you need to make 450 ml of a 4.5 m solution of sodium chloride. the only
available solution is 8.6 m. determine the volume of the stock solution needed and
the amount of water needed.
choose 2 answers!

The correct value of the product of a and b is 224

Taking the prime factorization of 161 reveals that it is equal to 23*7. Therefore, the only ways to represent 161 as a product of two positive integers are 161*1 and 23*7. Because neither 161 nor 1 is a two-digit number, the only two-digit factor of 161 is 23, we know that a and b are 23 and 7. Because 23 is a two-digit number, we know that a, with its two digits reversed, gives 23.

Therefore, a = 32 and b = 7. Multiplying our two correct values of a and b yields.

The correct product must have been

a*b =32*7

=224

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33 x 12 = 396

19 x 17 = 323

396 + 323 = 719

The approximate area under the curve of f(x) from x=0 to x=2 using a right-hand sum with four intervals is 4.25.

To approximate the area under the curve of the function f(x) = 4 - x^2 from x=0 to x=2 using a right-hand sum with four intervals, we first need to divide the interval [0, 2] into four equal subintervals of length h = (b-a)/n = (2-0)/4 = 0.5. The four subintervals are [0, 0.5], [0.5, 1], [1, 1.5], and [1.5, 2].

Next, we find the height of the curve at the right endpoint of each subinterval and multiply it by the width of the subinterval to get the area of the rectangle that approximates the region under the curve. Using the right endpoints of the subintervals, we have:

f(0.5) = 4 - (0.5)^2 = 3.75

f(1) = 4 - (1)^2 = 3

f(1.5) = 4 - (1.5)^2 = 1.75

f(2) = 4 - (2)^2 = 0

area of each rectangle:

A1 = f(0.5) * h = 3.75 * 0.5 = 1.875

A2 = f(1) * h = 3 * 0.5 = 1.5

A3 = f(1.5) * h = 1.75 * 0.5 = 0.875

A4 = f(2) * h = 0 * 0.5 = 0

the approximate area under the curve of f(x) from x=0 to x=2:

A ≈ A1 + A2 + A3 + A4 = 1.875 + 1.5 + 0.875 + 0 = 4.25

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Answer:

Vertically Opposite Angles are the angles opposite each other when two lines cross "Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down.

Step-by-step explanation:

Answer:

You would need to include in your description, angle of rotation, direction and center of rotation

Step-by-step explanation:

we know that

When the triangle is rotated,every point on the triangle is turned by an angle about a center of rotation.  The center of rotation is the point that a triangle rotates about. If the rotation is in the same direction as the hands of a clock, the direction is clockwise. If the rotation is in the opposite direction as the hands of a clock, the direction is counter-clockwise

so

To describe a rotation, we need to say what angle the triangle has been turned by, the direction and where the center of rotation is.

therefore

You would need to include in your description, angle of rotation, direction and center of rotation

The sample size that would be required for the width of 99% is 2653.

The number of subjects involved in a sample size is referred to as the sample size in market research. A set of people chosen from the general community who are thought to be a representative sample size for that particular study is referred to as the sample size.

The following details are given:

Margin of error, E = 0.025; Significance Level, = 0.01

The proportion p is estimated to be p = 0.53.

The significance level with a critical value of 0.01 is 2.58.

The smallest sample size needed to estimate the population proportion p within the necessary margin of error is determined using the formula shown below:

n >= p*(1-p)*(zc/E)2 n = 0.53 *(1 - 0.53*)2 n = 2652.97 *(1-p)*(2.58/0.025)2

As a result, we determine that n = 2653 is the minimal sample size needed to satisfy the criteria that

n >= 2652.97 and that it must be an integer value.

Sample size is 2653.

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The graph of f(x) = -x² + 2x + 1 and g(x) = 2ˣ, have the same y-intercept of (0, 1)

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the polynomial function f(x) = -x² + 2x + 1 and an exponential function g(x) = 2ˣ

From the graph of f(x) = -x² + 2x + 1 and g(x) = 2ˣ, have the same y-intercept of (0, 1)

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Answer: C

Step-by-step explanation:

The volume of a sphere is defined to be:

\(Volume=\frac{4}{3} \pi r^3\)

Plug in the values to get:

\(Volume=\frac{4}{3} (3.14)(3.5)^3=179.5in^3\)

The correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E. Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

She will be receiving a 2% raise per year. Her salary will increase $14,000 every year. The percent increase of her salary is 120% every year. Her salary is always 0.2 times the previous year's salary. The percent increase of her salary is 20% every year.

To calculate the salary of the vice president after n years of becoming a vice president, we use the given formula:

S(n) = 70000(1.2)

S(n) = 84000

The salary of the vice president after one year of becoming a vice president: S(1) = 70000(1.2)

S(1) = 84000

The percent increase of her salary is: S(n) = 70000(1.2)n

S(n) - S(n-1) / S(n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = (70000(1.2)n) - (70000(1.2)n-1) / (70000(1.2)n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = 20%

Therefore, the correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E.

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Answer:

7-n

Step-by-step explanation:

n-number 7 take away n

A correlation coefficient of 0.05 indicates a very weak positive correlation between the number of bedrooms and selling price.

When Bob calculates the correlation between the number of bedrooms in a home and its selling price and obtains a value of only 0.05, he can conclude that there is little to no linear relationship between the two variables.

Correlation is a statistical measure that indicates the degree to which two variables are related and the direction of the relationship. A correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

A correlation coefficient of 0.05 is very close to 0, indicating that there is almost no linear relationship between the number of bedrooms in a home and its selling price.

However, it is important to note that a low correlation coefficient does not necessarily mean that there is no relationship between the variables, as there could be a non-linear relationship or other types of relationships that cannot be captured by a correlation coefficient.

Therefore, Bob should further analyze the data set and explore other statistical measures or techniques to fully understand the relationship between the number of bedrooms in a home and its selling price.

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Answer:

\(\frac{27}{26}\) or 1\(\frac{1}{26}\)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Because the square root of 50 is 7.07 and 7.07 is less than 8.34.

Answer:

4 pounds

Step-by-step explanation:

16 ÷ 4 = 4

Answer:

D. 1/2 ≈ 0.083

Step-by-step explanation:

So for the coin there is a 1/2 chance because there are two sides, and only one will be "right." For the side-sided dice, there is a 1/6 chance using the same thinking as the coin.

We can multiply them by each other,

1/2 * 1/6 = 1/12

So the correct answer is D. 1/2 *about* 0.083

I hope this helps, have a nice day! :D

The model rocket reaches its maximum height after 23 seconds. B.

The time when the model rocket reaches its maximum height, we need to find the x-value of the vertex of the parabolic function given by F(x).

The x-value of the vertex can be found using the formula: x = -b/2a, where a and b are the coefficients of the quadratic function F(x) = \(ax^2 + bx + c.\)

For the function F(x) = \(-2x^2+ 92x + 24\), a = -2 and b = 92.

Using the formula x = -b/2a, we get:

x = -92 / 2(-2) = 23

The x-value of the vertex of the parabolic function indicated by F(x) must be determined at the moment the model rocket reaches its highest point.

The formula x = -b/2a, where a and b are the coefficients of the quadratic function, may be used to get the x-value of the vertex. F(x) = \(ax^2 + bx + c.\)

F(x) = for the function

\(-2x^2+ 92x + 24\),

, a = -2 and b = 92.

x = -92 / 2(-2) = 23 is the result of using the formula x = -b/2a.

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Answer:

Step-by-step explanation:

I belive the answer would be 18.30$, because if 1 hat is 6.70$ you mutiply it by 13 and which is 87.10$ -  325$ overall and the which is 237.9 then diveied that by 13 and get 18.30$ for each ball?

The value of a = -2 and b = 3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: 3a - 5b = -26, a + 2b = 6

We have to solve this equation.

3a - 5b = -26...(1)

a + 2b = 6...(2)

Now we multiply equation (1) by 2 and equation (2) by 5 and we get

6a - 10b = -52....(3)

5a + 10b = 30....(4)

After solving equations (3) and (4), we get

11a = -22

a = -2

Now we put the value of 'a' in equation(3) and we get

6(-2) - 10b = -52

-10b = -52 + 12

-10b =  -30

b = 3

Hence, the value of a = -2 and b = 3.

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Answer: 6

Step-by-step explanation:

A function is a function that represents the area under a curve. In this case, f is the curve being considered. The function a(x) represents the area under the curve of f from x=0 up to x.

So, if we want to find the area under the curve of f from x=0 up to x=3, we would evaluate a(3) - a(0). This would give us the total area under the curve of f from x=0 to x=3. Similarly, if we have another area function, say b(x), that represents the area under the curve of f from some other starting point (e.g. from x=1), we would use b(x) to find the area under the curve of f from x=1 up to some other x value.
The graph of f, displayed in the figure to the right, represents a function that can be analyzed using various mathematical concepts. In this case, we can consider two area functions for f, denoted as A(x) and B(x), which would allow us to evaluate the areas under the curve of the graph with respect to the x-axis. These area functions can be used to understand properties and behaviors of the function f in different regions of the graph.

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The IS relation is given by: Y = (intercept value rounded to two decimal places) + (slope value rounded to two decimal places) in the numerical example of the IS-LM model.

To derive the IS relation, we need to equate aggregate demand (AD) to aggregate supply (AS). Aggregate demand consists of consumption (C), investment (I), government spending (G), and net exports (NX). In this case, we assume net exports to be zero.

Given:

C = 233 + 0.47YD

I = 143 + 0.22Y - 1,094i

G = 299

T = 239

Aggregate demand (AD) = C + I + G

Substituting the given equations into AD:

AD = (233 + 0.47YD) + (143 + 0.22Y - 1,094i) + 299

Simplifying:

AD = 233 + 143 + 299 + 0.47YD + 0.22Y - 1,094i

Combining like terms:

AD = 675 + 0.47YD + 0.22Y - 1,094i

Since we want an equation with Y on the left side, we need to express YD in terms of Y by substituting YD = Y - T.

AD = 675 + 0.47(Y - T) + 0.22Y - 1,094i

AD = 675 + 0.47Y - 0.47T + 0.22Y - 1,094i

Combining like terms again:

AD = (0.47Y + 0.22Y) + (675 - 0.47T - 1,094i)

AD = 0.69Y - 0.47T - 1,094i + 675

Comparing with the IS relation Y = a + bAD, we have:

Y = 0.69Y - 0.47T - 1,094i + 675

Rearranging terms to have Y on the left side:

Y - 0.69Y = -0.47T - 1,094i + 675

0.31Y = -0.47T - 1,094i + 675

Dividing both sides by 0.31:

Y = (-0.47T - 1,094i + 675) / 0.31

Now, we can calculate the intercept and slope terms:

Intercept term = (-0.47T - 1,094i + 675) / 0.31

Slope term = 1 / 0.31

Rounding these values to two decimal places, the IS relation is:

Y = Intercept term + Slope term = (intercept value rounded to two decimal places) + (slope value rounded to two decimal places).

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If the device shows the zero vector, it means that the gradient at that location is zero.

To find the direction to walk in order to go directly downhill based on the gradient information from the device, you would need to follow the direction opposite to the gradient vector. The gradient vector points in the direction of the steepest uphill ascent, so walking in the opposite direction would take you downhill.

Here's a step-by-step process to determine the direction:

Stand at a particular location on the mountain.

Check the reading on the device, which gives you the gradient vector at that point.

Reverse the direction of the gradient vector to point in the opposite direction.

Move in the direction indicated by the reversed gradient vector. This will guide you downhill.

If the device shows the zero vector, it means that the gradient at that location is zero. In other words, the terrain is flat or level at that point. In this case, you are already at the lowest point of that local area, and any direction you choose to walk will keep you at the same altitude. It suggests that you are standing on a plateau or a local minimum.

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Answer:

the answer would -3/1 or -3

THIS IS THE CORRECT ANSWER!!!

If A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6. If the rank of A is less than 6, then the dimension of the row space will be less than 6.

The row space of a matrix is the span of its row vectors. Therefore, the dimension of the row space is equal to the number of linearly independent rows of the matrix.

For a 9x6 matrix A, the largest possible dimension of the row space is 6. This is because there can be at most 6 linearly independent rows in a 9x6 matrix. If there were more than 6 linearly independent rows, then the matrix would have rank greater than 6, which is impossible since the maximum rank of a 9x6 matrix is 6.

For a 6x9 matrix A, the largest possible dimension of the row space is also 6. This is because the number of linearly independent rows cannot exceed the number of columns in the matrix.

Therefore, if A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6.

However, if the rank of A is less than 6, then the dimension of the row space will be less than 6.

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To make the augmented matrix correspond to a consistent system, we need to ensure that the third row is a linear combination of the first two rows. Let's denote the entries in the third row as a, b, and c, respectively. Then, the equation involving g, h, and k that makes the matrix consistent is:

-4g + 3h + 5k = a

7g - 5h - 9k = b

In a consistent system, all rows of the augmented matrix must be linearly dependent. This means that the third row should be a linear combination of the first two rows. By equating the corresponding entries in the third row to variables, we can find an equation involving g, h, and k that satisfies this condition.

In the given augmented matrix, the third row is represented by the variables g, h, and k. We denote the entries in the third row as a, b, and c, respectively. To create a consistent system, we need to find a relationship between these variables and the entries in the first two rows.

By comparing the entries in the first and second columns, we can set up the following equations:

-4g + 3h + 5k = a (equation 1)

7g - 5h - 9k = b (equation 2)

These equations ensure that the augmented matrix corresponds to a consistent system. If we substitute the values of g, h, and k into equations 1 and 2, the resulting values in the third row will satisfy the entries a and b, respectively.

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26

Step-by-step explanation:

3x + 2x = 50 = 180

5x = 130

x = 26

To find the quantity that will maximize profit, we need to first calculate the total revenue and total cost functions. Total revenue is given by the product of the price and quantity, which is p*x.

Therefore, the total revenue function is R = (700-1/2x)*x = 700x - 1/2x^2. Total cost is given by the sum of the average fixed cost and average variable cost, which is C = 400 + 2x. Therefore, total cost function is C = (400+2x)*x = 400x + 2x^2.

Next, we can find the profit function by subtracting total cost from total revenue:
P = R - C = 700x - 1/2x^2 - 400x - 2x^2 = -5/2x^2 + 300x.

To maximize profit, we need to take the first derivative of the profit function and set it equal to zero:
dP/dx = -5x + 300 = 0
x = 60

Therefore, the quantity that will maximize profit is 60 units.

To find the selling price at this optimal quantity, we can substitute x=60 into the demand function:
p = 700 - 1/2(60) = $670 per unit.

Therefore, the selling price at this optimal quantity is $670 per unit.

To find the maximum profit, we can substitute x=60 into the profit function:
P = -5/2(60)^2 + 300(60) = $12,000.

Therefore, the maximum profit is $12,000.

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Answer:

33 marks

Step-by-step explanation:

solution:

45%of 80 marks

45/100*50 marks

33 marks

Answer:

Step-by-step explanation:

u got it right the first time it is D