1. Simplify and show your work.
3(2x^3y^5)^3
——————— or /
(2x^6y^3)^4

Answer:

[tex]y=3x-7[/tex]

Step-by-step explanation:

Parallel lines, by definition, never intersect. They have the same slope but different y-intercepts (otherwise they would be the same line) on a graph.

Slope-Intercept Form:

Slope-Intercept form is expressed as: [tex]y=mx+b[/tex], where

This form is super useful for linear equations as it gives us the two key features of a linear equation. It's how each of the options are formatted, so we know we'll have to use this form.

The line is parallel to [tex]y=3x-4[/tex], meaning it has a slope of 3, but also a y-intercept other than -4 (otherwise they would be the same equation).

So we can generally form an equation: [tex]y=3x+b\text{, }b\ne-4[/tex], so we can plug any value for "b" here (except -4) and have a parallel line

Since we not only want to find a parallel line, but also one that passes through a specific point, we can use our general parallel equation: [tex]y=3x+b\text{, }b\ne-4[/tex], and plug in known values. We of course already have the slope plugged in, but now we have a (x, y) coordinate, which we can plug in for x and y in the equation.

Original Equation:

[tex]y=3x+b[/tex]

Point given: (3, 2), substitute in x=3 and y=2:

[tex]2=3(3)+b[/tex]

Simplify:

[tex]2=9+b[/tex]

Subtract 9 from both sides:

[tex]-7=b[/tex]

Now we can take this value. and plug it back into the general equation:

[tex]y=3x+(-7)\implies y=3x-7[/tex]

Now we have our answer!

Answer:-12.168

Step-by-step explanation: multiply it regularly, then count how many decimals are after the numbers, in this case, 3. cus it’s 2 after 1.56 and one after 7.8

Answer: x=5

Step-by-step explanation:

Solve the rational equation by combining expressions and isolating the variable (x)

The slope of the relation is 1/4

You should know that slope is the rate of change of y with respect to x.  slope is denoted by change in y over change in x

The table of values is given as:

x −2 −1 0 1 2

y −13 −9 −5 −1 3

The slope is calculated as:

Slope = y₂ - y₁/x₂ - x₁

So, we have

Slope = 2 - 1/3 + 1

Evaluate the like terms

Slope = 1/4

In conclusion, the slope of the relation is 1/4

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An area surrounding a measurement that indicates how accurate it is called a confidence interval.

Let X = The proportion of n randomly selected consumers who receive the discount. So, X = B(n, p), where p is the likelihood that a consumer will receive the discount.

Back-up Theory 100(1 - α) % Confidence Interval for the population proportion, p is:

p ± Zα/2[√{P(1 –p)/n}] ……(1)

where

Zα/2 is the upper (α/2)% point of N(0, 1),

pcap = sample proportion, and

n = sample size.

One can conclude with 100(1 - )% confidence that the population proportion, p, is p if a 100(1 - )% Confidence Interval for p holds a specific hypothesized value of p…………. (2)

Now to work out the solution,

The given confidence interval is: 0.12 ± 0.05 i.e., [0.07, 0.17] or [7%, 17%]……………………. (3)

for Part (a)

equation (2) and (3), [7%, 17%] holds 15%. Hence the statement is NOT valid.

for Part (b)

equation(2) and (3), [7%, 17%] holds 15%. Hence the statement is valid.

For Part (c)

Margin of error is: Zα/2[√{P(1 –P)/n}]

If the sample sizes under Part (c) and (a) are respectively, n2 and n1, the ratio of respective margin of errors would be

[Zα/2.√t{P(1 –P)/n2}]/[Zα/2√{P(1 –P)/n1}]

= √(n1/n2)

= 1/√6 [given the second sample size is 6 times the first sample size]

= 0.4082

= > the margin of error under Part (c) = the margin of error under Part (c) x 0.4082

= 0.05 x 0.4082

= 0.020.

Thus, the margin of error when the sample size if 6-fold is 0.020.

For Part (d)

The revised Confidence Interval from Part (c) is 0.12 ± 0.02 or [0.10, 0.14], which does not hold 0.15 as a result, according to (2), the program is NOT operating as anticipated.

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Answer: A

Step-by-step explanation: 2.5 inches = 63.5 millimeters

Answer:1 roll of ribbon left

Step-by-step explanation:

Answer: 35 would be the median

Step-by-step explanation: Put the numbers in order and whichever one is the middle value is the median

Answer:

35

Step-by-step explanation:

The median is the middle price when listed from smallest to largest

31, 34,   35,    48, 50

The middle price is 35

The median is 35

The scale of measurement most reasonably applies to Confidence in Science is ordinal.

The basic  four scales used in measurements are continuous, discreet, ordinal and nominal. The continuous measurement scale is used to take the values in between a permitted range. For example weight, height, sales, rate etc.

In discreet measurements only take the whole numbers within a permitted range. For example, count of people, number of objects etc. Ordinary, logically ordered categorical values. For example, the size of clothes,

Nominal measurements include not logically ordered categorical values. For example, nationality, language etc.  The scale of measurements most reasonably applies to Confidence in Science is ordinal.

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The solution to the equation x³ + x - 4 = 0 is x = 1.38

From the question, we have the following parameters that can be used in our computation:

x^3 + x - 4 = 0

Express the exponents as proper superscript

So, we have the following representation

x³ + x - 4 = 0

Next, we solve the equation using a graph

i.e. we plot the graph of x³ + x - 4 = 0

See attachment for the graph of x³ + x - 4 = 0

The points where the graph of x³ + x - 4 = 0 crosses the x-axis are the solution

In this case, the point is 1.38

Hence, the solution is x = 1.38

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Answer:

58.8 feet per second

CONVERTING MPH TO FPS

If you are moving at the rate of 40MPH, how many feet do you travel in a second? At 40 miles per hour, you are traveling 58.8 feet per second. To convert miles per hour to feet per second, multiply the miles per hour figure by 1.47. There are 5280 Feet in a mile and 3600 Seconds in an hour.

On solving the provided question, we cans ay that - in given inequality equation to -7 < x < -2; -2 < x < 3

A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.

-7 < x < -2

-2 < x < 3

and 3 > x > 8

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The product of given equation is      [tex]6t^{4} + 6t^{2} bs-8bst^{2} -8b^{2} s^{2}[/tex] .

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

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.

[tex]=(6t^{2} -8bs) (t^{2} + bs)[/tex]

[tex]=6t^{2} (t^{2} + bs) -8bs(t^{2} + bs)[/tex]

[tex]=6t^{4} +6t^{2}bs -8bst^{2} -8b^{2} s^{2}[/tex]

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Answer: The statement you've provided describes the economic concept of elasticity. Elasticity is a measure of how responsive the quantity demanded or supplied of a good or service is to a change in its price. It measures the responsiveness of the consumers' and producers' behaviors to changes in price, in other words, how sensitive the consumers or producers are to changes in the good or service prices.

There are different types of elasticity, such as price elasticity of demand and price elasticity of supply. Price elasticity of demand measures how much the quantity demanded of a good changes in response to a change in its price. If a good has a high price elasticity of demand, then a small change in its price will result in a large change in the quantity demanded of the good. On the other hand, price elasticity of supply measures how much the quantity supplied of a good changes in response to a change in its price. A good with a high price elasticity of supply will see a large increase in the quantity supplied in response to a small price increase.

Elasticity is a very important concept in economics because it helps to understand how consumers and producers will react to changes in prices and how it would affect the overall economy.

Step-by-step explanation:

Analysing the given figures of the triangles ABC and A'B'C' , the required transformation for changing the traingle ABC to A'B'C' is the translation.

In a two-dimensional space, a translation transformation can be represented by a matrix of the form [1 0 Tx], [0 1 Ty], where Tx and Ty are the horizontal and vertical translation values, respectively. The matrix shows the movement of an object in the x and y directions, with Tx representing the horizontal shift and Ty representing the vertical shift.

A translation transformation moves an object from one position to another without changing its size or orientation. The shape and size of the object remain the same, but its position changes. The object is moved along a specific direction by a certain distance, and the position of the object within a coordinate system is changed. The effect of a translation can be visualized as sliding an object along a surface, while keeping its orientation and size unchanged.

As we can see from the given graph that the traingle ABC has moved straight downward without any changes in the orientation and the size of the traingle while being transformed to traingle A'B'C', Hence the transformation is translation transformation.

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3/4 > 1/5
6/9 > 2/5
6/7 > 3/10
2/11 < 4/9

Answer:

3/4 > 1/5

6/9 > 2/5

6/7 > 3/10

2/11 < 4/9

Step-by-step explanation:

Manera facil de comparar fracciones:.

3/4    1/5

Multiplica el denominador (numero abajo) de cada fraccion por el numerador de la otra fraccion y escribe el producto arriba del numerador.

El numero mas grande esta arriba de la fraccion mas grande.

5 x 3 = 15 arriba  de 3/5

4 x 1 = 4 arriba de 1/5

Como 15 > 4, 3/4 > 1/5

30      18

6/9    2/5

6/9 > 2/5

 60     21

6/7    3/10

6/7 > 3/10

18       44

2/11   4/9

2/11 < 4/9

The probability of tossing 3 heads in a row is P = 0.125, and after that, because the events are independent, the probability of getting heads (or tails) still is p = 0.5

Assuming that we have a fair coin, we assume that both outcomes have the same probability, so:

P(tails) = 0.5

P(heads) = 0.5

Then the probability of getting heads 3 times in a row, is the product of the probability of getting heads 3 times, this will be:

P(3 heads) = 0.5*0.5*0.5

P(3 heads) = 0.5^3

P(3 heads) =  0.125

Now, after this point, what is the probability of getting heads or tails?

Remember that each toss of the coin is independent of the previous one, so the probability of getting tails still is 0,5, and the same for the probability of getting heads.

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The percent of change can be calculated by taking the difference between the new value and the original value, divided by the original value, and then multiplying by 100 to express the result as a percentage.

In this case, the original value is 1 cup of cocoa and the new value is 2 cups of cocoa (since Troy added another cup). The difference between the two values is 1 cup.

So the percent of change would be:

(1 / 1) * 100 = 100%.

This means that the quantity of cocoa increased by 100% by adding 1 cup cocoa.

If earning 3250 per month over 10year period, At the end of 10th year, the amount on the account will be 390,000

To multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem. In the multiplication problem, 6 × 9 = 54, the numbers 6 and 9 are the factors, while the number 54 is the product.

The amount earned In a month is 3250.

There are 12 months In a year.

The total month in 10 years = 10× 12 = 120 months

The total amount in the account for 10years = 120×3250 = 390,000

Therefore there will be 390000 in the account at the end of 10th year.

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Answer:

Basically, LON would be 8z + 112 + 6z - 17

So, our equation will look like this

8z + 112 + 6z - 17 = -1z + 65

Subtract the 6z from the 8z

2z + 112 - 17 = -1z + 65

112 - 17 = 95

2z + 95 = -1z + 65

add the 1z

3z + 95 = 65

subtract the 95

-30

3z = -30

The answer is -10 :)

Step-by-step explanation:

Answer:

LON=75

Step-by-step explanation:

LON= LOM=NOM

-1z+65=8z+112-6z-17

-1z+65=2z+95

3z=-30

z=-10

LON= -1z+65

       = -1(-10)+65

       = 10+65

LON= 75

If the amount of time in seconds, t, it takes for a bungee jumper to free fall is given by the function t equals the square root of the quantity d over 16. The distance the jumper fall is: A 400 feet.

Using this formula to find the distance by solving for d

t=√d/q

Where:

t = Time = 5 seconds

d = Distance = ?

q = Quantity = 16

So,

5 seconds=√d/16

d=16x5²

d=16 × 25

d= 400 feet

Therefore we can conclude that the correct option is A.

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The measure of the angle (θ) is equivalent to sin⁻¹(6.3/14.5).

The Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. Mathematically, it can be written as -

(hypotenuse)² = (base)² + (perpendicular)²

Given is a right angle triangle with hypotenuse as 14.5 meters and

opposite side as 6.3 meters.

We can write sine of the angle (θ) as -

sin(θ) = P/H

sin(θ) = Opposite side/Hypotenuse

sin(θ) = 6.3/14.5

(θ) = sin⁻¹(6.3/14.5)

Therefore, the measure of the angle (θ) is equivalent to sin⁻¹(6.3/14.5).

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Answer:

6 is the missing number

Step-by-step explanation:

Solve what is inside of the parenthesis, then evaluate.

N x (8) = (30) + (18)

8N = 48

Solve for N.

N = 48/8

N = 6

Therefore , the solution to the given problem of interest comes out to be $272.

Simple interest is calculated by dividing initial capital by the interest rate, the duration, and other variables. The formula employed in marketing is simple return = principle + interest plus hours. This approach is the simplest way to calculate interest. Calculating interest as a percentage of the principle sum is the most common approach. For instance, he may only pay his portion of the interest if he borrowed $100 from a friend and agreed to pay it back with 5% interest. $100 (0.05) = $5. You should pay interest when you make loans, and you also must pay interest when you lend it. Usually, interest is calculated as a portion of a loan.

Here,

Given: $250 in principal

a 2.2% interest rate

and a 4-year term

To discover the basic interest:

Using this formula

Simple interest is equal to

=>P*R*T/100,

=> 250*2.2*4/100

=> 22.

Total amount after 4 years = 250 + 22 =272

Therefore , the solution to the given problem of simple interest comes out to be $272.

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Calculating the ratio between each pair of values in a table allows you to determine whether a proportional relationship is present. The table depicts a proportional relationship if all of those ratios are the same.

y = k x, where is the proportionality constant, is the equation that depicts a proportional relationship, or a line. Find k and create the equation by using k = y x from a table or graph. Tables, graphs, and equations can all be used to depict proportional relationships.

The equation y = kx represents a proportional relationship between two quantities y and x that have the same proportionality constant, k.

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Answer:

(2m + 1) * x ^ 2 - (2m + 5) * x + (2m + 1) = 0

2mx^2+x^2-2mx+5x+2m+1=0

3mx^2+5x+1=0

That's as far as you can get simplifying it.

Step-by-step explanation:

For the given issue, x has a value of 4. The offered solution is the solution extraneous .

When we solve equations, we often obtain values that aren't actually the answer to the equation.

A root of a transformed equation that isn't a root of the previous iteration because it was left out of the original equation's domain is known as a extraneous solution.

√(11x + 5) = 7

(11x + 5) = 7²

11x + 5 = 49

11x = 49 - 5

11x = 44

x = 4

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The answer to the stated domain range puzzle is 0.

both domain and range. The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x).  The values that the function outputs when we enter an x value are in this set.

The collection of all possible inputs and outputs constitutes a function's domain and range, respectively. Important features of a function are the domain and range.

(f(g)(x) = (√x)² - 1

(f(g)(x) = x - 1

(f(g)(x)(1)  = 1 - 1 = 0

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