a) let f(x) = |x| and define f(x) = ) x −1 f. find a piecewise algebraic formula for f(x) for all x. where is f continuous? where is f differentiable? where does f (x) = f(x)?

Answer:

1. b

2. -16

Step-by-step explanation:

1. -1+2 is equal to 1 so it works

You plug in each of the coordinates x and y variables on the graph and find one that satisfies the equation.

2. -(-4)(-5) is -20

-(-4) is = 4

-20+4 is -16

The probability that an incoming call to the customer service center will be from a customer who is either moderately satisfied or very satisfied with the service given by the call center is 0.480 or 48.0%.

To find the probability that an incoming call to the customer service center will be from a customer who is either moderately satisfied or very satisfied, we need to calculate the probability separately for each district and then sum them up.

Let's denote the events:

M: Call from a customer who is moderately satisfied.

V: Call from a customer who is very satisfied.

We are interested in finding P(M or V), which is the probability of the event M or the event V occurring.

For District A:

P(M) = 33%

= 0.33

P(V) = 11%

= 0.11

For District B:

P(M) = 34%

= 0.34

P(V) = 20%

= 0.20

Now, let's calculate the probability for each district by considering the proportions of calls from each district:

For District A:

P(A) = 60%

= 0.60

For District B:

P(B) = 40%

= 0.40

To find the overall probability of a call being moderately satisfied or very satisfied, we can use the law of total probability:

P(M or V) = P(A) * (P(M) + P(V)) + P(B) * (P(M) + P(V))

P(M or V) = (0.60 * (0.33 + 0.11)) + (0.40 * (0.34 + 0.20))

Calculating the values, we get:

P(M or V) = 0.60 * 0.44 + 0.40 * 0.54

= 0.264 + 0.216

= 0.480

Therefore, the probability that an incoming call to the customer service center will be from a customer who is either moderately satisfied or very satisfied with the service given by the call center is 0.480 or 48.0%.

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Answer:

C

Step-by-step explanation:

Ed2021

The solutions of the given trigonometric equation are 60°, 180°, 300°.

A trigonometric equation is an equation that consists of one or multiple trigonometric ratios of unknown angles.

The given trigonometric equation is:

cos (x/2) - sin (x) = 0

⇒ cos (x/2) - 2sin (x/2) cos (x/2) = 0

⇒ cos (x/2) [1 - 2sin (x/2)] = 0

Therefore,  cos (x/2) = 0 = cos (90°)  (x/2 can't be 270°)

⇒ x = 180°

Again,  [1 - 2sin (x/2)] = 0

⇒ 2sin (x/2) = 1

⇒ sin (x/2) = 1/2

⇒ (x/2) = 30°, 150°

⇒ x = 60°, 300°

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Answer:

The rate of customers entering the store would be 3 minutes per customer.

Step-by-step explanation:

3 customers entered over the course of 9 minutes

We can simplify 3/9 to 1/3. That would mean 1 customer enters every 3 minutes.

Answer:

\(x^{2} + x -3\)

Step-by-step explanation:

1. Write out the equation

\((x-2)+( x^{2} -1)\\\)

2. Add like-terms

\(x^{2} +x-3\)

Step-by-step explanation:

(X^2-1+x-2)

(X^2+x-2x-2)

X(x+1)-2(x+1)

(X-2)(x+1)

The subject with the maximum average is Mathematics, while the subject with the minimum average is Social studies; moreover, there is a difference of 6 between Hindi and English.

Based on the graph and the values given about each subject, it can be concluded that the subject with the maximum average is Mathematics which has an average of 91, while the subject with the minimum average is social studies with an average of 55.

English average: 62

Hindi average: 56

62 - 56 = 6

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Answer:

The percentage increase is 70%

Step-by-step explanation:

There is a calculator that solves the problem for you just enter the 2 values that they ask for

Using the division, 12 times will Pogo fetch the frisbee in 444 minutes.

In the given question we have to find how many times will Pogo fetch the frisbee in 4 minutes.

As given that the double number line shows that in 2 minutes, Pogo the dog can fetch a frisbee 6 times.

As given that in 2 minutes Pogo the dog fetch a frisbee = 6 times

So in 1 minutes Pogo the dog fetch a frisbee = 6/2 times

In 1 minutes Pogo the dog fetch a frisbee = 3 times

We have to find in 4 minutes how many frisbee Pogo the dog fetch

In 4 minutes Pogo the dog fetch a frisbee = 3*4 times

In 4 minutes Pogo the dog fetch a frisbee = 12 times

Hence, 12 times will Pogo fetch the frisbee in 444 minutes.

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The right answer is;

The double number line shows that in 2 minutes, Pogo the dog can fetch a frisbee 6 times.

Based on the ratio shown in the double number line, how many times will Pogo fetch the frisbee in 4 minutes?

When the process of observing or measuring yields results that consistently deviate in some way from the true value, this is known as observer/measurement bias. Because of the systematic mistake this adds into the data, the conclusions are incorrect or unreliable.

Observer/measurement bias is a sort of systematic error that happens when the technique used for observation or measurement yields results that consistently deviate in some way from the true value. The observer's own preconceived ideas or expectations, the measurement equipment, and the environment in which the observation or measurement is being conducted can all contribute to this form of bias.An observer's bias, for instance, could cause them to see or measure something in a way that favours one particular result or outcome over another. Similar to how external influences like noise, light, or temperature can skew results, the environment in which the observation or measurement is taking place may add a bias. If feasible, results that are inaccurate or unreliable because of observer/measurement bias should be avoided because they can lead to incorrect inferences about the data.

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$ 410

hi there !

80% ................. $328

100% .................$ x

x = 100×328/80

= 32800/80

= $ 410

Good luck !

In order for a 22% probability that a gallon of gas costs less than 1.80, the standard deviation have to be 39.21 cents.

Given data,

The average retail price of gasoline (all types) for the first half of 2005 was 212.2 cents.

Round z-value calculations to two decimal places and final answer to the nearest cent.

Method First, we have to calculate the z-value of 1.80.

Mean = 212.2 cents Standard deviation = ?

Value = 180 cents

Z = (x - μ) / σ

where, x = 180

μ = 212.2

σ = standard deviation of price distribution

Z = (180 - 212.2) / σ0.22 = P(z < (180 - 212.2) / σ)From standard normal distribution table (attached),

P(z < 0.84) = 0.7995.0.22 = 0.7995(180 - 212.2) / σσ = (180 - 212.2) / (0.22 × 0.7995)σ = 39.21 cents

Hence, the standard deviation have to be 39.21 cents in order for a 22% probability that a gallon of gas costs less than 1.80.

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Answer:

B.)8ft

Step-by-step explanation:

Set up a proportional to the roof slope:

2/5 = x/20

Cross multiply:

40/5 = 5x/5

x=8ft

Answer: B) 8 ft

Step-by-step explanation:

\(\frac{2}{5}*\frac{4}{4} =\frac{8}{20}\)

The graph with x 3 is called a cubic graph.

A graph is a visual representation of data, usually plotted on a two-dimensional plane. When graphing a function, the x-axis is used to represent the independent variable and the y-axis is used to represent the dependent variable. A graph with x 3 is a graph that shows the relationship between the independent variable, x, and the dependent variable, x3. This type of graph is called a cubic graph, as the graph follows a cubic equation.

The graph with x 3 is called a cubic graph.

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The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,

To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.

1) So, perimeter = 3:1

The ratio of areas between two similar polygons is equal to the square of the scale factor.

Since the scale factor is 3:1, the ratio of their areas is:

(Ratio of areas) = (Scale factor)² = 9/1 = 9:1

Similarly,

2) Perimeter = 7:4

Area = 49/16

Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

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Answer:

Step-by-step explanation:

∠ABD is a straight angle then it measures m∠ABD = 180°

On the other hand , m∠ABD = m∠DBC + m∠CBE + m∠ABE

Therefore, (we get this equation)

m∠DBC + m∠CBE + m∠ABE = 180°

Solving the equation:

m∠ABE = 180 - (m∠DBC + m∠CBE)

              = 180 - (115 + 20)

              = 180 - 135

              = 45°

If ∠ABD is a straight line, then the sum of the measures of ∠ABE, ∠EBC, and ∠CBD should be equivalent to 180°. Therefore,

\(\implies \angle ABE + \angle EBC + \angle CBD = 180\°\)

We are given the following measures:

Now, plug the measures into the equation [∠ABE + ∠EBC + ∠CBD = 180°]

\(\implies \angle ABE + \angle EBC + \angle CBD = 180\°\)

\(\implies \angle ABE + 20 + 115 = 180\)

Now, simplify by adding:

\(\implies \angle ABE + 20 + 115 = 180\)

\(\implies \angle ABE + 135 = 180\)

Furthermore, to determine the measure of ∠ABE, isolate it on one side of the equation. This can be done by subtracting 135 on both sides.

\(\implies \angle ABE + 135 - 135 = 180 - 135\)

\(\implies \boxed{\angle ABE = 45\°}\)

To solve the inequalities -2x + 4 < 8 and 3x + 4 ≤ -5, we will solve them individually and then represent the solutions on a number line.

For the first inequality, -2x + 4 < 8, we will isolate x:

-2x + 4 - 4 < 8 - 4

-2x < 4

Dividing both sides by -2 (remembering to reverse the inequality when multiplying/dividing by a negative number):

x > -2

For the second inequality, 3x + 4 ≤ -5, we isolate x:

3x + 4 - 4 ≤ -5 - 4

3x ≤ -9

Dividing both sides by 3:

x ≤ -3

Now we represent the solutions on a number line. We mark -2 with an open circle (since x > -2), and -3 with a closed circle (since x can be equal to -3). Then we shade the region to the right of -2 and include -3 to represent the solutions.

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The nature of roots of quadratic equation x² = -2x + 1 is real and distinct.

The standard form of a quadratic equation is:

ax² + bx + c = 0

The discriminant is defined as:

D = b² - 4ac

Using  the value of discriminant, we can determine the nature of roots of a quadratic equation.

If:

D > 0, the quadratic equation has two distinct real roots or the roots are real and distinct.

D = 0, the quadratic equation has 1 real equal roots or the roots are unique

D < 0, the quadratic equation has complex conjugate roots or the roots are imaginary.

In this case, the quadratic equation is:

x² = -2x + 1

transform it into the standard form:

x² + 2x - 1 = 0

Calculate the discriminant:

D = 2²  - 4 (-1) = 8

Since D > 0, the roots are two distinct real roots.

Your question is incomplete, but most probably your question was:

What is the nature of roots of quadratic equation x² = -2x + 1?

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Answer:

3 rounds

Step-by-step explanation:

Variable x = number of rounds

2x + 13 = 3x + 10

13 = x + 10

3 = x

Answer:

Step-by-step explanation:

Answer:

The answer is B!

Step-by-step explanation:

Using the vertical line test, two points meet while up and down. It'd be B.

Jim decorates the front of the house with the ribbon.

In the figure, the dimension of the parts are given

The ribbon used to decorate the front of the house will be equal to the perimeter of the given figure.

Calculate the perimeter of the figure

So Jim needs 30.6 in of ribbon to decorate the house.

1) Coordinates are (2,-6) and (1,-1)

2) Points are (1,2) and (2,8).

You do the reverse to determine a point's coordinates in a coordinate system. Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there. To get the y-coordinate, repeat the previous step while adhering to a horizontal line.

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

Given,

Function:

1) f(x) = -x² - 2x + 2

Let x be 1

y = -(1)² - 2(1) +2

y = -1 -2 + 2

y = -1

Points are (1, -1)

Let x be 2

y = -(2)² - 2(2) + 2

y = -4 -4 + 2

y = -6

Points are (2,-6)

2) f(x) = -2x²

Let x be 1

y = 2(1)²

y = 2

Let x be 2

y = 2(2)²

y = 8

So,

Coordinates are (1,2) and (2,8)

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To determine the margin of error in a confidence interval estimate, we need to use the given information of the sample size (375 games) and the confidence level (90%) to calculate the margin of error.

To calculate the margin of error in a confidence interval estimate, we use the formula: Margin of Error = Critical Value multiplied by Standard Error. Given that the sample size is 375 games and the confidence level is 90%, we can determine the critical value using a standard normal distribution or a t-distribution, depending on the sample size and assumptions.

Since the sample size is relatively large (375 games) and we don't have information about the population standard deviation, we can use the standard normal distribution. For a 90% confidence level, the critical value for a standard normal distribution is approximately 1.645. Now, to calculate the standard error, we use the formula: Standard Error = under root [(pmultiplied by (1 -p)) / n], where p is the sample proportion and n is the sample size.

In this case, the sample proportion is calculated as 300/375 = 0.8. Using the given information, the standard error is calculated as under root [(0.8 multiplied by (1 - 0.8)) / 375] ≈ 0.0231. Finally, we can calculate the margin of error by multiplying the critical value and the standard error: Margin of Error = 1.645 multiplied by 0.0231 ≈ 0.0380. Therefore, the margin of error in a 90% confidence interval estimate of the true proportion of games won by the team leading at the end of the third quarter is approximately 0.0380.

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Answer:

25+144+X=180°

169+X=180°

X= 180-169

Therefore, x= 11°

checking process: (25+144+11= 180°)

Answer:

x = 11 i beileve!

Step-by-step explanation:

(2/3)x = 7 + 2

(2/3)x = 9

2x = 9 × 3

x = 27/2

:. x = 13 1/2

Given:-

Solution:-

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Therefore , it will take her to read 1428 pages in 34 days.

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hope it helps! :)

Answer: 13 units

Step-by-step explanation:Given that Point C is the midpoint of AB and point B is between points A and D. If AD = 17 and BD = 9

According to definition midpoint, AC = CB

According to definition of segment addition postulate, AD = AB + BD

AB = AD - BD

AB = 17 - 9

AB = 8

Again, AB = AC + CB

Therefore, CB = AB/2

CB = 8/2 = 4

Now, CD = CB + BD = 4 + 9

CD = 13 units

Hence, length of CD = 13 units

From the shadow of the flagpole, we can build a right triangle that will allow us to estimate the angle of elevation of the sun.

The shadow on the ground will be one hick of the triangle, and the flagpole will be the other hick. The hypotenuse will be the line connecting the tip of the flagpole and the tip of the shadow. The angle of elevation is the one formed between the ground and the hypotenuse.

With that, the adjacent hick will be the shadow in the ground (22 ft long), and the opposite hick is the flagpole itself (45 ft tall). The tangent of an angle is the ratio of the opposite hick to the adjacent hick. Let's call the angle of elevation α. Then:

To find the value of α we use the function inverse tangent:

Then, the angle of elevation is approximately 63.9°. The correct answer is option A.

The point of concurrency determined by the three altitudes of any triangle is called the orthocenter of the triangle.

The orthocenter is the intersection of the three altitudes of the triangle. It is a point on the plane of the triangle that is equidistant from the three sides of the triangle.

To find the orthocenter of a triangle, you can draw the altitudes of the triangle and find the point where they intersect. The orthocenter is the point of concurrency for the three altitudes.

An orthocenter of a triangle is a point where the three lines that are perpendicular to the sides of the triangle intersect. These lines are called altitudes of the triangle.

Alternatively, you can use the following formula to find the coordinates of the orthocenter:

Let's say that the vertices of the triangle are A(x1, y1), B(x2, y2), and C(x3, y3). The coordinates of the orthocenter (H) can be found using the following formula:

Hx = ( (y1 - y3) (x1^2 + y1^2 - x3^2 - y3^2) - (y1 - y2) (x1^2 + y1^2 - x2^2 - y2^2) ) / (2 * (y1 - y3) - 2 * (y1 - y2))

Hy = ( (x1 - x3) (x1^2 + y1^2 - x3^2 - y3^2) - (x1 - x2) (x1^2 + y1^2 - x2^2 - y2^2) ) / (2 * (x1 - x3) - 2 * (x1 - x2))

Therefore, The point of concurrency determined by the three altitudes of any triangle is called the orthocenter of the triangle

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