What are the domain and range of the piecewise function

The expected number of hits

= ∑x P (X=x) = 0.96

Here, we have, to solve

Let X be a Binomial random variable that denotes the number of hits

where the parameters are n = 3, p = 0.320

P(X = x) , x = 0,1,2,3

(a) The probability distribution of X is

P(X = 0) = 0.3144

P(X = 1) = 0.4439

P(X = 2) = 0.2089

P(X = 3) = 0.0328

X 0 1 2 3

P(X = x) 0.3144 0.4439

0.2089

0.0328

(c) Expected number of hits

= ∑x P (X=x) = 0.96

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complete question:

Percents (round to 1. Jing has a .320 on-base percentage. Over the course of a 3-game series, Jing will bat 14 times. Assume that the chance of getting on base a fixed number of times is a binomial distribution. *tel Is the distribution for Jing getting on base symmetric, skewed right or skewed left?

The value of x, y and z in the line is as follows:

x = 55°

y = 125°

z = 55°

When lines intersect, angle relationships are formed such as vertically opposite angles, adjacent angles etc.

Therefore, let's use the angle relationship to find the angles x, y and z in the line.

Hence,

y = 125 degrees(vertically opposite angles)

Therefore,

x = 180 - 125(angles on a straight line)

x = 55 degrees

Therefore,

x = z(vertically opposite angles)

Vertically opposite angles are congruent.

Hence,

z = 55 degrees.

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The equation to model the given work is 5.4 liters / 10 teams = 0.54 liters per team, and 0.54 liters per team × 920 grams per liter = 497.28 grams per team.

The teams will share 5.4 liters of olive oil. To find out how much each team will receive, we can divide the total amount of olive oil by the number of teams:

5.4 liters ÷ 10 teams = 0.54 liters per team

However, it's usually more convenient to express this in grams for equation, so we need to convert liters to grams.

The conversion factor for olive oil is approximately 0.92 grams per milliliter (or 920 grams per liter). So, we can multiply 0.54 liters per team by 920 grams per liter to get:

0.54 liters per team × 920 grams per liter = 497.28 grams per team

Therefore, each team will receive 497.28 grams of olive oil as per the work.

Equation: 5.4 liters / 10 teams = 0.54 liters per team, and 0.54 liters per team × 920 grams per liter = 497.28 grams per team.

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The word that best describes line segment ID in the image given showing a circle is: a chord.

A chord can simply be described as a line segment in a circle that connects two points on the circumference of a circle to each other.

The largest chord in a circle is a the diameter. A circle can have as many chords as possible.

Considering the image given above, ID is a line segment which connects points I and D which are on the circumference of the circle together. Therefore, ID can best be described as a chord.

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The decimal number 0.044 in the fraction form will be 11/250.

Given that:

Decimal number = 0.044

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Multiply and divide the decimal number by 1,000. Then we have

⇒ 0.044 x 1,000 / 1,000

⇒ 44 / 1,000

⇒ 11 / 250

The decimal number 0.044 in the fraction form will be 11/250.

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The shape of the data that we have here is skewed to the right

A dataset is considered to be right-skewed (sometimes known as excessively positive) when the greater portion of its data points are concentrated on the lower end, forming an asymmetrical distribution that has a long tail to the right.

As such, the mean (average) within these distributions generally surpasses the median in value, with the latter also exceeding the mode.

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If Angel bought a $600 phone in Toronto instead of San Antonio, he pays $28.50 more sales tax, based on the subtraction operation.

Subtraction operation is one of the four basic mathematical operations, including addition, multiplication, and division.

Subtraction operation involves the subtrahend, the minuend, and the difference.

Sales tax rate in San Antonio Texas = 8.25%

Sales tax rate in Toronto Ontario = 13%

The cost of a phone bought by Angel = $600

The sales tax in dollars in San Antonio Texas = $49.50 ($600 x 8.25%)

The sales tax in dollars in Toronto Ontario = $78.00 ($600 x 13%)

The difference in tax between Toronto and San Antonio = $28.50 ($78.00 - $49.50).

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The solution is, the value of the variables are x = 40 and, y = 160.

Notice that "x" and "3x+20" are supplementary angles so their sum is 180°

(x) + (3x + 20) = 180

4x + 20 = 180

4x = 160

x = 40

To solve for "y", you have 2 options: either notice that "x" and "y-20" are supplementary angles so their sum is 180° or notice that "3x + 20" and "y - 20" are vertical angles so are equal to each other. I am going to solve using the first option because it is less work.

(x) + (y - 20) = 180°

40 + y - 20 = 180

y + 20 = 180

y = 160

Answer: x=40, y=160

The solution is, the value of the variables are x = 40 and, y = 160.

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complete question:

Find the value of each variable

There is no calculation required. The bearing of U is 32° Southwest from T.

A bearing is the angle in degrees measured clockwise from north in mathematics. Bearings are often specified in three figures. 30° clockwise from north, for example, is generally represented as 030°.

Bearings are used to identify both the direction and the angle of a certain landmark. In surveying and aviation, a true bearing is the angle formed by a path or line with a fixed north-south line. A correct bearing ALWAYS measures clockwise from North. In a true bearing, for example, we would measure this obtuse angle and claim it has a bearing of °T.

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The values of angle x is 140⁰.

The values of angle y is 108⁰.

The values of angle x and angle y is calculated by applying intersecting chord theorem.

The intersecting chord theorem states that the angle at tangent is half of the arc angle of the two intersecting chords.

Angle opposite arc 50 = ¹/₂ x 50 = 25⁰

Angle opposite arc 50 = ¹/₂ x 30 = 15⁰

angle x = 180 - (25 + 15) ( sum of angles in a triangle )

x = 140⁰

The value of angle y is calculated as follows;

minor arc = y

major arc = 50 + 30 + 140 = 220⁰

56 = ¹/₂ (220 - y)

2(56) = 220 - y

112 = 220 - y

y = 108⁰

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Answer: 0.3 and 3/10

Step-by-step explanation:

its 3 tenths

One shirt costs $6.99

One shirt costs $4.74

In the question that we have here we need to obtain the cost of a shirt. When we want to get the cost of just one item from the cost of a given number of the same item we are said to be  trying to obtain the unit cost.

Hence in this problem, we are trying to find the unit cost without adding the cost of the one-time design fee as such we are going to have in this case that;

Cost of one shirt in case 1 = $349.50/50 = $6.99

Cost of one shirt in case 2 =  $2370/500 = $4.74

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The cost of cone is $4.66 and cost of sundaes $4.54.

Assume,

cost of 1 cone = x

cost of 1 sundaes = y

Then according to the question

5x + 8y = 59.82 ....(i)

7x + 6y = 59.62  ....(i)

Now from 7x(i)  - 5x(ii)

⇒ 26 y = 118.24

⇒      y = 4.54

Put value of y into (i),

⇒ 5x + 36.32 = 59.62

⇒               5x = 23.3

⇒                 x = 4.66

Thus, x = 4.66 and  y = 4.54

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The surface area of the solid is 281 ft².

Given that, a solid figure made of a rectangular prism and a square pyramid,

We need to find its surface area,

To find the same, we will find the lateral surface area of square pyramid, and total surface area of rectangular prism,

So,

Surface area = 2×side×slant height + 2(length·width+width·height+height·length)-base area of the square pyramid,

= 2×5×5 + 2(4·12+12·5+4·5)-5²

= 50+256-25

= 281 ft²

Hence the surface area of the solid is 281 ft².

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The graph that represents the function f(x) = [tex]\frac{1}{x - 3} - 2[/tex]  is shown below.

We are given a function f(x) = [tex]\frac{1}{x - 3} - 2[/tex] and we have to plot a graph that represents this function.

The function we have is f(x) = [tex]\frac{1}{x - 3} - 2[/tex]  . We will now find the domain of the function. A set of input values for which the function is real and has defined values is called the domain of the function. So, The given function will be undefined at x = 3

Therefore, the domain is x < 3  or x > 3.

Now, we will look for the range of the given function. The range is the set of values of the dependent variable for which the function is defined. If we inverse the given function, we get

y = [tex]\frac{(3x + 7)}{(x + 2)}[/tex]

We will find the domain of this inverse function. The domain is f(x)  < -2 or f(x) > -2. Now, we will find x-intercepts and y-intercepts. The x-intercept is the point where y = 0 and the y-intercept is where x= 0

Let f(x) = y

Then y = [tex]\frac{1}{x - 3} - 2[/tex]

Put x = 0

thus y-intercept is (0, -7/3)

Now put y = 0

Then  x-intercept is (7/2, 0)

Now, we will calculate the horizontal and vertical asymptotes.

Vertical asymptotes,

Now, we will go over every undefined point and check if at least one of these statements is satisfied.

[tex]lim_{x - > a^{-}} f(x) = \pm\infty[/tex]

[tex]lim_{x - > a^{+}} f(x) = \pm\infty[/tex]

Therefore, the vertical asymptotes are x = 3

and For horizontal asymptotes,

Check if  [tex]x - > \pm\infty[/tex] the function y = [tex]\frac{1}{x - 3} - 2[/tex] behaves as a line y = mx + b.

Therefore, we have y = -2 as horizontal asymptotes.

The plotted graph that represents the given function is shown below.

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The complete question is "Which graph represents the function f(x)=1/x+3-2 "

The values of the function will be 15, -69, 68 and 24

The function, f(x) = (-x)³ - x² - x + 15, is able to be evaluated with specific values of x. Taking the value of x as 0, the result is acquired to be f(0) = (-0)³ - 0² - 0 + 15 = 15, thus yielding a value of 15.

Substituting the number 4 in place of x yields f(4) = (-4)³ - 4² - 4 + 15 = -64 - 16 - 4 + 15 = -69. In this way, it can be deduced that the value for f(4) is -69.

Likewise, through substituting the value -4 instead of x into the f(x) expression, one can calculate f(-4): f(-4) = (-(-4))³ - (-4)² - (-4) + 15 = 64 - 16 + 4 + 15 = 67. This then shows that the response for f(-4) is 67.

Similarly, by adding together the evaluations for f(2) and f(-2), there will be a summation involving both numbers: f(2) + f(-2) = (-2)³ - 2² - 2 + 15 + (-(-2)³ - (-2)² - (-2) + 15). Consequently, when combined, the final addition renders 24.

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The area of the right triangle, using the two formula gave the same result as (25√3)/2 squre units.

A right triangle is a triangle in which one angle is a right angle.

Area of a triangle can be calculated using:

A = 1/2 × b × h

Where b and h are base and height respectively.

From the diagram:

Base b = 5

Height h = 5√3

Area = ?

Plug these values into the above formula and solve for area.

A = 1/2 × b × h

A = 1/2 × 5 × 5√3

A = (25√3)/2

Now, using a second formula to verify if we get the same result.

A = 1/2 × ab × sinC

From the image:

a = 5√3

b = 5

Angle C = 90

Plug in the values:

A = 1/2 × ab × sinC

A = 1/2 × 5√3 × 5 × sin( 90° )

A = 1/2 × 5√3 × 5 × 1

A = (25√3)/2

Therefore, the area of the triangle is (25√3)/2 squre units.

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The true statement is, The difference between the mean is about 2 times the mean absolute deviation of the data sets.

Mean absolute deviation (MAD) is defined as the average value of the absolute deviations from the mean.

Difference of the means is found by subtracting the two means.

Each mean is found by adding the data points and then dividing by the number of data sets.

The relationship between the difference of means and the MAD of two sets is,

The difference between the mean is about 2 times the mean absolute deviation of the data sets.

Hence the correct option is B.

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Answer:

Step-by-step explanation:

It’s not clear what you’re referring to by “surveying”. However, here are some questions that you can ask yourself while reading to help you better understand what you’re reading1:

a. The value of the mean is µ = 15

The value of the standard deviation is 2.74

b. Values of 9.52 girls or greater are significantly low.

Values of 20.48 girls or greater are significantly high

c.  The result of 25 girls is significantly high because it is greater than 20.48.

a. The mean for the number of girls in a group of 30 births is:

a. µ = np

= 30(0.5)

The value of the mean is µ  = 15

The standard deviation is:

a. σ = √(np(1-p))

= √(30(0.5)(0.5))

The value of the standard deviation = 2.74 (rounded to two decimal places)

b. Using the range rule of thumb, we can say that significantly low results are those that are less than 15 - 2.74(2) = 9.52, and significantly high results are those that are greater than 15 + 2.74(2) = 20.48.

c. The result of 25 girls is significantly high because it is greater than 20.48. This suggests that the method may be effective in increasing the likelihood of having a girl.

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Financial advantage (disadvantage) of making the 40,000 starters instead of buying them from an outside supplier is: $89,700.

Here, we have,

Financial advantage (disadvantage)

First step is to calculate the relevant cost of making starters

Relevant cost= Direct materials+ Direct labor+ Variable manufacturing overhead+ Supervision

Relevant cost=($4×69,000)+ ($3.20×69,000) +($0.60×69,000) + $117,300

Relevant cost=$276,000+$220,800+$41,400+$117,300

Relevant cost=$655,500

Second step is to calculate the relevant cost of buying starters

Relevant cost=$10.80 × 69,000

Relevant cost=$745,200

Third step is to calculate the financial advantage

Financial advantage=$745,200-$655,500

Financial advantage=$89,700

Therefore the financial advantage is $89,700.

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The equation 2x + (2x + 8) + x + (x - 32) = 360° can be used to solve for x which makes option D correct. The variable x for the arc angles is equal to 64.

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.

The arcs together is the circumference of the circle O and they subtends the angle at the center of the circle which is 360° so;

2x + (2x + 8) + x + (x - 32) = 360°

6x - 24 = 360

6x = 360° + 24 {collect like terms}

6x = 384

x = 384/6 {divide through by 6}

x = 64

Therefore, the equation 2x + (2x + 8) + x + (x - 32) = 360° can be used to solve for x, and the variable x for the arc angles is equal to 64.

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The equation has exactly one real solution is - 2.41.

Since the equation is an expression that shows the relationship between two or more numbers and variables.

There are an infinite number of x values so, these two can easily be ruled out. there is no solution because the x values cancel each other out.

6x + 13 = -6x - 16

6x + 6x = -16 - 13

12x = -29

x = -29/12

x = - 2.41

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Answer:

I think it will be 4x^2+4x+7/4x+1

correct me if I'm wrong

If Lydia had ²/₃ of a bag of flour and she used ³/₅ of it to make loaves of bread, the fraction of the whole bag that she used was ²/₅.

A fraction is a portion or part of a whole.

Fractions are classified into proper, improper, and complex fractions, depending on the value of the numerator and denominator.

The fractional value of the bag of flour = ²/₃

The fraction of the bag that she used to make bread = ³/₅ of ²/₃

Comparatively, the proportion of the bag that she used was = ²/₅ (³/₅ of ²/₃)

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The equation written in point-slope form is:

y + 50 = (-1/3)*(x - 80)

A linear equation with a slope a that passes through a point (x₁,y₁) is written in the point-slope form as:

y -  y₁ = a*(x - x₁)

And the slope for a line that passes through  (x₁,y₁) and (x₂, y₂) is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we can identify the points (-70, 0) and (80, -50)

Then the slope is:

a = (-50 - 0)/(80 + 70) = -50/150 = -1/3

Using the red point (80, -50)

We can write the equation as:

y + 50 = (-1/3)*(x - 80)

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There are three primary sorts of operations done on sets in a set theory, such as:

Sets' union (∪)

Sets intersecting (∩)

Set difference (- )

Sets help in the identification of related groupings of objects. Set operations such as relations and functions are used to connect and manipulate sets.

Bowls, glasses, cups, and saucers are kept separate from plates, while pans and utensils have their own compartments. Cooking utensil sets and other collections are separated in storage. As seen above, there are countless examples of sets in our daily lives.

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