is the value of 2a+3b Prime or composite when a=11 & b=7​

Answer:

It would be 37 mnths

Step-by-step explanation:

They will have the same amount of money in their bank accounts after 26 months.

Algebra is the branch of mathematics that uses letters and variables to represent the missing information in a given mathematical expression, to find the solution.

Here,

Amount of money added by Neil in January = £32

Amount of money added by Amber in January = £240

Amount of money added by Neil at the end of every month = £50

Amount of money added by Amber at the end of every month = £42

According to the given data, after a number of months, the amount of money in their bank accounts must become same.

Let n be the number of months,

(£32 + n£50) = (£240 + n£42)

n£50 - n£42 = £240 - £32

n£8 = £208

So, n = 208/8

n = 26

Hence,

They will have the same amount of money in their bank accounts after 26 months.

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The candy store will use 103 grams of sugar in 10 hours.

To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).

To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.

We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.

So the calculation would be:

10.3 grams/hour x 10 hours = 103 grams

Therefore, the candy store will use 103 grams of sugar in 10 hours.

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From the information provided:

We have that those angles are corresponding angles, and thus:

*The two lines that must be parallel are:

So, line m should be parallel with line n.

Answer:

1:8 or 1/8

Step-by-step explanation:

That's your answer.....

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.105ft2 is the area of given figure.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

The given figure has rectangle and semi circle.

Area of rectangle=length * Breadth

=10*8

=80 ft2

Area of semicircle=1/2πr2 (r=4ft)

=1/2*3.14*(4)^2

=3.14*4*2=25.12ft2

Therefore area of figure is

=Area of rectangle+Area of semicircle

=80ft2+25.12ft2

=105ft2.

Therefore area of figure is 105ft2.

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The pickup truck travels 19\(\frac{2}{7}\) Miles in gallon.

A unit rate means a rate for one of something.

Given that a pickup truck travels 45 miles on 2\(\frac{1}{3}\) gallons of gas,

Since there are 45 miles in 7/3 gallons

So, 45*3/7 in one gallon = 19\(\frac{2}{7}\) Miles in one gallon

Hence, The pickup truck travels 19\(\frac{2}{7}\) Miles in gallon.

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Answer: 13. 30

Step-by-step explanation:

13. Area = 18x * 10y = 180xy

Length = 6th

With ?

180xy = 6xy x width

180 x/6xy

Width = 30

14. 3^(9-5)= 3^4 = 81 the truck weighs 81 times as the driver

3^5

The present value with interest rate is 14% is $1810.92.

The future value is $4892.

The interest rate is 14% per year.

The time period is 16 years.

To calculate the present value, we can use the following formula:

present value = future value / (1 + interest rate)**number of years

Plugging in the values for the future value, interest rate, and time period, we get:

present value = 4892 / (1 + 0.14)**16 = 1810.92

Therefore, the present value of $4892 if the interest rate is 14% and the number of years is 16 is $1810.92.

In words, the present value is calculated by dividing the future value by the factor that is 1 plus the interest rate raised to the power of the number of years. In this case, the future value is $4892, the interest rate is 14%, and the time period is 16 years. Therefore, the present value is $1810.92.

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The correct answer is B) II only.

The condition that checks that the sampling distribution of the sample proportion is approximately normal is II only, which is np0≥10 and n(1−p0)≥10 for sample size n.

Option I is not sufficient by itself to ensure normality of the sampling distribution. While random sampling is important for reducing bias in the sample, it does not guarantee that the sample proportion will have a normal distribution.

Option III is not relevant to the normality of the sampling distribution, as it pertains to the sample size relative to the population size and not the distribution of the sample proportion.

Therefore, the correct answer is B) II only.

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The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.


The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.

To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.

Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.

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The conversion of a fraction number with denominator 5 and numerator 2 , 2/5 in decimals is equals to the 0.4 value.

A decimal number can be defined as a number whose whole number part and fractional part are separated by a decimal point. Writing 2/5 as a decimal number by converting the denominator to powers of 10. We multiply the numerator and denominator by a number so that the denominator is a power of 10.

2/5 = (2 × 2) / (5 × 2) = 4/10

Now move the decimal point to the left as many places as there are zeros in the denominator, which is a power of 10.

The decimal moved one place to the left because the denominator was 10. Therefore, 4/10 = 0.4. Hence, required value is 0.4.

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If the columns of A are linearly independent, then it directly follows that the columns of A^2 span R**n.

A is the right response. It is obvious that the columns of A2 encompass Rn if the columns of A are linearly independent.

If the sections of A are linearly independent, you can see why this is the case. A linear combination of the columns of A can then be used to describe any vector x in Rn. The meaning of this is that there are scalars c1, c2,..., cn such that x = c1a1 + c2a2 +... + cnan, where a1, a2,..., an are the columns of A.

Consider the item A2 right now. Aej, where ej is the j-th standard basis vector in Rn, gives the j-th column of A2, which is provided by Aej, Which means that A2 = [Ae1 | Ae2 |... | Aen].

However, A2's columns can be written as linear combinations of the columns of A^2, and so the columns of A^2 span R^n.

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Answer:

Yes. Her answer is reasonable.

Step-by-step explanation:

Since sea level is at an elevation of 0 feet, we can express Coachella Valley as being -215 feet because it is 215 feet bellow sea level. If it were to be able sea level then it would be positive.

Answer:

\(d = \frac{4 - 3c}{c + 1} \)

Step-by-step explanation:

To make d the subject of formula, we need to rearrange the equation such that we arrive at d= _____.

\(c = \frac{4 - d}{d + 3} \)

Remove the fraction by multiplying (d +3) on both sides:

\(c(d + 3) = 4 - d\)

Expand:

\(cd + 3c = 4 - d\)

Bring all the d terms to one side and move the others to the other side of the equation:

\(cd + d = 4 - 3c\)

Factorise d out:

\(d(c + 1) = 4 - 3c\)

Divide by (c +1) on both sides:

\(d = \frac{4 - 3c}{c + 1} \)

Find the natural cubic spline, we need to construct a piecewise cubic polynomial that passes through each data point and has continuous first and second derivatives. The natural cubic spline that interpolates the given data points f(0) = 0, f(1) = 1, and f(2) = 2 can be determined.

To find the natural cubic spline, we need to construct a piecewise cubic polynomial that passes through each data point and has continuous first and second derivatives.

In this case, we have three data points: (0, 0), (1, 1), and (2, 2). We can construct a natural cubic spline by dividing the interval [0, 2] into two subintervals: [0, 1] and [1, 2]. On each subinterval, we define a cubic polynomial that passes through the corresponding data points and satisfies the continuity conditions.

For the interval [0, 1], we can define the cubic polynomial as

s1(x) = a1 + b1(x - 0) + c1(x - 0)^2 + d1(x - 0)^3,

where a1, b1, c1, and d1 are the coefficients to be determined.

Similarly, for the interval [1, 2], we define the cubic polynomial as

s2(x) = a2 + b2(x - 1) + c2(x - 1)^2 + d2(x - 1)^3,

where a2, b2, c2, and d2 are the coefficients to be determined.

By applying the necessary calculations and solving the system of equations, we can determine the coefficients of the cubic polynomials for each interval. The resulting natural cubic spline will be a function that satisfies the given data points and exhibits a smooth interpolation between them.

Since the given data points f(0) = 0, f(1) = 1, and f(2) = 2 define a simple linear relationship, the natural cubic spline interpolating these points will be a straight line passing through them.

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Answer:

Step-by-step explanation:

Given function in the vertex form is,

f(x) = (3x + 13)² + 89

    = \(9(x+\frac{13}{3})^{2}+89\) --------(1)

Vertex of the parabola → \((-\frac{13}{3},89)\)

If the standard equation of this function is,

f(x) = 9x² + 2x + 1

We will convert it into the vertex form,

f(x) = 9x² + 2x + 1

    = \(9(x^{2}+\frac{2}{9}x)+1\)

    = \(9[x^{2}+2(\frac{1}{9})x+(\frac{1}{9})^{2}-(\frac{1}{9})^2]+1\)

    = \(9[x^{2}+2(\frac{1}{9})x+(\frac{1}{9})^{2}]-9(\frac{1}{9})^2+1\)

    = \(9[x^{2}+2(\frac{1}{9})x+(\frac{1}{9})^{2}]-(\frac{1}{9})+1\)

    = \(9(x+\frac{1}{9})^2+\frac{9-1}{9}\)

    = \(9(x+\frac{1}{9})^2+\frac{8}{9}\) -------(2)

Vertex of the function → \((-\frac{1}{9},\frac{8}{9})\)

Equation (1) and (2) are different and both the equations have different vertex.

Therefore, given equation doesn't match the equation given in the vertex form of the function.

Answer:

y = -1/5 + 7

Step-by-step explanation:

Substitute the point (1,2) for the x and the y in the equation, set the 4 to b since we are solving for b.

2 = -5(1) + b  now solve for b

2 = -5 + b

+5   +5

7 = b

we know that the slope must be the reciprocal for it to be perpendicular

y = -1/5 + 7 add b (7) to the equation and change the reciprocal

Answer:

x < -8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

3 - (2x - 5) < -4(x + 2)

Step 2: Solve for x

Here we see that any value x smaller than -8 would work as a solution in the inequality.

The machine is working properly, the likelihood of it filling cans to 13.5 oz or less, based on a sample of 25 cans, is approximately 0.0062 or 0.62%.

To calculate the likelihood, we need to determine the probability of observing a sample mean of 13.5 oz or less, assuming that the machine is working properly.

Since we have a sample size of 25, we can use the Central Limit Theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases.

To find the probability, we need to standardize the sample mean using the z-score formula: z = (X - μ) / (σ / sqrt(n)), where X is the sample mean (13.5 oz), μ is the population mean (16 oz), σ is the population standard deviation (5 oz), and n is the sample size (25).

Calculating the z-score:

z = (13.5 - 16) / (5 / sqrt(25))

= -2.5 / (5 / 5)

= -2.5

Using a standard normal distribution table or a statistical calculator, we can find the probability associated with a z-score of -2.5. The probability of observing a sample mean of 13.5 oz or less, given that the machine is working properly, is approximately 0.0062 or 0.62%.

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Answer:

7 and 1

Step-by-step explanation:

Answer:

5ft= 60in

3/4 inch = 0.75 inch

=> 60/0.75 = 80 movies

Step-by-step explanation:

Answer:

Coefficients » 6 and 11

terms » a and n

constants » 5

Step-by-step explanation:

\(.\)

Answer:

2 and 1/6 feet

Step-by-step explanation:

To do this you would just put aside 17 and 14 and you would subtract 5/12 by 5/8. To subtract these you would just find the lcm which is 48 and that would be denominator and to make the top the same as the bottom you would just multiply how much it took the denominator and multiply the numerator. So to subtract them you would get 20/48 for 5/12 and 30/48 for 5/8. When you subtract them you get -10/12 so then you will subtract 17 and 14 which is 3 then you will subtract 3 - 10/12 and you would get 2 and 2/12 which can simplify to 2 1/6 feet

The difference in the lengths of alligators in zoos and Florida is 2.79 feet.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

Given that

The length of an alligator in a Zoo = 14 5/8 feet.

The length of an alligator in Florida =  17 5/12 feet.

Convert fractions into decimals, and we get

The length of an alligator in a Zoo = 14.625 feet.

The length of an alligator in Florida =  17.416 feet.

So the difference in their lengths = 17.416 - 14.625

So the difference in their lengths = 2.79 feet

Therefore, the difference in the lengths of alligators in zoos and Florida is 2.79 feet.

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Therefore, there are no solutions to the given quadratic equation. 57 and −2. Yes, there are two real roots in the given equation.

The formula for determining the roots is x = (-b  (b2 - 4ac))/2a. D = b2 minus 4ac is the discriminant. The equation has two real and distinct roots if D is greater than zero.

As a result, this equation does not have any actual roots.

Quadratic equations can be solved in three basic ways: completing the square, using the quadratic formula, and factoring.

When a given quadratic equation is multiplied by ax 2 + bx + c=0, we obtain a=2, b=7, and c=5.

Now, x x x using the quadratic formula.

= \s2×3 \s−7± \s7 \s2 \s −4×3×−5

= \s6 \s−7± \s49+60

= \s6 \s−7± \s109

= \s6 \s−7+ \s109

​ \s and x= \s6 \s−7− \s109

=0.57 and x=−2.91

Therefore, 0.57 and 2.91 are the answers to the given quadratic equation.

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Full Question = Solve the following equations.

3x 2 +7x−5=0

Show all your working and give your answer correct to 2 decimal places.

1. Markway can borrow $667,500 if each bond is sold at a premium of $30.

2. Markway can borrow $621,000 if each bond is sold at a discount of $10.

3. Markway can borrow $656,250 if each bond is sold at 92% of par.

4. Markway can borrow $773,250 if each bond is sold at 103% of par.

1. When each bond is sold at a premium of $30, the total premium amount is $30 x 750 = $22,500. The face amount of each bond is $900, so the borrowing amount would be $900 x 750 + $22,500 = $667,500.

2. When each bond is sold at a discount of $10, the total discount amount is $10 x 750 = $7,500. The face amount of each bond is $900, so the borrowing amount would be $900 x 750 - $7,500 = $621,000.

3. When each bond is sold at 92% of par, the selling price per bond is 92% x $900 = $828. The borrowing amount would be $828 x 750 = $656,250.

4. When each bond is sold at 103% of par, the selling price per bond is 103% x $900 = $927. The borrowing amount would be $927 x 750 = $773,250.

In each scenario, the borrowing amount is determined by multiplying the selling price per bond by the number of bonds. The presence of a premium or discount affects the borrowing amount accordingly.

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Answer:

The real number is - 6 and the imaginary number is 2.

Answer:

Step-by-step explanation:

the real numbers are -6 and 2

the imaginery is i

The reduced gradient is analogous to the residual for linear models.

In linear regression, the residual represents the difference between the observed values and the predicted values of the dependent variable. Similarly, in optimization, the reduced gradient represents the difference between the current solution and the optimal solution. It is a measure of how far the current solution is from the optimal solution in the direction of the search. By minimizing the reduced gradient, we can move closer to the optimal solution.

The reduced gradient is a widely used optimization technique in non-linear programming that allows for efficient computation of the descent direction at each iteration while accounting for constraints. It involves calculating a partial derivative of the objective function with respect to the variables that are not restricted by the constraints, and then projecting the resulting gradient onto the space defined by the constraints. The resulting vector is called the reduced gradient, and it points in the direction of the steepest descent that is feasible.

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The given parametric equations are, x = t³ - 3t, y = ²2²-6 Now, to find the tangent to a curve we must differentiate the equation of the curve, then to find the point where the tangent is horizontal we must put the first derivative equals to zero (0), and to find the point where the tangent is vertical we put the denominator of the first derivative equals to zero (0).

The first derivative of x is:x = t³ - 3t  dx/dt = 3t² - 3 The first derivative of y is:y = ²2²-6   dy/dt = 0Now, to find the point where the tangent is horizontal, we put the first derivative equals to zero (0).3t² - 3 = 0  3(t² - 1) = 0 t² = 1 t = ±1∴ The values of t are t = 1, -1 Now, the points on the curve are when t = 1 and when t = -1. The points are: When t = 1, x = t³ - 3t = 1³ - 3(1) = -2 When t = 1, y = ²2²-6 = 2² - 6 = -2 When t = -1, x = t³ - 3t = (-1)³ - 3(-1) = 4 When t = -1, y = ²2²-6 = 2² - 6 = -2Therefore, the points on the curve where the tangent is horizontal are (-2, -2) and (4, -2).

Now, to find the points where the tangent is vertical, we put the denominator of the first derivative equal to zero (0). The denominator of the first derivative is 3t² - 3 = 3(t² - 1) At t = 1, the first derivative is zero but the denominator of the first derivative is not zero. Therefore, there is no point where the tangent is vertical.

Thus, the points on the curve where the tangent is horizontal are (-2, -2) and (4, -2). The tangent is not vertical at any point.

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Because the graph always has a consistent slope of +2, the table x|y-2| 4|0| 6|2| is an illustration of a linear function table.

In order for a table to represent a linear function, there must be a constant rate of change (slope) between any two points on the graph. In other words, the relationship between the x-values and y-values should follow a consistent pattern.

The correct table that represents a linear function is: x|y-2| 4|0| 6|2|This is because there is a constant rate of change of +2 between any two points on the graph. For example, when x goes from 2 to 4, y increases from -2 to 0. When x goes from 4 to 6, y increases from 0 to 2.

This constant rate of change indicates that the relationship between x and y is linear.

In summary, a table represents a linear function when there is a constant rate of change between any two points on the graph. The table x|y-2| 4|0| 6|2| is an example of a linear function table because there is a consistent slope of +2 between any two points on the graph.

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The correct option is that C. Player A is the most consistent, with an IQR of 2.5.

The IQR is a spread metric that is less influenced by extreme values. It is the difference between the third (Q3) and first (Q1) quartiles. The quartiles for Player A are as follows:

Q1 = 2

Q3 = 4

IQR = Q3 - Q1 = 4 - 2 = 2

The quartiles for Player B are as follows:

Q1 = 2

Q3 = 5.5

IQR = Q3 - Q1 = 5.5 - 2 = 3.5

The IQR is regarded a better indicator of variability than the range since it is less impacted by extreme results. As a result, we may infer that the interquartile range is the best measure of variability for this data.

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