5. Find an expression to represent the area that is shaded
r

The graph represents the system of inequalities: y ≤ −3x − 1 and y ≤ −x + 4.

The graph represents the system of inequalities: y ≤ −3x − 1 and y ≤ −x + 4.

Let's analyze the given information step by step:

Line f(x) goes through the points (0, 4) and (4, 0) and is shaded below the line.

This means that the region below line f(x) is labeled A.

Since line f(x) is solid, the inequality associated with it must be y ≤ −3x − 1.

Line g(x) goes through the points (0, -1) and (2, 5) and is shaded below the line.

This means that the region below line g(x) is labeled B.

Since line g(x) is also solid, the inequality associated with it must be y ≤ −x + 4.

The shaded area where f(x) and g(x) have shading in common is labeled AB.

This means that the overlapping region satisfies both inequalities.

Combining the information, we find that the system of inequalities represented by the graph is:

y ≤ −3x − 1 (corresponding to line f(x))

y ≤ −x + 4 (corresponding to line g(x))

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The number of coffee shops per capita in the city is approximately 0.000124.

To calculate the number of coffee shops per capita in the given city, we divide the total number of coffee shops by the total population and round the result to six decimal places.

Number of coffee shops: 99

Population: 801,100

Coffee shops per capita = Number of coffee shops / Population

Coffee shops per capita = 99 / 801,100

Coffee shops per capita = 0.000123719

Rounding the result to six decimal places, the number of coffee shops per capita in the city is approximately 0.000124.

This means that for every person in the city, there are approximately 0.000124 coffee shops available. Another way to interpret this is that, on average, each person in the city can expect to have access to 0.000124 coffee shops.

Please note that this calculation assumes an equal distribution of coffee shops throughout the city and does not take into account factors such as location, density, or other variables that may affect coffee shop accessibility.

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Answer:

probability that the claim will be accepted, assuming the actual probability of cure is 65%, is approximately 0.9631 or 96.31%.

Step-by-step explanation:

Apologies for the confusion earlier. Let's calculate the probabilities based on the given information:

1) Find the probability that the claim will be rejected, assuming that the manufacturer's claim is true:

Using the normal approximation, we can find the z-score corresponding to X = 139. We standardize the random variable as follows:

Z = (X - μ) / σ

Z = (139 - 150) / sqrt(37.5) ≈ -1.795

Now we can find the probability using the standard normal table or a calculator:

P(Z < -1.795) ≈ 0.0369

Therefore, the probability that the claim will be rejected, assuming the manufacturer's claim is true, is approximately 0.0369 or 3.69%.

2) Find the probability that the claim will be accepted, assuming that the actual probability that the drug cures the skin disease is 65%:

Using the normal approximation, we can find the z-score corresponding to X = 139:

Z = (139 - 150) / sqrt(37.5) ≈ -1.795

Now we can find the probability:

P(Z > -1.795) ≈ 1 - P(Z < -1.795) ≈ 1 - 0.0369 ≈ 0.9631

Therefore, the probability that the claim will be accepted, assuming the actual probability of cure is 65%, is approximately 0.9631 or 96.31%.

chatgpt

Answer:

(A) -76

(B) 4/81

(C) -1/16

(D) 3

Step-by-step explanation:

It is given that u and v are functions of x and are differentiable at x=0 and that u(0) = -8, u'(0) = -4, v(0) = 9, and v'(0) = 5. We are asked to find the following derivatives at x=0.

(A) - [tex]\dfrac{d}{dx}[uv][/tex]

(B) - [tex]\dfrac{d}{dx}\Big[\dfrac{u}{v} \Big][/tex]

(C) - [tex]\dfrac{d}{dx}\Big[\dfrac{v}{u} \Big][/tex]

(D) - [tex]\dfrac{d}{dx} [-5v-7u][/tex]

[tex]\hrulefill[/tex]

Part (A) - Using the product rule.

[tex]\dfrac{d}{dx}[uv]=uv'+vu'[/tex]

Substituting in our values:

[tex](-8)(5)+(9)(-4)\\\\\\\therefore \boxed{=-76}[/tex]

Part (B) - Using the quotient rule.

[tex]\dfrac{d}{dx}\Big[\dfrac{u}{v} \Big]=\dfrac{vu'-uv'}{v^2}[/tex]

Evaluating at x=0:

[tex]\dfrac{(9)(-4)-(-8)(5)}{(9)^2}\\\\\\\therefore \boxed{=\frac{4}{81} }[/tex]

Part (C) - Using the quotient rule.

[tex]\dfrac{d}{dx}\Big[\dfrac{v}{u} \Big]=\dfrac{uv'-vu'}{u^2}[/tex]

Evaluating at x=0:

[tex]\dfrac{(-8)(5)-(9)(-4)}{(-8)^2}\\\\\\\therefore \boxed{=\frac{-1}{16} }[/tex]

Part (D) - Deriving the function.

[tex]\dfrac{d}{dx} [-5v-7u]=-5v'-7u'[/tex]

Substituting in our values:

[tex]-5(5)-7(-4)\\\\\\\therefore \boxed{=3}[/tex]

Thus, all parts have been solved.

Answer:

The slope of a line parallel to the equation y = (6/5)x - 2 is 6/5.

Step-by-step explanation:

In general, when two lines are parallel, they have the same slope. Therefore, any line that is parallel to the given equation will have a slope of 6/5.

Answer:

2/3

Step-by-step explanation:

The value x = 3 should be excluded from the solution set because it would result in a division by zero in the equation.

To determine the values that should be excluded in the equation x/(x - 3) + 1/3 = 1, we need to find the values of x that would make the equation undefined or result in a division by zero.

In this case, the expression x - 3 appears in the denominator, so we need to find the values of x that would make x - 3 equal to zero.

x - 3 = 0

x = 3

Therefore, the value x = 3 should be excluded from the solution set because it would result in a division by zero in the equation.

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The equation that represents the given sentence "Don's score decreased by 23 is 43" is d - 23 = 43, where d represents Don's score.

To translate the given sentence into an equation, let's break it down:

"Don's score" can be represented by the variable d.

"Decreased by 23" indicates a subtraction operation. So we subtract 23 from Don's score.

"Is" signifies the equal sign in the equation.

"43" is the result or value that Don's score decreased by 23 should be equal to.

Combining all the information, we can write the equation:

d - 23 = 43

This equation states that when we subtract 23 from Don's score (represented by d), the result should be equal to 43. This equation accurately represents the given sentence.

To find the value of Don's score (d), we can solve the equation by isolating the variable:

d - 23 = 43

Adding 23 to both sides of the equation:

d - 23 + 23 = 43 + 23

Simplifying:

d = 66

Therefore, Don's score, represented by the variable d, is equal to 66 based on the given equation.

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The point of intersection of line m and line n is: Line W

The intersection of two lines is defined as the point where the two lines intersect or intersects.

Line segments m and n are assumed to intersect. That is, they must eventually intersect.

In this question we need to find the intersection of lines l and m.

And suppose lines  A and B intersect.

From the given figure, we can see that in plane A, lines m and n intersect at point W. The point W is therefore the intersection of the two lines m and n.  

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The set A U U is:

A U U = {a, b, c, d, e, f, g, h}

A set is a collection or grouping of distinct objects, which are called elements or members of the set. These objects can be anything: numbers, letters, shapes, or even other sets.

We have:

A= {c, d, g, h}

U= {a, b, c, d, e, f, g, h}

A U U is the set of all elements (letters) that appear in both A and U. Thus, we can say:

A U U = {a, b, c, d, e, f, g, h}

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The effect on the graph of f(x) = x² when it is transformed to h(x) = 3x² - 7 is described by option B. The graph of f(x) is vertically stretched by a factor of 3 and shifted 7 units down.

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Evaluating when [tex]\( n = 1 \)[/tex], the value of S is: S = 1

Evaluate:

[tex]\[ S = 108(2)^{n-1} \][/tex]

When n = 1.

Remember: For a geometric series, the sum can be calculated using the formula:

[tex]\[ S = 108(2)^{n-1} \][/tex]

In this case, we have r = 2, since each term is multiplied by 2 to get the next term.

Substituting the values into the formula, we get:

[tex]\[ S = \frac{{(1 - 2^n)}}{{1 - 2}} \][/tex]

Simplifying further:

[tex]\[ S = \frac{{1 - 2^n}}{{-1}} \][/tex]

Since the denominator is -1, multiplying the numerator and denominator by -1, we get:

[tex]\[ S = 2^n - 1 \][/tex]

Therefore, when [tex]\( n = 1 \)[/tex], the value of S is:

S = [tex]2^1[/tex]- 1 = 2 - 1 = 1

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None of the answer choices provided (O (-5, -1), O (-1, 5), O (-1, -5), O (-5, 1)) are correct, as the concept of a center does not apply to Linear functions.

To determine the center of the function f(x), we need more information about the function. The expression given, 2x-1, represents a linear function, which is in the form y = mx + b, where m is the slope and b is the y-intercept.

The center of a function is typically associated with quadratic or circular functions and is not applicable to linear functions. Therefore, we cannot determine the center of the function f(x) = 2x - 1 based on the given information.

Thus, none of the answer choices provided (O (-5, -1), O (-1, 5), O (-1, -5), O (-5, 1)) are correct, as the concept of a center does not apply to linear functions.

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The two points are the tips of the vertical dotted line which represents the measure of the rectangles width and the base of the triangle. To obtain the area of the composite figure, calculate and add the area of each shape.

The figure given is a composite figure which consists of a rectangle and triangle. The polygon could be broken into two pieces by drawing a vertical line from the endpoint of the 28cm line segment of the rectangle.

2.)

To obtain the area of the composite figure, we need to calculate the area of the rectangle and triangle separately and then add them together.

Hence, adding the area of each shape gives the area of the composite figure.

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Answer: correct answer is B

Step-by-step explanation:

I did the assignment

The correct length of side k in triangle JKL is approximately 35.15 units.

The correct answer is option E.

The length of side k in triangle JKL using the correct values for sin(52°) and sin(97°).

Given:

m∠J = 97 degrees

m∠L = 31 degrees

J = 44

According to the Law of Sines, we have:

sin(∠J) / J = sin(∠K) / k

Substituting the given values:

sin(97°) / 44 = sin(∠K) / k

Now, let's solve for k:

k = (44 * sin(∠K)) / sin(97°)

Using a calculator:

k = (44 * sin(52°)) / sin(97°)

k ≈ (44 * 0.79) / 0.99

k ≈ 35.1

Therefore, the correct length of side k in triangle JKL is approximately 35.15 units making option E the correct answer.

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The question probable may be:

Triangle JKL has the following measures :m∠J=97degree, m∠L=31degree, and j=44. What is the length of side k?

A. 46.3

B. 52.0

C. 22.8

D. 34.9

E. 35.1

The property represented by the equation (8 x 5) x 6.75 = 8 x (5 x 6.75) is the associative property of multiplication.  The associative property of multiplication states that when three or more numbers are multiplied, the product is the same regardless of the grouping of the factors.

This means that if there are multiple numbers to multiply, it does not matter which numbers you multiply first.Here, both sides of the equation are equal: (8 x 5) x 6.75 = 340.5, and 8 x (5 x 6.75) = 340.5.

This shows that you can multiply the numbers in any order and still end up with the same product. Therefore, this equation represents the associative property of multiplication.

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Answer:

-----------------------

Apply the intersecting chords theorem, which states that:

It gives us the following equation:

Solve it for x:

The matching choice is C.

The calculated value of [-12] is (b) -12

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

[-12]

Remove the square bracket

So, we have

-12

The above expression cannot be further simplified

So, we have

[-12] = -12

Hence, the calculated value of [-12] is (b) -12

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Answer:

-12

Step-by-step explanation:

took the quiz

Answer: 147.57

Step-by-step explanation:

x - .26x = 109.20

0.26 = 26%

subtract 26% from 100% = 74%

109.20 / 0.74 = 147.57

Check work: 147.57 × .26 = 38.37

Then 147.57 - 38.37 = 109.20

The  12 feet of carpet is needed.

To round 11.5 feet to the nearest foot, we look at the decimal part, which is 0.5. According to the Rounding Rules, if the number being looked at is 5 or above, we round up by giving it a shove! Since 0.5 is exactly 5, we round up to the next whole number, which is 12 feet.

So, after rounding 11.5 feet to the nearest foot, we get 12 feet.

To determine how much carpet is needed, we use the rounded measurement, which is 12 feet.

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The value of the sum of 5 and the square of a number varies depending on the value of n. When n = 1, the result of the expression is 6, when n = 2, the result is 9, and when n = 3, the result is 14. The same applies when n is negative.

The sum of 5 and the square of a number is an expression that can be represented as (n² + 5), where n represents the number whose square is added to 5. The result of the expression varies depending on the value of n. In this answer, we will examine how to find the sum of 5 and the square of a number using various values of n.
If n = 1, then the square of n is equal to 1, and the sum of 5 and the square of n is equal to 6. Therefore, if n = 1, the result of the expression is 6.
If n = 2, then the square of n is equal to 4, and the sum of 5 and the square of n is equal to 9. Therefore, if n = 2, the result of the expression is 9.
If n = 3, then the square of n is equal to 9, and the sum of 5 and the square of n is equal to 14. Therefore, if n = 3, the result of the expression is 14.
If n = -1, then the square of n is equal to 1, and the sum of 5 and the square of n is equal to 6. Therefore, if n = -1, the result of the expression is 6.
If n = -2, then the square of n is equal to 4, and the sum of 5 and the square of n is equal to 9. Therefore, if n = -2, the result of the expression is 9.
If n = -3, then the square of n is equal to 9, and the sum of 5 and the square of n is equal to 14. Therefore, if n = -3, the result of the expression is 14.
In conclusion, the value of the sum of 5 and the square of a number varies depending on the value of n. When n = 1, the result of the expression is 6, when n = 2, the result is 9, and when n = 3, the result is 14. The same applies when n is negative.

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Answer:

30

Step-by-step explanation:

ahora:

edad de Kevin = k

edad de Gabriela = g

k = 2g

hace 12 años:

edad de kevin = k - 12

edad de gabriela = g - 12

k - 12 = 6(g - 12)

k = 2g

k - 12 = 6(g - 12)

2g - 12 = 6(g - 12)

2g - 12 = 6g - 72

4g = 60

g = 15

k = 2g = 2 × 15 = 30

It will take 14 days for 46 workers to build similar house.

When building a house, the number of days required to build is inversely proportional to the number of workers.

Therefore,

d α 1 / w

d = k / w

k = dw

where

Therefore,

k = 161 × 4

k = 644

Let's find the number of days to build similar house with 46 workers.

Therefore,

d = 644 / 46

d = 14 days

Therefore, it will take 14 days.

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Answer:

A) -5.44

Step-by-step explanation:

-7.94 + 2.5 = -5.44

 -7.94

+ 2.50

-------------

 -5.44

Hope this helps! :)

Answer:

-5.44

Step-by-step explanation:

Align the decimals.

since the greatest value (7.94) is having negative sign(-), your answer remains negative.

- 7.94

2.5

-5.44

The coordinate line such that it has a position s​=f(t)=t^2-6t+5 on the interval 0≤t≤8, body changes direction at `t=3s`.

Given that the position of the body is s = f(t) = [tex]t^2[/tex] − 6t + 5 on the interval 0≤t≤8 on a coordinate line.

Here, s is in meters and t is in seconds.

We need to find the following.

A) The body's displacement and average velocity for the given time interval.

B) The body's speed and acceleration at the endpoints of the interval.

C) The interval does the body change directionLet's solve each part.

A) Displacement is given by the formula:

[tex]$$\Delta s=f(t_2)-f(t_1)$$

$$\Delta s= f(8)-f(0)$$[/tex]

[tex]$$\Delta s=(8)^2-6(8)+5-[0^2-6(0)+5]$$

$$\Delta s=64-48$$

$$\Delta s=16m$$[/tex]

The average velocity is given by the formula:

[tex]$$\overline{v}=\frac{\Delta s}{\Delta t}$$[/tex]

where, [tex]$\Delta t$[/tex] is the time taken.

[tex]$$ \Delta t=8-0=8s$$

$$\overline{v}=\frac{16}{8}$$

$$\overline{v}=2m/s$$[/tex]

B) Speed is the magnitude of velocity.

The velocity is given by

The acceleration is given by [tex]v=\frac{ds}{dt}=f'(t)$$[/tex]

[tex]a=\frac{dv}{dt}=f''(t)$$[/tex]

Let's calculate the velocity at the endpoints of the interval.

[tex]$$v(0)=f'(0)=2(0)-6= -6m/s$$[/tex]

[tex]$$v(8)=f'(8)=2(8)-6= 10m/s$$[/tex]

Let's calculate the acceleration at the endpoints of the interval.

[tex]$$a(0)=f''(0)=2m/s^2$$[/tex]

[tex]$$a(8)=f''(8)=2m/s^2$$[/tex]

C) The body changes direction at the point where the velocity changes its sign.

Let's find the point where the velocity changes its sign.

[tex]$$v(t)=0$$

$$2t-6=0$$

$$2t=6$$

$$t=3s$$[/tex]

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(a) The body's displacement and average velocity for the given time interval is 21 m and  2 m/s respectively.

(b) The​ body's speed and acceleration at the endpoints of the interval is 10 m/s and  2 m/s² respectively.

(c) The interval at which the body changes direction is 0 ≤ t ≤ 3 s.

(a) The body's displacement and average velocity for the given time interval is calculated as follows;

s = f(t) = t² - 6t + 5

0 ≤ t ≤ 8 s

f(0) = 0 - 0 + 5 = 5 m

f(8) = 8²  - 6(8) + 5 = 21 m

displacement = 21 m - 5 m = 16 m

average velocity = ( 16 m ) / (8 s - 0 s ) = 2 m/s

(b) The​ body's speed and acceleration at the endpoints of the interval is calculated as;

v = f'(t) = 2t - 6

v(8) = 2(8) - 6 = 10 m/s

a = dv/dt = 2 m/s²

(c) the time to reach maximum height is calculated as;

v = 2t - 6

0 = 2t - 6

2t = 6

t = 3 s

Interval = 0 ≤ t ≤ 3 s

the height when the direction is changed;

f(3) = (3²) - 6(3) + 5

f(3) = - 4m

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Answer:

a) sum

b) shorter

c) longest

Step-by-step explanation:

a) sum

b) shorter

c) longest

Step-by-step explanation:

2). 5/2

3). 7/9

4). 12/5

5).5/6

Answer:

The list price would be $420.