Let sets A and B be defined as follows.
A is the set of integers greater than or equal to -9 and less than or equal to - 3
B=1-29, -26, -23, 30}
(a) Find the cardinalities of A and B.
n(A) =
n (B) =

Answer:

A

Step-by-step explanation:

The easiest way to see whether a table is a function is to check the Input and Output. If one Input has two outputs, then that table is not a function. So, the answer is A

Check the picture below.

Answer: 315

Step-by-step explanation:

(45 * 6) + 45

Since there are 45 pins and each takes 6 minutes, then you multiply those 2 first, and then each pin takes 1 minute each, so add 45 to your last answer, which will be your final answer of 315. :)

Answer:

315 minutes

Step-by-step explanation:

We know

One pin requires 6 minutes, with 1 minute per pin for placing stock in the lathe, which means 7 minutes to machine 1 pin.

7 times 45 = 315 minutes

So, it will take 315 minutes to machine 45 pins

A photo of a woman standing between two long rows of sewing machines in a factory. The factory owners relied on skilled workers to run the machines. Thus, option b is correct.

The manufacturing system's key advantages were lower costs for the business and increased worker productivity. The factory administration had direct control over the workers, allowing for regular monitoring of their output. Resources may be used more efficiently if they are shared across several employees.

First, equipment hastened the production of goods. This is because a machine might perform routine tasks skillfully and dependably. The ability of equipment to decrease the number of people required to complete a task is its second advantage. They were able to avoid paying employees by doing this, which allowed them to save money.

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The complete question is-

The photo shows a woman watching a row of machines in a factory. A photo of a woman standing between two long rows of sewing machines in a factory. what advantages did machinery provide for factory owners?

a. machines could do the work faster than skilled workers by hand.

b. factory owners relied on skilled workers to run the machines.

c. the machines produced a better product than skilled workers by hand.

d. factory owners needed more unskilled workers to run the machines.

Here's the completed table of values for y = 2x^2 + x

7,1,9

To find the value of y for each x, substitute x into the equation and simplify:

For [tex]x = -2: y = 2(-2)^2 + (-2) = 7[/tex]

For[tex]x = -2: y = 2(-2)^2 + (-2) = 7[/tex]

For[tex]x = 0: y = 2(0)^2 + 0 = 1[/tex]

For [tex]x = 1: y = 2(1)^2 + 1 = 4[/tex]

For[tex]x = 2: y = 2(2)^2 + 2 = 9[/tex]

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Part a: P2 processors therefore performs the best out of the three.

Part b: Number of Cycles are found.

Part c: New Clock rate for each processors is found.

High-speed data processing and intricate calculations are capabilities of high-performance computing (HPC).

1.

P1: 3GHz / 1.5 = 2 × 10^9 instructions / second

P2: 2.5GHz / 1.0 = 2.5 × 10^9 instructions  / second

P3: 4GHz / 2.2 = 1.82 × 10^9 instructions  / second

2. Number of Cycles:

P1: 3GHz × 10 = 3 * 10^10 cycles

P2: 2.5GHz × 10 = 2.5 × 10^10 cycles

P3: 4GHz ×10 = 4 ×  10^10 cycles

Number of instructions:

P1: 3GHz × 10 / 1.5 = 2 × 10^10 instructions

P2: 2.5GHz × 10 / 1.0 = 2.5 × 10^10 instructions

P3: 4GHz × 10 / 2.2 = 1.82 × 10^10 instructions

3. Execution time = (Number of instructions * CPI) / (Clock rate)

Therefore, if CPI rises by 20% but we aim to cut the execution time to 30%, we have:

Execution time × 0.7 = (Number of instructions  × CPI × 1.2) / (New Clock rate)

New Clock rate = Clock rate × 1.2 / 0.7 = 1.71 * Clock rate

New Clock rate for every processor:

P1: 3GHz × 1.71 = 5.13 GHz

P2: 2.5GHz × 1.71 = 4.27 GHz

P3: 4GHz × 1.71 = 6.84 GHz

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The correct question is-

Performance:

Consider three different processors, P1 P2 and P3, executing the same instruction set.

P1 has a 3 GHz clock rate and a CPI of 1.5. P2 has a 2.5 GHz clock rate and a CPI of 1.0.

P3 has a 4.0 GHz clock rate and a CPI of 2.2.

1. Which processor has the highest performance expressed in instructions per second?

2. If the processors each execute a program in 10 seconds, find the number of cycles and the number of instructions.

3. We are trying to reduce the execution time by 30% but this leads to an

increase of 20% in the CPI. What clock rate should we have to get this time reduction?

The probability of the sixth child being born as a boy is 0.5 or 50%. It is irrespective to the five boys born previously.

Since probability of a girl or boy being born is 50%,

Probability of Girl being born, P(G) = ½

Probability of boy being born, P(B) = ½

When one is calculating the probability of any one of the two events occurring or both evens have a chance of occurring, considering the events are non-mutually exclusive, the rule of addition is used.

Rule of addition: P(A or B)= P(A) + P(B) –P(A+B)

Where P(A)- probability that event A takes place

P(B)- Probability that event B takes place

P(A+B)-  probability of both events taking place.

In this case, both events cannot take place simultaneously, i.e., they are mutually exclusive, hence,

P(G or B)= ½ + ½ = 2/4 = ½ = 0.5.

Therefore, Probability of boy being born is 0.5

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The surface area is of the triangular prism is 121.8 cm²

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The surface area is gotten by adding each individual area of each surface of a three dimensional shape.

The area of the base is 6.9 cm². This is a triangular prism with height of 9 cm and each base side is 4 cm

The surface area = area of base + (9 cm * 4 cm) + (9 cm * 4 cm) + (9 cm * 4 cm) + area of base

Surface area = 6.9 + 6.9 + 36 + 36 + 36 = 121.8 cm²

The surface area is 121.8 cm²

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The slope of the given points is [tex]\frac{2}{5}[/tex] or 0.4.

Let (-7, 5) be ordered pair 1.

Let (-2, 7) be tordered pair 2.

Since point (-7, 5) is ordered pair 1: [tex]x_{1} =-7[/tex] and [tex]y_{1} =5[/tex].

Since point (-2, 7) is ordered pair 2: [tex]x_{2} =-2[/tex] and [tex]y_{2} =7[/tex]

Formula: [tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Substitute the variables in the formula by the identified coordinates in step 2 and calculate.

[tex]m=\frac{(7)-(5) }{(-2) -(-7) }=\frac{7-5}{-2+7}=\frac{2}{5}[/tex]

The slope of the given points is [tex]\frac{2}{5}[/tex].

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Answer: 2/5

Step-by-step explanation:

(-7,5) (-2,7)

change in y           2

------------------    =  -----

change in x           5

The new length of the living room floor would be 14.4 meters and the new width would be 6 meters.

1. Original Length = 12 meters  

2. Original Width = 5 meters

3. Increase by 20%

4. New Length = 12 + (20% of 12) = 12 + 2.4 = 14.4 meters

5. New Width = 5 + (20% of 5) = 5 + 1 = 6 meters

The original length of the living room floor was 12 meters and the original width was 5 meters. The owner decided to increase the living room dimensions by 20%, so the new length of the living room floor is 14.4 meters and the new width is 6 meters. This is calculated by adding 20% of the original length and width to the original values. For the length, this is 12 + (20% of 12) which is 12 + 2.4 = 14.4 meters. For the width, this is 5 + (20% of 5) which is 5 + 1 = 6 meters. The increase of 20% in the dimensions of the living room floor makes it look more spacious and inviting.

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The central angle is 63.6 degrees, which can be rounded to the nearest degree as 64 degrees.

The formula for the area of a sector of a circle is [tex]A = (θ/360) * π * r^2,[/tex] where θ is the central angle in degrees, π is 3.14, and r is the radius of the circle.

Given the area of a sector of a circle is [tex]56 cm^2[/tex] and the radius is 10 cm, we can solve for θ:

[tex]56 cm^2 = (θ/360) * 3.14 * 10^2\\56 cm^2 = (θ/360) * 314\\θ = (56 * 360) / 314\\θ = 63.6[/tex]

Therefore, the central angle is 63.6 degrees, which can be rounded to the nearest degree as 64 degrees.

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Answer: 2/6 or 2/12 (Go with 2/6)

Step-by-step explanation:

1/6 probability of rolling any one number. Add the probabilities for rolling a 3 (1/6) and rolling a 6 (1/6) and there is a 2/6 chance of rolling those numbers. it can also be 2/12 if you are looking at both dice rolls like one function.

it it is 1/6 because it the probability of rolling a 3 and then rolling a 6

The 30th term a30 of the sequence is -1445

The definition of the function is given as

arithmetic sequence of 1,-4,-9,-14

The above definitions imply that we simply subtract 5 from the previous term to get the current term

Using the above as a guide,

so, we have the following representation

First term, a = 1

Common difference, d = 5

An arithmetic sequence is represented as

a(n) = a + (n - 1)d

For the 30th term, we have

a(30) = a + 29d

So, we have

a(30) = 1 + 29 * -5

Evaluate

a(30) = -144

Hence, the value of a30 is -144

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Answer:

see below

Step-by-step explanation:

4 brothers in total, each saves 17 per week, in 3 weeks

314+(17*4)*3 =518

yes they do have enough

How many weeks will it take for them to save enough $ to buy the gift

515 = x *(17*4) + 314

How much each of them must save per week to have enough?

515= 3(x*4) +314

This model must be completed to represent 377 ÷ 12 as follows;

      30     1___

12 | 360  | 17 | 5.

In order to divide the given numbers by using the box method, we would write an expression to represent the number of times in which the number (377) can be divided by the number (12), while including the remainder (17) as follows;

377 ÷ 12 = (360 + 17) ÷ 12

377 ÷ 12 = (360 ÷ 12) + (17 ÷ 12)

377 ÷ 12 = 30 + (17 ÷ 12)

Note: 12 would divide 17 to give an output of one (1) remainder five (5).

In this context, the above mathematical expression would be re-written as follows;

377 ÷ 12 = 30 + 1 R 5.

Where:

The variable R represents remainder.

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The value of z that corresponds to 68% of the observations falling below is 0.84, and the value of z that corresponds to 75% of the observations falling above is 1.15.

A. To find the value of z that corresponds to 68% of the observations falling below, we can use the z-score formula. The z-score formula is z = (x-μ)/σ, where x is the value we are looking for, μ is the mean of the normal distribution, and σ is the standard deviation. Using this formula and a standard normal table, we can find that the value of z is 0.84. This means that 68% of the observations fall below z = 0.84. We can sketch a standard normal curve with this value of z marked on the axis by drawing a bell-shaped curve with the value of 0.84 marked on the x-axis.

B. To find the value of z that corresponds to 75% of the observations falling above, we can use the same formula and a standard normal table. We can find that the value of z is 1.15. This means that 75% of the observations fall above z = 1.15. We can sketch a standard normal curve with this value of z marked on the axis by drawing a bell-shaped curve with the value of 1.15 marked on the x-axis.

The value of z that corresponds to 68% of the observations falling below is 0.84, and the value of z that corresponds to 75% of the observations falling above is 1.15.

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The simplified value of the expression  7/9 divided 578 + 2/9 + 578 is,

(27071271/46818).

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

The expression 7/9 divided 578 + 2/9 + 578 is,

= 7/9 ÷ 578 + 2/9 + 578

= (7/9) × (1/578) + 2/9 + 578.

= (7/5202) + (2 + 9×578)/9.

= (7/5202) + (5204/9).

= (7×9 + 5202×5204)/(5202×9).

= (63 + 27071208)/(46818).

= (27071271/46818)

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Answer:

y = (0,-2)

Step-by-step explanation:

change in y/ change in x.

-4/4 ---> slope is -1

plug x and y coordinates AND SLOPE into y=mx+b

-3= -4/4(1)+b

-3= -1 +b

-2=b

Answer:

Blue paint = %90, Red Paint = 10%

Step-by-step explanation:

Out of 100, blue takes up more of the equation. It's 7/8's of the equation while there's only a quarter for red paint, making this equation, Blue > Red, aka, 90 > 10

90 > 10 = 90% of blue paint and 10% of red paint

Answer:

So if there were -4+20 the answer would be 16. When you add things, it goes to the right of the number line. When you subtract stuff it goes to the left. Simple but there are more rules like when this happens: 6--4 the two minuses turn into a plus 6+4—and other stuff. So -8 you have 8 negative signs and 20 positive signs. When a positive and a negative are added together they cancel each other out so now you have 12. This is modeled on the attachment. Hope this helped!

Step-by-step explanation:

the Image of Point C(-5, 3) under a rotation 90° clockwise about the origin followed by a reflection about the x-axis will be  C'(3, -5).

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given A triangle BCD that has rotated clockwise 90° about the origin and then reflected about the x-axis.

Rule of reflection and rotation a point:

Rotation about 90° : (x, y) → For clockwise (y, -x) For counterclockwise (x, y)

Reflection about x-axis : (x, y) => (x, -y)

For point C (-5, 3):

After Rotation 90 about origin clockwise:

As per the rule mentioned above

C(-5, 3) => C" (3, 5)

After reflection about the x-axis:

As per the rule mentioned above

C" (3, 5) => C'(3, -5)

therefore, the Image of Point C  under a rotation 90° clockwise about the origin followed by a reflection about the x-axis will be  C'(3, -5).

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The number of dimes is 24.

The number of quarters is 20.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

10 dimes = $1

1 dime = $0.1

4 quarters = $1

1 quarter = $0.25

Now,

Number of dimes = x

Number of quarters = (5/6)x

Now,

Duretta has collected $7.40 in all.

This means,

0.1x + 0.25(5/6)x = 7.40

0.1x + 0.21x = 7.40

0.31x = 7.40

x = 7.40/0.31

x = 23.87

x = 24

And,

(5/6)x

= 5/6 x 24

= 20

We can cross-check.

24 x 0.1 + 20 x 0.25 = 7.40

2.4 + 5 = 7.40

7.40 = 7.40

Thus,

Number of dimes = 24

Number of quarters = 5/6 x 24 = 20

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The system of equations are solved and the number of regular and premium cards are 9 and 16 respectively

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , let the regular cards be x

And , the premium cards be y

The cost of one regular card x = $ 0.40

The cost of one premium card y = $ 0.65

The total cost = $ 14

The total number of cards = 25

Substituting the values in the equation , we get

x + y = 25   be equation (1)

0.40x + 0.65y = 14   be equation (2)

Multiply by 100 on both sides of equation (2) , we get

40x + 65y = 1400

Divide by 5 on both sides of the equation , we get

8x + 13y = 280   be equation (3)

Multiply equation (1) by 8 , we get

8x + 8y = 200   be equation (4)

Subtracting equation (4) from equation (3) , we get

13y - 8y = 280 - 200

5y = 80

Divide by 5 on both sides of the equation , we get

y = 16

So , the number of premium cards is 18

Substitute the value of y in equation (1) , we get

x + 16 = 25

Subtracting 16 on both sides of the equation , we get

x = 9

So , the number of regular cards is 9

Hence , the equations are solved

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The equations that could be used to solve for the unknown lengths of △ABC are cos45° = AC/9 and sin45° = BC/9.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecent/hypotenuse and

tan = opposite/adjacent.

The opposite side to the reference angle is BC and the adjacent is the height.

We know, cos = adjacent/hypotenuse

Therefore, To determine AC we'll use cos45° = AC/9.

Also, To determine BC we'll use sin45° = BC/9.

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As total = 4100

Insurance = 123/4100*100 = 3%

Housing = 574/4100*100 = 14%

Entertainment = 164/4100*100 = 4%

The function with the greater initial value is (a) the function A

The complete question is added as an attachment

The initial value of a function is calculated when

x = 0

From the table of values, we have

y = 8 when x = 0

For the other function, we have

y = 4x + 3

So, the initial value is

y = 4(0) + 3

Evaluate

y = 3

8 is greater than 3

Hence, the function with the greater initial value is the table of values

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Answer:A linear model is appropriate because the scatterplot shows a strong, positive linear relationship.

Step-by-step explanation:

The quadratic regression equation is given as follows:

y = -0.02x² + 0.14x + 19.6.

Regression equations are obtained inserting the points of a data-set into a calculator.

In this problem, we want to find the quadratic regression equation, hence a quadratic regression calculator is used.

The points for this problem are given as follows:

y = -0.02x² + 0.14x + 19.6.

Meaning that the fourth option is the correct option.

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The equation of line is y = 4.5x + 10 and the slope is m = 4.5

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the first point be P ( 6 , 37 )

Let the second point be Q ( 1 , 14.50 )

Let the third point be R ( 0 , 10 )

Now , the slope of the line be represented as m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 37 - 14.50 ) / ( 6 - 1 )

Slope m = ( 22.50 ) / 5

Slope m = 4.5

And , the equation of line is y - y₁ = m ( x - x₁ )

On simplifying the equation , we get

y - 10 = 4.5 ( x - 0 )

y - 10 = 4.5x

Adding 10 on both sides of the equation , we get

y = 4.5x + 10

Hence , the equation of line is y = 4.5x + 10 and the graph is plotted

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