whats the expression (2x+3)(2x-4)

The solution is, the salary of the Luke after 10 years is 98000 dollars & the salary of the Luke after t years is 53000+4500t .

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

Given data:

* The starting salary of the Luke in the new company was,

S1 = 53000

* The salary raise given to Luke each year is,

R = 4500

(a). The salary of the Luke after 10 years is,

S = S1 +R*10

S  = 53000 + ( 4500* 10)

S = 98000

Thus, the salary of the Luke after 10 years is 98000 dollars.

(b). After the t years,

S = S1 +R*t

S  = 53000 + ( 4500* t)

S = 53000+4500t

Thus, the salary of the Luke after t years is 53000+4500t .

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Answer:

x = 115°

y = 50°

Step-by-step explanation:

it is an isosceles triangle, the angles at the base are congruent, x is the opposite angle of 115°, therefore the same value, to find y we subtract the two 65° angles from the sum of the internal angles of the triangle (180°) and we have 50 ° which is the value of Y, look at the figure to understand better

Answer:

34.8 pounds

Step-by-step explanation:

The cat weighs 10.4. Which is 24.4 pounds less that the dog. So find the weight of the dog, we need to make an equation. This equation would be:

[tex]dog[/tex][tex]-24.4=10.4[/tex]

Solve:

[tex]dog-24.4=10.4[/tex]

      [tex]+24.4[/tex]     [tex]+24.4[/tex]

[tex]dog=34.8[/tex]

Hope this helped!
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Answer: The equation 9 = p - 12 can be solved for p by adding 12 to both sides:

p = 9 + 12 = 21.

So the correct answer to the question "29, 30, 31 with one is the answer" would be 30, as it is the only one that equals 21.

Step-by-step explanation:

Answer:

458210 in binary

10001111001102

To convert decimal number 4582 to binary, follow these steps:

Divide 4582 by 2 keeping notice of the quotient and the remainder.

Continue dividing the quotient by 2 until you get a quotient of zero.

Then just write out the remainders in the reverse order to get binary equivalent of decimal number 4582.

Using the above steps, here is the work involved in the solution for converting 4582 to binary number:

4582 / 2 = 2291 with remainder 0

2291 / 2 = 1145 with remainder 1

1145 / 2 = 572 with remainder 1

572 / 2 = 286 with remainder 0

286 / 2 = 143 with remainder 0

143 / 2 = 71 with remainder 1

71 / 2 = 35 with remainder 1

35 / 2 = 17 with remainder 1

17 / 2 = 8 with remainder 1

8 / 2 = 4 with remainder 0

4 / 2 = 2 with remainder 0

2 / 2 = 1 with remainder 0

1 / 2 = 0 with remainder 1

Then just write down the remainders in the reverse order to get the answer, The decimal number 4582 converted to binary is therefore equal to : 

1000111100110

Answer:

Step-by-step explanation:

-23 + 19 = -4

At noon the temperature was -4 degrees F.

Answer:2737

Step-by-step explanation:

B and D meet at a 75º, as does A and C

The probability of an event for rolling a die P(E) is 1/2.

What is the probability of an event?

The probability of an event is a number (always positive) that expresses the likelihood that the event will occur. The likelihood that an event will occur falls between zero and one. A certain occurrence has a probability of one while an impossible event has a chance of zero. As implied by its name, probability deals with uncertainty.

Given, E be the event defined as {3,4,6}

So, the total number of an event E, n(E) = 3

For a die, total events are {1,2,3,4,5,6}

So, the total number of rolls of a die event, n(T) = 6

Then,

P(E) = [tex]\frac{n(E)}{n(T)} = \frac{3}{6} = \frac{1}{2}[/tex]

So, the required value of P(E) is 1/2.

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The sine of the complementary angle of 68° is 0.375.

Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

The complementary angle of 68° is calculated as;

θ = 90 - 68°

θ = 22°

sin (22° ) = 0.375

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The only sort of proof among the following options in the question that is frequently employed in geometry is the 'two-column' proof.

Geometry is the area of mathematics that deals with the characteristics of space and the shapes of particular things as well as the interactions between them in space.

A two-column geometric proof consists of a list of assertions and the justifications for each one's truth.

The statements are listed in a left-hand column, while the justifications for the statements are listed in a right-hand column.

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the width of the frame is 0.806 inches.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given this, Travis decided to make a frame for his birthday. The frame will be cut out of a piece of steel, and the final area of the frame should be 30in².

Since,

Area of frame = total area - cut out area

In our case, it is given that,

Total area = (11+2x)(6+2x)in²

cut out area = 11*6 = 66

So,

30 = (11+2x)(6+2x) - 66  

(11+2x)(6+2x) = 96

66 + 12x +22x +4x² = 96

4x² + 34x -30 = 0

x = 0.806 in

therefore. the width of the frame is 0.806 inches.

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Complete question:

1 1/4 divided into three parts you mean? You can simply take 1 1/4 or 1.25 and divide that by 3.

By fraction, you would want to convert the mixed number into an improper fraction, that way, it's easier. 1 1/4 to an improper fraction is 5/4.

5/4 divided by 3

Now whenever you're dividing fractions, remember this tip: keep, change, flip. Keep the first fraction, change the division sign to a multiplication sign, and flip the second fraction.

So 3, or 3/1 is now 1/3 and the sign is now multiplication.

5/4 x 1/3 = 5/12

That's your answer!

Hope this helped!

The probability of a day in which the company receives 6 or more complaints is 0.3721 likely, or about 37.21%.

A subfield of mathematics called probability is concerned with the investigation of uncertain events. It is the measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1. The higher the probability, the more likely it is that the event will occur.

Given that the number of complaints per day follows a Poisson distribution with a rate parameter λ = 5.

Assume X is a random variable that represents the daily complaint rate.

The probability of receiving 6 or more complaints can be calculated as follows:

we can calculate the probability of X being less than 6 complaints per day as follows:

P(X < 6) = F(5) = e^(-λ) * Σ(λ^k / k!, k=0 to 5)

where e is the base of the natural logarithm, Σ denotes the sum from k=0 to 5, and k! denotes the factorial of k.

Substituting the value of λ = 5, we get:

P(X < 6) = e^(-5) * Σ(5^k / k!, k=0 to 5)

= 0.0337 + 0.1404 + 0.1755 + 0.1463 + 0.0916 + 0.0404

= 0.6279

Therefore, the probability of receiving 6 or more complaints in a day is:

= 1 - 0.6279

= 0.3721

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Answer:

The length is 52 meters and the width is 23 meters.

Step-by-step explanation:

Let l stand for length, and w stand for width.

l = 2w + 6

The length is 6 more than twice the width.

2l + 2w = 150

Twice the length plus twice the width is the perimeter of a rectangle.

2(2w + 6) + 2w = 150

4w + 12 + 2w = 150

6w + 12 = 150

6w = 138

w = 23

l = 2(23) + 6

l = 46 + 6

l = 52

The prima facie rule uses actual probability distributions to determine if hiring decisions have had adverse impact on minority groups.

The "prima facie" rule refers to a legal standard or a evidentiary standard used in the field of employment discrimination law. In the context of employment discrimination, a prima facie case refers to the minimum evidence required to establish a presumption of discrimination.

The term "prima facie" comes from Latin and means "at first sight" or "on its face." In other words, a prima facie case of discrimination is established if, at first sight, the evidence suggests that discrimination has taken place. Once a prima facie case has been established, the burden of proof shifts to the employer to provide a non-discriminatory explanation for the actions in question.

It is more commonly used in legal and ethical contexts to refer to a case or argument that is initially strong enough to establish a point, but may be challenged or overcome by further evidence or argument.

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Using the fact that P is the midpoint of the segment AB, we will see that its y-value is -4.

We know that point P partitions directed segment AB in the part to part ratio of 4:4.

Notice that the ratio is equivalent to 1:1

So point P is just the midpoint of the segment, remember that for a segment whose endpoints are (a, b) and (c, d), the midpoint is:

M= ( [a+ c]/2, [b + d]/2)

P is the midpoint of (5,-7) and (1,-1), then the value of the y-coordinate of P is:

y = (-7 + (-1))/2

y = (-7 - 1)/2

y = -4

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The farmer requests that the pen's length be 20 feet longer than its breadth. If we use the symbol w to indicate width. The length would then equal w + 20.

You play the part of a middle schooler who is attempting to make your family's farm profitable in Farmer Math.

The challenge first asks us to determine the longest length given that the fencing will not exceed 100 feet.

We are aware that a rectangular area's perimeter is 2l + 2w (where l is the length and w the width)

Therefore, 2l + 2w 100 would be required for the fencing.

In order to solve for w, we will use the values for l and w that we mentioned in the beginning:

2l + 2w ≤ 100

2(w+20) +2w ≤ 100

2w + 40 +2w ≤ 100

4w ≤ 100 - 40

4w ≤60

w ≤ 15

The breadth must therefore be less than or equal to 15.

The longest length is achieved when the width is at its greatest value because the length is 20 feet greater than the width.

This makes the length at w = 15 the longest it can possibly be, at 35.

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This question finds congruent triangles. A similarity statement relating the 3 triangles is ABC-DAC-DBA.

From the triangle ABC-DAC-DBA, it has conditions that can be said to be congruent, because it has side lengths with patterned comparisons if the magnitudes are not the same.

The conditions for two congruent plane shapes, namely:

The above conditions also apply to congruent triangles.

Two triangles are congruent if they have:

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The double number line is discussed below.

In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

Given is a double number line.

A double number line diagram uses a pair of parallel number lines to represent equivalent ratios.

The locations of the tick marks match on both number lines.

The tick marks labeled 0 line up, but the other numbers are usually different.

The lines in a double number line diagram are similar to the number lines students have seen in earlier grades in that -

Therefore, the double number line is discussed above.

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Answer:

The answer is in the attachment

Step-by-step explanation:

The area of the rectangle would be equal to the sum of the areas of these 12 squares.

The area of a rectangle is a measure of the amount of space it covers. It is calculated by multiplying the length and the width of the rectangle.

For a rectangle with sides of 3 cm and 4 cm, the area can be found by multiplying 3 by 4. The formula for finding the area of a rectangle is

=> A = l * w,

where l is the length and w is the width.

So, for the rectangle with sides 3 cm and 4 cm, the area would be

=> A = 3 * 4 = 12 square centimeters.

To visualize this, imagine a rectangle with sides of 3 cm and 4 cm. If you placed 12 squares of 1 cm each inside this rectangle, it would fill up the entire rectangle without any space left.

Complete Question:

Find the areas of the rectangles whose sides are:

(a) 3 cm and 4 cm

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The experimental probability of not selecting a heart is (D)P(not heart) = 77.5%

The experimental probability that a heart is selected is:

= Number of times hearts was selected / Number of times Lisa drew a card

= 9 / 40

This then means that the experimental probability of not selecting a heart is:

= 1 -  experimental probability of selecting a heart

= 1 - 9 / 40

= 31 / 40

= 0. 775

= 77. 5 %

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The question is:

Determine the experimental probability of not selecting a heart.

(A) P(not heart) = 9%

(B) P(not heart) = 10%

(C) P(not heart) = 67.5%

(D)P(not heart) = 77.5%

The probability of getting all 8 questions correct is 1/4096 or approximately 0.024%.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The probability of getting a True/False question correct is 1/2, since there are only two possible answers. The probability of getting a multiple-choice question correct is 1/4 since there are four possible answers.

So, for the first 4 True/False questions, the probability of getting them all correct is (1/2)⁴ = 1/16.

For the last 4 multiple-choice questions, the probability of getting them all correct is (1/4)⁴ = 1/256.

The total probability of getting all 8 questions correct is the product of the probabilities of getting each set of questions correct:

(1/16) x (1/256) = 1/4096

So, the probability of getting all questions correct is 1/4096 or about 0.024%.

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Answer:

A Set With One Element

So any set with one element will have 2 subsets.

Step-by-step explanation:

Answer:

5%

Step-by-step explanation:

Decreased amount = 40 - 38

                                 = £ 2

[tex]\sf \boxed{decreased \ percentage = \dfrac{decreased \ amount}{oringinal price}*100 }[/tex]

                                  [tex]= \dfrac{2}{40}*100\\\\= 5 \%[/tex]

The expression that will not be equivalent to the number given -(-20) is -20 (option D).

A number is said to be equivalent not only if the number is equal in value, for example, 15 = 10 + 5, but also if the negative or positive sign is equal, for example, 5 is not equal to -5.

The original expression is -(-20), this expression can be simplified as 20 or +20 considering that minus plus minus is equivalent to +. Based on this, the expression that is not equivalent is -20.

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The least common multiple of 3 and 5 is 15, so we convert 5 to 15/3.So the answer is 5/3.

The calculation in fractions:

1/3 of 20 = (1/3) * 20 = 20/3

5 subtracted from 1/3 of 20 = 20/3 - 5

To simplify the expression 20/3 - 5, we need to subtract 5 from 20/3 by finding a common denominator between 5 and 20/3. The least common multiple of 3 and 5 is 15, so we convert 5 to 15/3:

20/3 - 5 = 20/3 - 15/3 = (20 - 15)/3 = 5/3

So the answer is 5/3.

Fractions are a way of representing numbers as ratios of two integers. The top number of a fraction is called the numerator, and the bottom number is called the denominator. The numerator represents the number of parts of the whole that are being considered, and the denominator represents the number of equal parts that make up the whole.

For example, the fraction 1/2 represents 1 part out of 2 equal parts that make up the whole.

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Answer: $ 0.62

Step-by-step explanation:

First, find out the cost of each bottle:

$4.69/ 36 bottles = $0.1297

                             = $0.13

Therefore, the profit is:

$0.75 - $0.13 =  $ 0.62

Answer:

the shape is different

Step-by-step explanation:

you draw the shapes