Complete the following statement.

16 fl oz = pt

Solution:

Given the system;

Add equation1 to equation2, we have;

Substitute x = 5 in equation2;

ANSWER:

In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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The probability that a randomly chosen drone will fly between 4.70 and 4.8 is 0.9772, rounded to four decimal places.

The probability that a randomly chosen drone will fly between 4.70 and 4.8 is 0.9772. Let's first convert the given values to the z-score values. Here are the formulas used to convert values to the z-scores: z=(x-µ)/σ, where z is the z-score, x is the value, µ is the mean, and σ is the standard deviation.To calculate the z-score of the lower limit:z₁=(4.70-4.76)/0.04=−1.50z₁=−1.50.

To calculate the z-score of the upper limit:z₂=(4.80-4.76)/0.04=1.00z₂=1.00The probability that the drone will fly between 4.70 and 4.80 can be found using a standard normal table. Using the table, the area corresponding to z=−1.50 is 0.0668 and the area corresponding to z=1.00 is 0.1587.

The total area between these two z-values is:0.1587-0.0668=0.0919This means that the probability of a randomly chosen drone will fly between 4.70 and 4.80 is 0.0919 or 9.19%.

Therefore, the probability that a randomly chosen drone will fly between 4.70 and 4.8 is 0.9772, rounded to four decimal places.

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Answer:

x = 1/2

Step-by-step explanation:

x^3 = 1/8

Take the cube root of each side

x^3 ^ (1/3) = (1/8)^ (1/3)

Rewriting 8 as 2^3

x^3 ^ (1/3) = (1/2^3)^ (1/3)

x = 1/2

x³ = 1/8

8 can be written as 2³

x³ = 1/2³

(x)³ = (1/2)³

When exponents are same bases are taken and exponents are eliminated

x = 1/2

The total derivative of a function is not necessarily one-to-one. The total derivative represents the change in a function with respect to all of its input variables.

If a function has multiple input variables, the total derivative is a matrix, called the Jacobian matrix, whose entries represent the partial derivatives of the function with respect to each input variable.

A function with a non-invertible Jacobian matrix is not one-to-one, since multiple input values can result in the same output value. For example, consider the function f(x,y) = (x^2, y^2). The total derivative of f is given by the Jacobian matrix:

| 2x 0 |

| 0 2y|

This matrix is non-invertible when x=0 or y=0, since it has a determinant of zero. Thus, the function f is not one-to-one when x=0 or y=0.

In terms of polynomials, the total derivative is important for determining whether a polynomial has multiple roots. A root of a polynomial is a value of the input variable that causes the polynomial to equal zero. If a polynomial has multiple roots, it is not one-to-one, since different input values can result in the same output value.

The total derivative of a polynomial can be computed using the power rule of differentiation. For example, consider the polynomial p(x) = x^3 - 6x^2 + 11x - 6. The total derivative of p with respect to x is:

p'(x) = 3x^2 - 12x + 11

If p'(x) has multiple roots, then p(x) has multiple roots as well. In this case, p'(x) has roots at x=1 and x=11/3, so p(x) has multiple roots at x=1 and x=3. Thus, the total derivative is useful for identifying when a polynomial is not one-to-one.

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Is total derivative  is one-to-one? explain the significance of this result in terms of the derivative on polynomials.

The parabola narrows as the quadratic coefficient increases. The parabola's width increases as the quadratic coefficient decreases.

The graphs' width and whether or not they slant upward or downward depend on the quadratic term's coefficient, a for the parent function.

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Answer:

397

Step-by-step explanation:

Sea 'p (x)' el número que no es divisible por 4, 6, 9, 11 y 12 de manera que cuando se divide por estos números da un resto igual, tenemos;

Por teorema del resto, tenemos;

p (x) = (x - a) · Q (x) + R

Dónde;

p (x) = El número, que se divide

Q (x) = El cociente

(x - a) = El divisor

R = El resto

Dado que el número más pequeño es 4, el resto, 0 <R <4

Para el número entero más pequeño arriba (x - a) · Q (x), tenemos;

R = 1

Observamos que el mínimo común múltiplo de 4, 6, 9, 11 y 12 = 396, por lo tanto, podemos tener;

(x - a) · Q (x) = 396

R = 1, dar;

p (x) = 396 + 1 = 397

Por lo tanto;

El número que no es divisible por 4, 6, 9, 11 y 12, de manera que cuando se divide por estos números da residuos iguales, p (x) = 397

Answer:

I believe it's B

Step-by-step explanation:

when the square roots are the same, you just add the two numbers in front of the roots

Division of

704/46

divide by 2

= 352/23

352 = 23x 10 + 122

122= 23x5 + 7

Then 352/23 = 23x10 + 23x5 + 7 = 23x15 + 7

or is also equal to 23 7/15

Answer:

25 ( 5 width times 5 length)

Step-by-step explanation:

Answer: See below

Step-by-step explanation:

a) 3x-6y=-12

x-2y=-8  --> x=-8+2y

3x-6y=-12

3(-8+2y)-6y=12

-12+6y-6y=-12

-24=-12

The statement is false for any value of y

b) If you solve the equations for y into slope-intercept form, they have the same slope

--> 3x-6y=-12

6y=12-3x

6 ÷ (6y=-12+3x) ÷ 6

y=1/2x+2

--> y=1/2x+2

x-2y=-8

-2y=-8-x

2 ÷ (2y=8+x) ÷ 2

y=1/2x+4

Since the slopes of the 2 lines are the same, they are parallel, and will never intersect

False, The range for an exponential function does not include all real numbers but only real numbers greater than zero.

In mathematics, an exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Given statement,

The range for an exponential function includes all real numbers.

By the definition,

Exponential functions have the general form y = f (x) = aˣ,

where a > 0, a≠1, and x is any real number.

The reason a > 0 is that if it is negative, the function is undefined for -1 < x < 1. Restricting a to positive values allows the function to have a domain of all real numbers.

Thus the range is all real numbers greater than zero.

Hence, The range for an exponential function includes all real numbers is False because it includes real numbers greater than zero.

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Based on the information provided regarding same as cash loans, Chelsea won't be charged interest for the first 6 months of the loan, nor will she have to make payments for the first 6 months. (Option D)

A Same-As-Cash Loan refers to a short-term lending solution in which no interest or monthly payment are required to be paid during a set “Same-As-Cash” period. At the end of a predetermined period, the loan is paid off. Hence, the customer owes no interest or monthly payments during a set promotional period and pays the same amount on the loan as they would have paid up front with cash. These are interest deferred loans in which the loans interest still accrues during that promotional period, however if the customer pays off the entire principal balance before the period ends, they are not required to pay that interest. The advantage of these loans is that customers may spend the same amount they would have if they had paid with cash up front. Hence, if Chelsea opts for loan that offered 6 months, same as cash, there would be no requirement of payment or interest charged for the 6 months.

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The property that justifies the statement "If 2x+5=11, then 2x=6" is the subtraction property of equality.

The subtraction property of equality states that if two quantities are equal, subtracting the same number from both sides of the equation will still result in equality.

In the given equation, 2x+5=11, we can isolate the variable x by subtracting 5 from both sides of the equation. Applying the subtraction property of equality, we have:

2x+5-5 = 11-5

Simplifying, we get:

2x = 6

The subtraction property of equality allows us to subtract 5 from both sides of the equation without changing its validity. This property is a fundamental principle in algebra that allows us to perform operations on equations while maintaining equality. Therefore, the property justifying the statement "If 2x+5=11, then 2x=6" is the subtraction property of equality.

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To construct a confidence interval to estimate the true average tip with 90% confidence, we can use the following formula:
Confidence Interval = mean ± (critical value * standard deviation / sqrt(sample size))

In this case, the sample mean is 11.6% and the standard deviation is 2.5%. The critical value for a 90% confidence level is 1.645 (obtained from the z-table).

Plugging in the values, we have:

Confidence Interval = 11.6 ± (1.645 * 2.5 / sqrt(sample size))

Since the sample size is not mentioned in the question, we cannot calculate the exact confidence interval. However, you can use the formula provided above and substitute the actual sample size to obtain the interval. Remember to round the endpoints to two decimal places, if necessary.

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Step-by-step explanation:

2 q and 7 dimes kkkkkkkkk

Answer:

q = 2

d = 7

Step-by-step explanation:

System of Equations:

d + q = 9

10d + 25q = 120

Use Substitution:

let d = 9 - q

10(9 - q) + 25q = 120

90 - 10q + 25q = 120

15q = 30

q = 2

d = 7

Answer:

The pressure exerted by gas number 3 is 159 mmHg

Step-by-step explanation:

To answer this question, the law to Use is Dalton’s law of partial pressure

Dalton’s law of partial pressure states that for a mixture of gases which do not mix, the total pressure exerted by such gases is equal to the sum of the individual pressure.

Now for the three gases, the total pressure Pt is equal to P1 + P2 + P3

Now we have Pt = 950 mmHg, P1 = 335 mmHg and P2 = 456 mmHg

P3 = Pt-P1-P2

Plugging the values above, we have ; 950-335-456 = 159 mmHg

In regression analysis , the error term ε is a random variable with expected value of 0.

What is regression analysis?

A set of statistical procedures known as regression analysis is used to estimate the relationships between a dependent variable and one or more independent variables.

Main Body:

In regression analysis, the model in the form is called regression model.

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β0 + β1x, is known as regression equation.

So the answer  to error term is 0.

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The equation of the circle C is x² + y² = 80 when it passes through the tangent points (-20, 0) and (0, 10).

Equation of circle:

Equation of the circle refer the position of a circle on a cartesian plane.

Given,

C is a circle with center the origin.

A tangent to C passes through the points (-20, 0) and (0, 10)

Here we need to find the equation of the circle C.

In order to find the equation of our line:

We have to identify the y-intercept which is (0,10).

Now, we need to find the gradient of our line which is:

Than can be calculated by,

=> (10 - 0) / (0- (-20))

=>  10/20 = 0.5

Now, the equation of our line is written as,

y = 0.5x + 10

But, here we know the center of our circle is the origin:

Which is in the following form:

=> x² + y² = r²

where r refers the radius

So, here we need the line to meet our circle at one point, we can substitute the equation for our straight line in for y.

Then the equation of the circle is written as,

=> x² + (0.5x + 10)² = r²

When we simplify it, then we get,

=> x² + (0.5x + 10)(0.5x + 10) = r²

Now, we can expand and simplify the brackets to leave us with:

=> 1.25x² + 10x + 100 = r²

=> 1.25x² + 10x + 100 - r² = 0

Here we know that this is a tangent and so it only meets the circle at one point.

So, this equation should only have one solution.

Then it can be written as,

=> b² - 4ac = 0

=> 10² - 4(1.25)(100 - r²) = 0

When we simplify this one then we get the value of

=> r² = 90

Therefore the equation of the circle is x^2 + y^2 = 80.

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The uniform probability distribution is used with  option (d) a continuous random variable.

The uniform probability distribution is used for a continuous random variable, meaning that a variable can take on any value within a specified range, and the likelihood of any value within that range is equal. This distribution is often represented by a rectangle with height equal to the uniform probability density, and width equal to the range of the variable. In other words, if the range of a continuous random variable is from a to b, and we define the uniform distribution over this range, then the probability of any value between a and b is equal to (b-a)^-1. The uniform distribution is useful in various applications where the lack of knowledge of the underlying process leads to equal probabilities for all outcomes in a given range.

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Answer:

  50 cm²

Step-by-step explanation:

Given that the regular polygon is a square, there are multiple ways you can jump directly to the answer. Perhaps the simplest is to use the formula for the area of a rhombus:

  A = 1/2(d1)(d2)

where d1 and d2 are the lengths of the diagonals. Here, we see that half the diagonal is 5 cm, so the area is ...

  A = (1/2)(10 cm)(10 cm) = 50 cm² . . . . area of the polygon

__

Alternate solution

If you want to use the radius and the number of sides in a formula, you can consider the area of each triangle formed by radii and a side. That triangle has area ...

  A = 1/2r²sin(α)

where r is the radius and α is the central angle. For an n-sided polygon, the area is the sum of n of these triangles, and the central angle is 360°/n. Then the polygon area is ...

  A = n/2·r²·sin(360°/n)

For n = 4 and r = 5 cm, the area is ...

  A = (4/2)(5 cm)²(sin(360°/4)) = 2(5 cm)²(1) = 50 cm² . . . . area of square

_____

Additional comment

The formula is somewhat different if you start with the length of the apothem. One way to find the area is using the above formula and the relation between the radius and apothem:

  r = a·sec(180°/n)

Another formula uses the apothem directly:

  A = n·a²·tan(180°/n)

Answer:

4 option is a correct answer

Answer:

D

Step-by-step explanation:

V(x) = x³

substitute x = 2x into V(x)

V2(x) = (2x )³ = 2³x³ = 8x³

The volume has increased by a factor of 8 when the edge is doubled

Answer:

To find the best line model for the data, we will use linear regression analysis.

First, we need to calculate the mean of x and y:

mean of x = (0 + 2 + 4 + 6 + 8 + 10 + 12 + 24 + 14) / 9 = 8

mean of y = (9 + 9 + 10 + 11 + 11 + 12 + 13 + 13 + 14) / 9 = 11

Next, we need to calculate the deviations of x and y from their respective means:

deviation of x = x - mean of x

deviation of y = y - mean of y

x y deviation of x deviation of y (deviation of x)^2 deviation of x * deviation of y

0 9 -8 -2 64 16

2 9 -6 -2 36 12

4 10 -4 -1 16 4

6 11 -2 0 4 0

8 11 0 0 0 0

10 12 2 1 4 2

12 13 4 2 16 8

24 13 16 2 256 32

14 14 6 3 36 18

Then, we can calculate the slope (b) of the best-fit line using the formula:

b = sum of (deviation of x * deviation of y) / sum of (deviation of x)^2

b = (16 + 12 + 4 + 0 + 0 + 2 + 8 + 32 + 18) / (64 + 36 + 16 + 4 + 0 + 4 + 16 + 256 + 36) = 0.190

Next, we can calculate the y-intercept (a) of the best-fit line using the formula:

a = mean of y - b * mean of x

a = 11 - 0.190 * 8 = 7.48

Therefore, the equation of the best-fit line is:

y = 0.190x + 7.48

Finally, we can calculate the correlation coefficient (r) using the formula:

r = sum of (deviation of x * deviation of y) / (sqrt(sum of (deviation of x)^2) * sqrt(sum of (deviation of y)^2))

r = (16 + 12 + 4 + 0 + 0 + 2 + 8 + 32 + 18) / (sqrt(64 + 36 + 16 + 4 + 0 + 4 + 16 + 256 + 36) * sqrt(16 + 16 + 1 + 0 + 0 + 1 + 4 + 4 + 1)) = 0.905

Therefore, the best-fit line for the given data is y = 0.190x + 7.48, and the correlation coefficient is r = 0.905.

Step-by-step explanation:

Answer:

ik the answer

Step-by-step explanation:

Answer:

aproximantly 131.1701yen

Step-by-step explanation:

Answer:

15430 Japanese yen

Step-by-step explanation:

To find out how many Japanese yen you receive for 100 British pounds, we need to find the exchange rate between British pounds and Japanese yen in the table. From the table, we can see that the exchange rate between British pounds and Japanese yen is 154.43. Therefore, if you exchange 100 British pounds, you will receive 100 * 154.43 = 15430 Japanese yen.

(a) I have attached the graph.

(b) The function g(x) is given by g(x) = f(2x + 2)/3.  You can work this out algebraically.  You can also work this out by using the graph of the function.

(c) We can obtain the graph of y = g(x) from the graph of y = f(x) through the following transformations:

* stretch horizontally by a factor of 2

* stretch vertically by a factor of 3

* shift downwards by 2 units

Transformation doesn't depend on the shape of the figure if it has an overlap or not

The transformation \(8d\) can be applied to a figure with overlap or not with overlap.

Transformations are operations on a plane that change the position, shape, and size of geometric figures.

When a geometric figure is transformed,

its new image has the same shape as the original figure.

However,

it is in a new position and may have a different size.

Let's talk about different types of transformations.

Rotation:

It occurs when a shape is turned around a point, which is the rotation center.

Translation:

It moves the shape from one point to another on a plane.

Reflection:

It is an operation that results in the mirror image of the original shape.

Scaling:

The shape is transformed by changing the size without changing its orientation.

Transformation on \(8d\):

In the given problem, the transformation of \(8d\) can be applied to the figure with or without overlap.

This means that \(8d\) transformation doesn't depend on the shape of the figure if it has an overlap or not.

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Answer:

44t + 11

Step-by-step explanation:

11(4t + 1)

Distribute 11 amongst the values inside the parenthesis

11(4t) + 11(1)

Multiply

44t + 11

Hope this helps :)

Answer:

\(44t + 11\)

Step-by-step explanation:

\(11(4t + 1) \\ = 44t + 11\)