A number is chosen uniformly at random from among the positive integers less than $10^8$. Given that the sum of the digits of the number is 9, what is the probability that the number is prime

The parabola has an axis of symmetry at x= -1.

Step-by-step explanation:

Answer:

7.5

Step-by-step explanation:simply divide 30 and 4 and the answer is 7.5

Answer:

7) 9.135x10^10

8) 3.428x10^-2

9) 2.5x10^-7

10) 4x10^10

Step-by-step explanation:

You’re only supposed to have one number to the left of the decimal point in scientific notation.

7) 9.135x10^10

8) 3.428x10^-2

9) 2.5x10^-7

10) 4x10^10

Answer:

210/3+3/3

Step-by-step explanation:

210/3=70+3=73/3=71
213/3=71

The value of the definite integral is 68/15.

An area or an extended version of an area can be represented mathematically by an integral in calculus.

Let's start by making a substitution. Let u = x - 17, which means du/dx = 1 and dx = du. The integral can then be written as like this as well:

\(\int\limits {\sqrt{x-17} } \, dx\) with limit from 17 to 18.

=  \(\int\limits^1_0 {(u+17)\sqrt{u} } \, du\)  

using the substitution x = u + 17 and the new limits of integration

=  \(\int\limits^1_0 {u^{\frac{3}{2} } }+17u^{\frac{1}{2} } \, du\)

= \([\frac{2}{5}u^{\frac{5}{2} }+\frac{34}{3}u^{\frac{3}{2} } ]^{0} _{1}\)

= (2/5 + 34/3) - 0

= 68/15

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Answer:

119 is the value of x when y = 7

Step-by-step explanation:

Since y varies inversely with x, we can use the following equation to model this:

y = k/x, where

Step 1:  Find k by plugging in values:

Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality.  We can find k by plugging in 49 for y and 17 for x:

Plugging in the values in the inverse variation equation gives us:

49 = k/17

Solve for k by multiplying both sides by 17:

(49 = k / 17) * 17

833 = k

Thus, the constant of proportionality (k) is 833.

Step 2:  Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:

Plugging in the values in the inverse variation gives us:

7 = 833/x

Multiplying both sides by x gives us:

(7 = 833/x) * x

7x = 833

Dividing both sides by 7 gives us:

(7x = 833) / 7

x = 119

Thus, 119 is the value of x when y = 7.

The value of expression \((21.28)^{2}\) is \(452.83\)

Here we have to find the equivalent expression of  \((21.28)^{2}\).

What is equivalent expression?

Equivalent expression are expressions that work the same even though they look different.

Now, the value of given expression is;

⇒\((21.28)^{2} = 452.83\)

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The three conditions for a function to be continuous at a point x=a are:

a) The function is defined at x=a.

b) The limit of the function as x approaches a exists.

c) The limit of the function as x approaches a is equal to the value of the function at x=a.

The continuity of a function can be analyzed by observing its graph. However, as the graph is not provided, a specific discussion about its continuity cannot be made without further information. It is necessary to examine the behavior of the function around the point in question and determine if the three conditions for continuity are satisfied.

The function f(x) = { *** is not defined in the question. In order to discuss its continuity, the function needs to be provided or described. Without the specific form of the function, it is impossible to analyze its continuity. Different functions can exhibit different behaviors with respect to continuity, so additional information is required to determine whether or not the function is continuous at a particular point or interval.

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Based on the given values, we can compute the expected returns and expected standard deviations for different weightings of the stocks in the portfolio. The results are as follows:

a. When w1 = 1.00, the expected return of the two-stock portfolio is 0.13, and the expected standard deviation is 0.03.

b. When w1 = 0.65, the expected return of the two-stock portfolio is 0.1095, and the expected standard deviation is 0.0214.

c. When w1 = 0.60, the expected return of the two-stock portfolio is 0.104, and the expected standard deviation is 0.0222.

d. When w1 = 0.30, the expected return of the two-stock portfolio is 0.074, and the expected standard deviation is 0.0262.

e. When w1 = 0.10, the expected return of the two-stock portfolio is 0.038, and the expected standard deviation is 0.0324.

To calculate the expected return of the two-stock portfolio, we use the weighted average of the individual expected returns based on the given weights. For example, in part (a), where w1 = 1.00, the expected return is simply equal to E(R1) = 0.13.

To calculate the expected standard deviation of the two-stock portfolio, we use the formula:

σ = √(w1^2 * E(a1)^2 + w2^2 * E(q2)^2 + 2 * w1 * w2 * E(a1) * E(q2) * ρ)

where E(a1) is the expected standard deviation of stock 1, E(q2) is the expected standard deviation of stock 2, and ρ is the correlation coefficient.

Regarding the risk-return graph, without the specific details of the graph options provided, it is not possible to determine which graph is correct for the given weightings and correlation coefficient. The graph would typically depict the risk-return tradeoff for different weightings and correlation coefficients, showing the relationship between expected return and expected standard deviation of the portfolio.

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Answer:

36

Step-by-step explanation:

Unit price: 9 / 5 = 1.8

20 box price: 1.8 * 20 = 36

Answer: no its not a function  

Step-by-step explanation: i searched it up and all of them said no, hopr thid helps :)

A triangle is a three-edged polygon with three vertices. Only the law of Sine can be applied to solve the triangle.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

The sum of all three angles can be written as,

118° + 22° + x = 180°

x = 40°

For the sine rule to be applicable, two angles and a side or an angle and two sides are needed. Therefore, the law of Sine can be applied to solve the triangle.

For the cosine rule to be applicable, two sides and an angle between them is needed to be known, hence, the law of cosine can not be applied.

Hence, Only the law of Sine can be applied to solve the triangle.

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The percentage of people who were in favor of both propositions is 34%.

Given that 65% of the group were in favor of proposition A. Therefore, 35% of the group were not in favor of proposition A. Also, 72% of the group were in favor of proposition B. However, since we need a percentage value that represents only the people who favor either proposition A or proposition B, we subtract the percentage of people who do not favor either proposition from 100%.100% - 3% = 97%Therefore, the total percentage of people who favor either proposition A or B is 97%.Thus, the percentage of people who were in favor of both propositions is:

x = 97% - 65% - 72%x = 34%

Therefore, 34% of the total group were in favor of both propositions.

Let the total group be "x". We know that 65% of the group were in favor of proposition A. So the number of people in the group in favor of proposition A = (65/100) × x = (13/20) × x And, 72% of the group were in favor of proposition B. Therefore, the number of people in the group in favor of proposition B = (72/100) × x = (18/25) × x Let "y" be the number of people who were in favor of both propositions. Therefore, the number of people who were not in favor of either proposition = (3/100) × x The total number of people who favor proposition A, proposition B, and neither is given as:

(13/20) × x + (18/25) × x + (3/100) × x

= 140%

Therefore, (65/100) × x + (72/100) × x + (3/100) × x

= 140%[(65 + 72 + 3)/100] x

= 140%[140/100] x

= 140% × 100x = (140/140) × 100x

= 100 Thus, the total number of people in the group is 100.Now, we need to find the percentage of people who favor both proposition A and proposition B. Let "z" be the percentage of people who were in favor of both propositions. Hence, the percentage of people who are not in favor of either proposition will be (100 - z - 65 - 72)% = (3%) = (3/100) × 100% = 3%

Thus, (100 - z - 65 - 72)%

= 3%100 - z - 137% = 3%100 - 137% + 3% = zz

= 34%Therefore, 34% of the total group were in favor of both propositions.

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Answer:

A

Step-by-step explanation:

In this question, we are concerned with selecting which of the options best represents the difference of two squares.

Let’s have an exposition below as follows;

Consider two numbers, which are perfect squares and can be expressed as a square of their square roots;

a^2 and b^2

where a and b represents the square roots of the numbers respectively.

Inserting a difference between the two, we have;

a^2 - b^2

Now by applying the difference of two squares, these numbers will become;

a^2 - b^2 = (a + b)(a-b)

So our answer out of the options will be that option that could be expressed as above.

The correct answer to this is option A

Kindly note that;

x^2 -9 can be expressed as x^2 - 3^2 and consequently, this can be written as;

(x-3)(x + 3)

Answer:

i think 20 hours i believe is it

Answer:

20 hours

Step-by-step explanation:

The total expense for producing 2 widgets is $18,006.00.

To find the total expense for producing 2 widgets, we need to find the total revenue from selling 2 widgets and then subtract the total expense of producing them.

The total revenue from selling 2 widgets is simply the price per widget times the quantity demanded at that price. Since the price is not specified in the problem, we can use the demand function to find it.

We know that the quantity demanded when 2 widgets are produced is:

q = 2

So we can solve the demand function for p:

q = -112p + 4,500

2 = -112p + 4,500

-112p = -4,498

p ≈ 40.16

Therefore, the price per widget is approximately $40.16.

The total revenue from selling 2 widgets at this price is:

revenue = price × quantity demanded

revenue = $40.16 × 2

revenue = $80.32

Now we need to find the total expense of producing 2 widgets. The problem gives us an expression for the total expense:

E = 3.00q + 18,000

Substituting q = 2, we get:

E = 3.00(2) + 18,000

E = $18,006.00

Therefore, the total expense for producing 2 widgets is $18,006.00.

Finally, we can calculate the profit as the difference between the revenue and the expense:

profit = revenue - expense

profit = $80.32 - $18,006.00

profit ≈ -$17,925.68

Since the profit is negative, Willie's Widgets would not make any profit from producing 2 widgets at this price. They would lose money.

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Answer: $657.53

Step-by-step explanation:

Circumference of a circle = πd

But in this case, it's a semi circle, so the circumference will be:

= πd/2

= (3.142 × 31) / 2

= 97.402/2

= 48.701

Then, the total amount of the fencing will be:

= 48.701 + 31

= 79.701

Then, the fencing cost will be:

= 79.701 × $8.25

= $657.53

this should help

the formula is x = -b/2a

The given statements are correct or incorrect is given below:

1) Correct.

2) Correct.

3) Correct.

4) Correct.

5) Correct.

6) Incorrect.

7) Correct.

8) Correct.

9) Correct.

10) Incorrect.

Here, we have,

1) Correct. In a simple graphical method, a graph is plotted to show the relationship between water usage and population.

2) Correct. The pressure in a distribution system needs to be sufficient to allow for adequate hydrant flows in case of a fire.

3) Correct. The term "distribution system" refers to the infrastructure and facilities used to supply water from its source to the point of usage.

4) Correct. Brackish water is water that has a higher salinity level than fresh water and even higher than seawater.

5) Correct. Monthly variation in water usage can impact the design and capacity requirements of storage reservoirs.

6) Incorrect. Jordan is considered a "Water Scarce" country, as it faces significant challenges in terms of water availability and scarcity.

7) Correct. During a fire, a significant quantity of water needs to be supplied over an extended period, necessitating a high rate of hourly supply.

8) Correct. The Manning equation is commonly used in the design and evaluation of sanitary sewers.

9) Correct. If the diameter (d) is less than 200 mm, the pipe's final diameter (D) is set at 200 mm.

10) Incorrect. The diameter of the interceptor pipe is typically larger than the diameter of the lateral pipe. The interceptor pipe carries wastewater from multiple lateral pipes.

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a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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Most data is likely to be skewed following a particular trait because when considering real life data, it is likely that it may concentrate on one end of the values on the real line as there is high uncertainty that exists with real life.

There is very little confidence that the population would behave in expected ways.

The skewed distribution implies the distribution that is not symmetrical. If a distribution is skewed it can be skewed to the left i.e. mean lies to the left of the center or skewed to the right i.e. mean lies to the right of the center of the distribution.

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The equation that represents the line that is perpendicular is

3y + 5x = -42

The standard equation of a line in point-slope form is expressed as:

\(y-y_1=m(x-x_1)\)

Substitute the point (-12, 6) and the slope m = -5/3 into the equation above to have:

\(y-6=-5/3(x-(-12))\\3(y-6)=-5(x+12)\\3y-18=-5x-60\\3y = -5x - 60 + 18\\3y + 5x = -42\\\)

Hence the equation that represents the line that is perpendicular is

3y + 5x = -42

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The opportunity cost of spending $90,000 on advertising but only producing 12,000 units can be calculated by comparing the benefits of the advertising investment to the potential alternative uses of that money.

First, let's calculate the total cost of producing 12,000 units. Fixed costs amount to $48,000, and variable costs are $8 per unit, resulting in a total cost of $48,000 + ($8 × 12,000) = $144,000.

Next, we need to calculate the potential sales revenue without advertising. With a price of $16 per unit, the potential sales revenue would be $16 × 12,000 = $192,000.

Now, let's calculate the potential sales revenue after advertising. The advertising multiplier is given as (30,000 + advertising) / 30,000. In this case, the multiplier would be (30,000 + 90,000) / 30,000 = 4.

Therefore, the potential sales revenue after advertising would be $192,000 × 4 = $768,000.

The opportunity cost is the difference between the potential sales revenue after advertising ($768,000) and the potential sales revenue without advertising ($192,000), which is $768,000 - $192,000 = $576,000.

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Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

The shortest length of fence that the rancher can use is 6000 ft.

What is meant by length?

The measuring of one thing from finish to finish or on its longest aspect, or a measuring of a selected a part of one thing is known as length.

Main Body:

x = width of rectangle

y = length of rectangle

A = area of rectangle = xy = 1500000 ft^2

L = length of fencing needed = 2(x + y) + x = 3x + 2y

L = 3x + 2(1500000/x) = 3x + 3(10^6)x^(-1)

As x –> 0+, L –> +inf.

As x –> +inf, L –> (3x)+.

Sketch and see that there will be a minimum in Quadrant I.

dL/dx = 3 - 3(10^6)x^(-2)

Extrema occur when dL/dx = 0:

3 - 3(10^6)x^(-2) = 0

(10^6)x^(-2) = 1

x^2 = 10^6

x > 0, so x = 1000 feet for shortest length.

Hence,Shortest L = 3000 + 3(10^6)(10^3)^(-1) = 6000 feet.

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Answer:

20

Step-by-step explanation:

(72-60):60*100 =

(72:60-1)*100 =

120-100 = 20

Hope this helps :)

The three examples of exercises that develop cardiovascular endurance are hiking, cycling and running.

Exercises require constant supply of energy obtained through glucose metabolism. It is provided through combined efforts of cardiovascular system and respiratory system. So during strenuous exercises, cardiovascular endurance refers to the ability of body to respond well during these exercises.

The aerobic exercises help develop cardiovascular endurance. They can be medium to high intensity exercises. The examples are swimming, dancing and running.

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