adding probabilities common core algebra i

As per the given equation, the first plant is produce 2x+21 more items than second plant.

The term equation is known as a mathematical statement that shows that two mathematical expressions are equal.

Here we have given that the first plant produces 5x+14 items daily

And the second plant produces 3x-7 items daily

In order to find the number of items produced on first plant, then we have to calculate the differences between number of items by the two plants daily, then it can be written as by using the equations,

=> (5x+14) - (3x-7)

Now, we have to expand the equations, then we get

=> 5x+14 - 3x+7

=> 2x+21

Therefore, first plant produces 2x+21 more items daily than the second plant.

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4Answer:

Step-by-step explanation:

24 divided by 4 = 6

Based on the questions, 13 guests are attending her best friend’s baby shower.

Firstly, we need to write down the numbers that are already stated in the question.

43 + 9 × х = 160

Secondly, move the x to continue counting.

9x = 160 – 43

Thirdly, calculate the numbers above.

9x = 117

Then, move the X to get the answer.

X = [tex]\frac{117}{9}[/tex]

Lastly, try to finish the division.

X = 13

In conclusion, the result shows that 13 guests attend Mrs. Wright’s best friend's baby shower.

The above question is about the algebraic word problem.

A word problem is a math question written in a short story scenario. Usually, it is a simple short story that is easy to understand.

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 The answer is Option D) f(x)-3

In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as For x > 0, a > 0, and a ≠1, y= logₐ x if and only if x = a^y Then the function is given by f(x) = logₐ x The base of the logarithm is a. This can be read it as log base a of x.

Given here: f(x)=log2x

Now in the attached graph we clearly see that f(x)-3 is the graph that looks identical to the one given in the graph.

Hence, option D is the correct answer.

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Answer:

[tex]x=0,\;x=\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given equation:

[tex]\sqrt{x}=\sqrt{3}x[/tex]

Square both sides:

[tex]\implies \left(\sqrt{x}\right)^2= \left(\sqrt{3}x\right)^2[/tex]

[tex]\implies x= \left(\sqrt{3}\right)^2 \cdot \left(x\right)^2[/tex]

[tex]\implies x=3x^2[/tex]

Subtract x from both sides:

[tex]\implies x-x=3x^2-x[/tex]

[tex]\implies 0=3x^2-x[/tex]

[tex]\implies 3x^2-x=0[/tex]

Factor out the common term x:

[tex]\implies x(3x-1)=0[/tex]

Apply the zero-product property:

[tex]\implies x=0[/tex]

[tex]\implies 3x-1=0 \implies x=\dfrac{1}{3}[/tex]

Answer:

[tex] \sf \: x = \frac{1}{3} \: (or) \: x = 0[/tex]

Step-by-step explanation:

The equation given is,

→ √x = √3x

Now the value of x will be,

→ √x = √3x

→ x = (√3x)²

→ x = 3x²

→ 3x² = x

→ 3x² - x = 0

→ (3x - 1)(x) = 0

→ 3x - 1 = 0 || → x = 0

→ 3x = 0 + 1 || → [ x = 0 ]

→ 3x = 1 ||

→ [ x = 1/3 ] ||

These are the values of x.

Answer: There are 520 pounds of dog and cat food

Step-by-step explanation:

1. 14+12= 26

2. 26x20=520

Andrew would need to invest $61,300 for the account to reach $93,000.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

The equation to find final amount in compound interest is,

A = P (1 + r/n)^(n t)

Here A is the final amount, P is the initial amount, r is the rate of interest, n is the number of times compounding is done in a year, t is the time in years.

Given, A = $93,000

t = 19 years

r = 2.2% = 0.022

n = 4 (since compounding is quarterly)

93,000 = P [1 + (0.022/4)]^(4×19)

93,000 = P [1.0055]^(76)

93,000 = P (1.517)

P = 61,297.8516

To the nearest hundred dollars, P = $61,300

Hence the principal amount Andrew need to invest is $61,300.

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The total volume of the object  is 40 in³

The volume of a solid object encompasses the space and capacity that the object can occupy. Here, we have two shapes that make up the solid object, a cylinder, and a sphere. A cylinder is an object that resembles a tube and has two circular sides with the same radius linked by a flat round surface.

The volume of the cylinder is calculated by using the formula:

V = πr²h

V = 3 * 2² * 3         ..... (since radius r = d/2 = 4/2 = 2)

V = 3 * 4 * 3

V = 36 in³

The volume of the sphere = 4/3 πr³

V = 4/3 * 3 * 1³

V = 4 in³

The total volume of the object =  volume of the cylinder + volume of the sphere

The total volume of the object = 36 in³ + 4 in³

The total volume of the object = 40 in³

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Mr.Kimble spent an amount of $636.17 altogether on gas.

Today, the US Retail Gas Price is at a current level of 3.366, up from 3.331 last week and down from 3.381 one year ago. Hence, the amount of $3.366 will be used in our computation.

Data

He used 12.6 gallons of gas for each of his 15 trips.

The total amount of money spent altogether on gas if the price is $3.366, is computed as follows:

= ($3.366 * 12.6 gallons) * 15 trips

= $42.4116 * 15 trips

= $636.17400

= $636.17.

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Answer:

A) f(2) = 120, g(2) = 4.

B) f'(x) = 5x + 20

C) R - {-2}.

Step-by-step explanation:

A) Just apply given value and resolve:

[tex]f(2) = 20 \times 2 + 80 = 40 + 80 = 120 \\ g(2) = 2 + 2 = 4[/tex]

B) g(2) is 4, so just divide f(x) by 4:

[tex] \frac{1}{4} f(x) = \frac{1}{4} (20x + 80) = \frac{20}{4} x + \frac{80}{4} = 5x + 20[/tex]

C)

[tex] \frac{f(x)}{g(x)} = \frac{20x + 80}{x + 2} [/tex]

Polynomials have full domain. A Quotient of polynomials is defined when denominator is not zero. In this sample, denominator is zero when x = -2, so -2 is not part of the domain. All other real numbers are part, hence R - {2}.

1. The value of F(2) = 120 and g(2) = 4.

2. The division is 5(x+4)

3. The domain is real number except -2.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

The function f(x) = 20x + 80 represents the distance in miles a drone flew.

The function g(x) = x + 2 represents the time the drone flew in hours.

1. F(2)= 20(2)+ 80= 40+ 80= 120

and, g(2)= 2 + 2 = 4

2. The division is

= F(x) / g(2)

= (20x + 80)/ (2+2)

= 20 (x+4) / 4

= 5 (x+4)

3. The domain of F(x) / g(x) is all real number except -2.

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The exponential form of 8x8x8x8 is 2^(4*3) = 2^12.

Answer:

3x of 180=8x of 90

Use this equation

The maximum number of mangos that she could buy = 9

Let x represents the number of apples and y represents the number of mangos.

Given that:

the cost of each apple = $0.50

and the cost of each mango = $0.75

Camila has $7. 75 to spend.

This means, the total cost of apples and mangos together must be less than or equal to 7.75

So, we get an inequality,

0.50x + 0.75y ≤ 7.75

And she must buy no less than 11 apples and mangos altogether.

x + y ≥ 11

consider a system of equations.

0.50x + 0.75y = 7.75

x + y = 11

If we solve this system of equations we get x = 2 and y = 9

So, she can buy at most 9 mangos.

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The piece of wood is as long as 48 nails. It is the quotient of the length of wood by the length of nail. In calculation, they should have the same unit length, that is inch.

One foot is equal to 12 inches.

Mathematically, it is expressed as

1 ft = 12 in

A piece of wood is 12 feet long. The nail has the length of 3 inches. Find the number of the nails so it equals the length of the piece of wood!

The length of piece of wood in inches would be

12 feet = 12 × 12 inches

12 feet = 144 inches

The number of nails needed so that the length would be as long as a piece of wood is

= length of wood / length of nail

= 144 inches / 3 inches

= 48 nails

Hence, a piece of wood is equal to 48 nails.

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The reflection of (-3, 2) over the y-axis is (-3, -2).

The reflection of a point (x, y) over the y-axis is (x, -y).

Therefore, the reflection of (-3, 2) over the y-axis is (-3, -2).

To calculate the reflection of (-3, 2) over the y-axis, we first use the formula (x, -y).

In this case, x = -3 and y = 2, so the reflection of (-3, 2) over the y-axis is (-3, -2).

We can also calculate the reflection of (-3, 2) over the y-axis using the distance formula.

The distance formula  is d = √(x2-x1)2 + (y2-y1)2

In this case, x1 = -3, x2 = 0, y1 = 2, and y2 = 0.

Therefore, the distance d = √(02-(-3)2 + (02-2)2 = √(9 + 4) = √13

The reflection of (-3, 2) over the y-axis is (-3, -2). This can be verified using the distance formula.

d = √(x2-x1)2 + (y2-y1)2 = √(-3-0)2 + (-2-0)2 = √(9+4) = √13

The distance d is equal to the distance between (-3, 2) and (-3, -2). Hence, the reflection of (-3, 2) over the y-axis is (-3, -2).

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Therefore , the solution of the given problem of factorization comes out to be x=0 and x=1/3.

The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.

Here,

Given:

thus . We do factorization of given expression and

we come on a result

=>  3x - 9x²

=> 3x (1 -3x)

x=0 and x=1/3

Therefore , the solution of the given problem of factorization comes out to be x=0 and x=1/3.

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Answer:

J

Step-by-step explanation:

Short to the point way compare it by Up to Down

4/9

Answer:

G

Step-by-step explanation:

a proportional relationship is defined by

y = ax

that means, if x = 0, then also y = 0.

let's look at the slope (the constant of change) :

y coordinate change / x coordinate change

when going from 1 point to another in the line.

we see e.g. for (4, 9) and (5, 12)

x changes by +1 (from 4 to 5).

y changes by +3 (from 9 to 12).

the slope is +3/+1 = 3.

but the slope cannot be the "constant of proportionality" ("a" above), because starting e.g. from (2, 3) to get to x = 0 would mean

x has to change by -2 (= -2×1).

and then y has to change by -6 (= -2×3) to keep the same slope "alive".

and so, for x = 0, we would get y = -3. but not 0.

the only equation with slope 3 (the factor of x, yes) is in G.

therefore, G is the right answer.

we can also check, when using x = 4, x = 5 and x = 2, we get the given y-values (9, 12, 3) from y = 3x - 3.

so, it is correct.

On solving the provided question, we got to know that - they are perpendicular, they are perpendicular and they are intersecting lines

A straight line that intersects another straight line at a 90° angle is said to be perpendicular. A little square is placed in the middle of two vertical lines to represent a 90° angle, often known as a right angle, as illustrated. The two straight lines in this instance are perpendicular to one another since they connect at a right angle.

1) For this case, we have to define perpendicular lines:

Angle y = angle H

10x-27 - 2x + 29

x = 32

they are perpendicular

2) they are perpendicular

3)  they are intersecting lines

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The midpoint formula is used to find the center point of a line segment, given the coordinates of the two endpoints. The formula is as follows:

Midpoint = ( (x₁+ x₂) / 2, (y₁ + y2) / 2 )

Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints of the line segment.

To find the missing coordinate using the midpoint formula, you would need to have the coordinates of one endpoint, as well as the coordinates of the midpoint. Then, you can use the formula to solve for the missing coordinate.

For example, if you have the coordinates of one endpoint as (3, 5) and the coordinates of the midpoint as (4, 6), you can use the formula to solve for the missing endpoint:

Midpoint = ( (3 + x₂) / 2, (5 + y₂) / 2 )

(4, 6) = ( (3 + x₂) / 2, (5 + y₂) / 2 )

So, by solving above equation we can get the missing coordinate

(x₂, y₂) = (5,7)

In conclusion, the midpoint formula can be used to find the missing coordinate of a line segment by using the coordinates of one endpoint and the midpoint. It is a simple and efficient way to find the missing coordinate when working with geometric shapes.

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The equation which is use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice is  

y = 0.25*85.

What is percentage?

A number or ratio expressed as a fraction of 100 is known as a percentage in mathematics. Though the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. An amount that is a percentage is dimensionless and has no assigned measurement.

Given:

The current box holds 85 ounces, 25% less rice.

We have to find the equation which is use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice.

Let, y be the original amount of ounces of rice in a box.

The current box holds 85 ounces.

The 25% less than 85 ounces are 85*0.25.

So, the equation becomes y = 0.25*85.

Hence, the equation which is use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice is  

y = 0.25*85.

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18-12=6, peter now has 6 dimes left after buying a drink. Since the number he has left is ONE HALF of the number of pennies he has. 6x2=12.

peter has 12 pennies. hoped that helped

Answer:

x=6 z=73

Step-by-step explanation:

9x+53=6x+71

3x+53=71

3x=18

x=6

9(6)+53

54+53

107

107+z=180

z=73

Answer: 5x − 4 > 2x + 3

Step-by-step explanation:

The expression 5x − 4 > 2x + 3 looks like an equation but with the equals sign replaced by an arrowhead. It is an example of an inequality. This denotes that the part on the left, 5x − 4, is greater than the part on the right, 2x + 3.

Answer:

[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6} \vphantom{\dfrac12} x&-4&1&2&3&6 \\\cline{1-6} \vphantom{\dfrac12} f(x)&-20&5&10&15&30 \\\cline{1-6}\end{array}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=5x[/tex]

To complete the function table, substitute each given value of x into the given function:

[tex]x=-4 \implies f(-4)=5(-4)=-20[/tex]

[tex]x=1 \implies f(1)=5(1)=5[/tex]

[tex]x=2 \implies f(2)=5(2)=10[/tex]

[tex]x=3 \implies f(3)=5(3)=15[/tex]

[tex]x=6 \implies f(6)=5(6)=30[/tex]

Completed table:

[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6} \vphantom{\dfrac12} x&-4&1&2&3&6 \\\cline{1-6} \vphantom{\dfrac12} f(x)&-20&5&10&15&30 \\\cline{1-6}\end{array}[/tex]

An equation of the line that passes through the point (6, 0) and had a slope of -5/6 is y = -5x/6 + 5.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Given the following parameters:

Substituting the given parameters into the point-slope formula, the equation of the line is given by;

y - y₁ = m(x - x₁)

y - 0 = -5/6(x - 6)

y = -5x/6 + 5

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0 to the 0 exponents is undefined or indeterminate, and it's not considered as a valid mathematical operation.

The value of 0 to the 0 exponents is undefined or indeterminate. The reason for this is that the mathematical definition of exponentiation states that any number to the power of 0 is equal to 1, except for 0, which is undefined. However, when we try to apply this rule to 0 to the power of 0, it creates a paradox.

If we assume that 0 to the 0 exponents is 1, then any number raised to the power of 0 would be equal to 1, which is not true. For example, 2 to the power of 0 is not equal to 1, but 2, so this assumption doesn't hold true.

On the other hand, if we assume that 0 to the 0 exponents is 0, then any number multiplied by 0 would be 0, which is not true either. For example, 2 multiplied by 0 is not equal to 2.

Therefore, 0 to the 0 exponents is undefined or indeterminate, and it's not considered as a valid mathematical operation.

It's important to note that in some fields of mathematics such as limit, the value of 0 to the 0 exponent is defined as 1, but this is limited to the context of limit and not in general math.

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The correct graph is the third one: graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2.

News grapher using a function with inputs and outputs to depict a function. A function is a connection between two variables in which the input determines the output. In a graph, the y-axis shows the output, while the x-axis shows the input.

An unweighted, undirected graph with no graph loops or numerous edges is referred to as a simple graph (also known as a strict graph; Tutte 1998, p. 2; West 2000, p.

The line that connects the coordinates (x, y) = (-2, -3) and (y = 1/2x + 2) on this graph expresses the equation y = 1/2x + 2. (0, -2). When we enter those coordinates into the equation, we get the points on the graph, y = 1/2(-2) + 2 = -3 and y = 1/2(0) + 2 = 2.

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The mirrors image of points (2, 3) under the origin is (-2, -3)

What is a mirror image?

A mirror image is a reflected duplicate of a seemingly identical item that is turned the other way in the plane perpendicular to the mirror surface. It manifests as an optical effect as a result of reflection off of materials like a mirror or water.

Here,

We have to find the mirror image of points (2, 3) under the origin.

We concluded that the mirror image of a point(2,3) is (-2,-3).

The coordinates of the origin are denoted by (0, 0). It means that at origin, x=0 and y=0.

Hence, the mirrors image of points (2, 3) under the origin is (-2, -3)

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