A factory makes 1,200 shirts every 6 hours. The factory makes shirts for 63 hours each week. What are the fewest number of days the factory will need to make 12,600 shirts?

on solving the provided question, we can say that by equation we Consequently, he will sell 16 automobiles at this price.

A number, a variable, or a mix of both, combined with certain operation symbols, make up an expression. An equal sign is used to denote the separation of two expressions in an equation.

Here,

Given: Number of cars sell in a day = 12

Price of a car =[tex]$23,000[/tex]

For each $300 price reduction dealer can sell two more cars per day.

Solution: Let there be x unit 300 price reduction

2x unit increase in sale of car

[tex]|R(x)=(15000-300x)(12+2x)[/tex]

Cost

[tex]|C(x)=1000+12000 (12+2x)[/tex]

Profit

[tex]|P(x)=(15000-300x)(12+2x)-1000+12000 (12+2x)\\15000(12+2x)–12000 (12+2x)-300x(12+2x)-1000\\=180000-144000+30000x-24000x -3600x -600-1000\\=36000+2400x-600 = P'(x)=-1200x +2400 = P"(x)=-1200[/tex]

For critical points

[tex]P'(x)=0= -1200x + 2400=0= x=2[/tex]

Since P"(x) <0at x = 2it is max profit 12+2x=12+2(2)=16

16cars per day he will sell

[tex]Price = 15000-300*16 = $10200[/tex]

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There 9% represent babies born with a birth defect, and 09-99(9%) to represents babies without birth defects.

The percentage is defined as a ratio expressed as a fraction of 100.

According to one study, 45 out of every 500 babies born in the world have a serious birth defect.

Use two-digit numbers 00-99; let 00- represent babies born with some kind of major birth defect.

p = x/n

p = 45/500

p = 0.9 = 9%

So, the simplest way to assign random numbers to conduct a simulation based on this statistic, it can use 00-99(9%) to represent babies born with a birth defect, and 09-99(9%) to represent babies without birth defects.

Hence, the correct answer would be an option (B).

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The size of the angle between AB and the base of the pyramid 27.9⁰

You should know that a pyramid is a polyhedron with a base that is a polygon

using the figure, The volume of the pyramid is 1/3 Bh

the area of the pyramid is  12*D = 144 cm²

= 1/3 * 14 * h = 768

Making h the subject of the formula

h= 16 cm

BO = √2 * 12/2 ÷6√2

this implies that Tan∅ = BD/BO = 6√2/16

Tan ∅ = 3√2/8

∅= 27.9⁰

In conclusion the size of the angle is 27.9⁰

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Answer:

hope this helps

Step-by-step explanation:

To determine its end behavior, look at the leading term of the polynomial function. Because the power of the leading term is the highest, that term will grow significantly faster than the other terms as x gets very large or very small, so its behavior will dominate the graph

Answer:

x = 7 , x = 11

Step-by-step explanation:

x² - 18x + 81 = 4 ( subtract 81 from both sides )

x² - 18x = - 77

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 9)x + 81 = - 77 + 81

(x - 9)² = 4 ( take square root of both sides )

x - 9 = ± [tex]\sqrt{4}[/tex] = ± 2 ( add 9 to both sides )

x = 9 ± 2

then

x = 9 - 2 = 7

x = 9 + 2 = 11

The exact solution to the system of equations shown on the graph is

(-1 1/5, 4 3/5)

The solution of a graph is where the two graphs intersects. This point is known as point of intersection and at this point we have the solution

The point of intersection of the two graphs as shown are read, Knowing that all interval marked represents one unit

x intersection: the point is more than -1 and not up to -1.5, which is a value at exactly half of the two intervals hence the possible option is -1 1/5

y intersection: the point is more than 4 and more than to 4.5, which is a value at exactly half of the two intervals hence the possible option is

4 3/5

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Answer: The solution of the ordered pairs are (0,1) and (1,3).

Step-by-step explanation:

The equation here is 2+6n, where n=1/2

substituting the value of n in the equation, we get,

 2+6n

= 2+6x1/2   ......(adding value of n)

=2+6/2  .......(dividing 6 by 2)

=2+3

=5

therefore, the value of 2+6n is 5

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Proportional functions seem to be linear functions that contain the origin and can be written as y is kx.

Here all the 4 functions are not proportional because it does not satisfy the condition y = kx.

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Yosemite Falls in California is made of three smaller falls. The upper fall drops 1450 feet. The time it takes for the droplet to reach the next fall is 9.52 seconds.

Given data:

h(t)=-16 t²+1450

Where:

t = time in seconds after the initial fall

So,

0=-16 t²+1450

16 t² =1450

t² = 90.625

t =√90.625

t = 9.52 seconds

Therefore we can conclude that the time is 9.52 seconds.

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On solving the question, we can say that - herefore , the required inequality expression is 4.50x+1.75y ≤50

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations.. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

One cupcake costs $4.50,

So, “x” cupcakes cost = 4.50x.

One brownie cost $1.75,

so “y” brownies cost = 1.75y.

thus, the total 4.50x+1.75y  must be less or equal to $50.

Therefore , the required inequality expression is 4.50x+1.75y ≤50

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The width of the given rectangle would be 7 units.

Let the length of the rectangle = a

let the width = b

length of a rectangle is the sum of the width plus 2.

Thus;

a = b + 2

area of rectangle is;

A = length * width

Thus;

A = b(b + 2)

but A = 63 units

b(b + 2) = 63

b² + 2b - 63 = 0

(b + 9)(b - 7) = 0

b = 7

a = 7 + 2

therefore;

a = 9

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Answer: 12 feet and 1 inch

Step-by-step explanation:

3 feet 10 inches

4 feet 11 inches

3 feet 4 inches

3+4+3 = 10 feet

10+11+4 = 25 inches

1 foot = 12 inches

25 / 12 = 2 (rounded up) feet with 1 inch left

10 + 2 = 12 feet and 1 inch

Answer:

Step-by-step explanation:

$22.1

The money earned by Conor if he works 3.25 hours at $9 an hour is $29.25.

The fundamental concept of making the same number of additions repeatedly is represented by the action of multiplication. The results of multiplying two or more integers are known as the products, and the factors that are used in the multiplication are referred to as the factors.

Given:

The pay rate for the work, W = $9,

The time of work, t = 3.25 hours,

Calculate the money earned by Conor as shown below,

The money earned by Conor = The pay rate for the work × The time of work,

The money earned by Conor = 9 × 3.25

The money earned by Conor = 29.25

Thus, the money earned by Conor is $29.25.

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Answer:

Step-by-step explanation:

so hard bro !!!

Using the concept of fraction, the percentage edited on the video is 62.5 percent.

Percentage is a standard mathematical concept used to express a portion of a whole number in terms of a hundred. It is denoted by the symbol “%” and is often expressed as a fraction or a decimal. For example, 25% can be expressed as 0.25 or 1/4.

In this problem, Thorton has done a 2.5 hours work. The percentage he has edited can be calculated using fraction or ratio as;

percentage edited = (2.5 / 4) × 100

Percentage = 0.625 × 100

Percentage = 62.5 %

From the above, Thorton has edited 62,5 percent of the video for his school project.

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Answer:

Equation: y=-8x+19

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Triangle ABC≅ Triangle DAB

use pytahgorean theorem:

ac^2=ab^2+bc^2

ac=[tex]\sqrt{ab^2+bc^2\\][/tex]

ac=[tex]\sqrt{4^2+3^2}[/tex]

ac=[tex]\sqrt{16+9}[/tex]

ac=[tex]\sqrt{25}[/tex]

ac=5

ac=bd=5 by congruency rules

On solving the provided question, we can say that - the initial value in number line will jump to +12 value

A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.

here,

the initial value of the number line is = 15

and on adding 12

it will jump to = 15 + 12

= 27

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The required equation is y = 1.4x - 295 shows the amount that must be repaid, y, when x dollars are borrowed.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The table below shows the amount that must be repaid, y, when x dollars are borrowed.

Amount Borrowed     Amount Repaid

    $100                              $155

    $200                             $295

    $600                             $855

    $900                             $1275

y - 155 = [(1275 - 155)/(900-100)](x-100)

y - 155 = (1120/800)(x-100)

y - 155 = 1.4(x-100)

y = 1.4x - 140 + 155

y = 1.4x - 295

Thus, the required equation is y = 1.4x - 295.

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Answer: Y = 1.4x + 15

Step-by-step explanation:

Multiply amount borrowed by 1.4 and add 15 gives you the amount repaid.

Step-by-step explanation:

Let M be the number of multiple choice problems and S be the number of short answer problems.

We can set up the following system of equations to represent this situation:

M * 3 + S * 4 = 111

M + S = 32

The first equation represents the total number of points on the test, and the second equation represents the total number of problems on the test.

To solve this system of equations, we can use a method such as graphing, substitution, or elimination.

Using the substitution method, we can solve for one variable in terms of the other and substitute it into the other equation. For example, we can solve the first equation for M:

M = (111 - S * 4) / 3

Then, we can substitute this expression for M into the second equation:

(111 - S * 4) / 3 + S = 32

Solving this equation for S gives us the number of short answer problems:

S = 12

To find the number of multiple choice problems, we can substitute this value for S into the expression for M that we derived earlier:

M = (111 - 12 * 4) / 3

Solving this equation gives us the number of multiple choice problems:

M = 8

Therefore, there are 8 multiple choice problems and 12 short answer problems on the test.

The amount of wood that will be needed for the 4 props is 256 ft²

You should understand that the number of wood needed for props is the distance round all the lengths of the prop multiplied by four

The lengths give are (5ft +8ft +7ft +2ft +3ft +5ft) *2*4

The amount of wood will be 32*2*4

= 256 ft²

In conclusion 256ft wood will be needed for 4 props

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Answer: 936

Step-by-step explanation: I got it wrong by following other answers but this is confirmed correct on the test. Picture taken to ease worry.

Dimensions of the portrait are 12.25 cm to the nearest tenth of a centimeter.

What are Dimensions?

The dimension of a mathematical space is defined as the smallest number of coordinates required to specify each point within it.

To have the area of the mat equal to the area of the portrait, the portrait and the mat must have the same area. Since the mat is 7 cm wide, we can use that to find the dimensions of the portrait.

If the portrait is square, the side length will be the same as the width of the mat, plus the width of the portrait.

So, portrait width = 7 cm + portrait width

Solving for portrait width:

portrait width = 7 cm / 2 = 3.5 cm

So, the dimensions of the portrait are 3.5 cm x 3.5 = 12.25 cm

Therefore, dimensions of the portrait are 12.25 cm to the nearest tenth of a centimeter.

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thanks for the points heres the answer 2

                                                                 18

[tex]8\sqrt{3}-3\sqrt{6}[/tex]

=============================================

Work Shown:

[tex]\text{x} = 10\sqrt{3}-\sqrt{12}-3\sqrt{6}\\\\\text{x} = 10\sqrt{3}-\sqrt{4*3}-3\sqrt{6}\\\\\text{x} = 10\sqrt{3}-\sqrt{4}*\sqrt{3}-3\sqrt{6}\\\\\text{x} = 10\sqrt{3}-2\sqrt{3}-3\sqrt{6}\\\\\text{x} = (10\sqrt{3}-2\sqrt{3})-3\sqrt{6}\\\\\text{x} = (10-2)\sqrt{3}-3\sqrt{6}\\\\\text{x} = 8\sqrt{3}-3\sqrt{6}\\\\[/tex]

-------------------------------

Therefore,

[tex]10\sqrt{3}-\sqrt{12}-3\sqrt{6}\\ \ \text{simplifies to} \\ 8\sqrt{3}-3\sqrt{6}\\\\[/tex]

In other words we can say

[tex]10\sqrt{3}-\sqrt{12}-3\sqrt{6}=8\sqrt{3}-3\sqrt{6}\\\\[/tex]

--------------------------------

Verification:

Use a calculator to compute the following.

[tex]10\sqrt{3}-\sqrt{12}-3\sqrt{6} \approx 6.507937\\\\8\sqrt{3}-3\sqrt{6} \approx 6.507937\\\\[/tex]

Since we get the same approximate decimal value, it helps us confirm the answer is correct.

The functions graphed on the axes is expressed below:

F(x) = 2 for all x =  (-∞, 3) to (3, ∞)

F(X) = 5 for x = [3]

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.

Given, a function in the graph below that is a straight line of y equal to 2 on all values of x except the x = 3

Thus the inequality of the given graph is

F(x) = 2 for all x =  (-∞, 3) to (3, ∞)

F(X) = 5 for x = [3]

Therefore, the given graph is a straight line that shows a discontinuity at x =3.

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6. a) In 10 squares there are 22 dots

6. b) There are 102 squares are in the diagram which has 104 dots.

6. c) t(n) = a + (n - 1) d

7. a) mean = 6; median = 5

7. b) new card number = 14

This can be solved using geometic series concept.

A geometric series is one where each pair of consecutive terms' ratios is a fixed function of the summation index. The ratio is a rational function of the summation index in a more comprehensive sense. creates what is known as a hyper geometric sequence. It is arithmetic if there is a common difference between the sequences. You can bet that anything is geometric if it has a common ratio. Similar to how the word arithmetic series denotes that each phrase is the arithmetic mean of its two neighbors, the name geometric series denotes that each term is the geometric mean of its two neighbors.

6. In the given figure we see that the dots are present here form a series.

In 1 square there are 4 dots.

In 2 squares there are 6 dots.

In 3 squares there are 8 dots.

So, they form a series.

a)

In 10 squares there are 22 dots

b)

There are 102 squares are in the diagram which has 104 dots.

c)

The formula of the series is:

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

here a = 4 and d = 2

7.

a)

Jemina has 3 cards with the number of 5,2 and 11

Thus, mean = 5+2+11 /3 = 6

median = 5

b)

Next Jemina takes another card and the mean goes up by 2.

So, the number of new card:

2+5+x+11/4 = 8

or, 18 + x = 32

or, x = 14

So, new card number = 14

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Answer:

Step-by-step explanation:

6. a) In 10 squares there are 22 dots

6. b) There are 102 squares are in the diagram which has 104 dots.

6. c) t(n) = a + (n - 1) d

7. a) mean = 6; median = 5

7. b) new card number = 14

Answer:

  see attached

Step-by-step explanation:

You want to match the given word problem with a suitable equation for solving it.

The variable x is assigned to the larger of two numbers that differ by 2. That makes the smaller one (x -2). The sum of their squares is ...

  x² + (x -2)² = 394

Simplifying, we get ...

  x² +x² -4x +4 = 394

  2x² -4x -390 = 0 . . . . . . . matches the first equation

The numerator of the fraction is 5 more than its denominator, x, so will be (x +5). Adding 3 to numerator and denominator, we get ...

  [tex]\dfrac{(x+5)+3}{(x)+3}=\dfrac{4}{3}\\\\3(x+8)=4(x+3)\\\\\boxed{3x+24=4x+12}\qquad\textsf{matches the third equation}[/tex]

The sum of x and its inverse is 4/3, so we have ...

  x + 1/x = 4/3

Multiplying by 3x gives ...

  3x² +3 = 4x

  3x² -4x +3 = 0 . . . . . . . . . matches the second equation

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The correct representations of the inequality are  -6x + 15 < 10 - 5x and x <-5. Options C and D

Inequalities are described as mathematical relations that makes a non-equal comparison between two elements, variables, numbers or mathematical expressions.

They are often used to compare two numbers on the number line based their sizes.

From the information given, we have the inequality;

–3(2x – 5) < 5(2 – x)

expand the bracket

-6x + 15 < 10 - 5x

collect like terms

-6x + 5x < 10 - 15

add or subtract the like terms

-x < -5

Make 'x' the subject of formula

x < 5

Hence, the value is -6x + 15 < 10 - 5x

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The complete question:

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.