Find. What part of 40 is 16?

Answer:

w = 49

Step-by-step explanation:

\(21 = \frac{3}{7} w\)

\(147 = 3w\)

(multiply 7 to both sides)

\(w = 49\)

divide both sides by 3

The three computations covered by the reliability factor table are sample size, index of reliability, and index of precision. Sample size deals with the size of the sample being used in order to achieve a desirable level of reliability.

Index of reliability is used to measure the consistency of results achieved over multiple trials. It does this by calculating the total number of items that contribute significantly to the final result. Finally, the index of precision measures the effect size of the sample, which is determined by comparing the results from the sample with the expected results.

The sample size computation gives the researcher an idea of the number of items that should be included in a sample in order to get the most reliable results. This is done by taking into account a number of factors including the variability of the population, the type of measurements used, and the desired level of accuracy.

The index of reliability is commonly calculated by finding the ratio of the number of items contributing significantly to the total result to the total number of items in the sample. This ratio is then multiplied by 100 in order to get a final score.

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Answer:

27

Step-by-step explanation:

25(0.08)=2+25=27

25(0.08)+25=27

The graph of the given equation is plotted below.

The given equation is y=2/7 x.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

Graph the line using the slope and y-intercept, or two points.

Slope: 2/7

y-intercept: (0, 0)

Plot the points (0, 0) and (7, 2) on the graph

Hence, the graph of the given equation is plotted below.

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Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the length of the rectangle be=l

So, breadth is b=l−14

Perimetre= 2(l+b)=2(l+l−14)=180 cm

⟹4l−28=180cm

⟹l=52cm

And, b=52−14=38cm

Hence, Area=l×b=52×38=1976cm  

2

x^2(x-2)(-2x+1)(x-1)

how:

(x³-2x²-2x+1)(x-1)​

(x^3-2x^2) (-2x+1) (x-1)

x^2(x-2)(-2x+1)(x-1)

Answer:3

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

9w = 63

9w/9 = 63/9

w = 7

Answer:

I'm pretty sure it's 7. I hope that helps

Step-by-step explanation:

We can approximate the nonlinear system by a linear system at (0,0) using the Jacobian matrix and can find the eigenvalues using the formula det(J(0,0) - λI) = 0.

We have to approximate the nonlinear system by a linear system at (0,0) and find the eigenvalues.

Identify the nonlinear system.
First, you need to provide the nonlinear system of equations you're working with. The system should be in the form of:
dx/dt = f(x, y)
dy/dt = g(x, y)

Calculate the Jacobian matrix.
To linearize the system, compute the Jacobian matrix, J, which contains the partial derivatives of f and g with respect to x and y. The Jacobian matrix is given by:

J(x, y) = [ ∂f/∂x  ∂f/∂y ]
             [ ∂g/∂x  ∂g/∂y ]

Evaluate the Jacobian at (0,0).
Substitute the point (0,0) into the Jacobian matrix to obtain J(0,0).

Find the eigenvalues.
To find the eigenvalues, solve the characteristic equation, which is given by:
det(J(0,0) - λI) = 0

Here, λ represents the eigenvalues, and I is the identity matrix. Solve the resulting polynomial equation for λ to obtain the eigenvalues of the linearized system.

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The triangle is drawn and attached

The length of BC is 3.9 cm

The length of BC is solved using Pythagoras Theorem as follows hypotenuse² = opposite² + adjacent²

where

hypotenuse = AB = 2 + 2 = 4

the hypotenuse is the diameter of the circle while given side is the radius and radius + radius = diameter

opposite = AC = 1

adjacent = BC = ?

AB² = AC² + BC²

substituting in to the values

4² = 1² + BC²

rearranging the equation

BC² = 4² - 1²

BC² = 16 - 1

BC = √15

BC = 3.873

BC = 3.9 to one decimal place

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Answer:

Since the sample size is n=10 we can find the first quartile taking in count the first 5 observations from the data set ordered and we have this:

33  60  62  63  69

\( Q_1 =62\)

We can find the third quartile taking in count the last 5 observations from the data set ordered and we have this:

70  74  79 107 119

\( Q_3 =79\)

And finally the median can be calculated with the average of the two moddlie values and we got:

\( Median= \frac{69+70}{2} =69.5 \)

And the IQr would be:

\( IQR = 79-62= 17\)

Step-by-step explanation:

Assuming that 2 is not part of the data we have:

74, 63, 69, 62, 33, 79, 70, 60, 107, 119

We can sort the values on increasing order and we got:

33  60  62  63  69  70  74  79 107 119

Since the sample size is n=10 we can find the first quartile taking in count the first 5 observations from the data set ordered and we have this:

33  60  62  63  69

\( Q_1 =62\)

We can find the third quartile taking in count the last 5 observations from the data set ordered and we have this:

70  74  79 107 119

\( Q_3 =79\)

And finally the median can be calculated with the average of the two moddlie values and we got:

\( Median= \frac{69+70}{2} =69.5 \)

And the IQr would be:

\( IQR = 79-62= 17\)

Answer:

Step-by-step explanation:

13/3 is the answer

Answer:

13/3

Step-by-step explanation:

Step 1

Multiply the denominator by the whole number

3 × 4 = 12

Step 2

Add the answer from Step 1 to the numerator

12 + 1 = 13

Step 3

Write answer from Step 2 over the denominator

13/3

please mark as brainliest if it helped

:)

The effective interest method of amortization is a method used to allocate the cost of a bond over the bond's life, in order to determine the amount of interest expense to be recorded each period.

In the case of Bentley Corporation, since they issued $1,000,000 of 10-year, 8% bonds at 105, this means that they received $1,050,000 in cash from investors.

Since the market rate of interest was 7%, the bonds were sold at a premium, which means that the effective interest rate is less than the stated interest rate of 8%. The effective interest rate is the rate at which the present value of the bond's future cash flows equals the amount of cash received at the time of issuance.

Using the effective interest method of amortization, the premium of $50,000 will be amortized over the life of the bond, reducing the effective interest rate each year. The interest expense recorded on December 31, 2021, the first interest payment date, will be calculated as follows:

$1,050,000 x 7% = $73,500 (effective interest)
$73,500 - $80,000 (stated interest) = -$6,500 (amortization of premium)
$80,000 - $6,500 = $73,500 (interest expense)

The premium of $50,000 will be reduced by $6,500, leaving a balance of $43,500 at the end of the first year. This process will continue each year until the bond matures in 2031.

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The graph of the inequality y ≥ (1/2)x - 1 and x - y > 1 is attached. Shannon's graph is correct.

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Inequalities are used for the non equal comparison of numbers and variables.

Given the inequalities:

y ≥ (1/2)x - 1     (1)

and

x - y > 1     (2)

The graph of the inequality is attached. Shannon's graph is correct.

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Answer:

(5x−1)(5x−1)

Step-by-step explanation:

25x2−10x+1

=(5x−1)(5x−1)

The simple interest rate that will ensure that Bob's investment of R6,500 equals Alice's 3% compound interest per year investment is 3.2%.

The difference between simple interest and compound interest is that simple interest computes interest on the principal only for each period.

Compound interest computes interest on both the principal and accumulated interest for each period.

Alice:

Principal investment = R6,500

Compound interest rate per year = 3%

Investment period = 5years

Future value = R7,535.28 (R6,500 x 1.03⁵)

Total Interest R1,035.28 (R7,535.28 - R6,500)

Bob:

Principal invested = R6,500

The simple interest rate = r

Investment period = 5years

The future value of the simple interest investment, A = P(1+rt)

7,535.28 = 6,500(1 + 5r)

Dividing each side b 6,500:

1.15927 = (1 + 5r)

5r = 0.15927

r = 0.031854

r - 0.032

r = 3.2% (0.32 x 100)

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Calculate r, giving your answer correct to 1 decimal place.

The evaluation of P10–Focus 1 indicates that we get by using the equation for the volume of a cuboid and by calculus;

(a) \(L = 4\times x + 4\times 2\cdot x + 4\times \frac{81}{2\cdot x} =12\cdot x + \frac{162}{x^2}\)

(b) \(L_{min}\) = 54 cm

(c) L'' at x = 3, (where \(L_{min}\) = 54 cm) is positive, therefore, x = 3 is a minimum point

P10-Focus2

The area = \(2\times x \times y+\frac{\pi\cdot x^2}{4} =4\), therefore, \(y = \frac{16- \pi \cdot x^2}{8 \cdot x}\)

The minimum point, which is an extremum point is a point where the derivative of the function is 0.

(a) The length of the cuboid = 2·x

The width of the cuboid = x

The volume of the cuboid = 81 cubic centimeters

The thickness of the cuboid is therefore;

Thickness = 81/(2·x × x) = 81/(2·x²)

The sum of the length of the twelve edges, L, is therefore;

\(L=x + x + x + x + x + 2\cdot x + 2 \cdot x + 2 \cdot x + 2\cdot x + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2}\)

Therefore;

\(L=4\times x + 4\times 2\cdot x + 4\times \frac{81}{2 \cdot x^2} =12\cdot x + \frac{162}{x^2}\)

The sum of the lengths of the twelve edges, L, is \(L = 12\cdot x + \frac{162}{x^2}\)

(b) The minimum value of L can be found using calculus by finding the point at which dL/dx = 0 as follows;

\(\frac{dL}{dx} = 12 - \frac{324}{x^3} =0\)

Therefore;

\(12-\frac{324}{x^3}=0\)

\(12 = \frac{324}{x^3}\)

x³ = 324 ÷ 12 = 27

x = ∛(27) = 3

x = 3

The minimum value of L can be obtained when x = 3 as follows;

\(L = 12\cdot x + \frac{162}{x^2}\)

\(L_{min} = 12\times 3 + \frac{162}{3^2} = 54\)

The \(L_{min}\) = 54

The minimum value of L is 54 centimeters

(c) The value of the minimum value of L can be confirmed by further differentiation using the second derivative, L'' as follows;

At the x-value of a minimum point of a function, the value of the further derivative is larger than zero

The further derivative of the specified function is found as follows;

\(L'' = \frac{dL'}{dx} =\frac{972}{x^4}\)

At the critical number, x = 3, from the first derivative, we get;

\(L'' = \frac{972}{3^4} = 12 > 0\)

The value of the further derivative of the function at the point x = 3, is L'' = 12 > 0, therefore the point x = 3 is a relative minimum.

(b) The radius of the quarter circle = x

The area of the figure = 4 m²

The sum of the area of the composite figures are;

\(A = 2 \times x \times y + \frac{\pi \cdot x^2}{4} = 4\)

Therefore;

\(y =\frac{\left(4 - \pi \cdot \frac{x^2}{4}\right)}{2\cdot x} = 16 - \frac{\pi \cdot x^2}{8\cdot x}\)

Rearranging the right hand side expression as a fraction, we get;

\(y = \frac{16-\pi \cdot x^2}{8\cdot x}\)

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the average rate of change is 4/3

Explanation:

Function: f(x)=4/3x + 8​

rewriting in the form of equation of line: y = mx + c

m = slope = rate of change

c = intercept

Comparing with the given function:

m = 4/3

c = 8

Hence, the average rate of change is 4/3

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{ \: Rs \: 552.5}}}}}\)

Step-by-step explanation:

Given,

Discount percent = 15 %

Vat percent = 13 %

Discount amount = Rs 750

Vat amount = ?

Finding the Marked price ( MP )

\( \boxed{ \sf{Discount \: amount = \: discount\% \: of \: MP}}\)

⇒\( \sf{750 = 15\% \: of \: MP}\)

⇒\( \sf{750 = \frac{15}{100} \times MP }\)

⇒\( \sf{750 = \frac{3}{20} MP}\)

⇒\( \sf{ \frac{3}{20} MP = 750}\)

⇒\( \sf{MP = 750 \times \frac{20}{3} }\)

⇒\( \sf{MP = rs \: 5000}\)

Finding the selling price

\( \boxed{ \sf{Selling \: price = \: MP - \: discount \: amount}}\)

⇒\( \sf{5000 - 750}\)

⇒\( \sf{Rs \: 4250}\)

Finally, finding the Vat amount

\( \boxed{ \sf{Vat \: amount = Vat\% \: of \: selling \: price}}\)

⇒\( \sf{13\% \: of \: 4250}\)

⇒\( \sf{ Rs 552.5}\)

Vat amount = Rs 552.5

Hope I helped!

Best regards!!

Answer:

C

Step-by-step explanation:

Remember that we can use the discriminant to determine the amount of roots that a quadratic function has.

If the determinant equals 0, then we only have one real root.

Our function is given by:

\(f(x)=x^2+bx+9\)

Then the discriminant will be:

\(\Delta = b^2-4(1)(9)=b^2-36\)

We only have one real root, thus our discriminant must be 0:

\(0=b^2-36\)

Solve for b:

\(b^2=36\)

Thus:

\(b=\pm 6\)

The answer is both II and III.

The final answer, then, is C.

In summary, the balance at the end of 4 years is approximately $88,416.58, and the balance at the end of 15 years is approximately $63,082.89.

To find the balance at the end of 4 years and 15 years for a loan of $100,000 at 4 percent annual interest with monthly payments, we can use the formula for the remaining balance on a loan after a certain number of payments.

The formula to calculate the remaining balance (B) is:

B = P * [(1 + r)^n - (1 + r)^m] / [(1 + r)^n - 1]

Where:

P is the principal amount (loan amount)

r is the monthly interest rate

n is the total number of monthly payments

m is the number of payments made

Let's calculate the balance at the end of 4 years:

P = $100,000

r = 4% annual interest rate / 12 (monthly interest rate) = 0.3333%

n = 30 years * 12 (number of monthly payments) = 360

m = 4 years * 12 (number of monthly payments) = 48

Substituting these values into the formula:

B = $100,000 * [(1 + 0.003333)^360 - (1 + 0.003333)^48] / [(1 + 0.003333)^360 - 1]

B ≈ $88,416.58

Therefore, the balance at the end of 4 years is approximately $88,416.58.

Now, let's calculate the balance at the end of 15 years:

P = $100,000

r = 4% annual interest rate / 12 (monthly interest rate) = 0.3333%

n = 30 years * 12 (number of monthly payments) = 360

m = 15 years * 12 (number of monthly payments) = 180

Substituting these values into the formula:

B = $100,000 * [(1 + 0.003333)^360 - (1 + 0.003333)^180] / [(1 + 0.003333)^360 - 1]

B ≈ $63,082.89

Therefore, the balance at the end of 15 years is approximately $63,082.89.

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the point P_0(2,1,2) lies on the tangent plane, we can use it to find the equation of the normal line:

x - 2 = 2

We start by finding the characteristic equation:

r^2 + 4r + 3 = 0

Solving for r, we get:

r = -1 or r = -3

So the complementary solution is:

y_c(t) = c_1 e^{-t} + c_2 e^{-3t}

Next, we need to find the transfer function H(s):

s^2 Y(s) - s y(0) - y'(0) + 4s Y(s) - 4y(0) + 3Y(s) = 1/s + 1/(s-1)

Applying the initial conditions y(0) = 0 and y'(0) = 1, we get:

(s^2 + 4s + 3) Y(s) = 1/s + 1/(s-1) + 4

Y(s) = [1/(s+1) + 1/(s+3) + 4/(s^2 + 4s + 3)] / (s^2 + 4s + 3)

We can factor the denominator of the second term in the numerator:

Y(s) = [1/(s+1) + 1/(s+3) + 4/((s+1)(s+3))] / [(s+1)(s+3)]

Using partial fraction decomposition, we get:

Y(s) = [2/(s+1) - 1/(s+3) + 1/((s+1)(s+3))] / (s+1) + [-1/(s+1) + 2/(s+3) - 1/((s+1)(s+3))] / (s+3)

Taking the inverse Laplace transform, we get:

y(t) = 2e^{-t} - e^{-3t} + (1/2)(1 - e^{-t}) - (1/2)(1 - e^{-3t})

So the general solution is:

y(t) = y_c(t) + y_p(t) = c_1 e^{-t} + c_2 e^{-3t} + 2e^{-t} - e^{-3t} + (1/2)(1 - e^{-t}) - (1/2)(1 - e^{-3t})

To find a particular solution, we need to solve for the unknown coefficients. Using the initial conditions y(0) = 1 and y'(0) = 0, we get:

c_1 + c_2 + 3/2 = 1

-c_1 - 3c_2 - 1/2 = 0

Solving this system of equations, we get:

c_1 = -2/5

c_2 = 9/10

So the particular solution is:

y_p(t) = (-2/5) e^{-t} + (9/10) e^{-3t} + (1/2)(1 - e^{-t}) - (1/2)(1 - e^{-3t})

Finally, the tangent plane at P_0(2,1,2) is given by the equation:

2x + 4y + 3z = 24

which corresponds to option (B) in the given choices.

To find the normal line, we first need to find the normal vector to the tangent plane, which is simply:

n = <2, 4, 3>

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a. The truck rental cost when you drive 85 miles is  $85.7.

b. The number of miles driven when the cost is $65.96 is 0.42x.

a. To find the truck rental cost when driving 85 miles, we can substitute the value of x into the given function.

f(x) = 0.42x + 50

Substituting x = 85:

f(85) = 0.42(85) + 50

= 35.7 + 50

= 85.7

Therefore, the truck rental cost when driving 85 miles is $85.70.

b. To determine the number of miles driven when the cost is $65.96, we can set up an equation using the given function.

f(x) = 0.42x + 50

Substituting f(x) = 65.96:

65.96 = 0.42x + 50

Subtracting 50 from both sides:

65.96 - 50 = 0.42x

15.96 = 0.42x

To isolate x, we divide both sides by 0.42:

15.96 / 0.42 = x

38 = x

Therefore, the number of miles driven when the cost is $65.96 is 38 miles.

In summary, when driving 85 miles, the truck rental cost is $85.70, and when the cost is $65.96, the number of miles driven is 38 miles.

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Samantha and Jeanne's original fractions is \(\frac{5}{(2x+3)} - \frac{7}{(x-4)}\)

From the question, we have the following parameters that can be used in our computation:

\(\frac{-9x-41}{(2x+3)(x-4)}\)

Using Partial Fraction, we have

\(\frac{-9x-41}{(2x+3)(x-4)} = \frac{A}{(2x+3)} + \frac{B}{(x-4)}\)

So, we have

-9x - 41 = A(x - 4) + B(2x + 3)

Expand

-9x - 41 = Ax - 4A + 2Bx + 3B

By comparison. we hve

A + 2B = -9

-4A + 3B = -41

Using a graphing tool, we have

A = 5 and B = -7

So, we have

\(\frac{-9x-41}{(2x+3)(x-4)} = \frac{5}{(2x+3)} - \frac{7}{(x-4)}\)

Hence, the original fraction is \(\frac{5}{(2x+3)} - \frac{7}{(x-4)}\)

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Answer:

I'm sorry I wish if I could help you but not sure of the answe

Answer:

B.

Symmetric Property

Step-by-step explanation:

The equation of the second line would be y = -x + 2.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Two linear graphs intersect at (3, -1).

One of the graphs has equation y = x - 4 and the other one passes through (4, -2).

m = ( -2 + 1) / ( 4 - 3)

m = -1 / 1 = -1

The equation of the second line

y + 2 = m ( x - 4)

y + 2 = -1 ( x - 4)

y = -x + 2

Hence, the equation of the second line would be y = -x + 2.

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A large population with a sample size of 30 or more has the smallest standard deviation, as the standard deviation is inversely proportional to the sample size. A smaller standard deviation indicates more consistent data. To minimize the standard deviation, the sample size depends on the population's variability, with larger sizes needed for highly variable populations.

If the population is large, a sample size of 30 or more will give the smallest standard deviation to the statistic. The reason for this is that the standard deviation of the sample mean is inversely proportional to the square root of the sample size.

Therefore, as the sample size increases, the standard deviation of the sample mean decreases.To understand this concept, we need to first understand what standard deviation is. Standard deviation is a measure of the spread of a dataset around the mean. A small standard deviation indicates that the data points are clustered closely around the mean, while a large standard deviation indicates that the data points are more spread out from the mean. In other words, a smaller standard deviation means that the data is more consistent.

when we are taking a sample from a large population, we want to minimize the standard deviation of the sample mean so that we can get a more accurate estimate of the population mean. The sample size required to achieve this depends on the variability of the population. If the population is highly variable, we will need a larger sample size to get a more accurate estimate of the population mean. However, if the population is less variable, we can get away with a smaller sample size.

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