Solve for x: 4(x-5) 8. = 9y​

9514 1404 393

Answer:

  (C)   x^38

Step-by-step explanation:

The explanation speaks for itself. It is a restatement of the Order of Operations as it applies to this expression.

__

Written in plain text, the expression is ...

  ((x^6·x^10)/(x^-3))^2

The order of operations requires you evaluate the inner parentheses first. The exponential terms cannot be simplified, so you perform the product. The applicable rule of exponents is ...

  (a^b)(a^c) = a^(b+c)

So, you now have ...

  ((x^(6+10))/(x^-3))^2 = (x^16/x^-3)^2

Again, you perform the division inside parentheses before anything else. The applicable rule of exponents is ...

  (a^b)/(a^c) = a^(b-c)

So, you have ...

  (x^(16-(-3)))^2 = (x^19)^2

Now, you can perform the exponentiation. The applicable rule of exponents is ...

  (a^b)^c = a^(bc)

So, the final simplification is ...

  (x^19)^2 = x^(19·2) = x^38

_____

Comment on exponent rules

The rules of exponents follow directly from the fact that an exponent is a representation of repeated multiplication.

Product rule:

  (x^2)(x^3) = (x·x)(x·x·x) = x·x·x·x·x = x^(2+3) = x^5

Quotient rule:

  (x^3)/(x^2) = (x·x·x)/(x·x) = x = x^(3-2) = x^1

Power rule:

  (x^3)^2 = (x·x·x)^2 = (x·x·x)(x·x·x) = x^(3·2) = x^6

When a population is subjected to directional selection over time, the traits that are selected for will remain stable while the traits that are selected against will disappear.

Evolution is the study of how populations change over time. Most traits have multiple genes controlling their structure, function, appearance, and other characteristics. Single genes only very infrequently control a trait.

As a result, most traits have a tendency to be continuous in nature and to have a wide range of values. One side of these values will be picked against during directional selection, while the other side will be selected in favor of. Look at the illustration of a lemur's fur color below.

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The area of rhombus can be found using the formula A = (d1 x d2)/2, where d1 and d2 are the lengths of the diagonals. Using area formula, we get A = (24 x 18)/2 the area of the rhombus is 24√(119) square meters.

Let's start by finding the other diagonal of the rhombus.

We know that the perimeter of a rhombus is four times the length of one of its sides. So, if the perimeter is 80 m, then each side has a length of 80/4 = 20 m.

We also know that the diagonals of a rhombus are perpendicular bisectors of each other, and they divide the rhombus into four congruent right triangles. Therefore, each leg of one of these right triangles is half of one of the diagonals of the rhombus.

Let's call the other diagonal of the rhombus d. Then, using the Pythagorean theorem in one of the right triangles, we have

(20/2)² + (d/2)² = 24²

100 + d²/4 = 576

d²/4 = 476

d = 2√(119)

Now that we have both diagonals, we can find the area of the rhombus by multiplying them and dividing by 2

Area = (24 * 2√(119))/2

Area = 24√(119)

Therefore, the area of the rhombus is 24√(119) square meters.

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--The given question is incomplete, the complete question is given

"  The area of a rhombus whose perimeter is 80 m and one of whose diagonal is 24 m is ..........."--

To access the first element of an array of integers called "numbers," you can use the expression:
numbers[0]`
This expression uses the array name "numbers" and the index "0" to access the first element.

To access the last element of "numbers," assuming it contains 10 elements, use the expression:

`numbers[9]`

Here, we use the index "9" since arrays are zero-indexed, meaning the last element in a 10-element array has an index of 9.
To access the first element of the array called numbers, we would use the expression "numbers[0]."

To access the last element of the array, assuming it contains 10 elements, we would use the expression "numbers [9]" since arrays are zero-indexed in most programming languages.

To access the last element of the array regardless of its length, we can use the expression "numbers [numbers.length-1]," which subtracts 1 from the length of the array to access the last element.
To access the last element, regardless of its length, use the expression:

'numbers [numbers. length - 1]'

This expression uses the "length" property of the array to find the total number of elements and subtracts 1 to get the correct index for the last element.

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Answer:

Undefined

Step-by-step explanation:

If I am seeing the table right, 14 is the only y coordinate and 14 goes with all the x.

so the line would be horizontal

The equation of the first line is y = -1/3x - 4, while the equivalent equations of the second line are y = -2/3(x - 3)  and y = -2/3x + 2

The given parameters are

Slope, m = 5/4

Point, (x1, y1) = (1, 3)

A linear equation is represented as

y = m(x - x1) + y1

So, we have

y = 5/4(x - 1) + 3

This gives

y = 5/4x + 7/4

Hence. the linear equation is y = 5/4x + 7/4

Here, we have

(x, y) = (3, 0) and (0, 2)

A linear equation is represented as

y = m(x - x1) + y1

Where

m = (y2 - y1)/(x2 - x1)

So, we have

m = (2 - 0)/(0 - 3)

m = -2/3

So, we have

y = -2/3(x - 3)

The above equation can be rewritten as

y = -2/3x + 2

Hence, the equations are y = -2/3(x - 3)  and y = -2/3x + 2

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Answer:

the first one because when x=-1 y=-2 and that does not directly vary with x

Step-by-step explanation:

In this exercise, we are given two functions f and g, and an interval [a, b]. We are asked to find the area between the graphs of f and g from x=a to x=b using definite integrals and the Fundamental Theorem of Calculus. The process involves finding the antiderivatives of the functions f and g, and then subtracting the values of the antiderivatives at a and b.

In particular, for this problem, we have f(x) = 8(x) = 6 - |x - 2| and the interval [3, 7). We can split the interval into two parts: [3, 5) and [5, 7). On the first part, the function f(x) is equal to 8(x) = 6 - (2 - x) = x + 4. On the second part, the function f(x) is equal to 8(x) = 6 - (x - 2) = 8 - x. Therefore, we can write the integral for the area between the graphs of f and g as follows:

∫[3,5) [f(x) - g(x)] dx + ∫[5,7) [f(x) - g(x)] dx

Substituting the functions f and g, we get:

∫[3,5) [(x+4) - 3] dx + ∫[5,7) [(8-x) - 3] dx

Evaluating the integrals, we get:

[(1/2)x^2 + 4x - 3x] from 3 to 5 + [(8x - (1/2)x^2) - 15] from 5 to 7

Simplifying, we get:

8

Therefore, the exact area between the graphs of f and g from x=3 to x=7 is 8 square units.

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Answer:

Exact form: -87/16

decimal from -5.4375

mixed number form -5 7/16

Step-by-step explanation:

I'ma god at math

The steps for subtracting mixed numbers are the transformation of improper fractions, subtraction of denominator, then subtracting numerator, making it the smallest term, and reverse.

Finding the difference between two mixed numbers is required when subtracting mixed numbers. The steps for subtracting mixed numbers are as follows:

Step 1: Transform the mixed values into improper fractions in step 1. To achieve this, divide the total by the denominator, then add the numerator. The new numerator is the outcome, and it is positioned above the denominator.

Step 2: Identify a common denominator in step two. You must identify a common denominator to subtract fractions with various numerators.

Step 3: Subtract the fractions in step three. Subtract the numerators from the fractions while maintaining the same denominator.

Step 4: Make the outcome simpler. Simplify the outcome if you can by breaking the fraction down into its smallest terms. 13/4 in this instance may be expressed as 3 1/4.

Step 5: Reverse the incorrect fraction to a mixed number in step 5. Divide the numerator by the denominator to return the improper fraction to a mixed number. The full number serves as the numerator, and the remainder serves as the quotient.

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The question is -

How to Subtract mixed numbers?

The identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

ta: Mean time between calls to the center

tθ: Effective response time

∂a: Standard deviation of the time between calls to the center

∂θ: Standard deviation of the effective response time

ra: Rate of calls to the center (inverse of ta, i.e., ra = 1/ta)

rθ: Rate of effective response (inverse of tθ, i.e., rθ = 1/tθ)

Given information:

Mean time between calls to the center (ta) = 6 minutes

Standard deviation of time between calls (∂a) = 4 minutes

Effective response time (tθ) = 11 minutes

Standard deviation of effective response time (∂θ) = 20 minutes

Using this information, we can determine the values of the parameters:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/ta = 1/6 minutes^(-1)

rθ = 1/tθ = 1/11 minutes^(-1)

So, the identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

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Using the properties of exponents we can write the given expression as \(x^\frac{3}{2} y^\frac{5}{2}z^\frac{-2}{3}\). Therefore, option E is the correct answer.

The given expression is \(\frac{\sqrt{x^3} \sqrt{y^5} }{\sqrt[3]{z^2} }\).

We can square root as 1/2.

So the expression becomes \(\frac{x^\frac{3}{2} y^\frac{5}{2} }{z^\frac{2}{3} }\)

=  \(x^\frac{3}{2} y^\frac{5}{2}z^\frac{-2}{3}\)

Therefore, option E is the correct answer.

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Step-by-step explanation:

formula for trapezoid or trapezium=h/2 × (a+b)

1.5/2 ×(2+7)

0.75 ×9

3.25msquare

Using the given formula, the sum of S(n) for the arithmetic series is 565.5.

In the given question we have to find the sum S(n) for the arithmetic series

The given formula is S(n)=n/2 {a(1)+a(n)}

The given values are a(1)=12, a(n)=75,n=13

We just have to put values in given formula

S(n)=n/2 {a(1)+a(n)}

S(n)=13/2 (12+75)

S(n)=6.5*87

S(n)=565.5

Hence, the sum of S(n) for the arithmetic series described is 565.5.

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Answer: 9 hours

Step-by-step explanation:

Answer:

Part A: (C) 16 square inches

Part B: (C) 36 square inches

The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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Using the slope value of the functions, the rate per day of hedge trimmer is greater than that of Lawn mower.

The cost function for renting hedge trimmer and Lawn mower :

Hedge trimmer :

Lawn Mower :

The rate per day is given by the slope value of the function.

Hence, the rate per day of hedge trimmer is greater than that of lawn mower.

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Answer:

A mile is equal to 5280 feet

You start off with

200 miles per hour

If you multiply 200 by 5280 you can find the speed in feet per hour

1,056,000 feet per hour

There are 60 minutes in an hour

If you divide 1,056,000 by 60 you can find the speed in feet per minute

So 17,600 feet per minute

Then if you divide that by 60 you can find the speed in feet per seconds

It is 293 1/3 or 293.333 feet per second.

Step-by-step explanation:

Inference is referred to as all the data collected in a particular study.

Etymologically, the word "infer" means to "carry ahead." Inferences are stages in reasoning that connect premises to logical conclusions. The dichotomy between deduction and induction in inference theory, which dates at least to Aristotle in Europe, is a classic one (300s BCE). Deduction is inference that results in logical conclusions from premises that are known to be true or that are presumed to be true, while the logic of correct inference is investigated. A universal conclusion is inferred by induction from specific evidence. Contradistinguishing abduction from induction, Charles Sanders Peirce is credited with identifying a third sort of inference. Researchers in the domains of logic, argumentation studies, and cognitive psychology traditionally study human inference (i.e., how people draw conclusions); artificial intelligence researchers create automated inference systems to mimic human inference.

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Answer:

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

40% of the total number is 6.

Find the total number x:

Answer:

the amount on your savings account ;

the amount of money in your piggy bank if you deposit the same amount each week (a bank account with regular deposits leads you to arithmetico-geometric sequences) ;

the size of a population in exponential growth, e.g. bacteria in a Petri dish (or in your leftovers if you find Petri dishes not "every day life" enough) ;

the intensity of radioactivity after n years of a given radioactive material (with application to determining the age of mommies!).

Answer:

7

Step-by-step explanation:

58 divided by 8 equals 7 use a calculator and you get your answer.hope it helps

The approach to probability exemplified by the formula Probability of an Event = Number of favourable Outcomes / Total number of possible outcomes is the Classical approach to probability.

The Classical approach to probability is based on the assumption of equally likely outcomes and is often used when dealing with simple and well-defined experiments or situations. It involves counting the number of favorable outcomes (those that satisfy the desired condition) and dividing it by the total number of possible outcomes. This approach assumes that all outcomes have an equal chance of occurring.

In contrast, the Empirical approach involves conducting experiments or observations to gather data and estimate probabilities based on the observed frequencies. The Subjective approach relies on personal judgments or subjective assessments of probabilities based on individual beliefs or opinions.

Therefore, the correct answer is A) Classical approach.

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Answer:

Domain: {-3, 5, 0, -1, -2, 1}

Range: {-6, -4, -2, 1, 3}

The relation is a function.

Step-by-step explanation:

The domain of this relation is the set of all x-values from the ordered pairs, which are:

Domain: {-3, 5, 0, -1, -2, 1}

The range of the relation is the set of all y-values from the ordered pairs, which are:

Range: {-6, -4, -2, 1, 3}

To determine if the relation is a function, we need to check if there are any repeated x-values with different y-values. If there are no such cases, then the relation is a function.

Looking at the domain and range, we can see that each x-value has only one corresponding y-value, so there are no repeated x-values with different y-values. Therefore, the relation is a function...

Yes, the probability assignments given to the four outcomes of an experiment are valid. Probabilities are calculated subjectively, and the decision maker assigned probabilities to the four outcomes of the experiment, which is perfectly acceptable.

Probability is a numerical measure of the likelihood of an event occurring, ranging from 0 to 1.

An event that is certain to happen has a probability of 1, while an event that is impossible has a probability of 0. The probability of any other event lies somewhere between 0 and 1.

Probability assignments, which are subjectively determined probabilities, are valid as long as they meet the following criteria:

In this case, the probability assignments are valid because they meet both of the above criteria. The probabilities assigned are between 0 and 1, and when the probabilities are added together, the sum is 1.

Therefore, the given probability assignments are valid.

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The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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