find H.C.F of 2x+4 and x^2-4​

Answer:

We can use the formula for compound interest to solve the problem:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, we know that P = $2,000, A = $6,883.55, n = 4 (quarterly compounding), and t = 16. We can solve for r by rearranging the formula as follows:

r = n[(A/P)^(1/nt) - 1]

Substituting the values, we get:

r = 4[(6,883.55/2,000)^(1/(4*16)) - 1] = 0.0522 or 5.22%

Therefore, the annual interest rate is approximately 5.22%

Answer= \(50cm^{2}\)

The most important details in this text are the calculation of Stock A's beta and the calculation of Stock A's new required rate of return if beta were 1.1. Beta is calculated using the equation of (Cov(Ra,Rm))/(Var(Rm)) where Ra = rate of return for Stock A, Rm = rate of return for the stock market, Cov(Ra,Rm) = covariance of Ra and Rm, and Var(Rm) = variance of Rm. If beta were 1.1, the new required rate of return for Stock A would be 12.7%.

a. Calculation of Stock A's beta:Beta (β) is used to evaluate the volatility of a stock relative to the stock market. A beta of 1.0 indicates that a stock has the same level of volatility as the entire stock market. Beta can be used to determine the degree of risk associated with a particular investment, and it can be calculated using the following equation:\($$\beta = \frac{Cov(R_a,R_m)}{Var(R_m)}$$\)

whereRa = rate of return for Stock A, Rm = rate of return for the stock market, Cov(Ra,Rm) = covariance of Ra and Rm, and Var(Rm) = variance of Rm.Given that, raF= 5%, ry= 12%, and rA = 13%.

Let us determine Stock A's beta.

Beta (β) =  (Cov(Ra,Rm))/(Var(Rm))

Given that Rm = ry = 12%Ra = rA = 13% Cov(Ra,Rm) = (Ra - raF) * (Rm - ry)Cov(Ra,Rm) = (0.13 - 0.05) * (0.12 - 0.05)Cov(Ra,Rm) = 0.0072Var(Rm) = (ry - raF)²Var(Rm) = (0.12 - 0.05)²Var(Rm) = 0.00049

Therefore, the beta for Stock A can be calculated as follows:

β =  (Cov(Ra,Rm))/(Var(Rm))

β = (0.0072)/(0.00049)

β = 14.69

Rounding β to two decimal places, we get Beta for Stock A = 14.69. Thus, the beta for Stock A is 14.69.b. Calculation of Stock A's new required rate of return:We need to determine Stock A's new required rate of return if beta were 1.1.The security market line (SML) can be used to determine a stock's required rate of return. The SML represents the required rate of return for a given level of risk (beta) in the market as a whole.

The SML can be represented by the following equation:\($$r_a = r_f + \beta*(r_m - r_f)$$\)

whereRa = required rate of return for Stock A, Rf = risk-free rate of return, Rm = expected market return, and β = beta of Stock A.Given that, Rf = raF = 5%, Rm = ry = 12%, and β = 1.1.Using the formula above, we can determine the new required rate of return for Stock A as follows:

r_a = r_f + β*(r_m - r_f)r_a

= 0.05 + 1.1*(0.12 - 0.05)r_a

= 0.05 + 1.1*0.07r_a

= 0.05 + 0.077r_a

= 0.127

Thus, if Stock A's beta were 1.1, the new required rate of return for Stock A would be 12.7%.

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Answer:

y = 17

Step-by-step explanation:

the absolute value always gives a positive value , that is

| - a | = | a | = a

given

y = | x | + 10 ( substitute x = - 7 into the equation )

y = | - 7 | + 10 = | 7 | + 10 = 7 + 10 = 17

Answer:

38°

Step-by-step explanation:

Using the Cosine rule in Δ ABC

cos A = \(\frac{b^2+c^2-a^2}{2bc}\)

where a, b and c are the sides of the triangle.

Here a = 5, b = 3 and c = 7 , thus

cos A = \(\frac{3^2+7^2-5^2}{2(3)(7)}\) = \(\frac{9+49-25}{42}\) = \(\frac{33}{42}\) , thus

∠ A = \(cos^{-1}\) (\(\frac{33}{42}\) ) ≈ 38°

Answer:

5.99

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the expression -2y-8+4y, we are to find the equivalent expressed is which other expression is similar to it. This can be expressed as shown below;

Step 1: Collect the like terms of the expression

= -2y-8+4y

= (-2y+4y)-8

Step 2: Sum up the terms in parenthesis:

=  (-2y+4y)-8

= 2y-8

Step 3: factor out the common terms

= 2y-8

= 2(y-4)

Hence the equivalent expression is 2(y-4).

Answer:

A and B

Step-by-step explanation:

On Khan Academy its right.

Answer:

jason shdudbuasd

Step-by-step explanation:

Answer:

0.625

Step-by-step explanation:

Answer:

0.625

Step-by-step explanation:

Answer:

Step-by-step explanation:

First look at the tangent function f(x) = tan x.  Its domain is restricted:  (-pi/2, pi/2).  There are no restrictions on the function value, so the range is (-infinity, +infinity).  The primary interval on which tan x is defined is (-pi/2, +pi/2, which has length pi.

In comparison, the domain of f(x) = tan 2x is only half as long as that of f(x) = tan x:  (-pi/4, +pi/4), with length pi/2.

Now, focusing on f(x) = 3cot(2x):  the range is the same:  (-infinity, +infinity).  The period is half that of tan x:  pi/2 instead of pi.  Remember that the cotangent function repeats itself every pi/2 radians.

Domain:  (-pi/4, +pi/4) (centered on the origin), (-3pi/4. 3pi/4), and so on, continuing to both the left and the right.

Range:  (-infinity, infinity)

Solution given:

R=rate=20%

T=time=45days =1month and 15 days =1 ½ months=⅛years

P=Principal=$31000

since bank gives/takes compound interest

so

interest=P((1+R/100)^T-1)

=31000((1+20/100)^⅛-1)=$714.6

I need to pay $ 714.6

For given function the rule obtained when finding f^(-1) is ±√[(x + 4)/3]

In this question, we have been given a function f(x) = 3x² - 4

We need to write the rule obtained when finding f^(-1)

Le f(x) = y          ........(1)

y =   3x² - 4

We find the value of x.

3x² = y + 4

x² = (y + 4)/3

x = ±√[(y + 4)/3]

From (1),

f^{-1}(y) = ±√[(y + 4)/3]

Since the choice of the variable is arbitrary, we can write this as ,

f^{-1}(x) = ±√[(x + 4)/3]

Therefore, for given function the rule obtained when finding f^(-1) is  ±√[(x + 4)/3]

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The 95%-confidence interval is:

Confidence Interval = [67.0 - 2.76, 67.0 + 2.76] ≈ [64.24, 69.76]

a) The estimate of the height can be found by taking the average of the measurements:

Height Estimate = (67+69+65+68+66)/5 = 67.0

Therefore, the estimated height of the building is 67 meters.

b) The 99%-confidence interval can be found using the formula:

Confidence Interval = [Height Estimate - Margin of Error, Height Estimate + Margin of Error]

where the Margin of Error is given by:

Margin of Error = Z * (Standard Deviation / sqrt(n))

Here, n = 5 (number of measurements), Z is the value from the standard normal distribution that corresponds to the 99% confidence level, and the standard deviation is given as 4.

Using a table or calculator, we find that Z = 2.576.

Plugging in the values, we get:

Margin of Error = 2.576 * (4 / sqrt(5)) ≈ 4.14

Therefore, the 99%-confidence interval is:

Confidence Interval = [67.0 - 4.14, 67.0 + 4.14] ≈ [62.86, 71.14]

c) To estimate the standard deviation, we can use the sample standard deviation formula:

Sample Standard Deviation = sqrt(1/(n-1) * Sum((Xi - Xbar)^2))

where Xbar is the sample mean, Xi are the individual measurements, and n is the sample size.

Plugging in the values, we get:

Xbar = (67+69+65+68+66)/5 = 67.0

Sample Standard Deviation = sqrt(1/(5-1) * ((67-67)^2 + (69-67)^2 + (65-67)^2 + (68-67)^2 + (66-67)^2)) ≈ 1.58

Therefore, the estimated standard deviation for the measurement error is 1.58.

d) To find the 95%-confidence interval when the standard deviation is unknown, we can use the t-distribution with n-1 degrees of freedom. The formula for the confidence interval is:

Confidence Interval = [Height Estimate - Margin of Error, Height Estimate + Margin of Error]

where the Margin of Error is given by:

Margin of Error = t * (Sample Standard Deviation / sqrt(n))

Here, n = 5 (number of measurements), t is the value from the t-distribution that corresponds to the 95% confidence level and 4 degrees of freedom (n-1), and the sample standard deviation is 1.58 (calculated in part c).

Using a table or calculator, we find that t = 2.776.

Plugging in the values, we get:

Margin of Error = 2.776 * (1.58 / sqrt(5)) ≈ 2.76

Therefore, the 95%-confidence interval is:

Confidence Interval = [67.0 - 2.76, 67.0 + 2.76] ≈ [64.24, 69.76]

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Answer:

It is 40

Step-by-step explanation:

10 x 8 divided by 2 is 40

Answer:

the one that charges $9.50 for each shirt

Step-by-step explanation:

It is because, for the first one, you need to add $20 to prepare it and an additional $9.00. Altogether, you need $29 for EACH shirt. But for the second company, you just need to play $9.50 for each shirt. The Second company is cheaper and therefore better

The probability that 5 hearts are chosen when 7 cards are drawn from a well-shuffled deck of 52 playing cards is option (d) 0.00000962.

Step 1: Determine the total number of ways to choose 7 cards from a deck of 52 playing cards, which can be calculated using the combination formula: C(52, 7) = 52! / (7! * (52 - 7)!), where "!" denotes the factorial.

Step 2: Determine the number of ways to choose 5 hearts from the deck. There are 13 hearts in a standard deck, so we can calculate the number of ways to choose 5 hearts from 13: C(13, 5) = 13! / (5! * (13 - 5)!).

Step 3: Calculate the probability by dividing the number of favorable outcomes (choosing 5 hearts) by the total number of possible outcomes (choosing 7 cards from the deck): P(5 hearts) = C(13, 5) / C(52, 7).

Step 4: Evaluate the probability numerically using a calculator or math software, and the result is approximately 0.00000962.

Therefore, the correct answer is option (d) 0.00000962.

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Answer:

1

Step-by-step explanation:

Answer:

Hey there!

p(x)=7x+25

7x+25=60

7x=35

x=5

Let me know if this helps :)

Answer:

y=1/4x+1/4

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

It's D on Enginuity

The graph of the function in the coordinate plane is f(x) = –5x – 19.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

As per the given diagram:

The x intercept of the line = -ve

The y intercept of the line = -ve

For f(x) = 3x - 11

x intercept = +ve

y intercept = -ve

Hence, not possible

For f(x) = -4x + 12

x intercept = +ve

y intercept = +ve

Hence, not possible

For f(x) = 4x + 13

x intercept = -ve

y intercept = +ve

Hence, not possible

For f(x) = -5x - 19

x intercept = -ve

y intercept = -ve

Hence, possible

The function plotted on the coordinate plane is f(x) = –5x – 19.

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Answer:

She spends 45 hours practicing her culinary skills in 5 weeks.

Answer:

T=-80

Step-by-step explanation:

P=kr/T when p=4 T=20 r= 2 k=40 so when p=-5,r=10 then T=-80

Step 1: The negative on the exponent means this thing is on the wrong side of the fraction.  Since there is no fraction written, it's by default in the top of a fraction over 1.

    \((-4)^{-3} = \dfrac{(-4)^{-3}}{1}\)

So, move that to the bottom of the fraction and make sure the exponent becomes positive:

    \(\dfrac{(-4)^{-3}}{1} =\dfrac{1}{(-4)^{3}}\)

Now you have to decide what \((-4)^3\) is.

Answer: 92

Step-by-step explanation:

Answer:

123

Step-by-step explanation:

did it in my head

Minimum sample size (n) = 15

To determine the minimum sample size required, we can use the formula:

n = (Zα/2 * σ / E)^2

Where:
- n is the minimum sample size
- Zα/2 is the z-score at the 95% confidence level, which is 1.96
- σ is the population standard deviation, which is given as 3.8
- E is the maximum error we can tolerate, which is 2 units in this case

Substituting the values, we get:

n = (1.96 * 3.8 / 2)^2
n = 27.44

Rounding up to the nearest whole number, we get a minimum sample size of 28.

Therefore, we need to sample at least 28 individuals from the normally distributed population to be 95% confident that the sample mean is within two units of the population mean, assuming a population standard deviation of 3.8.

To determine the minimum sample size required for a 95% confidence level, we'll need to use the following formula:

n = (Z * σ / E)^2

where:
- n is the minimum sample size
- Z is the Z-score corresponding to the desired confidence level (1.96 for a 95% confidence level)
- σ is the population standard deviation (3.8 in this case)
- E is the margin of error (2 units in this case)

Step 1: Identify the values
Z = 1.96 (from the 95% confidence level)
σ = 3.8
E = 2

Step 2: Plug the values into the formula
n = (1.96 * 3.8 / 2)^2

Step 3: Calculate the result
n = (7.528 / 2)^2
n = (3.764)^2
n ≈ 14.15

Since the sample size must be a whole number, round up to the nearest whole number to ensure the desired level of confidence is achieved.

Minimum sample size (n) = 15

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Answer:

x = 3

Step-by-step explanation:

2x - 1 = 5 ( add 1 to both sides )

2x = 6 ( divide both sides by 2 )

x = 3

Answer:

J

Step-by-step explanation: