120.
In a survey of adults who follow more than one sport, 30% listed football as their favorite sport. You survey 15 adults who follow more than one sport. What is the probability rounded to the nearest tenth that fewer than 4 of them will say that football is their favorite sport?
Answer: 0.5
Step-by-step explanation:
Binomial probability formula :-
[tex]P(x)=^nC_x\ p^x(q)^{n-x}[/tex], where P(x) is the probability of getting success in x trials , n is the total trials and p is the probability of getting success in each trial.
Given : The probability that the adults follow more than one game = 0.30
Then , q= 1-p = 1-0.30=0.70
The number of adults surveyed : n= 15
Let X be represents the adults who follow more than one sport.
Then , the probability that fewer than 4 of them will say that football is their favorite sport,
[tex]P(X\leq4)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)\\\\=^{15}C_{0}\ (0.30)^0(0.70)^{15}+^{15}C_{1}\ (0.30)^1(0.70)^{14}+^{15}C_{2}\ (0.30)^2(0.70)^{13}+^{15}C_{3}\ (0.30)^3(0.70)^{12}+^{15}C_{4}\ (0.30)^4(0.70)^{11}\\\\=(0.30)^0(0.70)^{15}+15(0.30)^1(0.70)^{14}+105(0.30)^2(0.70)^{13}+455(0.30)^3(0.70)^{12}+1365(0.30)^4(0.70)^{11}\\\\=0.515491059227\approx0.5[/tex]
Hence, the probability rounded to the nearest tenth that fewer than 4 of them will say that football is their favorite sport =0.5
A total of 363 were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold?
Answer:
The number of adult tickets sold was 121
Step-by-step explanation:
The general equation is: S + A = T ;where S means student tickets, A means adult tickets and T means total tickets. We know that S is two times A and T is 363. So, S will be 2x and A will be x. Then, the new equation is 2x + x = 363.
S + A = T
2x + x = 363
3x = 363
x = 363 / 3
x = 121
Adult tickets: A = x = 121
Student tickets: S = 2x = 2 * 121 = 242
Final answer:
To solve for the number of adult tickets sold, set the number of adult tickets as x, the student tickets as 2x, and use the total of 363 tickets to create the equation 3x = 363. Solving for x, you find that 121 adult tickets were sold.
Explanation:
The numerical problem given is about determining the number of adult tickets and student tickets sold for a school play, with the total number of tickets sold being 363, and the number of student tickets being twice the number of adult tickets sold.
Let the number of adult tickets be x. Then the number of student tickets is 2x. The total number of tickets sold is the sum of the adult tickets and student tickets, which is x + 2x = 3x. Since we know that 363 tickets were sold in total, we can write the equation:
3x = 363
Now, solve for x:
Divide both sides of the equation by 3:x = 363 / 3x = 121Therefore, 121 adult tickets were sold.
Assume that on a standardized test of 100 questions, a person has a probability of 80% of answering any particular question correctly. Find the probability of answering between 74 and 84 questions
Answer: 0.7264
Explanation:
The number of independent questions (n) = 100
Probability of answering a question (p) = 0.80
Let X be the no. of questions that need to be answered.
[tex]\therefore[/tex] random variable X follows binomial distribution
The probability function of a binomial distribution is given as
[tex]P(X=x) = \binom{n}{x}\times p^{x}(1-p)^{n-x}[/tex]
Now , we nee to find P(74 ≤ X ≤ 84)
[tex]\therefore P(74\leq X\leq 84) = P(X=74) + P(X=75).........+ P(X=84)[/tex]
P(74 ≤ X ≤ 84) = [tex]\sum_{74}^{84}\binom{100}{x}\times (0.80)^{x}(0.20)^{100-x}[/tex]
P(74 ≤ X ≤ 84) = 0.7264
List all the bijections from A into B.
a) A={q,r,s} and B={2,3,4}
b) A={1,2,3,4} and B={5,6,7,8}
Answer:
The list of bijections from A into B are shown below.
Step-by-step explanation:
A function f is called one-to-one or injective, if and only if
[tex]f(x)=f(y)\Rightarrow x = y[/tex]
for all x and y in the domain of f.
A function f from X to Y is called onto or surjective, if and only if
for every element y∈Y there is an element x∈X with f(x)=y.
If a function is one-one and onto, then it is called bijective.
Part (a):
A={q,r,s} and B={2,3,4}
We need to find all the bijections from A into B.
(1) [tex]A\rightarrow B=\{(q,2),(r,3),(s,4)\}[/tex]
(2) [tex]A\rightarrow B=\{(q,2),(r,4),(s,3)\}[/tex]
(3) [tex]A\rightarrow B=\{(q,3),(r,2),(s,4)\}[/tex]
(4) [tex]A\rightarrow B=\{(q,3),(r,4),(s,2)\}[/tex]
(5) [tex]A\rightarrow B=\{(q,4),(r,2),(s,3)\}[/tex]
(6) [tex]A\rightarrow B=\{(q,4),(r,3),(s,2)\}[/tex]
Part (b):
A={1,2,3,4} and B={5,6,7,8}
We need to find all the bijections from A into B.
(1) [tex]A\rightarrow B=\{(1,5),(2,6),(3,7),(4,8)\}[/tex]
(2) [tex]A\rightarrow B=\{(1,5),(2,6),(3,8),(4,7)\}[/tex]
(3) [tex]A\rightarrow B=\{(1,5),(2,7),(3,6),(4,8)\}[/tex]
(4) [tex]A\rightarrow B=\{(1,5),(2,7),(3,8),(4,6)\}[/tex]
(5) [tex]A\rightarrow B=\{(1,5),(2,8),(3,6),(4,7)\}[/tex]
(6) [tex]A\rightarrow B=\{(1,5),(2,8),(3,7),(4,6)\}[/tex]
(7) [tex]A\rightarrow B=\{(1,6),(2,5),(3,7),(4,8)\}[/tex]
(8) [tex]A\rightarrow B=\{(1,6),(2,5),(3,8),(4,7)\}[/tex]
(9) [tex]A\rightarrow B=\{(1,6),(2,7),(3,5),(4,8)\}[/tex]
(10) [tex]A\rightarrow B=\{(1,6),(2,7),(3,8),(4,5)\}[/tex]
(11) [tex]A\rightarrow B=\{(1,6),(2,8),(3,5),(4,7)\}[/tex]
(12) [tex]A\rightarrow B=\{(1,6),(2,8),(3,7),(4,5)\}[/tex]
(13) [tex]A\rightarrow B=\{(1,7),(2,6),(3,5),(4,8)\}[/tex]
(14) [tex]A\rightarrow B=\{(1,7),(2,6),(3,8),(4,5)\}[/tex]
(15) [tex]A\rightarrow B=\{(1,7),(2,5),(3,6),(4,8)\}[/tex]
(16) [tex]A\rightarrow B=\{(1,7),(2,5),(3,8),(4,6)\}[/tex]
(17) [tex]A\rightarrow B=\{(1,7),(2,8),(3,6),(4,5)\}[/tex]
(18) [tex]A\rightarrow B=\{(1,7),(2,8),(3,5),(4,6)\}[/tex]
(19) [tex]A\rightarrow B=\{(1,8),(2,6),(3,7),(4,5)\}[/tex]
(20) [tex]A\rightarrow B=\{(1,8),(2,6),(3,5),(4,7)\}[/tex]
(21) [tex]A\rightarrow B=\{(1,8),(2,7),(3,6),(4,5)\}[/tex]
(22) [tex]A\rightarrow B=\{(1,8),(2,7),(3,5),(4,6)\}[/tex]
(23) [tex]A\rightarrow B=\{(1,8),(2,5),(3,6),(4,7)\}[/tex]
(24) [tex]A\rightarrow B=\{(1,8),(2,5),(3,7),(4,6)\}[/tex]
a b c or d pls helpp
Answer:
C (0, 9)
Step-by-step explanation:
First, X is reflected across the line x=2.
X(4, -7) becomes X'(0, -7).
Next, X' is reflected across the line y=1.
X'(0, -7) becomes X"(0, 9).
The size of a bicycle is determined by the diameter of the wheel. You want a 20-in bicycle for your birthday. What is the area of one of the wheels? 385.47 in2 314.16 in2 484.37 in2 345.54 in2
Answer:
314.16 in²
Step-by-step explanation:
If the diameter is 20", then the radius is 10" (1/2 the diameter).
Area of a circle is [tex]\pi r[/tex]²
So, π 10² = 100π = 314.16 in²
According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66 inches and a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X = height of the individual. A) Give the distribution of X.
X ~ _____ (____,____)
B) Find the probability that the person is between 64 and 69 inches.
Write the probability statement.
P(______
What is the probability?
The distribution of X is a normal distribution with a mean of 66 inches and a standard deviation of 2.5 inches. To find the probability that a person's height is between 64 and 69 inches, we need to determine the z-scores for each height value and use a z-table or calculator to find the probabilities.
Explanation:A) Give the distribution of X.
X ~ Normal(66, 2.5)
B) Find the probability that the person is between 64 and 69 inches.
P(64 ≤ X ≤ 69)
To find this probability, we need to calculate the z-score for each height value using the formula z = (X - μ) / σ. Then, we can use a z-table or a calculator to find the corresponding probabilities.
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The height X of Asian adult males follows a normal distribution with parameters X ~ N(66, 2.5). The probability that one randomly chosen male is between 64 and 69 inches tall can be found using Z-scores and the area under the normal curve.
The distribution of the height X for Asian adult males according to the given study is X ~ N(66, 2.5), where 66 is the mean height in inches and 2.5 is the standard deviation.
Probability that the height is between 64 and 69 inches
To find the probability that the height of a randomly chosen Asian adult male is between 64 and 69 inches, we can use the properties of the normal distribution. We first convert the raw scores to Z-scores using the formula Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.
The probability statement is P(64 < X < 69). To calculate this probability, we find the Z-scores for 64 and 69 inches and then find the area under the normal curve between these two Z-scores using a standard normal distribution table or a calculator with normal distribution functions.
The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the probability that the bulb will last less than 800 hours?
Answer: 0.5507
Step-by-step explanation:
The cumulative distribution function for exponential distribution:-
[tex]P(X\leq x)=1-e^{-\lambda x}[/tex]
Given : The life of a light bulb is exponentially distributed with a mean of 1,000 hours.
Then , [tex]\lambda=\dfrac{1}{1000}[/tex]
Then , the probability that the bulb will last less than 800 hours is given by :-
[tex]P(X\leq 800)=1-e^{\frac{-800}{1000}}\\\\=1-e^{-0.8}=0.5506710358\approx0.5507[/tex]
Hence, the probability that the bulb will last less than 800 hours = 0.5507
The probability that the bulb will last less than 800 hours is 0.550
Further explanationAn incandescent light bulb is an electric light with a wire filament heated to such a high temperature that it glows with visible light. The filament of an incandescent light bulb is protected from oxidation with a glass or fused quartz bulb that is filled with inert gas or a vacuum. The exponential distribution is the probability distribution of the time between events in a Poisson point process. It is a particular case of the gamma distribution. While the arithmetic mean is the central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values
The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the probability that the bulb will last less than 800 hours?
What is the probability that the light bulb will have to replaced within 800 hours?
[tex]\lambda = \frac{1}{1000}[/tex]
[tex]P(x<=800) = 1 - e^{(-\lambda*x)} = 1-e^{[(-\frac{1}{1000} )*800]} = 1-e^{-0.8} = 1-0.449 = 0.550[/tex]
Learn moreLearn more about bulb https://brainly.com/question/9584045Learn more about hours https://brainly.com/question/1032699Learn more about mean https://brainly.com/question/3777157Answer details
Grade: 5
Subject: math
Chapter: probability
Keywords: mean, bulb, hours, exponential, light
Andrea has a jug containing 1.5 liters of chocolate milk. She fills one cup with 250 milliliters and another cup with 0.6 liters. How much chocolate milk is left in the jug in milliliters?
0.65 milliliters
249.1 milliliters
450 milliliters
650 milliliters
Answer:
650 milliliters.
Step-by-step explanation:
Amount in the Jug = 1.5 * 1000 = 1,500 mls.
She pours out 250 mls and 0.6 * 1000 = 600 mls
The amount left = 1500 - 250 - 600
= 650 milliliters.
The amount of chocolate milk left in the jug is; D: 650 milliliters
How do you convert units?
We are told;
Amount of chocolate milk in the jug = 1.5 litres
She fills one cup with 250 mL = 0.25 liters
She fills another cup with 0.6 liters
Thus;
Total amount used = 0.6 + 0.25 = 0.85 litres
Amount left = 1.5 - 0.85 = 0.65 Liters
Converting to mL gives; 650 milliliters
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Question 3: What is the x-intercept of the line 3x+4y=12?
Question 3 options:
(4, 0)
(3, 0)
(0, 4)
(0, 3)
Answer: First option.
Step-by-step explanation:
It is important to remember that the line intersects the x-axis when [tex]y=0[/tex].
So, given the line [tex]3x+4y=12[/tex], you need to substitute [tex]y=0[/tex] into the equation and solve for "x", in order to find the x-intercept of this line.
Therefore, this is:
[tex]3x+4y=12\\\\3x+4(0)=12\\\\3x+0=12\\\\3x=12\\\\x=\frac{12}{3}\\\\x=4[/tex]
Therefore, this line intersects the x-axis at this point:
[tex](4,0)[/tex]
Guesstimate how much total time do Americans spend driving in one year? Express the answer in hours, years and lifetimes.
How would one go about guestimating a problem like this.
Answer:
1,460 hours per year.
113,880 hours in a lifetime.
Step-by-step explanation:
Great question, it is always good to ask away and get rid of any doubts that you may be having.
Let's assume that on an average day Americans drive 4 hours a day. This includes going and coming from work as well as any groceries they might need to do. Since there are 365 days in a year we can multiply this by the hours a day driven.
[tex]365*4 = 1,460[/tex]
We can "guesstimate" that on average an American drives 1,460 hours per year.
Based on my research the average lifetime of an American is 78 years old. We can now multiply this by the number of hours driven in a year to have an idea of the number of hours driven in a lifetime.
[tex]1,460*78 = 113,880[/tex]
On average we "guesstimate" that an American drives 113,880 hours in a lifetime.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Certain functions obey the property f(m + n)=f(m)f(n) for all positive numbers and n.Can you think of a function that obeys this property? Hint: Functions that obey this property ill be familiar from ordinary pre-calculus algebra courses. Same question, but this time, the property is f(mn) f(m) +f(n) . (Note, don't expect f to be integer-valued. The hint from the first part applies here too.) m
Answer:
Given
[tex]f(m+n)=f(m)f(n)[/tex]
If we assume
[tex]f(x)=ae^{x}\\\\f(m+n)=ae^{m+n}\\\\\therefore f(m+n)=ae^{m}\times ae^{n}(\because x^{a+b}=x^{a}\times x^{b})\\\\\Rightarrow f(m+n)=f(m)\times f(n)[/tex]
Similarly
We can generalise the result for
[tex]f(x)=am^{x }[/tex] where a,m are real numbers
2)
[tex]f(m\cdot n)=f(m)+f(n)\\\\let\\f(x)=log(x)\\\therefore f(mn)=log(mn)=log(m)+log(n)\\\\\therefore f(mn)=f(m)+f(n)[/tex]
Two vectors A⃗ and B⃗ are at right angles to each other. The magnitude of A⃗ is 5.00. What should be the length of B⃗ so that the magnitude of their vector sum is 9.00?
Answer:
Length of B is 7.4833
Step-by-step explanation:
The vector sum of A and B vectors in 2D is
[tex]C=A+B=(a_1+b_1,a_2+b_2)[/tex]
And its magnitude is:
[tex]C=\sqrt{(a_1+b_1)^2+(a_2+b_2)^2} =9[/tex]
Where
[tex]a_1=Asinx[/tex]
[tex]a_2=Acosx[/tex]
[tex]b_1=Bsin(x+90)[/tex]
[tex]b_2=Bcos(x+90)[/tex]
Using the properties of the sum of two angles in the sin and cosine:
[tex]b_1=Bsin(x+90)=B(sinx*cos90+sin90*cosx)=Bcosx[/tex]
[tex]b_2=Bcos(x+90)=B(cosx*cos90-sinx*sin90)=-Bsinx[/tex]
Sustituying in the magnitud of the sum
[tex]C=\sqrt{(Asinx+Bcosx)^2+(Acosx-Bsinx)^2} =9[/tex]
[tex]C=\sqrt{A^2sin^2x+2ABsinxcosx+B^2cos^2x+A^2cos^2x-2ABsinxcosx+B^2sin^2x} =9[/tex]
[tex]C=\sqrt{A^2(sin^2x+cos^2x)+B^2(cos^2x+sin^2x)}[/tex]
[tex]C=\sqrt{A^2+B^2} =9[/tex]
Solving for B
[tex]A^2+B^2 =9^2[/tex]
[tex]B^2 =9^2-A^2[/tex]
Sustituying the value of the magnitud of A
[tex]B^2=81-5^2=81-25=56[/tex]
[tex]B= 7. 4833[/tex]
The calculation reveals that vector B should be approximately 7.48 in length when magnitude of A s 5.00 and magnitude of their vector sum is 9.00.
The subject question asks for the length of vector B given that it is at right angles to vector A, whose magnitude is 5.00, to ensure that the magnitude of their vector sum is 9.00. To solve this problem, we can use the Pythagorean theorem because the vectors are at right angles to each other.
Let's designate the magnitude of vector B as |B|. According to the Pythagorean theorem for right-angled triangles, we have:
|A|² + |B|² = |A + B|²
So, if |A| = 5.00 and the resultant |A + B| = 9.00, we can substitute these values to find |B|:
5.00² + |B|² = 9.00²
|B|² = 9.00² - 5.00²
|B|² = 81.00 - 25.00
|B|² = 56.00
Therefore, |B| = √(56.00)
|B| = 7.48.
So the length of B should be approximately 7.48 to get a resultant magnitude of 9.00 when added to A.
What are the coordinates of the x-intercept and y-intercept of the line -3y-x=-9
Answer:
Step-by-step explanation:
The x-intercept exists when y = 0; the coordinate takes on the form ( , 0)
The y-intercept exists when x = 0; the coordinate takes on the form (0, ).
We will fill in the blanks in a sec.
If the x-intercept exists when y = 0, then we fill in 0 for y and solve for x:
-3(0) - x = -9 so
-x = -9 and
x = 9
The coordinate is (9, 0) for the x-intercept.
If the y-intercept exists when x = 0, then we fill in 0 for x and solve for y:
-3y - 0 = -9 so
-3y = -9 and
y = 3
The coordinate is (0, 3) for the y-intercept.
john bates invested $5,000.00 in an account that paid 5% interest annually and is compounded anually.what is the amount after 2years
Answer:$500
Step-by-step explanation:
How many triangles can be made from the following three lengths: 3.1 centimeters, 9.8 centimeters, and 5.2 centimeters?
one
none
more than one
Answer:
none
Step-by-step explanation:
We have three sides
Adding the two smallest sides together must be bigger than the third side
3.1+5.2 > 9.8
8.3> 9.8
This is false, so we cannot make a triangle
1. Using the Euclidian algorithm, compute (91,39) and (73,21)
Answer:
HCF(91,39) = 13 and HCF(73,21) = 1
Step-by-step explanation:
As per euclidian algorithm, a = bq + r, where a is dividend, b is divisor, q is quotient and r is remainder.
We can use euclidian algorithm to find the HCF of numbers.
To find: HCF ( 91, 39 ):
On dividing 91 by 39, we get
91=39×2+13
Here, remainder = 13 [tex]\neq 0[/tex]
So, again applying division algorithm on 39 and 13, we get
[tex]39=13\times 3+0[/tex]
As remainder = 0 and divisor at this step is equal to 13, HCF = 13 .
To find: HCF ( 73, 21 )
On dividing 73 by 21, we get
[tex]73=21\times 3+10[/tex]
Here, remainder = 10 [tex]\neq 0[/tex]
On applying division algorithm on 21 and 10, we get
[tex]21=10\times 2+1[/tex]
Here, remainder = 1 [tex]\neq 0[/tex]
On applying division algorithm on 10 and 1, we get
[tex]10=1\times 10+0[/tex]
As remainder = 0 and divisor at this step is 1, HCF = 1
When situations arise in which your organization cannot meet one or more standards immediately, it is vitally important to recognize an exception to standards to determine where problems may exist. Answer: A Reference: p 159 True False
Answer:
open fb and search ravi verma
Step-by-step explanation:
send friend request
A given binomial distribution has 10 trials and probability of success p=1/3. Compute the standard deviation and explain your solution
Answer: 1.49
Step-by-step explanation:
We know that the standard deviation in a binomial distribution is given by :-
[tex]\sigma=\sqrt{n\cdot p\cdot (1-p)}[/tex], where n is the number of trials and p is the probability of success.
Given : The number of trials : [tex]n=10[/tex]
The probability of success = [tex]p=\dfrac{1}{3}[/tex]
Then , the standard deviation will be :-
[tex]\sigma=\sqrt{10\cdot \dfrac{1}{3}\cdot (1-\dfrac{1}{3})}\\\\\Rightarrow\ \sigma=1.490711985\approx1.49[/tex]
The standard deviation of a given binomial distribution with 10 trials and a probability of success of 1/3 is calculated using the formula σ = √npq, resulting in approximately 1.49. This value helps us understand the spread of successes in the experiment.
Explanation:To compute the standard deviation of a given binomial distribution with 10 trials and a probability of success p=1/3, we first identify the probability of failure, which is q=1-p=2/3. The formula for the standard deviation (σ) of a binomial distribution is σ = √npq, where n is the number of trials, p is the probability of success, and q is the probability of failure.
By substituting the given values into the formula:
n = 10p = 1/3q = 2/3We get σ = √(10)(1/3)(2/3) = √(20/9) ≈ 1.49. Therefore, the standard deviation of the binomial distribution is approximately 1.49.
This calculation helps us understand the dispersion or spread of the distribution of successes in our binomial experiment, indicating how far the number of successes can deviate from the expected value on average.
In terms of explaining the probability of assignment to trial arms in consent forms, ICH notes that is should be included...True or False
Answer: True, hope this helps! :)
Timelimit: 15 minutes. 11:08 remaining, x A radio tower is located 250 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 38 and that the angle of depression to the bottom of the tower is 27. How tall is the tower? Preview feet Points possible: 1 This is attempt 1 of 1. Submit
Answer:
The height of tower is 322.7 feet.
Step-by-step explanation:
Given
Distance between a building and tower= 250 feet
BCDE is a rectangle .Therefore, we have BC=ED and CD=BE=250 feet
In triangle ABE
[tex]tan\theta=\frac{perpendicula \; side }{hypotenuse}[/tex]
[tex]\theta=38^{\circ}[/tex]
[tex] tan38^{\circ}=\frac{AB}{BE}[/tex]
[tex]\frac{AB}{250}=0.781[/tex]
[tex] AB=0.781\times250[/tex]
AB=195.25 feet
In triangle EDC
[tex]\theta=27^{\circ}[/tex]
[tex]tan27^{\circ}=\frac{ED}{CD}[/tex]
[tex]\frac{ED}{250}=0.509[/tex]
[tex]ED=250\times0.509[/tex]
ED=127.25 feet
ED=BC=127.25 feet
The height of tower=AB+BC
The height of tower=195.25+127.25=322.5 feet
Kelly price sells college textbooks on commission. She gets 8 % on the first $7500 of sales, 16% on the next $7500 of sales, and 20% on sales over $ 15,000. In July of 1997 $9500, ShelbyShelby's sales total was
What was ShelbyShelby's gross commission for July 1997?
Answer:
The commission would be $ 920.
Step-by-step explanation:
Given,
Sales in 1997 = $ 9500,
Since, there is a commision of 8 % on the first $ 7500 of sales, 16% on the next $ 7500 of sales, and 20% on sales over $ 15,000,
If x represents the total sales,
Commission for x ≤ 7500 = 8% of x = 0.08x,
Commission for 7500 < x ≤ 15000 = 8% of 7500 + 16% of (x-7500)
= 600 + 0.16(x-7500),
Commission for 7500 < x ≤ 15000 = 8% of 7500 + 16% of 7500 + 20% of (x-15000)
= 600 + 1200 + 0.20(x-15000)
= 1800 + 0.20(x-15000)
Thus, the function that shows the given situation,
[tex]f(x)=\left\{\begin{matrix}0.08x & x \leq 7500\\ 600+0.16(x-7500) & 7500 < x \leq 15000\\ 1800+0.20(x-15000) & 15000 < x\end{matrix}\right.[/tex]
Since, 9500 lies between 7500 and 15000,
Therefore, the commission would be,
f(9500)= 600 + 0.16(9500 - 7500) = 600 + 320 = $ 920
Shelby's gross commission for July 1997 on sales of $9500 is calculated as $920.
Kelly Price sells college textbooks on commission, and the structure of her commission is a tiered rate: 8% on the first $7500 of sales, 16% on the next $7500 of sales, and 20% on sales over $15,000.
For Shelby’s sales totaling $9500 in July 1997, we must calculate her gross commission for that month.
Here is the step-by-step calculation:
Calculate the commission on the first $7500 at 8%, which is $7500 * 0.08 = $600.Now, since Shelby's total sales are $9500, we subtract the first tier limit of $7500 to find the remaining sales amount, which is $9500 - $7500 = $2000.Next, calculate the commission on the remaining $2000 at the second tier rate of 16%, which is $2000 * 0.16 = $320.Add the two commission amounts together to find the total commission: $600 + $320 = $920.Therefore, Shelby’s gross commission for July 1997 is $920.
Express the following repeating decimal as a fraction in simplest form.
0.342 repeating (line over entire decimal)
Final answer:
The repeating decimal 0.342 can be expressed as the fraction 38/111 in simplest form, by using algebraic methods to eliminate the repeating pattern and then simplifying the resulting fraction.
Explanation:
Expressing the repeating decimal 0.342 as a fraction involves using algebra to convert the decimal into a form that can be simplified into a fraction. First, we set the repeating decimal equal to a variable:
Let x = 0.342
To remove the repeating part, we multiply x by a power of 10 that corresponds to the number of digits in the repeating sequence. Since there are three digits repeating (342), we multiply by 1000:
1000x = 342.342
We now subtract the original equation (1x) from this new equation (1000x) to get rid of the decimal:
1000x - x = 342.342 - 0.342
999x = 342
Now we simplify by dividing both sides by 999:
x = 342 / 999
This fraction can be further simplified by dividing both the numerator and denominator by their greatest common divisor:
x = 38 / 111. Therefore, the fractional form of 0.342 is 38/111 in its simplest form.
To convert the repeating decimal 0.342 (with 342 repeating indefinitely) to a fraction, let's follow these steps:
1. Let x equal the repeating decimal:
\( x = 0.342342342... \)
2. Recognize the pattern: the digits 342 repeat every three places. To isolate the repeating sequence, we need to multiply x by a power of 10 that has the same number of digits as the repeating sequence.
3. The repeating sequence has three digits, so we'll multiply x by \( 10^3 = 1000 \):
\( 1000x = 342.342342... \)
4. Now, subtract the original number x from this new number to remove the repeating part:
\( 1000x - x = 342.342342... - 0.342342342... \)
5. Notice that on the right-hand side, the repeating decimals cancel each other out, leaving whole numbers:
\( 999x = 342.000000... \)
6. Now solve for x:
\( x = \frac{342}{999} \)
7. To simplify the fraction, we find the greatest common divisor (GCD) of the numerator (342) and the denominator (999).
To find the GCD, we can list the factors of each:
Factors of 342 include: \( 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342 \).
Factors of 999 include: \( 1, 3, 9, 27, 37, 111, 333, 999 \).
The largest factor that appears in both lists is 9.
8. Divide both the numerator and the denominator by their GCD:
\( x = \frac{342 ÷ 9}{999 ÷ 9} \)
9. Doing the division:
\( x = \frac{38}{111} \)
Thus, the repeating decimal 0.342 (with a line over the entire decimal) can be expressed as the fraction \( \frac{38}{111} \) in its simplest form.