plot the numbers -1.5, 3/2,-3/2

If increasing the sides of a square field by five feet will increase the area by 245 ft², then the area of the original square is 484 ft².

To find the area of the original square, we can use the following formula:

Area of the original square = x²

where x is the original length of the square field.

Given that the increase in the length and width of the square field is 5 ft, the side length of the new square is (x + 5) ft. Therefore, the area of the new square is (x + 5)² ft².

Given that the area of the new square is 245 ft² more than the area of the smaller square, we can write:

(x + 5)² = 245 + x²

Expanding the left-hand side of the equation and simplifying, we get:

x² + 10x + 25 = 245 + x²

Solving for x, we get:

10x + 25 = 245

x = 22

Plugging x = 22 into the formula, we can find the area of the original square:

Area of the original square = x² = 22² = 484 ft²

Therefore, the area of the original square is 484 ft².

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Answer: Hypotheses followed by a conclusion is called an If-then statement or a conditional statement.

Step-by-step explanation: Yes I used google, but reworded it.

Answer:

A conditional statement is a math statement that uses the "if" and "then" that join two things together.

Step-by-step explanation:

Example:

if p... then q...

hope this helps!

have a good day :-)

Answer: 5

Step-by-step explanation: you subtract 12.14 from 19.44 to get the amount of money he paid for the toppings alone which is 7.4. Then do 7.4/1.44 to get 5 toppings.

The statement holds true for the base case and it holds true for any k=n assuming it holds true for k=n, we can conclude that the statement holds true for all positive integer values of k. Hence, if we remove the root of a \($\mathrm{k}^{\text {th }}$\) order binomial tree, it results in k binomial trees of the smaller orders.

The statement to be proven is: "If we remove the root of a \($\mathrm{k}^{\text {th }}$\) order binomial tree, it results in \($\mathrm{k}$\) binomial trees of the smaller orders."

We will prove this statement by mathematical induction.

Base case k=1 :

Inductive step:

Suppose the statement holds true for some \($\mathbf{k}=\mathbf{n}$\), i.e., if we remove the root of an \($\mathbf{n}^{\text {th }}$\) order binomial tree, it results in \($\mathrm{n}$\) binomial trees of the smaller orders. We need to show that it also holds true for \($\mathbf{k}=\mathbf{n}+1$\)

using definition of mathematical induction.

Consider a \($(\mathrm{n}+1)^{\text {th }}$\) order binomial tree, which can be formed by joining two \($\mathrm{n}^{\text {th }}$\) order binomial trees. If we remove the root of this \($(\mathrm{n}+1)^{\text {th }}$\) order binomial tree, we are left with two nth order binomial trees. By the induction hypothesis, each of these \($\mathbf{n}^{\text {th }}$\) order binomial trees will result in n binomial trees of the smaller orders. Hence, the result of removing the root of the \($(n+1)^{\text {th }}$\) order binomial tree will be n + n = 2n binomial trees of the smaller orders, which implies that the statement holds true for \($\mathrm{k}=\mathrm{n}+1$\) as well.

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At constant temperature and pressure, for ideal gas mixtures (GI) and for ideal solutions (SI), it is always true that the value of delta Hmixing is 0.

In both ideal gas mixtures (GI) and ideal solutions (SI), the value of delta Hmixing is 0 because there is no heat involved in the mixing process at constant temperature and pressure. In an ideal gas mixture, the individual gas molecules do not interact with each other and behave independently. Therefore, when the gases are mixed together, there is no change in energy or enthalpy. Similarly, in an ideal solution, the solute particles and solvent particles do not interact with each other and mix uniformly. The mixing process does not involve any heat transfer, so the enthalpy change (delta Hmixing) is zero.

This is due to the fact that at constant temperature and pressure, the only forces that matter are the forces of attraction and repulsion between the particles. In an ideal gas mixture, the individual gas molecules do not attract or repel each other, resulting in no change in energy during mixing. Similarly, in an ideal solution, the solute particles do not attract or repel the solvent particles, leading to no change in enthalpy during mixing. As a result, the value of delta Hmixing is always zero for both ideal gas mixtures and ideal solutions at constant temperature and pressure.

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The mean and standard deviation of the total time are µx = 66 and σx = 3.17, so the correct answer is (D) µx= 66 σx= 3.17.

To find this:

The total time to complete all three tasks is the sum of the time taken for each task. The mean time to complete all three tasks (µx) can be calculated by adding the mean time for each task: µx = 36 + 22 + 8 = 66. The standard deviation (σx) of the total time can be calculated using the standard deviation of each task and the square root of the number of tasks (n).

Using the formula: \(\sigma x = \frac{\sqrt{\sigma1^2 + \sigma2^2 + \sigma3^2}}{\sqrt n}\),

where σ1, σ2, σ3 are the standard deviations of each task, n = 3.

Plugging in the values, we get

\(\sigma x = \sqrt(2.5^2 + 1.8^2 + 0.75^2)/\sqrt3 \\= \sqrt{6.25 + 3.24 + 0.5625}/\sqrt3 \\= \sqrt{10.0525}/\sqrt3 = 3.17\)

Hence, the mean and standard deviation of the total time are µx = 66 and σx = 3.17, so the correct answer is (D) µx= 66 σx= 3.17.

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The set of polynomials is not closed under division.

A set is said to be closed under an operation if the result of that operation on elements of the set is always an element of the set. For example, the set of natural numbers is closed under addition because the sum of two natural numbers is always a natural number.

In the case of polynomials, the set of polynomials is closed under addition, subtraction, and multiplication. This means that if you have two polynomials, you can add, subtract, or multiply them and the result will be another polynomial.

However, when it comes to division, the set of polynomials is not closed. When you divide two polynomials, the result is not always a polynomial. The result can be a polynomial plus some remainder. For example, dividing x^2 + 2x + 1 by x + 1 will give you x + 1 with a remainder of 1.

Therefore, the set of polynomials is not closed under division because the result of dividing two polynomials is not always a polynomial.

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Answer:

Its either c or b

Step-by-step explanation:

sorry if its wrong

Answer:

that library has only 3 books? it needs to open a book raising fund

The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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Answer:

32 degrees.

Step-by-step explanation:

The probability of meeting a pupil who is a boy is 0.80

From the question, the given parameters are:

Population = 600

Girls = 120

Start by calculating the number of boys

This is represented as

Boys = Population - Girls

So, we have

Boys = 600 - 120

Evaluate

Boys = 480

The probability of a meeting a boy is then calculated as

P = Boys/Population

So, we have

P = 480/600

Evaluate

P = 0.80

Hence, the probability of a boy is 0.80

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A unit vector parallel to the tangent line of the parabola y = x² at the point (3, 9) is (1/√(37), 6/√(37)).

To find a unit vector parallel to the tangent line of the parabola y = x² at the point (3, 9), we need to determine the slope of the tangent line at that point and then normalize it to obtain a unit vector.

The slope of the tangent line can be found using the derivative of the function y = x². Taking the derivative with respect to x:

dy/dx = 2x

Substituting x = 3 into the derivative, we get:

dy/dx = 2(3) = 6

This slope represents the slope of the tangent line to the parabola at the point (3, 9).

Now, to obtain a unit vector parallel to this line, we normalize the vector (1, 6). Dividing each component of the vector by its magnitude:

Magnitude of (1, 6) = √(1² + 6²) = √(37)

Unit vector = (1/√(37), 6/√(37))

Therefore, a unit vector parallel to the tangent line of the parabola y = x² at the point (3, 9) is (1/√(37), 6/√(37)).

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Answer:

5.2

Step-by-step explanation:

adding all the numbers together and dividing it by 10.

Answer:

mean = 5.2

Step-by-step explanation:

The mean (or average) of a group of numbers is defined as the value calculated by adding all the given numbers together and then dividing the result by the number of numbers given.

Therefore,

\(\boxed{\mathrm{mean = \frac{sum \ of \ the \ numbers}{number \ of \ numbers}}}\).

In the question, the numbers given are: 3, 7, 2, 4, 7, 5, 7, 1, 8, and 8.

Therefore,

sum = 3 + 7 + 2 + 4 + 7 + 5 + 7 + 1 + 8 + 8

       = 52

There are 10 numbers given in the question. Therefore, using the formula given above, we can calculate the mean:

\(\mathrm{mean = \frac{52}{10}}\)

            \(= \bf 5.2\)

Hence, the mean of the given numbers is 5.2.

Answer:

F= 1 /4 y+ 9 /4

Step-by-step explanation:

brainliest?

The company's claim can be evaluated using a hypothesis test. The null hypothesis, denoted as H0, assumes that the true proportion of chips that do not fail in the first 1000 hours is 55% or lower.

Ha stands for the alternative hypothesis, which assumes that the real proportion is higher than 55%. This test has a significance level of 0.01.

A sample of 800 chips was taken based on the information provided, and it was discovered that 60% of them do not fail in the first 1000 hours. A one-sample percentage test can be used to verify the assertion.  The test statistic for this test is the z-score, which is calculated as:

\(\[ z = \frac{{p - p_0}}{{\sqrt{\frac{{p_0(1-p_0)}}{n}}}} \]\)

If n is the sample size, p0 is the null hypothesis' assumed proportion, and p is the sample proportion.

If we substitute the values, we get:

\(\[ z = \frac{{0.6 - 0.55}}{{\sqrt{\frac{{0.55(1-0.55)}}{800}}}} \]\)

The z-score for this assertion is calculated, and we find that it is approximately 2.86.

In order to determine whether there is sufficient data to support the company's claim, we compare the computed z-score with the essential value. At a significance level of 0.01 the critical value for a one-tailed test is approximately 2.33.

Because the estimated z-score (2.86) is larger than the determining value (2.33), we reject the null hypothesis. Therefore, the company's assertion that more than 55% of the chips do not fail in the first 1000 hours of use is supported by sufficient data at the 0.01 level.

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To compute the probability of selecting a certain number of white or black balls from the urn after a certain number of trials, we can use the concept of conditional probability. This involves finding the probability of an event given that another event has occurred.

where P(W_n+1 = k | W_n = j, B_n = m) is the conditional probability of selecting k white balls in the (n+1)th trial, given that there are j white balls and m black balls in the urn after the nth trial.

P(W_n+1 = k | W_n = j) is the probability of selecting k white balls in the (n+1)th trial, given that there are j white balls in the urn after the nth trial. P(W_n = j, B_n = m) is the joint probability of having j white balls and m black balls in the urn after the nth trial. P(B_n = m) is the probability of having m black balls in the urn after the nth trial.

Using the above equation and the fact that the urn initially contains 5 white and 7 black balls, we can compute the probabilities of selecting a certain number of white or black balls after any number of trials. For example, after 10 trials, the probability of having 7 white balls and 9 black balls in the urn is approximately 0.055.

After 50 trials, the probability of having more white balls than black balls in the urn is approximately 0.989. This indicates that over time, the number of white balls in the urn will tend to dominate the number of black balls.

Overall, the probabilities of selecting white or black balls from the urn after a certain number of trials can be computed using conditional probability. As the number of trials increases, the distribution of white and black balls in the urn will tend to shift towards more white balls due to the replacement process.

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In this case, the mean absolute deviation of 8.5 indicates that, on average, the data points deviate from the mean by about 8.5 units.

Mean absolute deviation (MAD) is a statistical measure that represents the average distance between each data point and the mean of the data set. It is calculated by finding the absolute value of the difference between each data point and the mean, and then taking the average of these absolute differences. MAD is a useful measure of the variability or spread of a data set, and is often used as an alternative to the more common measure of standard deviation. Like standard deviation, MAD gives an indication of how spread out the data is, but unlike standard deviation, MAD is less sensitive to extreme values or outliers.

Here,

To find the mean absolute deviation of the data, we first need to calculate the mean (average) of the data:

Mean = (46 + 54 + 43 + 57 + 50 + 62 + 78 + 42) / 8

Mean = 52

The mean of the data is 52.

Next, we need to calculate the absolute deviation of each data point from the mean. The absolute deviation is simply the absolute value of the difference between each data point and the mean:

|46 - 52| = 6

|54 - 52| = 2

|43 - 52| = 9

|57 - 52| = 5

|50 - 52| = 2

|62 - 52| = 10

|78 - 52| = 26

|42 - 52| = 10

Now, we can calculate the mean absolute deviation by taking the average of the absolute deviations:

Mean Absolute Deviation = (6 + 2 + 9 + 5 + 2 + 10 + 26 + 10) / 8

Mean Absolute Deviation = 8.5

The mean absolute deviation of the data is 8.5.

Interpretation: The mean absolute deviation represents the average distance between each data point and the mean of the data. In this case, the mean absolute deviation of 8.5 indicates that, on average, the data points deviate from the mean by about 8.5 units. This means that the data points are relatively spread out, with some points being much higher or lower than the mean.

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Answer:

Lucy's dog needs to gain 6 pounds.

Step-by-step explanation:

Lucy's dog lost 6 pounds so the dog will have to gain 6 pounds.

The Dog need to gain 6 pounds for net change of zero pounds.

We have Lucy's whose dog lost 6 pounds.

We have to find out how much weight does her dog need to gain in order to have a net change of 0 pounds.

Number of toffees left after loosing 'y' toffees = x - y

The number of toffees to buy = x - (x - y) = x - x + y = y

A/Q -

Let the Dog's initial weight be -  W

After loosing 6 pounds, the weight will be -   W - 6

For a net change of zero pounds, he needs to add = W - (W - 6) = W - W + 6 = 6 Pounds.

Hence, he need to gain 6 pounds for net change of zero pounds.

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To find the number of bicycles that must be manufactured to minimize the cost, we need to determine the value of x that corresponds to the minimum point of the cost function C(x).

We can find this by taking the derivative of C(x) with respect to x and setting it equal to zero. Let's differentiate C(x):

C'(x) = 6x - 1500

Now we set C'(x) = 0 and solve for x:

6x - 1500 = 0

6x = 1500

x = 250

Therefore, the number of bicycles that must be manufactured to minimize the cost is 250 bicycles.

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The margin of error for a 99% confidence interval estimate is approximately 0.0838 or 8.38%.

To calculate the margin of error for a 99% confidence interval estimate, we can use the formula:

Margin of Error = Z * sqrt(p_hat * (1 - p_hat) / n)

Where:

Z is the z-value corresponding to the desired confidence level (99% confidence level corresponds to a z-value of approximately 2.576).

p_hat is the sample proportion (percentage of apples with bruises), which is calculated as the number of apples with bruises divided by the total sample size.

n is the sample size.

Given:

Sample size (n) = 100

Number of apples with bruises = 12

Calculating the sample proportion:

p_hat = 12 / 100 = 0.12

Using the z-value for a 99% confidence level (z = 2.576), we can calculate the margin of error:

Margin of Error = 2.576 * sqrt(0.12 * (1 - 0.12) / 100)

Calculating the margin of error:

Margin of Error = 2.576 * sqrt(0.12 * 0.88 / 100)

Margin of Error = 2.576 * sqrt(0.1056 / 100)

Margin of Error = 2.576 * sqrt(0.001056)

Margin of Error ≈ 2.576 * 0.0325

Margin of Error ≈ 0.0838

Therefore, the margin of error for a 99% confidence interval estimate is approximately 0.0838 or 8.38%.

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Answer:

the answer is c. y=3x-6

Step-by-step explanation:

Hi there! Hopefully this helps!

----------------------------------------------------------------------------------------------------------

First we need to substitute the value of the variable into the expression and simplify.

b-(b+a×4c÷4) = 1 - (1 + -6 × 4(2) ÷ 4).

Now we need to solve 1 - (1 + -6 × 4(2) ÷ 4).

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1 - (1 + -6 × 4(2) ÷ 4)

|

|  First, we cancel out 4 and 4.

\/

1 - (1 - 6 × 2)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Next, we multiply -6 and 2 to get -12.

1 - (1 - 12)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Then we subtract 12 from 1 to get -11.

1 - (-11)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The opposite of -11 is 11.

1 + 11.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Answer:

Answer: 12

Hope this helps

Answer:

9.45g= 28.2

Divide through by 9.45

g=28.2/9.45

g=2.98 to 2s.f

As the answer is 9.45g=28.2, we can figure out easily that g is just 28.2 divide by 9.4. or 28.2/9.4

Dividing this we can get 3 easily, this is simple division.

If you have any question just ask in the comments.

Answer:

the equation D ) would cause a consistent-independent system.

Step-by-step explanation:

A ) 5 x + y = 7  /*( -2 )

    10 x + 2 y = 14

    --------------------

    - 10 x - 2 y = - 14

      10 x + 2 y = 14

   ------------------------

       0 x = 0  ( Dependent system )

B ) 5 x + y = 7  / *  3

    - 15 x - 3 y = - 6

    --------------------------

    15 x + 3 y  = 21

    - 15 x - 3 y = - 6

  -------------------------

        0 x = 15 ( Inconsistent system )

C )   5 x + y = 7

       5 x + y = - 7  / * ( - 1 )

       ---------------------------

       5 x + y = 7

      - 5 x - y = 7

    ------------------

        0 x = 14  ( Inconsistent system )

D ) 5 x + y = 7  / * ( - 2 )

     6 x + 2 y = 7

     ------------------

      - 10 x - 2 y = - 14

        6 x   + 2 y = 7

      -----------------------

       - 4 x = - 7;     x = 7/4;   y = - 7/4

These tasks involve analyzing various aspects of cost-volume-profit relationships, sensitivity to changes, and resource constraints to gain insights into the financial performance and operational efficiency of the company.

1) To prepare a contribution margin income statement, you need to classify the costs as variable or fixed and calculate the contribution margin for each product. Subtracting the total variable costs from the total sales revenue will yield the contribution margin, which can be used to determine the operating profit.

2) The weighted average contribution margin ratio can be calculated by dividing the total contribution margin by the total sales revenue. This ratio indicates the average contribution margin earned per dollar of sales.

3) The break-even point in sales dollars can be determined by dividing the total fixed costs by the contribution margin ratio. It represents the level of sales required to cover all costs and achieve a zero-profit position.

4) To earn an annual profit of $400,000, you would need to add this profit amount to the total fixed costs and divide the sum by the contribution margin ratio to find the required sales dollars.

5) By increasing or decreasing the plane sales price by 10 percent while keeping the total sales units constant, you can calculate the impact on the operating profit by multiplying the change in sales price by the total sales units and the contribution margin ratio.

6) If the sales mix shifts more towards the car product, the break-even point in units may decrease. This is because the car product has a lower labor hour requirement per unit compared to the other two products, potentially reducing the total fixed costs and contributing to a lower break-even point.

7) To optimize the use of limited labor hours, you would calculate the contribution margin per labor hour for each product by dividing the contribution margin by the labor hours required per unit. This information can guide decision-making on the allocation of labor hours to maximize profitability.

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The distance between the skew lines is √14 units.

we need to find the shortest distance between any two points on the two lines. Let's choose two points, one from each line, and then calculate the distance between them. For the first line with parametric equations:

x = 3 + t

y = 3 + 6t

z = 2t

Let's choose a point on this line with t = 0:

Point A: (x₁, y₁, z₁) = (3 + 0, 3 + 6(0), 2(0)) = (3, 3, 0)

For the second line with parametric equations:

x = 2 + 2s

y = 5 + 15s

z = -3 + 6s

Let's choose a point on this line with s = 0:

Point B: (x₂, y₂, z₂) = (2 + 2(0), 5 + 15(0), -3 + 6(0)) = (2, 5, -3)

Now, we can calculate the distance between these two points using the distance formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Substituting the values:

Distance = √[(2 - 3)² + (5 - 3)² + (-3 - 0)²]

         = √[(-1)² + (2)² + (-3)²]

         = √[1 + 4 + 9]

         = √14

Therefore, the distance between the skew lines is √14 units.

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Answer:

40

Step-by-step explanation: