A candidate for congress is trying to decide what to focus her campaign on in order to win the election. Describe how she might obtain a random sample to know what issues are important to her constituents.

Answer:

y

≤

−

x

−

2

(1)

y

≥

−

5

x

+

2

(2)

First graph the 2 linear functions by intercepts:

a. y1 = - x - 2

Make x = 0 --> y-intercept is -2

Make y = 0 --> x-intercept is - 2

b. y2 = -5x + 2

Make x = 0 --> y-intercept is 2

Make y = 0 --> x-intercept is

2

5

Graphically solve the 2 linear inequalities (1) and (2).

The solution set of (1) is the area below the line y1. Color it.

The solution set of (2) is the area above the line y2. Color it.

The combined solution set of the system is the area commonly shared by the 2 above solution set areas.

graph{-x - 2 [-10, 10, -5, 5]}

graph{-5x + 2 [-10, 10, -5, 5]}

Answer:

X=60°

Step-by-step explanation:

Because the sum of angle of all side of a triangle is 180°

and

if that goes on

the equation become

x°+75°+45°=180°

x°+120°=180°

x°=180°-120°

x°=60° hence prove

a. F is concave up on (-∞, 0) ∪ (6, ∞) and concave down on (0, 6).

b. The inflection points are (0, -2) and (6, -226).

a) To determine the intervals of concavity, we need to find the second derivative of f:

f(x) = (x⁴)/4-3x³-2f'(x) = x³ - 9x²f''(x) = 3x² - 18x

The second derivative f''(x) is a polynomial. We need to find the values of x for which f''(x) is zero or undefined.3x² - 18x = 3x(x - 6)f''(x) = 0 when x = 0 or x = 6.

Now we can determine the intervals of concavity by testing the sign of f''(x) in each interval:

Interval (-∞, 0):f''(-1) = 3(-1)² - 18(-1) = 21 > 0, so f is concave up on (-∞, 0).

Interval (0, 6):f''(1) = 3(1)² - 18(1) = -15 < 0, so f is concave down on (0, 6).

Interval (6, ∞):f''(7) = 3(7)² - 18(7) = 63 > 0, so f is concave up on (6, ∞).

Therefore, f is concave up on (-∞, 0) ∪ (6, ∞) and concave down on (0, 6).

B. The inflection points occur where the concavity changes, which are at x = 0 and x = 6.

The ordered pairs for the inflection points are (0, f(0)) and (6, f(6)).

f(0) = -2 and f(6) = -226, so the inflection points are (0, -2) and (6, -226).

c) To find the critical points, we need to find the values of x for which f'(x) = 0 or f'(x) is undefined:

f'(x) = x³ - 9x² = x²(x - 9)

f'(x) = 0

when x = 0 or x = 9.f''(0) = 0,

so we can use the First Derivative Test to determine that f has a relative maximum at x = 0.f''(9) = 36 &

gt; 0 so we can use the Second Derivative Test to determine that f has a relative minimum at x = 9.

Therefore, the relative extrema are:

Relative maximum at x = 0.

Relative minimum at x = 9.

d) To find where f'(x) has relative maxima and minima, we need to find the values of x for which f''(x) = 0 or f''(x) is undefined:

f''(x) = 3x² - 18x = 3x(x - 6)f''(x) = 0 when x = 0 or x = 6.

We can use the First Derivative Test to determine the nature of the relative extrema:

For x &

lt; 0, f'(x) is negative, then f'(x) is increasing from negative to zero as x approaches 0 from the left.

Therefore, f'(x) has a relative minimum at x = 0.

For 0 < x < 6, f'(x) is positive, then f'(x) is increasing from zero to positive as x increases.

Therefore, f'(x) has a relative maximum at x > 0.

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a. F is concave up on (-∞, 0) ∪ (6, ∞) and concave down on (0, 6).

b. The inflection points are (0, -2) and (6, -226).

How to determine the intervals of concavity?

a) To determine the intervals of concavity, we need to find the second derivative of f:

f(x) = (x⁴)/4-3x³-2f'(x) = x³ - 9x²f''(x) = 3x² - 18x

The second derivative f''(x) is a polynomial. We need to find the values of x for which f''(x) is zero or undefined.3x² - 18x = 3x(x - 6)f''(x) = 0 when x = 0 or x = 6.

Now we can determine the intervals of concavity by testing the sign of f''(x) in each interval:

Interval (-∞, 0):f''(-1) = 3(-1)² - 18(-1) = 21 > 0, so f is concave up on (-∞, 0).

Interval (0, 6):f''(1) = 3(1)² - 18(1) = -15 < 0, so f is concave down on (0, 6).

Interval (6, ∞):f''(7) = 3(7)² - 18(7) = 63 > 0, so f is concave up on (6, ∞).

Therefore, f is concave up on (-∞, 0) ∪ (6, ∞) and concave down on (0, 6).

B. The inflection points occur where the concavity changes, which are at x = 0 and x = 6.

The ordered pairs for the inflection points are (0, f(0)) and (6, f(6)).

f(0) = -2 and f(6) = -226, so the inflection points are (0, -2) and (6, -226).

c) To find the critical points, we need to find the values of x for which f'(x) = 0 or f'(x) is undefined:

f'(x) = x³ - 9x² = x²(x - 9)

f'(x) = 0

when x = 0 or x = 9.f''(0) = 0,

so we can use the First Derivative Test to determine that f has a relative maximum at x = 0.f''(9) = 36 &

gt; 0 so we can use the Second Derivative Test to determine that f has a relative minimum at x = 9.

Therefore, the relative extrema are:

Relative maximum at x = 0.

Relative minimum at x = 9.

d) To find where f'(x) has relative maxima and minima, we need to find the values of x for which f''(x) = 0 or f''(x) is undefined:

f''(x) = 3x² - 18x = 3x(x - 6)f''(x) = 0 when x = 0 or x = 6.

We can use the First Derivative Test to determine the nature of the relative extrema:

For x &

lt; 0, f'(x) is negative, then f'(x) is increasing from negative to zero as x approaches 0 from the left.

Therefore, f'(x) has a relative minimum at x = 0.

For 0 < x < 6, f'(x) is positive, then f'(x) is increasing from zero to positive as x increases.

Therefore, f'(x) has a relative maximum at x > 0.

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Answer:

man its

C

hope I heped

Step-by-step explanation:

Answer:

34 pages

Step-by-step explanation:

For the first three pages, Sonia is already down 13 dollars.

106-13=93 dollars left

93/3 dollars per page =31

31+those three first pages=34 pages

Answer:

34

Step-by-step explanation:

When you subtract 13 by 106 you will receive 93. Then you divide 93 by 3 and get 31. Add 3 pages to 31 and get 34. (If you're wondering where i have gotten the 3 it is from the first 3 pages Sonia paid for)

Hope this helped.

Answer:

D

Step-by-step explanation:

The probability that among the first two songs played, exactly 1 of the 4 songs you like is played is 0.452 or 45.2%.

Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

There are 4 songs that you like out of the 14 total songs, so the probability of selecting a song that you like on the first draw is 4/14.

On the second draw, the probability of selecting a song that you like is 3/13, since there are now 3 songs that you like out of the remaining 13 songs.

The probability of selecting exactly 1 of the 4 songs you like in the first two draws is given by:

P(exactly 1 like in first two draws) = (4/14) ×(10/13) + (10/14) × (4/13) = 0.452

Therefore, the probability that among the first two songs played, exactly 1 of the 4 songs you like is played is approximately 0.452 or 45.2%.

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The value of x is 33.4

To determine the value in the green box, we need to know that there are six different trigonometric identities.

These identities are enumerated as;

Using the sine identity, we have;

sin θ = opposite/hypotenuse

We have that;

θ = 64 degrees

Opposite = 30

Hypotenuse  = x

Substitute the values, we have;

sin 64 = 30/x

cross multiply

x = 30/0. 8987 = 33. 4

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The interval notation for the solution set is (-∞, -4] and the number line is on the image at the end.

Here we want to find the solution set of the inequality below:

x ≤ -4

First let's do the interval notation. This will be the set that contains all the numbers from negative infinity to -4 (with -4 included, so  we need to have a closed set at that end)

This is written as:

(-∞, -4]

The use of the symbols [ ] means that the element belongs to the set.

Now to the number line, we will have a closed circle at x = -4 (because it is a solution) and a line that goes to the left of it. You can see an example in the graph at the end.

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For the statement "If a polygon lacks right angles, then it is a parallelogram.", the counter example is -

Option A : a right triangle

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

A counterexample for a conditional statement is an example that satisfies the hypothesis (the first part of the statement) but does not satisfy the conclusion (the second part of the statement).

In this case, the statement is "If a polygon lacks right angles, then it is a parallelogram."

A right triangle is a polygon that lacks right angles, but it is not a parallelogram.

Therefore, a right triangle is a counterexample for this statement.

A square, a regular hexagon, and a rectangle all have right angles, so they are not counterexamples for this statement.

Therefore, the triangle is the counterexample.

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The probability of getting 3 heads in 4 coin tosses, given that we get at least 2 heads, is 4/11 or 0.364.

To solve this problem, we can use the conditional probability formula. Let A be the event of getting 3 heads in 4 coin tosses, and let B be the event of getting at least 2 heads in 4 coin tosses. Then we want to find P(A|B), the probability of getting 3 heads in 4 coin tosses given that we get at least 2 heads.

By the definition of conditional probability, we have:

P(A|B) = P(A and B) / P(B)

To find P(B), the probability of getting at least 2 heads in 4 coin tosses, we can use the complement rule and find the probability of getting 0 or 1 heads:

P(B) = 1 - P(0 heads) - P(1 head)

To find P(0 heads), the probability of getting 0 heads in 4 coin tosses, we use the binomial probability formula:

P(0 heads) = (4 choose 0) * (0.5)^0 * (1-0.5)^(4-0) = 1/16

Similarly, we can find P(1 head):

P(1 head) = (4 choose 1) * (0.5)^1 * (1-0.5)^(4-1) = 4/16

So,

P(B) = 1 - P(0 heads) - P(1 head) = 11/16

To find P(A and B), the probability of getting 3 heads in 4 coin tosses and getting at least 2 heads, we can use the binomial probability formula again:

P(A and B) = (4 choose 3) * (0.5)^3 * (1-0.5)^(4-3) = 4/16

Therefore,

P(A|B) = P(A and B) / P(B) = (4/16) / (11/16) = 4/11

So the probability of getting 3 heads in 4 coin tosses, given that we get at least 2 heads, is 4/11 or approximately 0.364.

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Answer:

25%

Step-by-step explanation:

Answer:

a=92  b=37  c=51

Step-by-step explanation:

a= 7x-6

b=3x-5

c=4x-5

7x-6+3x-5+4x-5=180

14x-16=180

14x=196

x=14

The measure of side length EF in the right triangle is 24.

The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c²  = a² + b²

From the diagram:

Hypotenuse DE = c = 26

Leg DF = a = 10

Leg EF = b = ?

Plug in the values and solve for b:

c²  = a² + b²

26²  = 10² + b²

676  = 100 + b²

b² = 676  - 100

b² = 576

b = +√576 ( we take the positive value since we are dealing with dimensions)

b = 24

Therefore, the length EF is 24.

Option C)24 is the correct answer.

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Answer: 7ft/s

Step-by-step explanation: 7ft x 10 sec =70 seconds

Answer:

2x ( -3x + 14)

Step-by-step explanation:

Distribution property is used in a format like a ( b + c ). To simplify these kinds of expressions, we multiply the outside term by each of the inside terms. So in this instance, a ( b + c ) is equal to ab + ac.

3x ( 2x - 8 ) + 4x

Let's use what we learned above, and multiply the outside term (-3x) by each of the inside terms.

-3x · 2x + (-3x) · (-8) +4x

Simplify by multiplication:

-6x² + 24x +4x

Finally, we add:

-6x² +28x

Now, to simplify further, we can look for terms that show up in numbers.

We can see that the variable x is present in each of the terms, so we can factor that out, removing it from the term as follows:

x ( -6x + 28)

We can look and see that 2 is also a common factor between the two terms, so we can take that out too.

2x ( -3x + 14)

This is the most simplified it can get.

Part a: Carl earning per hour is $18.

Part b: More Money is earned by Carl.

Part c: The  graph that represents Carl's earnings is drawn.

For the given question,

The amount of the money Louis have is defined by the equation.

Carl's Earnings

Time (h)  Hours      3     5     8    10

Money earned($)  54 90 144 180

Part a: Carl earning per hour.

For 3 hours Carl earns $54.

For one hour-$54/3 = $ 18.

Part b: More Money is earned by-

For 1 hours Carl earns $8.

For 1 hour Louis earning is y = 14×1 = $14.

Thus, Carl earns more.

Part c: The  graph that represents Carl's earnings over time in hours is drawn.

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Answer:

A

Step-by-step explanation:

You can't square a negative number, so the number must be non real.

Answer:

Step-by-step explanation:

The equation of the line with the given points is y = 6x - 4. This can be derived by calculating the slope of the line, which is 6, and then using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the given points are (x1, y1) = (1, 10), so the equation of the line is y - 10 = 6(x - 1) or y = 6x - 4.

Answer y == 3

+7

Step-by-step explanation:

The graph of a linear relationship contains the points (1, 10) and (3, 16).

Write the equation of the line in slope-intercept fo

Step-by-step explanation:

the general slope-intercept form is

y = ax + b

a is the slope, which is the ratio of "y coordinate change / x coordinate change" when going from one point to another on the line.

b is the y-intercept - the y value when x = 0.

for the slope we see

x changes by +2 (from 1 to 3)

y changes by +6 (from 10 to 16)

so, the slope a is +6/+2 = 3

and the semi-ready equation is

y = 3x + b.

now we use one of the points in the equation to solve for b. I picked (1, 10) :

10 = 3×1 + b = 3 + b

b = 7

so, the full equation is

y = 3x + 7

Answer:

27

Step-by-step explanation:

Answer:

18Πin3

Step-by-step explanation:

Answer:

8/3

9/11

try it. and send money :)

Answer:

2+2 = 4

Step-by-step explanation:

Let's visualize this using # signs

we have two groups of two # signs, so let's map that out

##

##

If you count the individual # signs, it is 4. You can also use this model to figure out 2 *2 (4)

I hope this helps :)

Answer:

4

Step-by-step explanation:

2+2

2+1+1

3+1

4

Answer:

0.9, 0.89, 0.81, 0.8, 0.79, 0.09, 0.08

Step-by-step explanation:

Answer: 0.09 , 0.89 , 0.81, 0.08, 0.79 , 0.9, 0.8

Step-by-step explanation:

First find the greatest

0.09, 0.89,0.81, 0.08, 0,79

Then the least

0.9 .0.8

Now put it all together  

0.09, 0.89. 0.81 , 0.08, 0.79 , 0.9, and lastly 0.8

Answer:

-1/2

Step-by-step explanation:

To find f(f^-1(-1/2)), we need to first find the inverse of f, which is denoted as f^-1. The inverse of a function f is another function that undoes the effect of f. In other words, if y = f(x), then x = f^-1(y).

The inverse of f is given by:

f^-1(y) = (y - 5) / 2

Now we can substitute -1/2 for y in this expression to find f^-1(-1/2):

f^-1(-1/2) = (-1/2 - 5) / 2

f^-1(-1/2) = (-11/2) / 2

f^-1(-1/2) = -11/4

Now that we have found f^-1(-1/2), we can substitute this value into the original function f to find f(f^-1(-1/2)):

f(f^-1(-1/2)) = f(-11/4)

f(f^-1(-1/2)) = 2(-11/4) + 5

f(f^-1(-1/2)) = -11/2 + 5

f(f^-1(-1/2)) = -1/2

Therefore, f(f^-1(-1/2)) = -1/2

The amount of fewer euros he would receive as a result of the delay is 20 E.

The percentage loss that was caused by the delay is -4%.

Exchange rate is the rate at which one unit of a currency can buy another currency. In this question, the value of Euros appreciated by Monday. This is because $1 buys less Euros on Mondays. On the hand, dollars depreciates in value.

Amount of fewer Euros received = value of euros if it were exchanged on Friday - value of euros if it was exchanged on Monday

Value of euros if it were exchanged on Friday = 1.25 x 400 = 500 E

Value of euros if it was exchanged on Monday = 1.20 x 400 = 480 E

Difference = 500 E - 480 E = 20 E

Percentage loss = (Euros received on Monday / Euros that would have been received on Friday) - 1

Percentage loss = (480 / 500) - 1 = -0.04 = -4%

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Answer:

3×1/2 = 1.5km per week

14÷1.5=9.33 if you round it it would take 9weeks