Find the coordinates of the midpoint between (8, 1) and (0, - 9).

Answer:

2 + 2 ㏑2

Step-by-step explanation:

y = x (e^x)

to dy/dx (slope), we need to perform the product rule:

if y = f(x) g(x), where both f(x) and g(x) are functions in x, then dy/dx = f(x) g'(x) + f'(x) g(x).

let u = x (dy/dx = 1) and v = e^x ( dv/dx = e^x).

then dy/dx = u (dv/dx) + v (du/dx)

= x (e^x) + e^x. this is the slope.

at x = ㏑2:

dy/dx = ㏑2 (e^㏑2) + e^㏑2

= ㏑2 (2) + 2

= 2 + 2 ㏑2

A. The solution to the congruence 3x - 107 ≡ 0 (mod 12) is x ≡ 1 (mod 12).

B. The solution to the congruence 5x + 3 - 102 ≡ 0 (mod 7) is x ≡ 6 (mod 7).

C. The solution to the congruence 66 + 9 ≡ 0 (mod 11) is x ≡ 4 (mod 11).

To solve modulo equations or congruences, we need to find values of x that satisfy the given congruence.

A. For the congruence 3x - 107 ≡ 0 (mod 12), we want to find an x such that when 107 is subtracted from 3x, the result is divisible by 12. Adding 107 to both sides of the congruence, we get 3x ≡ 107 (mod 12). By observing the remainders of 107 when divided by 12, we see that 107 ≡ 11 (mod 12). Therefore, we can rewrite the congruence as 3x ≡ 11 (mod 12). To solve for x, we need to find a number that, when multiplied by 3, gives a remainder of 11 when divided by 12. It turns out that x ≡ 1 (mod 12) satisfies this condition.

B. In the congruence 5x + 3 - 102 ≡ 0 (mod 7), we want to find an x such that when 102 is subtracted from 5x + 3, the result is divisible by 7. Subtracting 3 from both sides of the congruence, we get 5x ≡ 99 (mod 7). Simplifying further, 99 ≡ 1 (mod 7). Hence, the congruence becomes 5x ≡ 1 (mod 7). To find x, we need to find a number that, when multiplied by 5, gives a remainder of 1 when divided by 7. It can be seen that x ≡ 6 (mod 7) satisfies this condition.

C. The congruence 66 + 9 ≡ 0 (mod 11) states that we need to find a value of x for which 66 + 9 is divisible by 11. Evaluating 66 + 9, we find that 66 + 9 ≡ 3 (mod 11). Hence, x ≡ 4 (mod 11) satisfies the given congruence.

Modulo arithmetic or congruences involve working with remainders when dividing numbers. In a congruence of the form a ≡ b (mod m), it means that a and b have the same remainder when divided by m. To solve modulo equations, we manipulate the equation to isolate x and determine the values of x that satisfy the congruence. By observing the patterns in remainders and using properties of modular arithmetic, we can find solutions to these equations.

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Answer:

55

Step-by-step explanation:

15+10d

15+10(4)

15+40

55 minutes

It will take 55 minutes for Mark to bake 48 cookies.

15+10d

15+10(4)

15+40

55 minutes

Simply put, you can expect to bake cookies at 350 degrees Fahrenheit for 8-12 minutes. However, there are some things to consider when baking biscuits. The type of biscuit, the size of the biscuit, and the content of the fabric.

Preheat the oven to 350 ° F (or 325 ° F for a non-stick baking sheet). Place the cookie dough base about 2 inches apart on a non-oiled sheet pan. BRAKE for 10-14 minutes or until light brown. Cool 2 minutes; Remove from the top plate.

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Answer:

the answer is 21.6%

Step-by-step explanation:

(a) The rate of change of the sound pressure with respect to time is approximately 0.0694 dB/second.

(b) The rate of change of the sound pressure at r = 1 second is 0 dB/second.

(a) The rate of change of the sound pressure with respect to time (dp/dt), we can use the chain rule. The given formula for sound pressure is P = 10 log(W/W₀), where W is the sound power and W₀ is the reference threshold.

Given:

W = 7.2 Watts (sound power)

dW/dt = 0.5 Watts/second (rate of change of sound power with respect to time)

Using the chain rule, we have:

dp/dt = (dP/dW) × (dW/dt)

The derivative of P with respect to W can be found by differentiating the logarithmic function:

dP/dW = 10 × (1/W) × (dW/dt)

Substituting the given values:

dp/dt = 10 × (1/W) × (dW/dt)

= 10 × (1/7.2) × 0.5

= 0.0694 dB/second

Therefore, the rate of change of the sound pressure with respect to time is approximately 0.0694 dB/second.

(b) Given:

W = 1² + 1 + 1

t = 3 seconds

To find the rate of change of the sound pressure at t = 3 seconds (dp/dt), we need to differentiate the formula for sound pressure with respect to time.

Using the chain rule, we have:

dp/dt = (dP/dW) × (dW/dt)

The derivative of P with respect to W is:

dP/dW = 10 × (1/W)

The derivative of W with respect to t can be found by differentiating the given formula:

dW/dt = d/dt (1² + 1 + 1)

= 0

Substituting the values:

dp/dt = (dP/dW) × (dW/dt)

= 10 × (1/3) × 0

= 0

Therefore, the rate of change of the sound pressure at t = 3 seconds is 0 dB/second.

(c) Given:

W = cos(0.2)

r = 1 second

To find the rate of change of the sound pressure at r = 1 second (dp/dt), we need to differentiate the formula for sound pressure with respect to time.

Using the chain rule, we have:

dp/dt = (dP/dW) × (dW/dt)

The derivative of P with respect to W is:

dP/dW = 10 × (1/W)

The derivative of W with respect to t can be found by differentiating the given formula:

dW/dt = d/dt (cos(0.2))

= 0

Substituting the values:

dp/dt = (dP/dW) × (dW/dt)

= 10 × (1/cos(0.2)) × 0

= 0

Therefore, the rate of change of the sound pressure at r = 1 second is 0 dB/second.

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Answer:

\( - 3x = 4.2 \\ - x = \frac{4.2}{3} \\ - x = 1.4 \\ x = - 1.4 \\ thank \: you\)

Answer:

1/12clay each bowl

Step-by-step explanation:

Since we know she used 1/3, simply divide 1/3 by 4 to get your answer.

1/3 / 4/1

1/3 * 1/4

1/12

1/12 is the amount of clay which Bianca use for each bowls

A division is a process of splitting a specific amount into equal parts.

Given that Bianca uses 1/3 of clay to make 4 bowls.

Bianca  uses the same amount of clay for each bowl.

We have to find the amount of  clay does Bianca use for each bowls.

To find this we have to divide 1/3 by 4.

When a fraction is divided by whole number, the denominator of the fraction is multiplied with the whole number.

(1/3)/4

1/3×1/4

One divided by three times of one by four we get one by twelve.

1/12

Hence, 1/12 is the amount of clay which Bianca use for each bowls

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Answer:

The answer is 45

Step-by-step explanation:

Follow the steps:

set it up:

18/? = 40%/100%

18 x 100= 1800

1800 divided by 40 equals 45

Hope this helps! :)

It is not an entity that can take on different values, the consistency in measurement, the strength of the relationship between variables, or the truth of a measurement.

Validity is concerned with the degree to which a measure or conclusion accurately represents the concept or phenomenon it is intended to assess or describe. It focuses on the appropriateness and accuracy of inferences or interpretations based on the measurement or observation. Validity addresses the question of whether a measure or conclusion captures the intended construct or relationship and provides meaningful and reliable information.

Validity is distinct from other concepts mentioned. While an entity can take on different values, it is not synonymous with validity. Consistency in measurement refers to reliability, which is a separate concept related to the consistency and stability of measurements. The strength of the relationship between two variables is typically referred to as the correlation or association, but it is not directly related to validity. Lastly, the truth of a measurement is a broader philosophical concept, but validity specifically relates to the accuracy and appropriateness of a measure within a specific context or purpose.

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Note that after 15 minutes, Liam is 25 blocks away from his house. This prompt is a distance - time graph problem.

A distance-time graph depicts how far an object has moved in a given amount of time. It is a basic line graph that depicts distance versus time findings. The Y-axis represents distance. The X-axis represents time.

It should be noted that a distance-time graph depicts how the distance and speed of an item vary over time. The movement of three items over time is depicted in this graph. The slope, or steepness, of each line shows the speed of the item. In general, the quicker the item, the steeper the slope.

Note that by the 13th minute, Liam had already covered 25 blocks but remained stationary at that location for 3 minutes.

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The value of the ratio x : y : z is 1/2 : /3 : 5/18

From the question, we have the following parameters that can be used in our computation:

x:y = 1/2:1/3 and y:z = 1/5:1/6

Express the ratio properly

So, we have the following representation

x : y = 1/2 : 1/3 and y : z = 1/5 : 1/6

Multiply the ratio y : z = 1/5 : 1/6 by 5/3

So, we have

y : z = 1/3 : 5/18

So, we have

x : y : y : z = 1/2 : 1/3 : 1/3 : 5/18

Remove the repetition

This gives

x : y : z = 1/2 : /3 : 5/18

Hence, the ratio is 1/2 : /3 : 5/18

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Answer:

Yes

Step-by-step explanation:

Yes because if you insert -39 for x and 42 for y then your equation is:

42 = -39 + 81

If you were to solve this equation it would be true.

The solutions for the equation sinx = √1 - cosx in the interval [0, 2π) are x = 0, π/2, and 3π/2.

To solve this equation, we first need to square both sides:
sin^2x = 1 - cosx
Next, we can use the identity sin^2x + cos^2x = 1 to substitute sin^2x with 1 - cos^2x:
1 - cos^2x = 1 - cosx
Now we can simplify by moving all the terms to one side:
cos^2x - cosx = 0
Factorizing, we get:
cosx(cosx - 1) = 0
So the solutions are when cosx = 0 or cosx = 1. In the interval [0, 2π), the solutions for cosx = 0 are x = π/2 and 3π/2. The solution for cosx = 1 is x = 0. Therefore, the solutions for the equation sinx = √1 - cosx in the interval [0, 2π) are x = 0, π/2, and 3π/2. We express these solutions in radians in terms of π.

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x is greater than eleven thirds.

Inequality are expression that have <, > , ≤ and ≥ .

Therefore,

1 / 5 (5x) + 10 + 5x > 32

Hence,

1 / 5 × 5x + 10 + 5x > 32

x + 10 + 5x >32

combine like terms

x + 10 + 5x >32

x + 5x + 10 > 32

Therefore,

x + 5x + 10 > 32

6x + 10 > 32

subtract 10 from both sides

6x + 10 - 10 > 32 - 10

6x > 22

divide both sides by 6

x > 22 / 6

x > 11 / 3

Therefore, x is greater than eleven thirds.

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This is voluntary response bias. The result overestimates true support for firing the coach.

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Risk reduction can be defined as the strategy that reduces risk by minimizing the chance that the loss occurs or reduces the value lost. That is option B.

Risk reduction is defined as the strategy that can be used to make risk less severe through taking some clearly defined actions.

The strategies that can be used include the following:

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Polygon pairs are dissimilar because their proportions are not equal.So,

\(\frac{8}{5}\neq \frac{15}{12}\)

Congruent polygons are exactly the same size and fit perfectly because all corresponding parts are congruent (equal). Conversely, similar polygons have the same shape but not the same size (that is, one larger than the other).

That is, if two polygons are similar, their corresponding angles are congruent and their corresponding sides are proportional.

So if we find that the corresponding angles here match, we know if the corresponding sides are proportional. The angles are coincident, but the sides are not proportional.

how \(\frac{17}{13}\) , \(\frac{15}{12}\) , \(\frac{8}{5}\)

You can see that the ratios are not equal. Therefore, polygon pairs are dissimilar. 

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The answer is option A) similar; the corresponding angles are congruent and 8/5 = 17/13.

What is meant by congruent angles?

Congruent angles are two angles that have the same measure in degrees or radians. In other words, if two angles are congruent, they have the same angle measurement and can be superimposed on each other. When two angles are congruent, they will look exactly the same and will have the same degree or radian value.

We can see that the given polygons are right angled triangles.

To check if the two right triangles are similar, we can use the Pythagorean theorem to confirm that the ratio of the sides is consistent between the two triangles.

For Triangle 1:

Base = 8

Height = 15

Hypotenuse = 17

For Triangle 2:

Base = 5

Height = 12

Hypotenuse = 13

Using the Pythagorean theorem, we can find that the length of the missing side (the side perpendicular to the hypotenuse) for Triangle 1 is:

\(\sqrt{(17^2 - 8^2)\) = \(\sqrt{(225)\) = 15

Using the Pythagorean theorem, we can find that the length of the missing side (the side perpendicular to the hypotenuse) for Triangle 2 is:

\(\sqrt{(13^2 - 5^2)\) = \(\sqrt{(144)\) = 12

Now we can compare the ratios of the corresponding sides:

Triangle 1:

Base/Height = 8/15

Height/Hypotenuse = 15/17

Base/Hypotenuse = 8/17

Triangle 2:

Base/Height = 5/12

Height/Hypotenuse = 12/13

Base/Hypotenuse = 5/13

We can see that the ratios of the corresponding sides in the two triangles are equal:

Base/Height: 8/15 = 5/12

Height/Hypotenuse: 15/17 = 12/13

Base/Hypotenuse: 8/17 = 5/13

Therefore, the two triangles are similar and the answer is A) similar; the corresponding angles are congruent and 8/5 = 17/13.

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The solutions to the equations are

1. x = 4

2. x = -12

3. x = 0 and x = 4

The solutions to the inequalities are

4. -5 < x < 1

5. x ≤ -3 and x ≥ 4

From the question, we have the following equations

1. 4x + 6 = 8x - 10

2. -3/4x - 2 = -1/2x + 1

3. |4 - 2x| + 5 = 9

Next, we split the equations to 2

So, we have

1. y = 4x + 6 and y = 8x - 10

2. y = -3/4x - 2 and y = -1/2x + 1

3. y = |4 - 2x| + 5 and y = 9

Next, we plot the system of equations (see attachment) and write out the solutions

The solutions are

1. x = 4

2. x = -12

3. x = 0 and x = 4

From the question, we have the following inequalities

4. x² + 4x - 5 < 0

5. x² - x - 12 ≥ 0

Next, we plot the system of inequalities (see attachment) and write out the solutions

The solutions are

4. -5 < x < 1

5. x ≤ -3 and x ≥ 4

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The variable assigned to strgrade when intscore equals 90 would likely be 'A'.

When the variable intscore equals 90, the corresponding value assigned to the variable strgrade would typically be 'A'. This suggests that a score of 90 is associated with the highest grade achievable in the given context. The specific mapping between integer scores and letter grades may vary depending on the grading system or criteria in place. It is important to note that without further information about the grading scale or specific rules defined within the system, it is difficult to determine the exact value of strgrade assigned to intscore of 90.

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Complete Question

David bought a chain of fast food restaurants that operated 200 stores in 2009. The number of restaurants has grown at a rate of 12% annually.how many stores does the restaurant operate in 2020?

Answer:

\(N_{11} \approx 749\)

Step-by-step explanation:

From the question we are told that:

Number of Fast Food Restaurants \(P=200\)

Number of years \(t=11yrs\)

Rate \(r=12%\)

Generally the equation for the Number of restaurant in operation in 2020 is mathematically given by

 \(N(t)=Pe^{rt}\)

Therefore

For t=11

 \(N_{11}=200*e^{0.12*11}\)

 \(N_{11}=748.7\)

 \(N_{11} \approx 749\)

Answer:c

Step-by-step explanation:

Answer: C

Step-by-step explanation:

find the slope of 4x + 3y equals to​

I will assume a value of a

so

4x+3y=a

Isolate the variable y

3y=-4x+a

y=-(4/3)x+a/3

therefore

Note: the value of the slope not depend of the value of a

15 candy bars must be bought at the cost of $0.72 per piece to bring the average down to $0.80.

To find the number of candy bars needed to bring the average cost down to $0.80, we can use the formula for average:

(sum of costs)/(number of candy bars).

Let's denote the number of candy bars needed as x. We know that the sum of costs for the group of ten candy bars is 10 * $0.89 = $8.90.

To bring the average down to $0.80, the sum of costs for the x candy bars must be (10 * $0.89 + x * $0.72).

Now we can set up the equation:

(10 * $0.89 + x * $0.72)/(10 + x) = $0.80.

Simplifying this equation, we get:

8.9 + 0.72x = 0.8(10 + x).

Solving for x, we find that x = 15.

Therefore, 15 candy bars must be bought at the cost of $0.72 per piece to bring the average down to $0.80.

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complete question:

A group of ten candy bars has an average cost of $0.89 per candy bar. How many bars must be bought at the cost of $0.72 a piece to bring the average down to $0.80?

Remaining uranium after 20 days: 47.84 lbs (initial: 60 lbs, decay rate: 0.4% per day).

To solve this problem, we need to use the formula for exponential decay:

\(y = a(1 - r)^t\)

where y is the final amount, a is the initial amount, r is the decay rate (as a decimal), and t is the time elapsed.

In this case, we are given that the initial amount is 60 pounds, the decay rate is 0.4% or 0.004 per day, and the time elapsed is 20 days. Therefore, we can plug these values into the formula to get:

y =\(60(1 - 0.004)^20\)

Simplifying the equation, we get:

\(y = 60(0.996)^20\)

Using a calculator, we find that:

\(y ≈ 47.84\)

Therefore, the amount of uranium that will still remain after 20 days is approximately 47.84 pounds.

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Answer is the coordinates of endpoint F(6, 4).

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

let coordinate of F is (x,y).

4= (x + 2)/2

8= x +2

x = 6

6= (y +8)/2

12 = y + 8

y = 4

Answer is the coordinates of endpoint F(6, 4).

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For a data set with an odd number of observations that have been sorted from smallest to largest values, the median is located at \(\frac{x+1}{2}\)

Given,

The conditions

We know,

Median is the middle number of ordered data set.

Consider the number of observations as x

Then the median is located at \(\frac{x+1}{2}\)

Hence, for a data set with an odd number of observations that have been sorted from smallest to largest values, the median is located at \(\frac{x+1}{2}\)

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Answer:

Story

Jane is 1.7 m tall.  She stands 250 m away from the base of the Eiffel tower and looks up at the top of the building.  The angle of elevation from her eyeline to the top of the building is 45°.

Question

Calculate an estimate of the height of the building. Give your answer to the nearest meter.

Calculation

Label the sides of the triangle O, A and H (where O is the side opposite to the angle, A is the side adjacent to the angle and H is the hypotenuse).

In the triangle, the angle and side A is known, and O must be calculated.

Therefore, use the trig ratio tan(x) = O/A:

⇒ tan(40) = O/250

⇒ 250tan(40) = O

⇒ O = 209.7749078...

Assume Jane's eye-level is approximately 1.5 m above the ground.

Therefore, the Eiffel tower is approximately:

209.7749078... + 1.5 = 211.2749078.. meters tall

Rounding to the nearest meter ⇒ 211 m