The sum of the positive divisors of a positive integer of the form $2^i3^j$ is equal to $600$. What is $i j$

A) The polynomial is:

f(x) = x^3 - 5*x^2 + 7x - 3

B) There are no breaks in the domain of the piecewise function.

We know that f(x) is a polynomial function with the zeros:

Then we can write the polynomial f(x) as:

f(x) = a*(x - 3)*(x - 1)*(x - 1)

Where a is the leading coefficient of the polynomial, which is not given in the problem.

Expanding that, we get:

f(x) = a*x^3 - a*5*x^2 + a*7x - a*3

That is the polynomial in the expanded form, where if we take a = 1, we get:

f(x) = x^3 - 5*x^2 + 7x - 3

B) h(x) is a piecewise function, such that the two domains are:

h(x) = f(x)     if x < 0

h(x) = g(x)    if x ≥ 0

Where g(x) = ∛(x - 4)

First, bot functions (polynomial and the cubic root) have the set of all real numbers as their domain, so the domain of the piecewise function is the set of all real numbers.

clearly, we can see that:

f(0) = -3

g(0) =  ∛(- 4)

So we will only have a jump at x = 0, but there are no breaks.

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Answer:

x = -22/3, y = -17/2

Step-by-step explanation:

Here the parameters, p =0.489 and n=15, and the probability of winning more than 8 times is  0.17946

while you playing an arcade game, there are two possible outcomes: win or lose, which is related to the binomial distribution, such as :

P= \(C_{n,k}\) \(p^{n}\) \(q^{n-k}\)

where C is the  combination, p is the probability of success and the q is the complement of the p (q=1-p) .Here we are given that the probability of winning an arcade game is 0.489 and  the probability of losing is 0.511.  So p=  0.489, since the number of the trial are 15, we need to  find the probability for more  than 8 times, which means

P(X>8)= P(X=9)+P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)              P(X>8)=P(X>=8)- P(X=8)  

           = 0.34328- 0.16382  

            =0.17946

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Answer:

The independent variable is the variable that is manipulated or changed during an experiment. In this case, the independent variable is represented by the x-values of the given points.

So, the answer would be option A: {-2, 3, 1, 5}

Step-by-step explanation:

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Answer:

The coordinates of the point is (3,5 , 400)

Step-by-step explanation:

The question is incomplete as the graph is not given in the question. Lets complete the question first. I have attached the graph related to this question below.

We can see in the graph that x-axis represents the years while the y-axis represents the pennies collected by Harry.

We have to find the coordinates of the point where he is able to collect 400 pennies.

As y-axis represents pennies, and the point to be found is at 400 pennies, so the y-coordinates of the point is 400.

Harry collects 400 pennies when he is halfway through 4rth year, which means that he has been collecting for:

3 years + Half of 4rth year = 3.5 years.

As x-axis represents the year and the point to be found is at 3.5 years, so the x-coordinate of the point is 3.5.

So, the coordinates of the point is (3,5 , 400)

This point can be seen in the second graph

Answer:

7

Step-by-step explanation:

Answer:

7-8

Step-by-step explanation:

with this is basd

The equation of the other line of the triangle is x + 2y - 18 = 0.

A right triangle is formed by the y-axis, the line y = 2x + 4 and another line. If the legs of the right triangle intersect at (2, 8), then the point of intersection of the legs of the right triangle is (2, 8) which is also the vertex of the right triangle.

Let the equation of the other line be y = mx + c. The slope of the line passing through the point (2, 8) and the point of intersection of line y = 2x + 4 with x-axis is -1/2.

Slope of line y = 2x + 4 is 2. Therefore, the slope of the line perpendicular to y = 2x + 4 and passing through the point (2, 8) is (-1/2). Thus, the equation of the line is y - 8 = (-1/2)(x - 2) which simplifies to 2y - 16 = - (x - 2) and further simplifies to x + 2y - 18 = 0.

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Factored form of an expression is writing it in the terms of multiplication of factors. The factors of given expression are: (3x-1) and (x-4)

If the given quadratic expression is of the form \(ax^2 + bx + c\),

then its factored form is given by \((x - \alpha)(x-\beta)\)

such that

\(b =\alpha+\beta\\ac = \alpha \times \beta\)

For the given case, the expression is \(3x^2 + 11x - 4\)

If we take

\(\alpha = 12\\\beta = -1\), then we get 12-1 = 11, and 12 times -1 = -12 = -4 times 3

Thus,

\(3x^2 + 11x - 4 = 3x^2 + 12x - x - 4 = 3x(x-4) + 1(x-4) = (3x-1)(x-4)\\3x^2 + 11x - 4 = (3x-1)(x-4)\)

(these factors represent the side length of the region whose area is modeled by the considered expression since area of rectangle is product of its length and width (assuming region was rectangle) ).

Thus, The factors of given expression are: (3x-1) and (x-4)

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Answer:

my best advice: look at the y-intercepts!

Step-by-step explanation:

when the equations are set out like this, the last number (in this case "+4" and "-2"), represents where they cross the y axis. this gives you a great place to start.

if you plot (0, 4) for the first equation, you can then move right one square and down one square to get the next point in the equation.

the next one starts with (0, -2) and goes right one square and up two

let's pick a number, hmmm say number "a", and let's increase it twice by 5%.

\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of a}}{\left( \cfrac{5}{100} \right)a}\implies 0.05a~\hfill \stackrel{a+0.05a}{1.05a}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of 1.05a}}{\left( \cfrac{5}{100} \right)1.05a}\implies 0.0525a~\hfill \stackrel{1.05a+0.0525a}{1.1025a} \\\\[-0.35em] ~\dotfill\\\\ 1.1025a~~ - ~~a~~ = ~~\stackrel{difference}{0.1025}\qquad \qquad \stackrel{\textit{converting to \%}}{0.1025\cdot 100}\implies \stackrel{\%}{10.25}\)

To find the surface area of the figure, we need to consider the individual surfaces and add them together.

First, let's identify the surfaces of the figure:

The lateral surface area of the larger prism (excluding the base)

The two bases of the larger prism

The lateral surface area of the smaller prism (excluding the base)

The two bases of the smaller prism

The lateral surface area of a prism is given by the formula: perimeter of the base multiplied by the height.

The bases of the prisms are rectangles, so their areas can be calculated by multiplying the length by the width.

To find the missing prism's surface area, we need to consider that it is a smaller prism nested inside the larger prism. The lateral surface area and bases of the missing prism should also be included.

Once we have calculated the individual surface areas, we add them together to find the total surface area of the figure.

Without specific measurements or dimensions of the figure, it is not possible to provide a numerical answer. Please provide the necessary measurements or dimensions to calculate the surface area.

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Answer:

0.5

Step-by-step explanation:

Note that sides AD and BE are perpendicular on the same side AC. So the angles CAD and CBE, both are equal to 90 degrees.

Beig the corresponding angles, ADC and BEC are also equal.

And the angle ACD is the common angle in both the triangles.

Therefore by the AAA criteria, the triangles CAD and CBE are similar.

So their corresponding sides must be proportional,

Answer:

m = -3/4

Step-by-step explanation:

Take any two points on a line to find the slope. Here they give you the points

(0, 5) and (4, 2).

Put these points into the slope formula.

y₂ - y₁/x₂ - x₁

2 - 5/4 - 0

-3/4

The slope of this line is -3/4.

Answer: 4 pieces? If you multiple 5 by .25 (1/4 as a decimal) you get the answer 1.25. The answer 1.25 times 4 is equal to 4.

Minimization of  f(x) = |x+3| + x^3 at the endpoints (-2 and 6)  the minimum value of the function is approximately 3.84, which occurs at x= \sqrt{1/3}

within the given interval.

To minimize the function subject to the constraint f(x) = |x+3| + x^3 that x lies in the interval [-2, 6], we need to find the value of x that minimizes f(x) within that interval.

First, let's analyze the function f(x). The absolute value term |x+3| can be rewritten as:

|x+3| =

x+3 if x+3 >= 0

-(x+3) if x+3 < 0

Since the interval [-2, 6] includes both positive and negative values of x+3, we need to consider both cases.

Case 1: x+3 >= 0

In this case, f(x) = (x+3) + x^3 = 2x + x^3 + 3

Case 2: x+3 < 0

In this case, f(x) = -(x+3) + x^3 = -2x + x^3 - 3

Now, we can find the minimum of f(x) within the given interval by evaluating the function at the endpoints (-2 and 6) and at any critical points within the interval.

Calculating the values of f(x) at x = -2, 6, and the critical points, we can determine the minimum value of f(x) and the corresponding value of x.

Since the equation involves both absolute value and a cubic term, it is not possible to find a closed-form solution or an exact minimum value without numerical methods or approximation techniques.

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The first quartile is always equal to one of the values in the sample when the sample size is a multiple of 4.

This is because the first quartile is the median of the lower half of the data set, and when the sample size is a multiple of 4, there is anThe first quartile is always equal to one of the  valuesin the sample when the sample size is a multiple of 4. This is because the first quartile is the median of the lower half of the data set, and when the sample size is a multiple of 4, there is an even number of values in the lower half of the data set. Therefore, the first quartile will be one of the values in the sample. For example, if the sample size is 8, the first quartile will be the median of the first 4 values, which will be one of the values in the sample.

In summary, the first quartile is always equal to one of the values in the sample when the sample size is a multiple of 4. of values in the lower half of the data set. Therefore, the first quartile will be one of the values in the sample. For example, if the sample size is 8, the first quartile will be the median of the first 4 values, which will be one of the values in the sample.
In summary, the first quartile is always equal to one of the values in the sample when the sample size is a multiple of 4.

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In this code, we initialize a variable `count` to keep track of the number of blank spaces. Then, we iterate through each character in the string using a `for` loop. Inside the loop, we check if the current character `char` is equal to a blank space, which is represented by `" "` in Python. If it is, we increment the `count` by 1.

To determine the number of blank spaces in a string called "wow," you need to iterate through each character in the string and count the occurrences of blank spaces.

Here's an example of how you can do this in Python:

```python

string = "wow"

count = 0

for char in string:

   if char == " ":

       count += 1

print("Number of blank spaces:", count)

```

In this code, we initialize a variable `count` to keep track of the number of blank spaces. Then, we iterate through each character in the string using a `for` loop. Inside the loop, we check if the current character `char` is equal to a blank space, which is represented by `" "` in Python. If it is, we increment the `count` by 1.

Finally, we print the value of `count`, which represents the number of blank spaces in the string "wow".

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Answer:

Step-by-step explanation:

Population growth or decay exponential function is represented by the following equation:

Therefore, for the function for the population:

Yes it is correct that the expected value of a random variable can be interpreted as a long-run average.

The expected value of a random variable is a concept used in probability theory and statistics. It is a way to summarize the average behavior or central tendency of the random variable.

To understand why the expected value represents the average value that the random variable would take in the long run, consider a simple example. Let's say we have a fair six-sided die, and we want to find the expected value of the outcomes when rolling the die.

The possible outcomes when rolling the die are numbers from 1 to 6, each with a probability of 1/6. The expected value is calculated by multiplying each outcome by its corresponding probability and summing them up.

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Answer:

length is 12 feet and the width is 6 feet

Step-by-step explanation:

w=width  l=length

l=2w

2l+2w=36ft

4w+2w=36ft

6w=36ft

w=6ft

l=2*6=12ft

Answer:

114. There is something wrong with the options im 100% sure its 114 talk to your teacher.

The solution is just to substitute

Answer:

Unit rate per fluid ounce = $0.15

Step-by-step explanation:

Given that:

Cost of one quart bottle of juice = $4.80

We know that:

One quart = 32 ounces

Unit rate is the rate in which two quantities are compared and one of them is one.

Unit rate = \(\frac{4.80}{32}\)

Unit rate = $0.15 per fluid ounce

Hence,

Unit rate per fluid ounce = $0.15

In order to convert from rectangular to polar, we can use the following relations:

So, using these values of x and y in the given equation, we have:

Answer:

3 minutes to 10 minutes

Step-by-step explanation:

15 : 50. Both can be divided by 5

3 : 10

Answer:

B) 7.8 and 7.9

Step-by-step explanation:

Taking the square root of 61, we can conclude that the decimal form is 7.810, which falls between the range of 7.8 and 7.9

Answer:

√61 lie between 7.8 and 7.9