Arithmetic Series
Evaluate:

Answer:

The answer is 6x²+x+7

Step-by-step explanation:

(3x²+3) + (3x²+x+4)

3x²+3 + 3x²+x+4

COLLECT LIKE TERMS

3x²+3x²+x+3+4

ADD UP LIKE TERMS

6x²+x+7

The quotient is [tex]2\frac{2}{25}[/tex]. The quotient is a mixed number.

What is a fraction bar?

With mathematics, a fraction bar is a visual representation of fractions that aids in fraction comparison and fraction operations. A part-to-whole representational model is fraction bars or fraction strips. Each fraction bar segment represents one unit of a larger whole.

Given that [tex]2\frac{3}{5}[/tex] divide by [tex]1\frac{1}{4}[/tex].

The mathematical representation is

  [tex]2\frac{3}{5}[/tex]  ÷  [tex]1\frac{1}{4}[/tex]

Convert the mixed fraction to improper fraction:

= (2×5 + 3)/5  ÷ (1×4+1)/4

=(13/5) ÷ (5/4)

To convert the division sign into a multiplication sign, take the reciprocal of 5/4.

= (13/5) × (4/5)   [Reciprocal of 5/4 is 4/5]

= 52/25

If 52 is divided by 25, the quotient is 2 and the remainder is 2.

Convert 52/25 into a mixed fraction:

52/25 =[tex]2\frac{2}{25}[/tex].

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Answer:

say there are 2 colors, it is 50/50.

if there are 3 it would be a 1/3. 4 colors would be 1/4. now multiply your probability by two. i.e: 1/4 ×2 = 2/8

Answer:

One solution:

[tex]\boxed{x = 0,\;y = -\dfrac{6}{5}}[/tex]

Step-by-step explanation:

The solution strategy is to isolate one of the variables by eliminating the other. There are several ways to do this. This is my preferred way

The equations are

[tex]5y = x-6 \cdots[1]\\\\4x - 10y = 12 \cdots[2]\\\\[/tex]

Transform equation [1] into the same form as [2] with x and y variables on the left and the constant on the right:

Subtract x from both sides of equation [1]:

[tex]-x + 5y = -6\cdots[3][/tex]

Multiply equation [3] by 2 to get the coefficients of y the same
[3] x 2 gives

[tex]-2x + 10 y = -12\cdots[4][/tex]

In equations [2] and [4], the coefficients of y are the same but of opposite sign

Add equations [2] and [4] to get

[tex]4x - 10y + (-2x + 10y) = 12 + (-12)\\\\4x - 10y -2x - 10y = 12 -12\\\\4x - 2x -10y + 10y = 0\\\\2x = 0\\\\x = 0\\\\[/tex]

Substitute for x = 0 in any of the equations [1] or [2] and solve for y
Let's pick equation 1

Substitute for x = 0 in [tex]5y = x - 6\\[/tex]

[tex]5y = 0 - 6\\\\5y = -6\\\\y = -\dfrac{6}{5}\\\\[/tex]

So this is a system of equations with one solution:
[tex]\boxed{x = 0,\;y = -\dfrac{6}{5}}[/tex]

With the amount of silk she has, she can create 48 garments.

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

According to our question-

She possesses 144 yards of silk cloth.

Each dress needs 3 yards of silk for the skirt and 1 yard for the bodice.

According to the data given, the calculation is as follows:

144/3

48

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Answer:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} \sf Pizza & \sf Drinks\\\cline{1-2} \vphantom{\dfrac12} 0& 30\\\cline{1-2} \vphantom{\dfrac12} 1& 20\\\cline{1-2} \vphantom{\dfrac12} 2& 10\\\cline{1-2} \vphantom{\dfrac12} 3& 0\\\cline{1-2} \end{array}[/tex]

See attachment for the graph of the inequality.

Step-by-step explanation:

Given information:

The inequality to represent the given information is:

To complete the given table, input p from 0 through 3 into the inequality and solve for d.

[tex]\begin{aligned}p=0 \implies 10(0) + d & \leq 30\\d & \leq 30\end{aligned}[/tex]

[tex]\begin{aligned}p=1 \implies 10(1) + d & \leq 30\\10+d & \leq 30\\d & \leq 20\end{aligned}[/tex]

[tex]\begin{aligned}p=2 \implies 10(2) + d & \leq 30\\20+d & \leq 30\\d & \leq 10\end{aligned}[/tex]

[tex]\begin{aligned}p=3 \implies 10(3) + d & \leq 30\\30+d & \leq 30\\d & \leq 0\end{aligned}[/tex]

Completed table:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} \sf Pizza & \sf Drinks\\\cline{1-2} \vphantom{\dfrac12} 0& 30\\\cline{1-2} \vphantom{\dfrac12} 1& 20\\\cline{1-2} \vphantom{\dfrac12} 2& 10\\\cline{1-2} \vphantom{\dfrac12} 3& 0\\\cline{1-2} \end{array}[/tex]

To graph the inequality:

Therefore, the expression for the total number of apples Laqueta has in the basket is (n+3) + m.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

A figure or a group of figures used to represent a mathematical item, an action on a mathematical object, a relationship between mathematical objects, or to organize other symbols that appear in a formula are known as mathematical symbols.

The total number of apples Laqueta has in the basket = n+m

When she puts 3 more red apples into the basket, the total number of red apples becomes n+3.

So,  the total number of apples Laqueta has in the basket is (n+3) + m.

This can be simplified as n+m+3.

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Answer:

20%

Step-by-step explanation:

The probability that the first unbelted driver is in the 6th car stopped is
(1 - 0.20)^5 * 0.20,
where 0.20 is the probability that a driver does not wear their seatbelt (20%),
and (1 - 0.20)^5 is the probability that the first 5 cars stopped all have drivers who wear their seatbelts.

This simplifies to (0.8)^5 * 0.2 = 0.32768 * 0.2 = 0.065536.

Answer:

533

Step-by-step explanation:

Ends in an odd number

Answer:

the first one: 0533

Step-by-step explanation:

1,3,5,7,9 are basic odd numbers

2,4,6,8 are basic prime numbers

see what the last digit is aka the ones place

see if it ends in an odd or even

the only one that has the last digit as an odd number is the first one 0533, therefore it is the answer.

The people that developed pneumonia will be 78 people.

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

According to the CDC, 6% of people who contract measles also develop pneumonia. If there were 1,296 cases of the measles in the United States in 2019, the people that developed pneumonia will be:

= 6% × 1296

= 78 people.

The second question can't be solved as the information isn't given.

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Answer:

14:7, 42:21, 6:3, 48:24

Step-by-step explanation:

The ratio can be seen as 2:1 (from the provided 14:7 which is equal to 2), which would be in plums:grapes.

Your ratio of 42:21 is correct for the second column, so we can move on to the third and fourth.

We can use this equation to find your missing values for column 3:

[tex]\frac{14}{7}[/tex] = [tex]\frac{x}{3}[/tex]

Now, we can solve for x through cross multiplication:

7x = 14*3

7x = 42

x = 6

For column 4, we can set up the equation:

[tex]\frac{14}{7}[/tex] = [tex]\frac{x}{24}[/tex]

Now, let's solve for x:

7x = 336

x = 48

Therefore, your ratios will be:

14:7, 42:21, 6:3, 48:24.

The lines y = x + 3 and y = 2 · x + 2 pass through point (1, 4) on Cartesian plane.

In this problem we must graph two lines that pass through point (x, y) = (1, 4). Lines can be represented by equations of following form:

y = m · x + b

Where:

We must choose two slope-intercept combinations to generate two different lines: (x, y) = (1, 4)

Line 1

4 = m · 1 + b

4 = m + b

m = 1

4 = 1 + b

b = 3

y = x + 3

Line 2

4 = m · 1 + b

4 = m + b

m = 2

4 = 2 + b

b = 2

y = 2 · x + 2

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Answer:

I think it's b. when you have a negative and a negative it becomes a positive

Answer: it's C because 4% of 2170 is 86.8 and times 18 years is 1562.4 and 2170 minus 1562.4 equals 607.8. And C is the closest answer to that answer I gave.



Equation of the tangent to the curve at point (-1,1) is: y=2x+3

Given,

x=cos(t)+cos(2t)

y=sin(t)+sin(2t)

P(-1,1)

For the point(-1,1), the value of t satisfy the equations x=cos(t)+cos(2t) and y=sin(t)+sin(2t) is pi/2.

To find an equation of the tangent to the curve at the given point (x,y) where x=cos(t)+cos(2t) and y=sin(t)+sin(2t) and t= pi/2, we need to first find the slope of the tangent line at this point. To do this, we need to take the derivative of the x and y functions with respect to t:

dx/dt = -sin(t) + 2sin(2t)

dy/dt = cos(t) - 2cos(2t)

Now we can use this information to find the slope of the tangent line at the given point (x,y) where x=cos(t)+cos(2t) and y=sin(t)+sin(2t) and t= pi/2:

slope = dy/dx = (cos(t) - 2cos(2t)) / (-sin(t) + 2sin(2t)) evaluated at t = pi/2

slope = (cos(pi/2) - 2cos(2pi/2))/(-sin(pi/2) + 2sin(2pi/2)) = 0 - (-2)/0 + 0 = 2

Now, we can use this slope to find the equation of tangent using:

(y-y1)= m(x-x1)

=> y-1=2(x+1)

=>y=2x+3

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Whenever you want to add clarification, explanation, or a side remark to a statement, you should use parentheses ().

3(0.4h+5)=4(0.2h+7)

When adding extraneous information or an aside to a sentence, parentheses, a pair of punctuation marks, are most frequently utilized.

Two curving vertical lines can be seen in parentheses: ( ). Parenthesis refers to a single instance of this punctuation.

To the left, we reposition every term:

3(0.4h+5)-(4(0.2h+7))=0

Parentheses are increased.

0h-(4(0.2h+7))+15=0

-(4(0.2h+7)), which we calculate as follows:

4(0.2h+7)

Parentheses are increased.

0h+28

In addition, we add up all the numbers and variables.

h+28

Resuming the equation

-(h+28)

In addition, we add up all the numbers and variables.

h-(h+28)+15=0

Parentheses are removed.

h-h-28+15=0

In addition, we add up all the numbers and variables.

-13!=0

For this equation, there is no answer.

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Answer:

The slope is 1/2

Step-by-step explanation:

To find the slope of the line, put the equation in slope intercept form.

y= mx+b where m is the slope and b is the y intercept

4y -2x = -30

Add 2x to each side

4y -2x+2x = 2x-30

4y = 2x-30

Divide by 4

4y/4 = 2x/4 -30/4

y = 1/2x -15/2

The slope is 1/2

Answer:

0.5

Step-by-step explanation:

To find the slope of the line you have write this in slope intercept form.

That is,

Here,

m - Slope

c - y intercept

Now, to write this expression in slope intercept form, you have to make y the subject of this expression.

[tex] 4y - 2x = - 30[/tex]

Add 2x to both sides.

4y = 2x - 30

Now divide both sides by 4.

y = 2/4x - 30/4

Accordingly,

[tex]y = 0.5x - 7.5[/tex]

Slope of the line (m) = 0.5

The equation of the square coop is 4x = 20 and the length is 5yd .

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

20yd of fencing to build the walls of a square coop.

Therefore, the perimeter of the square coop is 20 yd .

Then the equation of the perimeter of the square coop is 4x = 20.

Solving the equation,

4x = 20

We get,

x = 5yd

The equation of the square coop is 4x = 20 and the length is 5yd .

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Correct option is B and C, Stocks have higher risk than bonds. A bond offers fixed interest income, while a stock may offer dividends to investors.

In general, stocks are riskier than bonds simply because they do not provide investors with guaranteed returns, as opposed to bonds, which do so through coupon payments. Bondholders, who are a company's creditors, get priority in being paid back in the case of a business bankruptcy, making stocks intrinsically more volatile than bonds. Owners of common stock, on the other hand, are last in line and risk losing everything if the business fails.

Bonds would be a preferable choice for risk-averse investors who want to safely invest their money and feel secure with more standardized payout schedules.

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Step-by-step explanation:

[tex]3x - y = 20 \\ y = 7 \\ 3x = 20 - 7 \\ 3x = 13 \\ x = \frac{13}{3} \\ x = 4.33[/tex]

The value o x for the given expression will be 9.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 3x - y = 20 the value of y is 7. The value of x will be calculated as:-

3x - y = 20

3x - 7 = 20

3x = 20 + 7

3x = 27

x = 27 / 3

x = 9

Therefore, the value of x will be 9.

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The dog moves quickly through 250-meter passes

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

According to our question-

dog run =11 metres per second

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Answer:

x= 18,0

Step-by-step explanation:

Answer: x⁰⁄₂ + 0 = y or x⁰⁄₂ = y

Step-by-step explanation:

Equation of a line is mx+b=y

m=slope

The slope is ʸ⁄ₓ or in this case ⁰⁄₂

b=where the line cross the y-axis which is 0, when it is 0 there is no use in write +0 after the equation, as there is no difference, but it is your choice

Answer:

Okay so, if he is getting a console for $17.50, then you first want to do is subtract that from the total amount that he has which is $49.

49 - 17.50 = $31.50

Now each game costs $5.25

You can either just keep adding 5.25 by itself until you get to 31.50, or you can just divide 31.50 by 5.25, but I am going to just multiply then by certain numbers until I get the result.

5.25 * 5 = 26.25 so we know he can buy more than 5.

5.25 * 6 = 31.50

He can buy 6 games!

Step-by-step explanation:

Hope it helps! =D

Answer: 8 employees doing both jobs.

Step-by-step explanation:

     If 4 do neither, we can subtract this from the total number of employees. This will give us the employees that work with customers, the warehouse, or both.

           36 - 4 = 32 employees

     Next, we need to find how many do both. We can add 29 and 11 together to find the total number of jobs worked in these sections (this will include employees doing both jobs).

           29 + 11 = 40 employees

     Lastly, we will subtract the total number of employees working in these sections from the number above to find how many are doing both jobs.

           40 - 32 = 8 employees doing both jobs.

Answer:

14

Step-by-step explanation:

35% of 40

= [tex]\frac{35}{100}[/tex] × 40

= 0.35 × 40

= 14

Answer:

[tex]l = \frac{P}{2} - w[/tex]

Step-by-step explanation:

[tex]P= 2(l+w)[/tex]

[tex]\frac{P}{2} = l +w[/tex]

[tex]l = \frac{P}{2} - w[/tex]

Answer:

20

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

30 minus 12 is 18 and 18 is 25% of 72

Answer: cubic inches

Step-by-step explanation: volume is cubed since it is 3 dimensions and it is in inches which are the units given