Please upload a picture of your work or type it. Answer this using the image below

The proper plot that graphs the given three functions in the same figure is shown below:Given functions are(())=(),(())=12log10(+1)and(ℎ())=1

By using the plot function in MATLAB software, the proper plot that graphs the given three functions in the same figure is shown below:MATLAB Code:clear all; close all; clc; x = -20:0.1:20;

f = x;

g = 12*log10(x+1);

h = 1./x; plot(x,f,'-k','LineWidth',2); hold on; plot(x,g,'-r','

LineWidth',2); plot(x,h,'-b','

LineWidth',2); grid on; xlim([-20,20]); ylim([-50,50]); xlabel('Abscissa (x)'); ylabel('Ordinate (y)'); title('Graphing Functions');

legend('f(x)=x',

'g(x)=12log_{10}(x+1)',

'h(x)=1/x','

Location','northwest');The plot that graphs the given three functions in the same figure is shown below:

Therefore, the proper plot that graphs the given three functions in the same figure is shown above.

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Answer:

36

Step-by-step explanation:

Quadrilateral's angels always add up to 360. Thus, 2x+5x+6x+7x=360

20x=360 (divide both sides by 20)

x = 18

To find the smallest angle, plugin x into 2x.

2(18)=36

Answer:

In the problem, the sum of the two functions is 2x + 2

Step-by-step explanation:

For this problem, we have to add together f(x) and g(x).

f(x) = 9 - 3x

g(x) = 5x - 7

(f + g)(x) = (9 - 3x) + (5x - 7)

Combine like terms.

(f + g)(x) = 2x + 2

So, when you combine the two functions together, you will get 2x + 2.

The value of f(x)+g(x) according to the question given is; 2x + 2.

To evaluate the sum of functions f(x) and g(x); we have;

Therefore;

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To find the cumulative distribution function (CDF) of Z = X + Y, where X is uniformly distributed over (0,1) and Y is exponentially distributed with parameter lambda = 2, we can use the properties of independent random variables.

For 0 < a < 1, we have:

P(Z ≤ a) = P(X + Y ≤ a)

Since X and Y are independent, we can write this as:

P(Z ≤ a) = ∫∫ P(X ≤ x, Y ≤ a - x) dxdy

Since X is uniformly distributed over (0,1) and Y is exponentially distributed with parameter lambda = 2, we have their respective probability density functions (PDFs):

fX(x) = 1, 0 ≤ x ≤ 1

fY(y) = 2e^(-2y), y ≥ 0

Now, we can calculate the CDF of Z:

P(Z ≤ a) = ∫∫ P(X ≤ x, Y ≤ a - x) dxdy

= ∫∫ fX(x) * fY(y) dxdy, since X and Y are independent

= ∫∫ 1 *\(2e^(-2y)\) dxdy, for 0 ≤ x ≤ 1 and y ≥ 0

Integrating with respect to x from 0 to 1 and with respect to y from 0 to a - x, we get:

P(Z ≤ a) = ∫[0,1]∫[0,a-x] 1 * 2\(e^(-2y)\)dydx

= ∫[0,1] [\(-e^(-2y)\)] [0,a-x] dx

= ∫[0,1] (1 - \(e^(-2(a-x)\))) dx

Evaluating the integral, we have:

P(Z ≤ a) = [x - \(xe^(-2(a-x))\)] [0,1]

= (1 - e^(-2a))

Therefore, the cumulative distribution function (CDF) of Z is:

P(Z ≤ a) = \((1 - e^(-2a)),\) for 0 < a < 1

For 0 < a < ∞, the cumulative distribution function of Z remains the same:

P(Z ≤ a) = (1 - e^(-2a)), for 0 < a < ∞

Now, let's move on to the cumulative distribution function of T = X/Y.

P(T ≤ a) = P(X/Y ≤ a)

Since X and Y are independent, we can write this as:

P(T ≤ a) = ∫∫ P(X/y ≤ a) fX(x) * fY(y) dxdy

Using the given information that X is uniformly distributed over (0,1) and Y is exponentially distributed with parameter lambda = 2, we can substitute their respective PDFs:

P(T ≤ a) = ∫∫ P(X/y ≤ a) * 1 * \(2e^(-2y)\)dxdy

= ∫∫ P(X ≤ ay) * 1 * \(2e^(-2y)\)dxdy

Now, we need to determine the range of integration for x and y. Since X is between 0 and 1, and Y is greater than or equal to 0, we have:

0 ≤ x ≤ 1

0 ≤ y

Using these limits, we can calculate the CDF of T:

P(T ≤ a) = ∫[0,1]∫[0,∞] P(X ≤ ay) * 1 * \(2e^(-2y)\) dydx

To evaluate this integral, we need to consider the range of values for ay. Since a can be any positive real number, ay can range from 0 to ∞.

P(T ≤ a) = ∫[0,1]∫[0,∞] P(X ≤ ay) * 1 * 2\(e^(-2y)\) dydx

= ∫[0,1]∫[0,∞] (ay) * 1 * 2\(e^(-2y)\) dydx, for ay ≥ 0

Integrating with respect to y from 0 to ∞ and with respect to x from 0 to 1, we have:

P(T ≤ a) = ∫[0,1]∫[0,∞] (ay) * 1 * 2\(e^(-2y)\)dydx

= ∫[0,1] (2a / (4 + a^2)) dx

Evaluating the integral, we get:

P(T ≤ a) = (2a / (4 + \(a^2)),\) for a > 0

Therefore, the cumulative distribution function (CDF) of T is:

P(T ≤ a) = (2a / (4 + \(a^2)),\) for a > 0

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Answer:

153/8

Step-by-step explanation:

The given statement is false.

In a two-tailed hypothesis test for a population mean, where the population standard deviation is known, the critical values are the values that divide the alpha (significance level) into two equal-tailed regions.

For a 1% level of significance (alpha = 0.01), a two-tailed test allocates half of the alpha to each tail of the distribution. In this case, each tail will have an area of 0.01/2 = 0.005.

The critical values are determined by the standard normal distribution (z-distribution) or by the t-distribution (if the sample size is small and the population standard deviation is unknown). These critical values represent the number of standard deviations away from the mean that correspond to the desired level of significance.

The specific critical values will depend on the sample size, distribution type (z or t), and the desired level of significance. To obtain the critical values, one would consult a standard normal distribution table or a t-distribution table, depending on the case.

In summary, the critical values in a two-tailed hypothesis test do not necessarily divide the area under the standard normal curve into a middle 0.98 area and two outside areas of 0.01. The allocation of the alpha (significance level) is determined based on the desired level of significance, and the critical values are obtained from the appropriate distribution table.

Therefore, the given statement is false

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Sin (30) = 1/2

1/2 = x^2

So you can square both sides and find X.

X =

\( \sqrt{ \frac{2}{2} } \) = 0.707106...Ans is 1 when rounded to the nearest whole number)

Answer:

Let x be the number of silver medals.

As there were two more gold medals than silver ones, gold medals are x+2

We also know that the number of bronze medals was 4 less than the sum of gold and silver, so if there are x + 2 of gold and x of silver, there are x+x+2-4 of bronze.

Now, we can do an equation, as we know there were a total of 28 medals:

x + x + 2 + x + x + 2 - 4 = 28

And we isolate x:

4x = 28

x = 28/4 = 7

There were 7 silver medals, so there were 9 gold ones (7-2) and 12 of bronze (9+7-4).

The number of Gold, Silver and Bronze medals are 9, 7 and 12 respectively.

Let the number of silver medals = s

Let the number of good medals = s + 2

Let the number of bronze medals = 2s - 2

Total medals = 28

Therefore, the value for each medal will be:

s + s+2 + 2s-2 = 28

Collect like terms

4s = 28 - 2 + 2

4s = 28

s = 28/4 = 7

Silver medals = 7

Gold medals = s + 2 = 7 + 2 = 9

Bronze medals = 2s - 2 = 2(7) -2 = 14 - 2 = 12

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The equation of parabola will be x^2 = 20y.

The given focus is (0, 5) and the given directrix is y = -5.

Let (x, y) be any point on the parabola.

The distance from (x, y) to the focus (0, 5) is given by:

sqrt((x-0)^2 + (y-5)^2)

The distance from (x, y) to the directrix y = -5 is simply |y - (-5)| = |y + 5|

By definition of a parabola, these distances are equal. Therefore, we have:

sqrt((x-0)^2 + (y-5)^2) = |y + 5|

Squaring both sides, we get:

\((x-0)^{2} + (y-5)^{2} = (y + 5)^{2}\)

Simplifying and rearranging, we get:

\(x^{2}\) = 4(5)y

Therefore, the equation of the parabola with focus (0, 5) and directrix y = -5 is:

\(x^{2}\) = 20y.

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Answer:

Step-by-step explanation:

so their is probably about 20 or 10 marbles in each bag so if they take them just kinda subtract the amount each kid got to see how many were left for emila to get I think that’s how you do if not then I was happy to help and I hope you get better help

Answer:

n = 12

Step-by-step explanation:

I assume in problem 4 the relation between miles and hours is proportional.

Set up a proportion.

45 miles is to 4 hours as 135 miles is to n hours.

45/4 = 135/n

Cross multiply.

45n = 4 × 135

n = 4 × 3

n  = 12

Answer:

12

Step-by-step explanation:

Because we can divide 45 and 4 and we get 11.25

Now we know that one hour is 11.25 miles. So just divide 135/11.25

and you get 12

im pretty sure thats the correct answer. Hope this helps

Answer:

r=b(w)-2x

Step-by-step explanation:

were solving for r so that is our end variable

sense we dont know how many boxes there are we just put b in the equation by itself, multiplying it with w since that represent the total number of waffles

b(w)

Ex: they buy 2 boxes and each box contains 24 waffles

b=2 and w=waffles

it then says each week they eat x amount of waffles, meaning its the same number for every week allowing us to multiply it with the number of weeks.

2x

Ex: say the family eats 10 waffles per week week, meaning x=10, well the we just multiply the 10 by the number of weeks

Answer: r = b(w) - 2x

The number of remaining waffles r, after 2 weeks is r=bw-2x.

Given that, a family buys b boxes of frozen waffles each containing w waffles.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The number of remaining waffles r, after 2 weeks.

Number waffles = Number of boxes × Number of waffles in each box

= b × w

= bw

Now, number of waffles left after 2 weeks = 2x

So, equation is r=bw-2x

Therefore, the number of remaining waffles r, after 2 weeks is r=bw-2x.

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Let's analyze the given information and the statements provided.

We are told that the integers r, s, and t all have the same remainder when divided by 5. This means that these integers can be written in the form:

r = 5n + k

s = 5m + k

t = 5p + k

where n, m, and p are integers representing quotients and k is the common remainder.

Statement (1) r + s = t:

If r + s = t, we can substitute the expressions for r and s:

(5n + k) + (5m + k) = 5p + k

Combining like terms:

10n + 10m = 5p

Dividing both sides by 5:

2n + 2m = p

From this equation, we can see that p must be an even number. However, we cannot determine the exact value of t based on this equation alone. Statement (1) is not sufficient to answer the question.

Statement (2) 20 ≤ t ≤ 24:

This statement provides a range for the possible values of t. Since t has the same remainder when divided by 5 as r and s, it must be congruent to k modulo 5. From the given range, the only number that satisfies this condition is t = 20.

However, we need to consider the combined information from both statements to reach a conclusion.

By considering both statements, we find that the only value that satisfies both conditions is t = 20.

the value of t is 20.

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Answer:

6.8 inches

Step-by-step explanation:

inch= 1 x

feet= 5 34

1×34÷5

Answer:

C=5π/2

Step-by-step explanation:

Given:

Last year Lira earned $12,000 less than her husband Todd.

Together they earned $75,000.

To find:

The amount earned by Lira in last year.

Solution:

Let x be the amount earned by Lira's husband inn last year.

Last year Lira earned $12,000 less than her husband Todd.

Amount earned by Lira = \(x-12000\)

Total amount earned by Lira and her husband = \(x+(x-12000)\)

                                                                             = \(2x-12000\)

Together they earned $75,000.

\(2x-12000=75000\)

\(2x=75000+12000\)

\(2x=87000\)

\(x=\dfrac{87000}{2}\)

\(x=43500\)

Now,

Amount earned by Lira = \(x-12000\)

                                       = \(43500-12000\)

                                       = \(31500\)

Therefore, the amount earned by Lira in last year is $31500.

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:

-6x+2=4

3(-3x+1)=6

-2(3x-1)=4

-3x=1

x=-1/3

Step-by-step explanation:

Answer:

98

Step-by-step explanation:

The formula for this situation = Cube volume - cone volume

Cube volume = 5.1 * 5.1 * 5.1 = 132.7 ( rounded )
Cone volume = pi × r^2 × h/3 = pi × 2.55^2 × 5.1/3 = 3.14 × 6.5025 × 1.7 = 34.7 ( rounded )

Total volume = 132.6 - 34.7 = 98

Notes for myself: Cube = 5.1 * 5.1 * 5.1
Problem Description:
the volume of the cube with the empty cone-shaped indentation is ___ cubic meters.

Use 3.14 for pi and round your answer to the nearest hundredth.
Hope this helped

Answer:

124 people

Step-by-step explanation:

Answer:

Answer: People 18 and over are considered adults​

Because more than or equal to 18

Good Luck!

Answer:

O#4,  People 18 and over are considered adults​.

Step-by-step explanation:

Since there is a line under it, it means greater than or equal to.

Answer:

Step-by-step explanation:

v(t) =  25,000×1.035^t

The function to model the value of home is v(t) = 25000 \((1+ 0.0.35)^t\).

The worth of a current asset at some point in the future based on an estimated rate of growth is known as future value (FV). For investors and financial planners, the future value is crucial because they use it to predict how much an investment made now will be worth in the future.

Investors can make wise investment choices based on their projected demands by knowing the future worth.

Given:

P = $25, 000.

The value of the home has increased by approximately 3.5% per year since.

So, using the future value the function to model the value of home

v(t) = 25000 \((1+ 0.0.35)^t\)

where t is time in years.

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If a marble is selected at random from Adrian's Bag of Marbles, then the probability that marble selected from Adrian's bag will not be red is 0.7.

The "Probability" of an "event-A" occurring is defined as the ratio of the number of favorable outcomes for event A to the total number of possible outcomes in a given sample space. It is denoted as P(A).

To find the probability that marble selected will not be red,

we need to find "total-number" of marbles in Adrian's bag and the number of marbles that are not red.

We know that,

⇒ Number of red marbles = 3,

⇒ Number of blue marbles = 7,

So, Total marbles in bag = Number of red marbles + Number of blue marbles,

⇒ 3 + 7 = 10,

The Number of marbles that are not red = Number of blue marbles = 7,

So, probability that marble selected will not be red is :

⇒ Probability (not red) = (Number of marbles that are not red)/(Total number of marbles),

⇒ 7/10,

⇒ 0.7

Therefore, the required probability is 0.7.

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The given question is incomplete, the complete question is

Adrian's Bag of marbles contain 3 Red and 7 Blue Marbles, If a marble is selected at random from Adrian's Bag of Marbles, then What is the probability the Marble selected will NOT be red?

The length of the ribbon to the nearest tenth is 50.3 inches.

To find the length of the ribbon that surrounds the edge of a circular hat that has a radius of 8 inches, we can use the formula for the circumference of a circle.

The formula for the circumference of a circle is given by the following:

C = 2πr

Where C represents the circumference of the circle, π represents the constant value of pi which is approximately equal to 3.14, and r represents the radius of the circle.

Given that the circular hat has a radius of 8 inches, we can use this value to find the circumference of the circle.

Hence, we have: r = 8 inches

C = 2πr

C = 2π(8)C = 16π

The length of the ribbon that surrounds the edge of the circular hat is equal to the circumference of the circle. Therefore, the length of the ribbon is:16π ≈ 50.3 inches (to the nearest tenth)

Therefore, the length of the ribbon to the nearest tenth is 50.3 inches.

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The true statements from the options provided are:

A. The product Ax is defined as a linear combination of columns of A with the corresponding entries of x as weights.

D. The product Ax is a vector in \(R^n\).

E. Ax is a vector whose ith entry is the sum of the products of the corresponding entries from row i of A and the vector x.

A linear combination in mathematics is an expression created from a group of terms by multiplying each component by a constant and combining the results (for example, an expression of the form axe + by, where a and b are constants, would be a linear combination of x and y).

The true statements from the options provided are:

A. The product Ax is defined as a linear combination of columns of A with the corresponding entries of x as weights.

D. The product Ax is a vector in \(R^n\).

E. Ax is a vector whose ith entry is the sum of the products of the corresponding entries from row i of A and the vector x.

These statements accurately describe properties and definitions related to matrix-vector multiplication. The product Ax is obtained by taking a linear combination of the columns of A, where the entries of x act as weights. The resulting product Ax is a vector in \(R^n\), and its entries are calculated by summing the products of the corresponding entries from row i of A and the vector x.

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Answer:

1. The estimate of the proportion of mosquitoes in the area that carry the disease is approximately 0.1606 or 16.06%

2. To check for accuracy of the of the value of proportion of disease carrying mosquito in the area

Step-by-step explanation:

The given parameters are;

The number of mosquitoes in the sample = 137

The number of mosquitoes that carry the disease = 22

1. The estimate of the proportion of mosquitoes in the area that carry the disease = (Number of mosquitoes with the disease)/(The number of mosquitoes in the sample)

The estimate of the proportion of mosquitoes in the area that carry the disease = 22/137 ≈ 0.1606 or 16.06%

2. The reason the scientist run the simulations to find additional possible proportions of mosquitoes in the area that carry the disease is to check for variability and accuracy of the proportion of disease carrying mosquito in the area.

1. The proportion of mosquitoes in the region that carry the illness is estimated to be 16.06%.

2. To ensure that the proportion of disease-carrying mosquitos in the region is accurate.

A ratio is an ordered pair of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two ratios are specified to be equal.

Given data;

There were 137 mosquitos in the sample,\(\rm N_s\)

The number of disease-carrying mosquitos is,\(\rm N_m\)=22

The estimated proportion of disease-carrying mosquitos in the region is found as;

\(\rm D_m=\frac{N_m}{N_s} \\\\ \rm D_m=\frac{22}{137} \\\\ D_m=16.06 \ %\)

2. The scientists used simulations to determine alternative probable proportions of disease-carrying mosquitos in the region in order to check for variability and accuracy in the proportion of disease-carrying mosquitos in the area.

Hence,the proportion of mosquitoes in the region that carry the illness is estimated to be 16.06%.

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Answer:

Step-by-step explanation:

\(V=\pi R^2\cdot H\\\\V=13\,816\ m^3\\R=20\,m\\H=??\\\\13\,816=\pi\cdot20^2\cdot H\\\\13\,816=400\pi H\\\\13\,816\approx1256.637 H\\\\H\approx10.994424\,m\)