Your friend claims that when a polynomial function has a leading coeffcient of 1 and the coefficients are all integers , every possible rational zero is an integer . Is your friend correct ? Explain your reasoning.

The portfolio's return can be calculated by multiplying the weights of each investment by their respective returns and summing them up. However, without information on the weights of the investments, the portfolio's return cannot be determined accurately.

To calculate the portfolio's return, we need to know the weights of each investment, which represent the proportion of the total portfolio value allocated to each asset. Without this information, we cannot determine the exact portfolio return.

However, if we assume equal weights for simplicity, the average return of the portfolio can be estimated. In this case, the portfolio consists of $1,000 invested in Disney with a 15% return and $5,000 invested in Oracle with an 18% return.

Using equal weights, the estimated portfolio return can be calculated as follows:

Portfolio return = (Weight of Disney × Return of Disney) + (Weight of Oracle × Return of Oracle)

Assuming equal weights, the portfolio return would be:

(0.5 × 15%) + (0.5 × 18%) = 7.5% + 9% = 16.5%

Therefore, with equal weights, the estimated portfolio return would be 16.5%. However, please note that without accurate information on the weights of the investments, the exact portfolio return cannot be determined.

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Step 1

Given;

Step 2

Find f(7)

Find g(-2)

Answers;

We will improve the argument by stating that two intersecting lines have vertically opposite angles equal in magnitude.

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Answer:

Step-by-step explanation:

log3 (4) = 1.262

log3 (-2) = -0.6309

The revenue earned per minute of the movie is approximately $8.9 x 10^7.

To calculate the revenue earned per minute of the movie, we need to divide the total revenue by the duration of the movie in minutes.

Revenue earned per minute = Total revenue / Duration of the movie

Total revenue = $81.1 x 10^9

Duration of the movie = 9.1 x 10^1 minutes

Revenue earned per minute = ($81.1 x 10^9) / (9.1 x 10^1)

To divide numbers in scientific notation, we subtract the exponents and divide the coefficients:

Revenue earned per minute = $81.1 x 10^(9-1) / 9.1

Simplifying the exponent:

Revenue earned per minute = $81.1 x 10^8 / 9.1

Dividing the coefficients:

Revenue earned per minute ≈ $8.9 x 10^7

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Answer:

350+150m=total money

11 months

Step-by-step explanation:

you just put in the number of months that have passed in for m and solve for total money.

After how many months will Paul have $2,000?

350+150m=2000

350-350+150m=2000-350

150m=1650

150m/150=1650/150

m=11

Answer:

20l 10w or it could be the other way around

The greatest area of water she can enclose is 2500 m².

A rectangle is a 2-dimensional quadrilateral with four right angles.

Perimeter of a rectangle = 2 x (length + width)

Area of a rectangle = length x width

In order to determine the greatest area of water the lifeguard can enclose, we have t determine the sum of the dimensions.

200m = 2( l + b)

l + b = 200m / 2

l + b = 100m

The second step is to determine the pair of dimensions that add up to 100.

90 x 10 = 900

80 x 20 = 1600

70 x 30 = 2100

60 x 40 = 2400

50 x 50  = 2500

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The χ2 values for interval estimation for a sample size of 12 at 95% confidence level are approximately 21.920 and 2.179.

For the χ2 values for interval estimation at a 95% confidence level for a sample size of 12, we need to determine the critical values associated with the chi-square distribution.

The chi-square distribution is determined by two parameters: the degrees of freedom (df) and the confidence level.

For interval estimation, the degrees of freedom are equal to the sample size minus 1, which in this case is 12 - 1 = 11.

To find the critical values, we need to identify the chi-square values that leave a total probability of 0.05 (5%) in the tails of the distribution.

Since we are interested in a two-tailed interval estimation, we need to divide this probability equally between the two tails, resulting in 0.025 (2.5%) in each tail.

Using statistical tables or software, we can find the chi-square value associated with a 2.5% probability in the upper tail of the distribution with 11 degrees of freedom.

Similarly, we can find the chi-square value associated with a 2.5% probability in the lower tail.

For a sample size of 12 and a 95% confidence level, the critical chi-square values would be approximately:

Upper tail (2.5%): χ2 = 21.920

Lower tail (2.5%): χ2 = 2.179

Therefore, the χ2 values for interval estimation at a 95% confidence level with a sample size of 12 are approximately 21.920 and 2.179.

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Answer:

Step-by-step explanation:

Hello : let  A(3,-8)    B(-1,-2)

the slope is :   (YB - YA)/(XB -XA)

(-2+8)/(-1-3)  = 6/-4 =-3/2

The quotient obtained from the division of given fractions is 23/18.

Given that, \(4\frac{5}{16}\) divided by \(3\frac{3}{8}\).

Dividing fractions is nothing but multiplying the fractions by reversing one of the two fraction numbers or by writing the reciprocal of one of the fractions. By reciprocal we mean, that if a fraction is given as a/b, then the reciprocal of it will b/a.

Here, 69/16 ÷ 27/8

= 69/16 × 8/27

= 23/2 × 1/9

= 23/18

Therefore, the quotient obtained from the division of given fractions is 23/18.

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The probability that a randomly selected resident is in favor of the dog park is 7/18.

Probability is used to calculate the chances that an event would happen. The probability the event occurs with certainty is 1 and the probability that the event does not occur with certainty is 0.

The probability that a randomly selected resident is in favor of the dog park = number of students in favor of the dog park / total number of residents

35/ 90

Express the fraction in its simplest form by dividing the numerator and the denominator by 5

= 7 / 18

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The F-distribution is used to test the significance of the population coefficient of determination (option D).

The coefficient of determination, denoted as R², measures the proportion of the variance in the dependent variable that is explained by the independent variables in a regression model. It ranges from 0 to 1, where 0 indicates no relationship and 1 indicates a perfect relationship.

To determine the significance of R², the F-distribution is used. The F-test compares the variation explained by the regression model (numerator) to the unexplained or residual variation (denominator). It calculates the F-statistic, which is the ratio of the two variances.

The F-distribution provides critical values that allow us to determine whether the observed F-statistic is statistically significant or not. By comparing the calculated F-value with the critical value from the F-distribution, we can assess whether the coefficient of determination is significantly different from zero, indicating the presence of a meaningful relationship between the variables. The correct option is d.

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Answer:

in explanation

Step-by-step explanation:

Input to output so for the input when it is 1=6 because it starts at 5 and then 8 what I mean is when the input comes out the output is going to be 3 more greater than last time.

So 1=6 so 6 is 5 more then

2 to 10=8 so 5 more went to 8 more.

Next is 3 and 14 so 3 more again because 8 + 3=11 so in that case that next number is 4 it will be 14 more

So 14 more than 4=18 and that is the output.

Also for the output it adds 4 for the numbers 6 + 4=10 + 4=14+ another 4=18.

And input is just plus 1.

Hope it helps have a great day:)

The substitution effect, denoted by ε*, measures the change in quantity demanded of q1 due to the relative price change, while the income effect, denoted by θξ, measures the change in quantity demanded of q1 due to the change in purchasing power. The total effect, denoted by ε, combines both the substitution and income effects.

To calculate the substitution effect, we need to evaluate the price elasticity of demand for q1, which measures the responsiveness of quantity demanded to a change in price. The income effect depends on the income elasticity of demand, which measures the responsiveness of quantity demanded to a change in income. These elasticities can be calculated using the given utility function, but specific price and income data are required.

Without the actual price and income data, it is not possible to provide the exact numerical values for the substitution, income, and total effects. The effects can only be determined with the necessary information and by performing the appropriate calculations using the utility function. The values of ε*, θξ, and ε will depend on the specific price and income changes that are considered.

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Answer: 28.1

Step-by-step explanation:

First, we have that the problem can be seeing as follows:Now, knowing this and the the properties of the diagonals we will have that [We use the law of cosines}:First diagonal [AC} is given by:So, one of the diagonals has an approximate length of 10.7 ft.Second diagonal [BD] is given by:So, the second diagonal has a length of approximately 28.1 ft.**Diagonals**

sorry if I’m wrong

Answer:

11x + 4y - y^2

Step-by-step explanation:

You plus the same variables, in this time you got 9x and 2x so it's 11x!

Answer:

11x + 4y - y²

Step-by-step explanation:

9x + 4y + 2x - y²

combine like terms

11x + 4y - y²

Answer:

(100)^0=1

Step-by-step explanation:

This follows the laws of indices

The investment problem is modeled by an initial value problem (IVP) where the rate of change of the investment is determined by the initial investment, monthly deposits, and the interest rate.

a) The investment problem can be modeled by an initial value problem where the rate of change of the investment, y(t), is given by the initial investment, monthly deposits, and the interest rate. The IVP can be written as:

dy/dt = 0.09y + 200, y(0) = 500.

b) To solve the IVP, we can use an integrating factor to rewrite the equation in the form dy/dt + P(t)y = Q(t), where P(t) = 0.09 and Q(t) = 200. Solving this linear first-order differential equation, we obtain the solution for y(t).

c) To find the value of the investment after 2 years, we substitute t = 2 into the obtained solution for y(t) and calculate the corresponding value.

d) After 2 years, the monthly deposit increases to $300. To find the value of the investment a year later, we substitute t = 3 into the solution and calculate the value accordingly.

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Answer:

83 percent is the answer

Answer:

8 km

Step-by-step explanation:

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

40 / 5 = 8km

Answer:

Base = 10 cm

Height = 6 cm

Step-by-step explanation:

Here is the formula for the area of a triangle.

 \(A=\frac{bh}{2}\)

We are given

\(A=30\)

\(b=h+4\)

Replace all occurrences of \(b\) with \(h+4\) in each equation.

\((h+4)*\frac{h}{2} =30\)

Apply the distributive property.

\(h(\frac{h}{2})+4(\frac{h}{2})=30\)

\(\frac{h*h}{2}+4(\frac{h}{2})=30\)

Use the power rule to combine exponents.

\(\frac{h^2}{2}+4(\frac{h}{2})=30\)

Factor 2 out of 4 .

\(\frac{h^2}{2}+2(2)(\frac{h}{2})=30\)

Cancel the common factor.

\(\frac{h^2}{2}+2h=30\)

Solve for h.

Multiply each term in  \(\frac{h^2}{2}+2h=30\)  by 2 to eliminate the fractions.

\(\frac{h^2}{2}*2+2h*2=30*2\)

Simplify each term.

Cancel the common factor of 2.

\(h^2+2h*2=30*2\)

\(h^2+4h=60\)

Subtract 60 from both sides of the equation.

\(h^2+4h-60=0\)

Factor using the AC method.

Consider the form \(x^2+bx+c\) . Find a pair of integers whose product is \(c\) and whose sum is \(b\) . In this case, whose product is − 60 and whose sum is 4 .

−6, 10

Write the factored form using these integers.

\((h-6)(h+10)=0\)

Set \(h-6\) equal to 0 and solve for h.

Then add 6 to both sides of the equation.

\(h-6=0\\h=6\)

Set \(h+10\) equal to 0 and solve for h.

Then subtract 10 from both sides of the equation.

\(h+10=0\\h=-10\)

The final solution is all the values that make \((h-6)(h+10)=0\) true.

\(h=6,-10\)

Given \(b=h+4\)

Replace all occurrences of h with 6 in each equation.

\(b=6+4\\b=10\\h=6\)

Answer:

s = 17units

Step-by-step explanation:

For this problem, we are trying to find a specific unknown side length.

We're actually given some extraneous information (information that is not needed to solve the problem):  It isn't necessary to know that BC is 5.

If the side AD with the unknown length is part of a right triangle (the triangle in red in the attached diagram), we can use the Pythagorean Theorem to solve for AD.

It isn't clear if the diagram you were provided gives ∠ABD as a right angle,  if it only gives ∠CBD as a right angle, or if it gives both as a right angle.  Below, we prove that it doesn't matter, because regardless, both must be right angles.

Is Triangle ABD a "right triangle"?

Since B is between A and C, then the two angles ∠ABD & ∠CBD form a linear pair, and by the linear pair postulate are supplementary.  Since they are supplementary, their measures add to 180°.  Using the fact that all right angles are 90°, substitution, the subtraction property of equality, arithmetic, the measure of ∠ABD is also 90°, and thus must be a right angle.  Thus, based on the given information, both ∠ABD & ∠CBD must be right angles.

Consequently, triangle ABD is a right triangle, by definition (it is a triangle that has a right angle).

Pythagorean Theorem

Since triangle ABD is a right triangle, the Pythagorean Theorem can be applied.

The Pythagorean Theorem states that \(a^{2} +b^{2} =c^{2}\) where "c" is the hypotenuse (the side across from the right angle) and "a" and "b" the the lengths of the two other sides (called legs) of the right triangle.  (Aside: Because of the commutative property of addition, it doesn't matter which of the two legs' lengths is used for a, and which is used for b.  The only thing that is required is that "c" be the length of the hypotenuse)

In our triangle, side AD, with unknown length "s" is the length of our hypotenuse, and sides AB and BD are the two legs.  Substituting values into the Pythagorean Theorem equation, we can solve for the unknown "s":

\(a^{2} +b^{2} =c^{2}\)

\((8)^{2} +(15)^{2} =(s)^{2}\)

\(64 +225 =s^{2}\)

\(289 =s^{2}\)

Applying the square root property...

\(\pm \sqrt{289} =\sqrt{s^{2}}\)

\(s=17 \text{ or } s=-17\)

Final Solution

We discard the negative solution we obtained, since s represents the length of the side of a triangle.

s = 17units

Answer:

17

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The postfix expression of "7+5-3*2(6*7)/4" is "7 5 + 3 2 * 6 7 * 2 * - 4 /". Evaluating the postfix expression gives the result of the expression. The prefix expression for the given infix expression is "/ - + 7 5 * 3 * 2 ( * 6 7 ) 4".

To convert the infix expression "7+5-3*2(6*7)/4" into postfix expression, we follow the rules of operator precedence and associativity. The postfix expression is obtained by placing operators after their operands.

The postfix expression for the given infix expression is:

"7 5 + 3 2 * 6 7 * 2 * - 4 /"

To evaluate the postfix expression, we use a stack data structure. We scan the postfix expression from left to right and perform the corresponding operations.

Starting with an empty stack, we encounter the operands "7" and "5". We push them onto the stack. Then we encounter the operator "+", so we pop the last two operands from the stack (5 and 7), perform the addition operation (7 + 5 = 12), and push the result back onto the stack.

We continue this process for the remaining operators and operands in the postfix expression. Finally, after evaluating the entire expression, the result left on the stack is the final answer.

To convert the infix expression into prefix expression, we follow similar rules but scan the expression from right to left. The prefix expression is obtained by placing operators before their operands.

The prefix expression for the given infix expression is:

"/ - + 7 5 * 3 * 2 ( * 6 7 ) 4"

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Using the vertical line test, the graph that represents a function is: Graph C.

A simple test we can carry out quickly to determine if a graph represents a function is the vertical line test.

Using the vertical line test, a vertical line is drawn across the curve in the given plane. If the vertical line intersect the curve more than once, it is not a function, but if it intersects the curve at just exactly one point, then the graph represents a function.

If we draw a vertical line across each of the given graphs, only the graph in option C will be intersected at exactly only one point.

Therefore, graph C represents a function.

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The chi-square distribution approaches symmetry as the number of degrees of freedom rises.

The distribution of the sum of the squares of k independent standard normal random variables continues to be the chi-squared distribution with k degrees of freedom.

A continuous, non-negative, positively skewed probability distribution is the chi-square distribution. Unlike the z and t scores used for quantitative variables, the Chi-square statistic can be used to compare the difference between the observed and expected frequencies of values of a categorical random variable.

The chi-square distribution changes from a descending slope to a hump form as the degrees of freedom (k) rise. The hump changes from being highly right-skewed to being roughly normal as the degrees of freedom rise.

As a result, the assertion is accurate.

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Answer:

The answer is 2.5

Step-by-step explanation:

Formula Used is is ½ x x+y

so it is ½ x 2 + 3

½ x 5 = 2.5

Answer:

2=2/1

3=3/1

multiplying both fractions by 10.

2*10/1*10

3*10/1*10

20/10 and 30/10

so nos are 21/10.......29/10

The value of the original number (represented by "x"), the final expression simplifies to 3. This demonstrates that the result is always 3 for this number trick.

Let's use algebraic expressions to illustrate the number trick.

Let's assume the original number is represented by the variable "x."

An amount that can fluctuate depending on the mathematical issue is referred to as a variable.

Subtract 7: x - 7

Multiply by 3: 3(x - 7) = 3x - 21

Add 30: 3x - 21 + 30 = 3x + 9

Divide by 3: (3x + 9) / 3 = x + 3

Subtract the original number: x + 3 - x = 3

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