Step-by-step explanation:
Let width of the rectangle be y
Length of rectangle = 3y + 12.1
Perimeter = 2(L + y) = 122.6
2 (4y + 12.1 ) = 122.6
8y + 24.2 = 122.6
y = 98.4 / 8
y (width) = 12.3
Length = 49
can someone do these 2 for me ?
says the answer needs to be 20 letters long so here are the 20 letters
Step-by-step explanation:
1. -3/7
2. x = 0, -3, -4
Find the smallest number to be divided by 768 to get a perfect square number. Also find the square root of the new number obtained
Answer: The smallest number to be divided by 768 is 768. The number obtained will be one and the square root of 1 is 1.
Step-by-step explanation:
We need to find a number that when being divided by 768 we will get a perfect square number. First list the perfect square numbers ,which starts from 1,4,9,16,25,36,49,64.....
In these perfect squares the least of them is 1, meaning that we need to find a number that when divided by 768 we will get 1. We know that when a number is divided by the same number we get 1. Meaning that the smallest number to be divided by 768 to get 1 is 768 itself.
The number obtained is 1 .
The square root of one is 1.
You are considering two assets with the following characteristics. E(R1) = 0.18 E(σ1) = 0.09 w1 = 0.7 E(R2) = 0.24 E(σ2) = 0.17 w2 = 0.3 Compute the mean and standard deviation of two portfolios if r1,2 = 0.30 and -0.45, respectively. Do not round intermediate calculations. Round your answers for the mean of two portfolios to three decimal places and answers for standard deviations of two portfolios to five decimal places. Mean of two portfolios: Standard deviation of two portfolios if r1,2 = 0.30: Standard deviation of two portfolios if r1,2 = -0.45: Choose the correct risk–return graph. The correct graph is . A. B. C. D. Explain the results. The negative correlation coefficient risk without sacrificing return.
The correct risk-return graph is option (A).This graph shows that for a negative correlation coefficient, an investor can reduce their risk without sacrificing return by investing in a portfolio that combines two negatively correlated assets. This is because when the assets have negative correlation, they are less likely to move in the same direction at the same time, resulting in a reduced overall portfolio risk.
The expected returns and standard deviations for two assets are as follows:E(R1) = 0.18 E(σ1) = 0.09 w1 = 0.7E(R2) = 0.24 E(σ2) = 0.17 w2 = 0.3Mean of two portfolios:There are two portfolios with a correlation coefficient r1,2, which is given as follows:r1,2 = 0.30Thus, the mean of the two portfolios is calculated as follows:Mean of portfolio 1: (w1 × E(R1)) + (w2 × E(R2))= (0.7 × 0.18) + (0.3 × 0.24)≈ 0.198Mean of portfolio 2: (w1 × E(R1)) + (w2 × E(R2))= (0.7 × 0.18) + (0.3 × 0.24)≈ 0.198Standard deviation of two portfolios if r1,2 = 0.30:The formula to calculate the standard deviation of two portfolios is given as follows:σp = √[w12 × σ1^2 + w22 × σ2^2 + 2w1w2σ1σ2r1,2]σ1 = 0.09σ2 = 0.17r1,2 = 0.30w1 = 0.7w2 = 0.3Thus, the standard deviation of two portfolios if r1,2 = 0.30 is calculated as follows:σp = √[(0.7)2 × (0.09)2 + (0.3)2 × (0.17)2 + 2 × (0.7) × (0.3) × (0.09) × (0.17) × (0.30)]≈ 0.11469 (rounded to 5 decimal places)Standard deviation of two portfolios if r1,2 = -0.45:Thus, the standard deviation of two portfolios if r1,2 = -0.45 is calculated as follows:r1,2 = -0.45σp = √[(0.7)2 × (0.09)2 + (0.3)2 × (0.17)2 + 2 × (0.7) × (0.3) × (0.09) × (0.17) × (-0.45)]≈ 0.08223 (rounded to 5 decimal places)The correct risk-return graph is option (A).
This graph shows that for a negative correlation coefficient, an investor can reduce their risk without sacrificing return by investing in a portfolio that combines two negatively correlated assets. This is because when the assets have negative correlation, they are less likely to move in the same direction at the same time, resulting in a reduced overall portfolio risk.
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Daily high temperatures in St. Louis for the last week were as follows: 92, 92, 93, 95, 95, 86, 95 (yesterday). a) The high temperature for today using a 3-day moving average =____ degrees (round your response to one decimal place).
The high temperature for today using a 3-day moving average is 92 degrees.
To calculate the high temperature for today using a 3-day moving average, we take the average of the temperatures from the past three days, including today.
Given the daily high temperatures in St. Louis for the last week:
92, 92, 93, 95, 95, 86, 95 (yesterday)
To find the 3-day moving average for today's high temperature, we consider the temperatures from yesterday, the day before yesterday, and three days ago.
(95 + 86 + 95) / 3 = 92
Therefore, the high temperature for today, calculated using a 3-day moving average, is approximately 92 degrees Fahrenheit, rounded to one decimal place.
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Factor 7x^2-24x + 9.
Help me plz
Answer:
(7x-3)(x-3)
Good Luck!!!
Have a wonderful day and here are free pts to make your day better <3 lvu and be safe
15 x 6 = ?
Answer:
80
Step-by-step explanation:
Answer:
well 5 x 6 is 30 carry the 3, 1 x 6 is 6 plus the 3 is 9 so ur answer is 90
Step-by-step explanation:
Find the distance between the two points rounding to the nearest tenth (if
necessary).
(8,-5) and (1,1)
Can someone please help me
Answer:
[tex]d=9.2[/tex]
Step-by-step explanation:
Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Simply plug in your 2 coordinates into the distance formula to find distance d:
[tex]d=\sqrt{(1-8)^2+(1-(-5))^2}[/tex]
[tex]d=\sqrt{(-7)^2+(1+5)^2}[/tex]
[tex]d=\sqrt{49+(6)^2}[/tex]
[tex]d=\sqrt{49+36}[/tex]
[tex]d=\sqrt{85}[/tex]
[tex]d=9.21954[/tex]
[tex]d=9.2[/tex]
how do i run a chi-square goodness of fit test with only one variable available?
The categories being mutually exclusive and independent observations. Violation of these assumptions may affect the validity of the test results.
To run a chi-square goodness-of-fit test with only one variable available, you can compare the observed frequencies of different categories with the expected frequencies under a specified distribution or hypothesis.
Here are the steps to conduct a chi-square goodness-of-fit test with one variable:
1. Define your null hypothesis (H₀) and alternative hypothesis (H₁). The null hypothesis typically states that the observed data follows a specific distribution or expected frequencies.
2. Determine the expected frequencies for each category under the null hypothesis. If you have a specific distribution in mind, such as a uniform distribution or a normal distribution, you can use the expected frequencies based on that distribution. If not, you can use the proportion of each category in the sample as the expected frequency.
3. Collect your observed data. This should consist of the frequencies or counts for each category in your single variable.
4. Calculate the chi-square test statistic. The chi-square test statistic measures the discrepancy between the observed and expected frequencies. It is calculated using the formula:
χ² = Σ((O - E)² / E)
where O is the observed frequency and E is the expected frequency for each category.
5. Determine the degrees of freedom (df) for the test. For a chi-square goodness-of-fit test with one variable, the degrees of freedom is equal to the number of categories minus 1.
6. Look up the critical value from the chi-square distribution table using the significance level (α) and the degrees of freedom. This critical value determines the threshold for rejecting the null hypothesis.
7. Compare the calculated chi-square test statistic with the critical value. If the calculated chi-square test statistic is greater than the critical value, you reject the null hypothesis. If it is less than or equal to the critical value, you fail to reject the null hypothesis.
8. Calculate the p-value associated with the chi-square test statistic. The p-value represents the probability of obtaining the observed data or more extreme results, assuming the null hypothesis is true. You can use a chi-square distribution table or statistical software to calculate the p-value.
9. Make a decision based on the p-value. If the p-value is less than the chosen significance level (α), typically 0.05, you reject the null hypothesis. If the p-value is greater than or equal to α, you fail to reject the null hypothesis.
Remember that the chi-square goodness-of-fit test assumes certain assumptions, such as the categories being mutually exclusive and independent observations. Violation of these assumptions may affect the validity of the test results.
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The table shows the weights of onions at a grocery store.
Answer:
Formula: 0.12x = y
Step-by-step explanation:
5 × 0.12 = 0.60
3 × 0.12 = 0.36
14 × 0.12 1.68
Graph f(x)=-1/2x-5
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Identify the domain of the function shown in the graph.
Describe and explain the difference between explicit formulas for arithmetic
sequences and explicit formulas for geometric sequences.
Answer:
Arithmetic sequence: [tex]a_{n}=a_{1}+(n-1)d[/tex]
Geometric sequence: [tex]a_{n}=a_{1}(r)^{n-1}[/tex]
Step-by-step explanation:
The arithmetic sequence: is the sequence whos terms increased or decreased by a constant amount.
Examples:
4, 7, 10, 13, 16, ........................ (increased by 3)25, 20, 15, 10, ......................... (Decreased by 5)The explicit formula for the nth term of the arithmetic sequence is:
[tex]a_{n}=a_{1}+(n-1)d[/tex] [tex]a_{1}[/tex] is the first termd is the constant difference between each two consecutive termsn is the position of the number in the sequence
The geometric sequence: is the sequence whos consecutive terms have a constant ratio
Examples:
1, 2, 4, 8, 16, ........................ (Multiplying by 2)625, 125, 25, 5, ......................... (Dividing by 5)The explicit formula for the nth term of the geometric sequence is:
[tex]a_{n}=a_{1}(r)^{n-1}[/tex] [tex]a_{1}[/tex] is the first termr is the constant ratio between each two consecutive termsn is the position of the number in the sequence* Arithmetic sequence →→→→→→ Geometric sequence
Has a constant difference →→→→→→ Has a constant ratio
[tex]a_{n}=a_{1}+(n-1)d[/tex] →→→→→→ [tex]a_{n}=a_{1}(r)^{n-1}[/tex]
[tex]d=a_{n}-a_{n-1}[/tex] →→→→→→ [tex]r=\frac{a_{n}}{a_{n-1} }[/tex]
The sum of three consecutive even numbers is 324. What are the three numbers?
Answer:
the ans is 108
Step-by-step explanation:
let the three consecutive no. be 'x'
by question:
x+x+x=324
or,3x=324
or,x =324÷3
or, x=108
checking this answer
108+108+108
=324
Write 27 as a product of three primes
Answer:
27 is a composite number. 27 = 1 x 27, or 3 x 9. Factors of 27: 1, 3, 9, 27. Prime factorization: 27 = 3 x 3 x 3, which can also be written 27 = 3³.
Answer:
3 x 3 x 3
Step-by-step explanation:
ok so 27 can be broken down to 3 and 9
3 x 9
and 3 x 9 can be broken down to 3 and 3 and 3
3 x 3 x 3
Question 1(Multiple Choice Worth 3 points) (02.06)The table below shows that 1 day equals 24 hours. Notice that 12 hours is one-half of that. Use the table to help you determine how many days are equal to 54 hours. 1 day 24 hours 12 hours 12 hours days 2 days days PLEASE NEED HELP ASAP WILL GIVE BRAINLY AND STOP PUTTING RANDOM LETTERS JUST FOR THE POINTS
9514 1404 393
Answer:
2 1/4 days
Step-by-step explanation:
You could extend your table a bit to help answer this.
(days, hours)
(1, 24)
(1/2, 12)
(1/4, 6)
(2, 48)
Now, we observe that 54 hours is 6 more hours than 48 hours, so will be 1/4 day more than 2 days.
54 hours is 2 1/4 days
11. What is the slope of the line
represented by 5x – 10y = 30 ?
Answer:
Slope (m) = -1/2
Step-by-step explanation:
y = mx + b
5x – 10y = 30
-5x -5x
-10y = -5x + 30
y = -5x/ 10 + 30/10
y = -1/2x + 3
The black graph is the graph of
y = f(x). Choose the equation for the red graph.
Answer:
[tex]c. \: \: \: y + 3 = f(x)[/tex]
f(x) = -4x2 - 6x + 8.
Answer:
y intercept= (0, 8)
Step-by-step explanation:
x y
-3 10
-2 4
-3/4 41/4
0 8
1 -2
How many whole numbers are less than k, if k is a whole number?
The set of the whole numbers is the set of all the positive integers and the zero. So we can write it as:
{0, 1, 2, 3, 4, ...}
We will see that:
if k is a whole number, then there are k whole numbers that are smaller than k.
Let's see how we got that:
Now, we know that k is a whole number, then just let's assign different whole numbers to k and count how many whole numbers are smaller than k.
if k = 1
We have 1 whole number smaller than k, that is the zero.
if k = 2
We have 2 whole numbers smaller than k, the zero and the 1.
if k = 3
we have 3 whole numbers smaller than k, {0, 1, 2}
We already can see the pattern.
if k is a whole number, then there are k whole numbers that are smaller than k.
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A binary message source M2 outputs bytes (8 bit words) such as 11010010 with every byte being equally likely. A quaternary message source M4 produces words of length 8 with characters from the set {0,1,2,3}, such as 32100313, with all such words being equally likely. (a) What is the probability, p, that a word produced by M4 is a byte, i.e., every character in the word belongs to the set {0,1}? (b) If a word is equally likely to be drawn from either source, what is the probability it will be a byte? (c) Given that the word is a byte, what is the probability it came from M2?
a)The probability that a word produced by M4 is a byte is 1/4. b) the probability is 5/8 c) The probability it came from M2 is 1.
(a)To calculate the probability that a word produced by M4 is a byte, we need to determine the number of valid byte words and divide it by the total number of possible words in M4.
The valid byte words consist of two characters, either 0 or 1, and the remaining six characters can be any of the four options (0, 1, 2, or 3). Therefore, the number of valid byte words is 2^2 * 4^6.
The total number of possible words in M4 is 4^8 since each character can be one of the four options (0, 1, 2, or 3).
Thus, the probability p that a word produced by M4 is a byte is:
p = (2^2 * 4^6) / 4^8 = 2^2 / 4^2 = 1/4
(b) If a word is equally likely to be drawn from either source, we need to calculate the overall probability of drawing a byte word.
The probability of drawing a byte word from M2 is 1, as all words produced by M2 are bytes.
The probability of drawing a byte word from M4 is p, which we calculated in part (a) as 1/4.
Since the word can be drawn from either source with equal probability, the overall probability of drawing a byte word is:
(1/2) * 1 + (1/2) * (1/4) = 5/8
(c) Given that the word is a byte, we need to find the probability that it came from M2.
The probability that a byte word came from M2 is 1, as all words produced by M2 are bytes.
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the sum of three consecutive numbers is 41 less than five times the largest number. find the largest number.
Answer:
19
Step-by-step explanation:
So:
x + (x + 1) + (x + 2) = 5 (x + 2) - 41
3x + 3 = 5x + 10 - 41
3x + 3 = 5x - 31
34 = 2x
17 = x
The numbers are 17, 18, and 19. The biggest is 19
Which two of the following terms describes the expression 2x - 4x² + 6?
Answer:
−2⋅(2x−3)⋅(x+1)
Step-by-step explanation:
What linear equation is represented by the table? 1
y= 4x - 2
y= 2x
y=4x
y=2x-2
Answer:
Y=4x-2
Step-by-step explanation:
You have to try it (x,y) (2,6)
y=4x-2
6=4(2)-2
6=8-2
Geometry question about finding missing angles!
Answer:
x = 38.5y = -12.5m∠EBD = 26°Step-by-step explanation:
The sum of the three angles is 180°.
(2x) +(x+y) +(52-2y) = 180
3x -y = 128 . . . . write in standard form
The congruent angles have equal measure.
2x = 52 -2y
x + y = 26 . . . . write in standard form
__
Adding these two standard-form equations, we get ...
(3x -y) +(x +y) = (128) +(26)
4x = 154
x = 38.5
x + y = 26
y = 26 -38.5 = -12.5
The values of interest are ...
x = 38.5y = -12.5m∠EBD = 26°Point Z is located at (-5, -3) on the coordinate plane. Point Z is reflected over the
y-axis to create point Z'. What ordered pair describes the location of Z'?
Answer:
(5,-3)
Step-by-step explanation:
Use the equation y=−3x+2 to find the missing value.
Given the dependent value = -28.
y=10y
x=86x
y=86y
x=10
Answer:
x =10
Step-by-step explanation:
Use the process of the elimination. Start with the first and work your way down.
y= -3(10) + 2
y= -30 + 2
y = -28
F(x)=3x 2 +9f, left parenthesis, x, right parenthesis, equals, 3, x, squared, plus, 9 and g(x)=\dfrac{1}{3}x^2-9g(x)= 3 1 x 2 −9g, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 3, end fraction, x, squared, minus, 9 Write simplified expressions for f(g(x))f(g(x))f, left parenthesis, g, left parenthesis, x, right parenthesis, right parenthesis and g(f(x))g(f(x))g, left parenthesis, f, left parenthesis, x, right parenthesis, right parenthesis in terms of xxx. f(g(x))=f(g(x))=f, left parenthesis, g, left parenthesis, x, right parenthesis, right parenthesis, equals g(f(x))=g(f(x))=g, left parenthesis, f, left parenthesis, x, right parenthesis, right parenthesis, equals Are functions fff and ggg inverses?
Answer:
[tex]f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252[/tex]
[tex]g(f(x)) = 3x^4 + 18x^2 + 18[/tex]
f(x) and g(x) and not inverse functions
Step-by-step explanation:
Given
[tex]f(x) = 3x^2 + 9[/tex]
[tex]g(x) = \dfrac{1}{3}x^2 - 9[/tex]
Required
Determine f(g(x))
Determine g(f(x))
Determine if both functions are inverse:
Calculating f(g(x))
[tex]f(x) = 3x^2 + 9[/tex]
[tex]f(g(x)) = 3(\frac{1}{3}x^2 - 9)^2 + 9[/tex]
[tex]f(g(x)) = 3(\frac{1}{3}x^2 - 9)(\frac{1}{3}x^2 - 9) + 9[/tex]
Expand Brackets
[tex]f(g(x)) = (x^2 - 27)(\frac{1}{3}x^2 - 9) + 9[/tex]
[tex]f(g(x)) = x^2(\frac{1}{3}x^2 - 9) - 27(\frac{1}{3}x^2 - 9) + 9[/tex]
[tex]f(g(x)) = \frac{1}{3}x^4 - 9x^2 - 9x^2 + 243 + 9[/tex]
[tex]f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252[/tex]
Calculating g(f(x))
[tex]g(x) = \dfrac{1}{3}x^2 - 9[/tex]
[tex]g(f(x)) = \frac{1}{3}(3x^2 + 9)^2 - 9[/tex]
[tex]g(f(x)) = \frac{1}{3}(3x^2 + 9)(3x^2 + 9) - 9[/tex]
[tex]g(f(x)) = (x^2 + 3)(3x^2 + 9) - 9[/tex]
Expand Brackets
[tex]g(f(x)) = x^2(3x^2 + 9) + 3(3x^2 + 9) - 9[/tex]
[tex]g(f(x)) = 3x^4 + 9x^2 + 9x^2 + 27 - 9[/tex]
[tex]g(f(x)) = 3x^4 + 18x^2 + 18[/tex]
Checking for inverse functions
[tex]f(x) = 3x^2 + 9[/tex]
Represent f(x) with y
[tex]y = 3x^2 + 9[/tex]
Swap positions of x and y
[tex]x = 3y^2 + 9[/tex]
Subtract 9 from both sides
[tex]x - 9 = 3y^2 + 9 - 9[/tex]
[tex]x - 9 = 3y^2[/tex]
[tex]3y^2 = x - 9[/tex]
Divide through by 3
[tex]\frac{3y^2}{3} = \frac{x}{3} - \frac{9}{3}[/tex]
[tex]y^2 = \frac{x}{3} - 3[/tex]
Take square root of both sides
[tex]\sqrt{y^2} = \sqrt{\frac{x}{3} - 3}[/tex]
[tex]y = \sqrt{\frac{x}{3} - 3}[/tex]
Represent y with g(x)
[tex]g(x) = \sqrt{\frac{x}{3} - 3}[/tex]
Note that the resulting value of g(x) is not the same as [tex]g(x) = \dfrac{1}{3}x^2 - 9[/tex]
Hence, f(x) and g(x) and not inverse functions
x + (x − 14) = 40. little confused
Answer:
27is answer
Step-by-step explanation:
x+ x - 14 = 40
or, 2x = 40+ 14
or, 2x = 54
or, x = 54
2
or, x= 27
Solve for t.
-9 = t/-9
Answer:
t = 81
Step-by-step explanation:
81/-9 = -9
Answer:
81 = t
Step-by-step explanation:
-9 = t/-9
To isolate x, multiply -9 on both sides.
-9 = t/-9
*-9 *-9
81 = t
Hope this helped you...have a great day! C:
Reduce the following fraction:
* 4b/4a
plz respond
Answer: b/a
Step-by-step explanation: 4/4 * b/a = 1 * b/a = b/a
a/b is the value of fraction. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
What is meant by Mathematical expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)
A mathematical expression shows the value of something by combining numbers, variables, and operators. A mathematical statement known as an equation involves setting two expressions equal to one another.
Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing. For instance, the mathematical equation for "4 added to 2" will be 2+4.
Given ,
4b/4a
When you divide both the numerator and the denominator by 4, you get:
Therefore b/a is the value of fraction.
The complete question is : Reduce the following fractions.
4a/4b
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