Select the correct answer. Rewrite the expression using only positive integer exponents. (m2/3n-1/3)^6
A. m9/n18
B. n18/m9
C. m4/n2
D. n2/m4

The probability that at least one component does not function properly when 2 components are randomly selected from 8 is 1/4, or 0.25.

The total number of ways to select 2 components from 8 is:

C(8,2) = 8! / (2! (8-2)!) = 28

Now, let's find the probability that at least one component does not function properly. We can find this probability by subtracting the probability that both components function properly from 1.

The probability that the first component functions properly is 7/8, since there are 7 working components out of 8. The probability that the second component also functions properly, given that the first component does, is 6/7, since there are 6 working components left out of 7. Therefore, the probability that both components function properly is:

(7/8) * (6/7) = 6/8 = 3/4

So the probability that at least one component does not function properly is:

1 - 3/4 = 1/4

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If Paul uses the function y = 8x + 38 to model the situation, then the model predicts a score of:

86 for 6 hours of homework.

In the given problem, we are given a linear equation of the form y = 8x + 38, where y represents the score obtained by Paul and x represents the number of hours of homework done by Paul.

To predict the score for 6 hours of homework, we need to substitute 6 for x in the equation and solve for y. By substituting x = 6 in the equation, we get:

Therefore, the model predicts a score of 86 for 6 hours of homework.

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The width in miles, of the park is equal to 5/6 miles.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Substituting the given points into the area of rectangle formula, we have the following;

25/54 = 5/9 × W

Width, W = 25/54 × 9/5

Width, W = 5/6 miles.

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Complete Question:

The area of a rectangular city park is 25/54 square miles. The length if the park is 5/9 of a mile. What is the width in miles, of the park?

The linear equation that shows the relationship between y and x is y = x - 5

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

The slope intercept form of an equation is:

y = mx + b

where m is the rate of change and b is the y intercept.

From the values given, using (1, -4) and (2, -3):

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-(-4)=\frac{-3-(-4)}{2-1} (x-1)\\\\y=x - 1-4\\\\y=x-5[/tex]

The linear equation is y = x - 5

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Answer: 29 yards

Step-by-step explanation:

    First, we want to find how much she spent. We will subtract the leftover from the original amount.

$15 - $9.49 = $5.51 spent

    Next, we will convert this value into cents.

$5.51 = 551 cents

    Last, we will divide this by the price per yard to find how many yards she bought.

551 / 19 = 29 yards

Answer:

29 yards

Step-by-step explanation:

$15.00 - $9.49= $5.51

$5.51 divide by .19 per yard = 29

With the root values 6 and 8 the quadratic equation is x² - 6x +8 = 0.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The roots of the quadratic equation are -

HCF of smallest prime number, LCM of smallest composite number

The smallest prime number is 2.

So, the HCF of 2 is 2.

The smallest composite number is 4.

So, the LCM of 4 is 4.

If m and n are the roots of a quadratic equation ax² + bx + c = 0, then the sum of the roots is (m+n) and the product of the roots is (mn).

And then the quadratic equation becomes x² - (m+n)x +mn = 0.

So, here m = 2 and n = 4.

The sum of roots is -

(m + n) = (2 + 4) = 6

The product of roots is -

(mn) = (2 × 4) = 8

So, the quadratic equation is x² - 6x +8 = 0.

Therefore, the equation is x² - 6x +8 = 0.

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A regular polygon with 18 sides has a central angle that is 20 degrees in size.

A polygon's total number of central angles equals 360 degrees.

As a result, the regular polygon's centre angle has a ratio of 360 to its number of sides. It may be expressed as,

[tex]$C_a=\frac{360}{n}[/tex]

Here, (n) denotes the regular polygon's number of sides.

The polygon in the provided issue has an overall total of 18 sides. Using the method above, it is possible to determine the polygon's centre angle, which has 18 sides. Thus,

[tex]$& C_a=\frac{360}{18} \\[/tex]

[tex]$& C_a=20^{\circ}[/tex]

Therefore, a regular polygon with 18 sides has a central angle that is 20 degrees in size.

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Answer:

-9+4-6+(-11)=-9+4-6-11=-22

first -9+4 is -5-6=-11then-11 = -22

The length of the radius of the circle is 7.5 inches.

The radius formula is easily obtained by halving the circle's diameter. The line segment created when we join a point on a circle's circumference to its exact center is referred to as the ring's radius. The radius of a circle is the separation between its centre and circumference. Always, the diameter is twice the radius. As a result, the formula is created by multiplying the diameter by two.

Given that the diameter of the circle is 15 inches.

The radius of the circle is half the measure of the diameter.

That is,

R = d/2

R = 15/2

R = 7.5 inches

Hence, the length of the radius of the circle is 7.5 inches.

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make brainalist keep smiling dude..!

Answer:

x=-2log10(12)

Step-by-step explanation:

12x10^x/2=1/12

x/2=-log10(12)

x=-2log10(12)

The standard form of the polynomial is given as follows:

-13m^4 - m² + 12m + 7.

Hence the degree of the polynomial is of:

4th degree.

The leading coefficient is of:

-13.

The standard form of the polynomial is obtained writing the polynomial in decreasing order of the exponents, hence:

-13m^4 - m² + 12m + 7.

Then the degree and the leading coefficient are given as follows:

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120 calories make up one cup amount of calories. Three cups of the cereal have 360 calories in them.

1. Determine how many calories are in a cup: 120 calories are in 3/4 cup; 3/4 cup is 120 calories.

2. Determine how many calories are in 3 cups: 3 cups at 120 calories each equals 360 calories.

You must divide the total amount of calories in a serving of 3/4 cup by 3/4 cup to determine the unit rate for calories per cup of a certain cereal. In this instance, a serving of the cereal that is 3/4 cup in size has 120 calories. As a result, 120 calories are the number of calories in a cup. You must multiply the unit rate for calories per cup (120 calories) by 3 cups to see how many calories are in 3 cups of cereal. This indicates that there are 360 calories in 3 cups of the cereal. In summary, there are 360 calories in 3 cups of cereal, or 120 calories per cup, at the unit rate.

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Answer: acute

Step-by-step explanation:

   This triangle does not have any right angles (90°), or any angles larger than a right angle, so it is an acute triangle.

The equation 2(x - 4) = 2x - 8 has infinitely many solutions.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given equation is 2(x - 4) = 2x - 8.

Solving this,

Using the distributive property, a (b + c) = ab + ac, 2(x - 4) = (2 × x) - (2 × 4).

Substituting in the original equation,

(2 × x) - (2 × 4) = 2x - 8

2x - 8 = 2x - 8

2x - 2x = -8 + 8

0 = 0

Right hand side and left hand side are equal if we put any value for x.

So it has infinitely many solutions for x.

Hence the given equation has infinitely many solutions.

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The coordinates of the other endpoint are (17, 3).

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and then divide by two (2):

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

Next, we would determine the coordinate of MP with midpoint M at (7, 3) as follows;

12 = (7 + x₂)/2

24 = 7 + x₂

x₂ = 24 - 7

x₂ = 17.

For the other co-ordinate of P on line segment MP, we have:

3 = (3 + y₂)/2

6 = 3 + y₂

y₂ = 6 - 3

y₂= 3.

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When x = 6 and y = 8, the expression that s given as x^2+y^2/10 is calculated by substituting the given values and it is equal to 42.4.

The expression to evaluate is: x^2 + y^2/10.

To evaluate this expression when x = 6 and y = 8, we substitute these values into the expression and then perform the arithmetic operations according to the order of operations (PEMDAS).

PEMDAS stands for Parentheses, Exponents, Multiplication and Division (performed left to right), and Addition and Subtraction (performed left to right). The order of operations ensures that we always evaluate expressions in a consistent and unambiguous manner.

So, we have:

x^2 + y^2/10 = 6^2 + 8^2/10

= 36 + 64/10

= 36 + 6.4

= 42.4

Therefore, when x = 6 and y = 8, the value of the expression x^2 + y^2/10 is 42.4.

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Answer:

The answer is 6 with a remainder of 2.

Step-by-step explanation:

3 times 6 is 18.

Then if you subtract 18 from 20 you get 2.

So 3 goes into twenty, 6 times, and you get a remainder of 2.

The pretax cost of the laptop is $1187.96. The solution has been obtained by using linear equation.

What is a linear equation?

This is the linear equation with the largest degree of one. This demonstrates that there are no variables in linear equations with exponents greater than 1. A straight line appears on the graph as a result of such an equation.

Let the price before tax be 'x'

So, tax = 7.6% * x

Tax = .076x

The total cost of computer is given by:

⇒Total cost = x + .076x

⇒Total cost = 1.076x

⇒1278.24 = 1.076x

⇒x = $1187.9553             (On dividing both sides by 1.076)

⇒x = $1187.96

Hence, the pretax cost of the laptop is $1187.96.

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The equation of line r is x = -3/2y + 5/2.

A line's equation is typically expressed in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. A line's equation expresses the y coordinate of any point on the line in terms of its x coordinate. In other terms, a line equation is a formula that can be used to compute the y coordinate of any point on a line given its x coordinate.

In the given question,

The equation of line r is y = -1/3x + 7.

Line r is perpendicular to line q, so the slopes of the two lines must be opposite reciprocals of one another. The slope of line q is 3, so the slope of line r must be -1/3.

To find the equation of line r, we can use the point-slope formula. The point-slope formula is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

In line r, (x1, y1) is (1, 3). The slope, m, is -1/3.

Substituting values into the point-slope formula, we have y - 3 = -1/3(x - 1).

Solving for y, we have y = -1/3x + 7.

This equation is written in slope-intercept form, which is the form y = mx + b, where m is the slope and b is the y-intercept.

In line r, the slope is -1/3 and the y-intercept is 7.

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4. The value of b is 180+2a (option C)

11. the distance between A and B is 4√2 (option A)

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn. Angles around a point add to 360 °.

The total angle at a point is 360°

therefore the third angle in the triangle = 180-(a+a) = 180-2a

therefore b = 360-( 180-2a)

b = 360-180+2a

b = 180+2a

If the volume of the cube is 64, then AB = √4²+4²

= √16+16 = √32

AB = √32

AB = √ 16×2

AB = 4√2

Therefore the distance between A and B is 4√2

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The tables/graphs with their equations are

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

Tables, Graphs and equations

Table (a)

Here, we notice that:

The output is the 5 less than three times the input

This is represented as

y = 3x - 5

Table (b)

Here, we notice that:

The output is the 2 more than negative 12 times the input

This is represented as

y = -12x + 2

Graph (c)

Here, we have the following points

(4, 0) and (0, -5)

A linear function is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx - 5

Using the other point, we have

0 = 4m - 5

This gives

m = 5/4

So, we have

y = 5/4x - 5

Graph (d)

Here, we have the following points

(0.5, 0) and (0, 3)

A linear function is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 3

Using the other point, we have

0 = 0.5m + 3

This gives

m = -6

So, we have

y = -6x + 3

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The customer had a 3-hour repair when paying $96 without a coupon.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

With a coupon, the customer paid $66 for a 3-hour repair.

The coupon gives a 40% discount on the inspection fee, so let's call the original inspection fee "x". Then the customer paid 0.6x + 14*3 = $66.

Solving for x, we get x = $30.

Without a coupon, the customer paid $96.

We want to find out how many hours of repair were done for $96.

Let's use a similar equation to solve for the number of hours:

Let's call the number of hours "h". Then the customer paid 30*0.6 + 14h = $96.

Solving for h, we get h = 3.

Therefore, the customer had a 3-hour repair when paying $96 without a coupon.

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The linear equation that gives the dollar value V of the product in terms of the year t is V = - $5600t + $344,000.

V(t) is a function of t that expresses the value in the year 2000+t.  

We know that the decrease is $5600 per year.

So,

V(t) = -$5600t + c  

where c is the constant.

V(15) =  -$5600 (15) + c = $260,000     [t = 15]

Hence, we can say that -  

c = $260,000 + $5600 (15)

c= $260,000 + $84,000

c= $344,000

Now we got the value of c. We can write the equation as follows -

V = - $5600t + $344,000

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Answer:

25%

Step-by-step explanation:

Let Dawn’s monthly allowance be 5x. Let Evelyn’s monthly allowance then be 8x.

Percentage increase by 20% is the same as multiplying a number by 1.2

To find the percentage decrease of Evelyn’s monthly allowance, we can equate their allowances after the change of their initial allowance.

1.2 * 5x = k/100 * 8x

k represents the percentage

6x = 8xk/100

Cancel the x’s from both sides

6 = 8k/100

600 = 8k

k = 75

Therefore since 75% of Evelyn’s monthly allowance is equal to Dawn’s increased monthly allowance, this means Evelyn’s monthly allowance was decreased by 25%.

Answer: 7,000,000

By the way: How do we have almost the same name?

Answer:

the answer is 7,000,000

Step-by-step explanation:

6,000,000+1,000,000=7,000,000

The value of m for which the parallelogram WXYZ will be a square is (a) 2 .

For the parallelogram WXYZ to be a square ,

We know that , if parallelogram WXYZ is a square all, then all the sides are equal ;

So , we write WX = XY = YZ = ZW ;

To find the value of "m" , we use WX = ZW ;

substituting the values of sides of square from the figure ,

we get ;

⇒ 2m + 4 = m + 6 ;

⇒ 2m - m = 6 - 4 ;

⇒ m = 2 ;

Therefore , the value of "m" for the square WXYZ is 2 .

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The given question is incomplete , the complete question is

What value of m would make parallelogram WXYZ a square ?

(a) 2

(b) 3

(c) 4

(d) 5

The point estimator for the proportion of registered voters expressed concern about a loosening of restrictions is 0.58. The margin of error for this poll is 3.6%.

The point estimator for the proportion of registered voters expressing concern about a loosening of restrictions is:

58/100 = 0.58 or 58%

To determine the margin of error for this poll assuming a confidence level of 95%, we can use the following formula:

margin of error = zsqrt(p(1-p)/n)

where z is the z-score for the desired confidence level (1.96 for 95%), p is the point estimator for the proportion (0.58), and n is the sample size (900).

So, the margin of error is:

1.96sqrt(0.58(1-0.58)/900) ≈ 0.036 or 3.6%

Therefore, the margin of error for this poll is 3.6%.

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____The given question is incomplete, the complete question is given below:

Read the following news article and then answer the two questions at the end According to an NBC News/Wall Street Journal poll released Sunday, 58 percent of registered voters expressed concern about a loosening of restrictions compared with 32 percent who worried that the restrictions would stay in place for too long 3 percent said they were concerned about both scenarios. A mere 3 percent said the pandemic had no impact on their lives, compared with 77 percent who said it had affected them either in a very major way" or "fairly major way The sample size was 900 registered voters a What is the point estimator for the proportion of registered voters expressed concern about a loosening of restrictions b. Determine the margin of error for this poll assuming a confidence level of 95%.