One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor. (a) Write a differential equation that is satisfied by y. (Use k for the constant of proportionality.) dy dt = ky 1-y. (b) Solve the differential equation. Assume y(0) = C. y = 1-ce-kt +1 (c) A small town has 1300 inhabitants. At 8 AM, 100 people have heard a rumor. By noon half the town has heard it. At what time will 90% of the population have heard the rumor? (Do not round k in your calculation. Round the final answer to one decimal place.) hours after the beginning

a) Angle of line of sightFrom a point O in the school compound, Adeolu is 100 m away on a bearing N 35° E and Ibrahim is 80 m away on a bearing S 55° E. (a) How far apart are both boys? (b) (c) What is the bearing of Adeolu from point O, in three-figure bearings? What is the bearing of Ibrahim from point O, in three-figure bearings?The angle of the line of sight of Adeolu from the point O is given by:α = 90 - 35α = 55°.The angle of the line of sight of Ibrahim from the point O is given by:β = 90 - 55β = 35°.a) By using the Sine Rule, we can determine the distance between Adeolu and Ibrahim as follows:$

\frac{100}{sin55^{\circ}} = \frac{80}{sin35^{\circ}

100 sin 35° = 80 sin 55°=57.73 mT

herefore, both boys are 57.73 m apart. b) The bearing of Adeolu from the point O can be determined as follows:OAN is a right-angled triangle with α = 55° and OA = 100. Therefore, the sine function is used to determine the side opposite the angle in order to determine AN.

Thus:$$sin55^{\circ} = \frac{AN}{100}$$AN = 80.71 m.

To find the bearing, OAD is used as a reference angle. Since α = 55°, the bearing is 055°.

Therefore, the bearing of Adeolu from the point O is N55°E. c) Similarly, the bearing of Ibrahim from the point O can be determined as follows:OBS is a right-angled triangle with β = 35° and OB = 80. Therefore, the sine function is used to determine the side opposite the angle in order to determine BS.

Thus:$$sin35^{\circ} = \frac{BS}{80}$$BS = 46.40 m.

To find the bearing, OCD is used as a reference angle. Since β = 35°, the bearing is 035°.Therefore, the bearing of Ibrahim from the point O is S35°E. A boy walks 5 km due North and then 4 km due East. (a) Find the bearing of his current posi- tion from the starting point.

(b) How far is the boy now from the start- ing point?The boy's position is 5 km North and 4 km East from his starting position. The Pythagorean Theorem is used to determine the distance between the two points, which are joined to form a right-angled triangle. Thus

:$$c^2 = a^2 + b^2$$

where c is the hypotenuse, and a and b are the other two sides of the triangle. Therefore, the distance between the starting position and the boy's current position is:$$

c^2 = 5^2 + 4^2$$$$c^2 = 25 + 16$$$$c^2 = 41$$$$c = \sqrt{41} = 6.4 km$$

Therefore, the boy is 6.4 km from his starting point. (a) The bearing of the boy's current position from the starting point is given by the tangent function.

Thus:$$\tan{\theta} = \frac{opposite}{adjacent}$$$$\tan{\theta} = \frac{5}{4}$$$$\theta = \tan^{-1}{\left(\frac{5}{4}\right)}$$$$\theta = 51.34^{\circ}$$

Therefore, the bearing of the boy's current position from the starting point is N51°E.

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Answer:

12

Step-by-step explanation:

To write the equation of a circle centered at (h, k) with a diameter of d, we can use the standard form of the equation:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) represents the center of the circle and r represents the radius.

In this case, the center of the circle is (-4, 4), and the diameter is 14. The radius is half of the diameter, so the radius would be 14 / 2 = 7.

Substituting the values into the equation, we have:

(x - (-4))^2 + (y - 4)^2 = 7^2

Simplifying further:

(x + 4)^2 + (y - 4)^2 = 49

Therefore, the equation of the circle centered at (-4, 4) with a diameter of 14 is:

(x + 4)^2 + (y - 4)^2 = 49

The slope of tangent line is, m= \(-\frac{1}{14}\)

Equation of tangent line, for m= \(-\frac{1}{14}\) and b= \(\frac{53}{7}\) is, 14y = -x + 106

The slope of a line is a measure of how steeply it rises or falls as it moves horizontally. It is calculated by dividing the change in the vertical coordinate by the change in the horizontal coordinate between two points on the line.

Slope of tangent, m = \(\frac{dy}{dx}\)

f(x) = y = \(\sqrt{57-x}\)

y = \((57-x)^{\frac{1}{2}}\)  

Differentiate the above equation y with respect to x.

\(\frac{dy}{dx} = \frac{1}{2} * (57-x)^{1-\frac{1}{2} }* (-1)\)

\(\frac{dy}{dx} = -\frac{1}{2} * (57-x)^{-\frac{1}{2} }\)

\(\frac{dy}{dx} = -\frac{1}{2\sqrt{57-x} }\)

Therefore, the slope (m) of tangent line f(x) at point (8, 7) is,

\(\frac{dy}{dx} | _{(8, 7)} = -\frac{1}{2\sqrt{57-8} } = - \frac{1}{14}\)

Equation of tangent line f(x) at point (8, 7) is,

y = mx + b

7 = \(-\frac{1}{14}\) × 8 + b

b = \(\frac{53}{7}\)

So, Equation is, y = \(-\frac{1}{14}x + \frac{53}{7}\)

Therefore, 14y = -x + 106

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Answer:

x<6

Step-by-step explanation:

The Product(multiplication) of -2 and a number(x) minus(-) six IS(=) greater than(>) -18.

Which gives you: -2x-6>-18

First step is to get the -2x by itself so we add 6 to both sides.

-2x>-12

We then want to get x by itself so we divide by -2 on both sides. Don't forget to flip the inequality sign because we are dividing by a negative.

x<6

The line of best fit for the set of data in this problem is given as follows:

y = 0.613x + 4.142.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) of the data-set in the calculator.

The points for this problem are given as follows:

(-2, 2.9), (-3.5, 2), (1.4, 4.8), (-4.2, 1.5), (0,4), (2.8, 6), (-1.5, 3.5).

Inserting these points into a calculator, the line of best fit is given as follows:

y = 0.613x + 4.142.

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Answer:

-1.25

Step-by-step explanation:

\(\boxed{slope = \frac{y1 - y2}{x1 - x2} }\)

☆ (x₁, y₁) is the 1st coordinate and (x₂, y₂) is the 2nd coordinate

Slope of line

\( = \frac{6 - ( - 4)}{1 - 9} \\ = \frac{6 + 4}{ - 8} \\ = - \frac{10}{8} \\ = - \frac{5}{4} \\ = - 1.25\)

The solution to the questions are

From the question, the given parameters are:

The volume of honey = 12 oz

The cost of the honey = $5.40

The cost of the honey per ounce is then calculated as

Cost = The cost of the honey/The volume of honey

Substitute the known values in the above equation

So, we have

Cost = 5.40/12

Evaluate

Cost = 0.45

In this case, we have

The amount of honey to buy is then calculated as

Amount = The volume of honey/The cost of the honey

Substitute the known values in the above equation

So, we have

Amount = 12/5.40

Evaluate

Amount = 2.22

In (a) and (b), we have

Cost = 0.45

Amount = 2.22

These equations are unit equations

When represented as linear equations, we have

c = 0.45h

h = 2.22c

Where h represent ounces of honey and c represents cost in dollars.

Here, we use

c = 0.45h

Next, we enter the equation in a graphical calculator, and attach the chart

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The multiplication expression with eight rational factors are ''positive''.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Jared writes a multiplication expression with eight rational factors. Half of the factors are positive and half are negative.

Since, Multiplication of four positive numbers are always gives a positive number and multiplication of four negative numbers are always gives a positive number.

Hence, The multiplication expression with eight rational factors are positive.

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B u A = 48

B = 45

The part of set B not included in A is B - A∩B  = 45 - 7 = 38

Since B u A = 48,  A must have 48-38 = 10 elements (3 exclusive of B, 7 shared with B).

------

Alternatively, the inclusion-exclusion principle may be used:   A  +  B  - (A ∩ B) = A u B  

  A + 45 - 7 = 48

  A  = 48 - 45 + 7  

   A = 10

NOTE that I'm using A and B  to indicate the number of elements in each set, respectively.

More formally, one would write |A|  and |B| to indicate the cardinality (number of elements) of the set.

Answer:

10

Step-by-step explanation:

Distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Let \((x_1,y_1)\) = (-4, 2)

Let \((x_2,y_2)\) = (2, -6)

Substituting given points into the formula:

\(\implies d=\sqrt{(2-(-4))^2+(-6-2)^2}\)

\(\implies d=\sqrt{(6)^2+(-8)^2}\)

\(\implies d=\sqrt{36+64}\)

\(\implies d=\sqrt{100}\)

\(\implies d=10\)

The correct option regarding the price is C. no; The packs of socks are marked up to $7 and then discounted to $4.20.

In this situation, a shoe store buys packs of socks wholesale for $5 each and marks them up by 40%. The price will be:

= Original price + Markup

= 5 + (40% × 5)

= 5 + 2

= $7

Then, the store decides to discount the packs of socks by 40%. This will give a price of:

= 7 - (40% × 7)

= 7 - 2.8

= $4.2

The price isn't discounted to $5.

In conclusion, the correct option is C.

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Answer:

19

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

2/3

Step-by-step explanation:

1 and 2 are taken away, therefore you have 3, 4, 5, and 6 left as options to roll. So the answer is 4/6 since there's 4 numbers, but simplified it's 2/3.

Answer:

There are six possible outcomes when rolling a die, each of which is equally likely. Of these six outcomes, three are greater than 2 (3, 4, 5) and three are not (1, 2, 6). Therefore, the odds in favor of rolling a number greater than 2 are 3 to 3, or simply 1 to 1. Alternatively, we could express this as a probability: the probability of rolling a number greater than 2 is 3/6, or 1/2, since there are three favorable outcomes out of a total of six possible outcomes.

Step-by-step explanation:

PRICES COUNTS COSTS

8 e 8e

10 420-e-t 10(420-e-t)

12 t 12t

420 3920

system%28e%2B420-e-t=5t%2C8e%2B10%28420-e-t%29%2B12t=3920%29

First equation gives highlight%28t=70%29.

Second equation simplifies to e-t=140.

Substitution gives highlight%28e=210%29.

Quantity of $10 tickets by difference, highlight%28140%29

Answer:its undefined

Step-by-step explanation:

Answer:

Plug this into the formula y2 - y1 / x2 - x1

-2 = x1, x2 = 2, y1 = -1, y2 = -3

-3 - (-1) / 2 - (-2)

-2 / 4

-1/2

The slope is -1/2.

Step-by-step explanation:

We are given that

We want to find h when t = 35

Solution

From

Therefore, h = 43

Using the unit circle to find sin 240 and cos 240, without using a calculator. The calculated results should match our approximations of -1/2 for sin 240 and -√3/2 for cos 240.

To find sin 240 and cos 240 without a calculator, we can use the unit circle, which is a circle with radius 1 centered at the origin in a two-dimensional coordinate system. The unit circle provides a convenient way to define the sine and cosine of an angle in terms of their coordinates on the circle.

The sine of an angle is the y-coordinate of the point on the unit circle corresponding to that angle, and the cosine of an angle is the x-coordinate of the point on the unit circle corresponding to that angle.

For an angle of 240 degrees, we can find the corresponding point on the unit circle by constructing a line from the origin to the point on the circle.

we can see that the y-coordinate of the point is negative, so sin 240 = -sin (240 - 180) = -sin 60 = -1/2.

The x-coordinate of the point is also negative, so cos 240 = -cos (240 - 180) = -cos 60 = -√3/2.

We can use a calculator to check our answers by entering sin(240) and cos(240) with parentheses around the 240, as requested by the calculator. The calculated results should match our approximations of -1/2 for sin 240 and -√3/2 for cos 240.

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The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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The purchasing power in five years will be $15,476.

To predict the purchasing power in five years, we can substitute the value of X as 5 into the equation y = 20000(0.95)^X.

Plugging in X = 5, we have:

\(y = 20000(0.95)^5\)

Calculating the expression, we find:

\(y ≈ 20000(0.774)\)

Simplifying further, we get:

\(y ≈ 15480\)

Rounding the result to the nearest dollar, the predicted purchasing power in five years would be approximately $15,480.

Therefore, the closest option to the predicted purchasing power in five years is $15,476.

So the correct answer is:

$15,476.

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Rounding to the nearest dollar, the predicted purchasing power in five years is approximately $15,480.

To predict the purchasing power in five years using the given equation, we substitute the value of x (representing the number of years) as 5 and calculate the result.

The equation provided is: y = 20000(0.95)^x

Substituting x = 5 into the equation, we have:

y = 20000(0.95)⁵

Now, let's calculate the result:

y ≈ 20000(0.95)⁵

≈ 20000(0.774)

y ≈ 20000(0.774)

≈ 15,480

This means that, according to the given equation, the purchasing power of $20,000, with an inflation rate of five percent, would be predicted to be approximately $15,480 after five years.

By changing the value of x (representing the number of years) to 5, we can use the preceding equation to forecast the buying power in five years.

The example equation is: y = 20000(0.95)^x

When x = 5 is substituted into the equation, we get y = 20000(0.95).⁵

Let's now compute the outcome:

y ≈ 20000(0.95)⁵ ≈ 20000(0.774)

y ≈ 20000(0.774) ≈ 15,480

This indicates that based on the equation, after five years, the purchasing power of $20,000 would be estimated to be around $15,480 with a five percent inflation rate.

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Answer:

The net present value of 1,500 a year from now at 5% interest is $1,428.57.

Step-by-step explanation:

NPV = 1,500 / 1.05 = 1,428.57

Answer:

Step completed incorrectly:  2

Correct Answer: y = -4x + 22

Step-by-step explanation:

The graph is a straight line through points M(4, -1) and N(8, 0).  Point Q is located at (6, -2).

To calculate the slope of the line, substitute the points into the slope formula:

\(\textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-(-1)}{8-4}=\dfrac{1}{4}\)

Therefore, the slope of MN is 1/4, so step 1 of Francisco's calculations is correct.

If two lines are perpendicular to each other, the slopes of these lines are negative reciprocals. The negative reciprocal of a number is its negative inverse.

The negative reciprocal of 1/4 is -4.

Therefore, the slope of the perpendicular line is -4.

So Francisco has made an error in his calculation in step 2 by not making the perpendicular slope negative.

Corrected work

\(\textsf{Step 1:} \quad \sf slope\;of\;MN:\; \dfrac{1}{4}\)

\(\textsf{Step 2:} \quad \sf slope\;of\;the\;line\;perpendicular:\; -4\)

\(\begin{aligned}\textsf{Step 3:} \quad y-y_1&=m(x-x_1)\;\; \sf Q(6,-2)\\y-(-2)&=-4(x-6)\end{aligned}\)

\(\textsf{Step 4:} \quad y+2=-4x+24\)

\(\textsf{Step 5:} \quad y+2-2=-4x+24-2\)

\(\textsf{Step 6:} \quad y=-4x+22\)

Therefore, step 2 has been completed incorrectly.

The correct answer is y = -4x + 22.

The average ticket cost for each concert is given as follows:

The ticket costs are obtained by a system of equations, for which the variables are given as follows:

It cost a total of $1707 to purchase six tickets for concert A and six tickets for concert B, hence:

6a + 6b = 1707

a + b = 284.5.

Three tickets for concert B cost a total of $687, hence the cost for concert B is of:

3b = 687

b = 287/3

b = $95.67.

Replacing into the first equation, the cost for concert A is given as follows;

a = 284.5 - 95.67

a = $188.83.

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Answer:

A sample of 217 is needed.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1-0.95}{2} = 0.025\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1-\alpha\).

So it is z with a pvalue of \(1-0.025 = 0.975\), so \(z = 1.96\)

Now, find the margin of error M as such

\(M = z*\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

If the population standard deviation is $3,750 how large should the sample be if margin of error is $500

We have that \(\sigma = 3750\).

We need a sample of n, and n is found when \(M = 500\). So

\(M = z*\frac{\sigma}{\sqrt{n}}\)

\(500 = 1.96*\frac{3750}{\sqrt{n}}\)

\(500\sqrt{n} = 1.96*3750\)

\(\sqrt{n} = \frac{1.96*3750}{500}\)

\((\sqrt{n})^{2} = (\frac{1.96*3750}{500})^{2}\)

\(n = 216.1\)

Rounding up

A sample of 217 is needed.

The completed table is as follows:

x | y

8 | 0

9 | 3

36 | 6

8 | 2√2

8 | -2√2

To solve the equation x = y², we can substitute the values of x and find the corresponding values of y in the table.

Let's fill in the missing entries one by one:

For x = 9, we need to find y. Since x = y², we take the square root of both sides to solve for y. So, y = √9 = 3. Therefore, the corresponding value for y is 3.

For x = 36, again, we apply the square root operation to both sides, giving y = √36 = 6. Hence, the corresponding value for y is 6.

For y = 2√2, we need to find x. Squaring both sides of the equation, we have \(x = (2\sqrt2)^2 = 4 \times 2 = 8\). Therefore, the corresponding value for x is 8.

For y = -2√2, we follow the same process as in step 3. Squaring both sides, we get \(x = (-2\sqrt2)^2 = 4 \times 2 = 8\). So, the corresponding value for x is 8.

After filling in the missing entries, the completed table is as follows:

x | y

8 | 0

9 | 3

36 | 6

8 | 2√2

8 | -2√2

Please note that there can be multiple valid solutions for this equation, but this table provides one possible solution.

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Answer:

The answer is X=10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

4x - 8 = 32

4x = 40

x = 10

Certainly! I'll be happy to solve and explain the given problem to you in a step-by-step manner.

In the given diagram, we have a triangle with two angles labeled as 4x° and (3x + 10)°. We need to solve for the value of x.

According to the properties of triangles, the sum of the interior angles of a triangle is always 180 degrees. Therefore, we can set up the following equation:

4x + (3x + 10) + 90 = 180

Let's simplify the equation:

4x + 3x + 10 + 90 = 180

7x + 100 = 180

Next, we'll isolate the variable term by subtracting 100 from both sides of the equation:

7x = 180 - 100

7x = 80

To solve for x, we'll divide both sides of the equation by 7:

x = 80 / 7

Now, let's calculate the value of x:

x ≈ 11.43

Therefore, the value of x is approximately 11.43.

Please note that this solution assumes the given diagram accurately represents the angle measurements, and the calculations provided are based on that assumption.

Answer : The number of capfuls of liquid soap needed to fill the rectangular soap dispenser are 12.

Step-by-step explanation :

First we have to calculate the volume of soap dispenser which is a cuboid.

Volume of cuboid = l × b × h

where,

l = length of cuboid = 16 cm

b = width of cuboid = 9 cm

h = height of cuboid = 4 cm

Now put all the given values in the above formula, we get:

Volume of cuboid = 16 cm × 9 cm × 4 cm

Volume of cuboid = 576 cm³

Now we have to calculate the volume of cap which is a cylinder.

Volume of cylinder = π r² h

where,

r = radius of cylinder = 2 cm

h = height of cylinder = 4 cm

Now put all the given values in the above formula, we get:

Volume of cylinder = 3.14 × (2 cm)² × 4 cm

Volume of cylinder = 50.24 cm³

Now we have to calculate the number of capfuls of liquid soap are needed to fill the rectangular soap dispenser.

Number of capfuls of liquid soap needed =  \(\frac{\text{Volume of soap dispenser}}{\text{Volume of cap}}\)

Number of capfuls of liquid soap needed =  \(\frac{576cm^3}{50.24cm^3}\)

Number of capfuls of liquid soap needed = 11.46 ≈ 12

Therefore, the number of capfuls of liquid soap needed to fill the rectangular soap dispenser are 12.