Distribute to create an equivalent expression with the fewest symbols possible.
\dfrac12(2a - 6b+ 8) =
2
1
​
(2a−6b+8

Answer:

To add or subtract fractions, they must have a common denominator. In this case, the denominators of the fractions are 2 and 8, which are not the same. To find the least common multiple of 2 and 8, we can list the multiples of each number and find the smallest one that is common to both:

2: 2, 4, 6, 8, 10, 12, 14, ...

8: 8, 16, 24, 32, ...

The least common multiple of 2 and 8 is 8. Therefore, to add or subtract the fractions, we must convert them to have a denominator of 8.

-3/2 = -12/8 and 3/8 = 3/8

So, -3/2 - 3/8 = -12/8 - 3/8

Now we can subtract the fractions directly:

-12/8 - 3/8 = -12 - 3 / 8

= -15/8

Therefore, the simplified form of -3/2 - 3/8 is -15/8

Answer: 7

Step-by-step explanation:

First, we need to prime factorize the number 189,

189 = 3 × 3 × 3 × 7 × m

From the factors we can see that there is no pair of same numbers for 7, so if we replace m with 7, we can get a perfect square.

Hence the answer is 7

If f(x) = x⁴ + 2, g(x) = x-6 and h(x) = √x , then the simplified form of f(g(h(x))) is f(g(h(x))) = (√x - 6)⁴ + 2.

What is the polynomial expression?

Any expression which consists of variables, constants, and exponents, and is combined using mathematical operators like addition, subtraction, multiplication, and division is a polynomial expression.

We can simplify f(g(h(x))) by first evaluating h(x), then substituting the result into g(x), and finally substituting the result into f(x).

Starting with h(x) = √x, we can substitute this into g(x) to get:

g(h(x)) = g(√x) = √x - 6

Next, we can substitute g(h(x)) = √x - 6 into f(x) to get:

f(g(h(x))) = f(√x - 6) = (√x - 6)⁴ + 2

Simplifying this expression requires some algebraic manipulation, but we can expand (√x - 6)⁴ using the binomial theorem or by using the method of FOIL (first, outer, inner, last) repeatedly. Either way, we will end up with a polynomial expression in x with terms of various degrees.

Therefore, the simplified form of f(g(h(x))) is f(g(h(x))) = (√x - 6)⁴ + 2.

To learn more about polynomial expression visit,

https://brainly.com/question/26489570

#SPJ1

Answer:

y = 5.25 [tex](8)^{x}[/tex]

Step-by-step explanation:

the general form of an exponential function is

y = a [tex](b)^{x}[/tex]

to find a and b , substitute the coordinates of the given points into the equation.

using (2, 336 )

336 = a b² → (1)

using (3, 2688 )

2688 = a b³ → (2)

divide (2) by (1)

[tex]\frac{ab^3}{ab^2}[/tex] = [tex]\frac{2688}{336}[/tex] ( cancel ab on numerator/denominator of left side )

b = 8

substitute b = 8 into (1) and solve for a

336 = a × 8² = 64a ( divide both sides by 64 )

5.25 = a

then exponential function is

y = 5.25 [tex](8)^{x}[/tex]

The margin of error, given the percentage who replied that Newton ate the apple, is 3.5%.

The margin of error is a measure of how much the sample results are likely to vary from the true population value.

To calculate the margin of error, you need to know the sample size, the proportion of the sample that gave a particular response, and the level of confidence.

The formula for the margin of error is:

Margin of Error = z x √(p x ( 1 - p) / n)

where:

z = the critical value from the standard normal distribution table

p = the proportion of the sample that gave a particular response

n = the sample size

The margin of error for Newton eating the apple is therefore:

Margin of Error = 1.96 x √(0.28 x (1 - 0.28) / 581)

Margin of Error = 1.96 * √(0.00035)

Margin of Error = 1.96 * 0.018

Margin of Error = 0.035

The margin of error is therefore 3.5%.

Find out more on Margin of Error at https://brainly.com/question/29328438

#SPJ1

If the Colossus Ferris wheel debuted at the 1984 New Orleans World's Fair and the ride is 180 ft tall, and passengers board the ride at an initial height of 15 ft above the ground. The period of the sine function model is: 2/3 minutes.

Given equation:

h=-82.5 cos 3pi(t)+97.5

Where:

h= height of the passenger above the ground measured in feet

t = time of operation of the ride in minutes

So,

h=-82.5× cos  [2 × π ×t /T) +97.5

2 ×π / T = 3 × π

T = 2/3 minutes

Therefore the period of the sine function model is: 2/3 minutes.

Learn more about period of the sine function model here:https://brainly.com/question/23713359

#SPJ1

Answer: <3, 1>

Step-by-step explanation: A translation of a vector is simply moving it a certain distance in a certain direction. In this case, the first translation of  <6, -4> moves the vector 6 units to the right and 4 units down. The second translation of <-3, -5> then moves the vector an additional 3 units left and 5 units down. The net result of these two translations is to move the vector 3 units to the right and 1 unit up, which is equivalent to a single translation of <3, 1>.

The coordinates of the fourth vertex is (1,-8).

As three of a parallelogram's vertices, we were given:

(3,-2), (-1,-4), (5,-6). (5,-6).

We see that (3,-2) and (-1,-4) form a diagonal after charting the points as in the attachment.

The midpoint formula determines what point on this diagonal is in the middle.

Keep in mind that both diagonals' midpoints are identical.

Specify the coordinates of the fourth point (x,y).

As a result of once more applying the midpoint formula to (3, -2), we get:

x=1 and y=-8

The fourth point's locational details are as follows:

(1,-8).

To learn more about vertex refer to:

https://brainly.com/question/29030495

#SPJ1

The complete question is,

A good can be produced for a total cost of 600 or 850 when making 100 units and 150 units, respectively. Discover an equation for TC in terms of Q, the number of generated units, presuming that the total cost function is linear.

The average income per household that is causing an increase in both the number of cars owned and the average number of citizens with health insurance.

The correlation of variables is the statistical relationship between two variables.

A correlation is positive if both variables move in the same direction and negative if the variables move in different directions - as one variable increases, the other decreases.

Correlation does not imply causation: This means that one can not legitimately associate a cause-and-effect relationship between the two variables.

In this example, it cannot be legitimately shown that increasing the number of cars per household would cause members of the community members to purchase health insurance, but when we bring in the lurking variable.

which is the increase in average income per household, we can see that this possibility might cause more people to buy more health insurance even after they have purchased cars, because they have more money to spend.

To know more about scatterplot:

https://brainly.com/question/17255485

#SPJ4

G(:,:) returns the matrix G in its original form. This command takes all elements of G and reshapes them into a single row vector. This means that all elements of G are included in the output, and the output is in the same shape as the original matrix.

G(:) reshapes all elements of G into a single column vector. This command takes all elements of G and places them into a single column. This means that all elements of G are included in the output, and the output is in a column vector.

G(7,6) returns an indexing error. This command attempts to access an element outside of the range of the matrix G. Since G is a 6 x 6 matrix, there is no element at the index (7,6).

max(G) returns the maximum entry in each column of G. This command takes the maximum value from each column and returns them as a single row vector. This means that the output contains the maximum value from each column and the output is in a single row vector.

sum(G) returns the sum of the entries in each column of G. This command takes the sum of all entries in each column and returns them as a single row.

Learn more about MATLAB:

https://brainly.com/question/27854252

#SPJ4

The simple random sample of 200 eggs

Statistic=Proportion of eggs in the sample that contain salmonella.

p = 0.045

The population is the individuals that are being studied.

population=All eggs in one day

A sample is the part of the population of which information was actually collected.

Sample=The simple random sample of 200 eggs

A parameter is a descriptive measure for a population.

Parameter=Proportion of eggs shipped that day that contain salmonella.

p = 0.1 % =0.001

A statistic is a descriptive measure for a sample.

STATISTIC=Proportion of eggs in the sample that contain salmonella.

p=9÷200 = 0.045

learn more about Statistic.

https://brainly.com/question/29093686

#SPJ4

50 breaks do they make.

An equation is a mathematical statement that shows the relationship between two values, or variables. It is formed by using an equal sign between two expressions that have the same value. Equations are used to solve for unknown values, or to describe a relationship between two or more variables. Equations can be used to solve for a single variable or multiple variables, and can be used to solve problems in both mathematics and science.
To find the answer to this question we must use the formula V = L x W x H. In this case, V = 10 x 9 x 4 = 360. We now know that there is 360 cubic inches in each brick. To find the total number of bricks that can be made from 18,000 cubic inches of concrete, we must divide 18,000 by 360. The answer is 50, which means that the company can make 50 concrete bricks from 18,000 cubic inches of concrete.

To know more about Equation click-
https://brainly.com/question/2972832
#SPJ1

Mario can mail the books in the box, as the weight of the books is less than the weight of the box.

The total weight is obtained applying proportions, converting the fractions to decimal, dividing the numerator by the denominator.

The weights of each book are given as follows:

Hence the total weight for the books is given as follows:

0.625 + 0.4375 + 0.75 = 1.8125 pounds.

The weight of the box is given as follows:

2 + 0.5 = 2.5 pounds.

Hence Mario can mail the books in the box, as the weight of the books is less than the weight of the box.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

I tink D?

Step-by-step explanation:

The function after the reflection over y-axis is f' ( x ) = √( -x )

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = √x

Now , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y)

So , the reflected function is f' ( x ) = √( -x ) and the graph is plotted

Hence , the reflected function is f' ( x ) = √( -x )

To learn more about reflection click :

https://brainly.com/question/4681298

#SPJ2

The following congruence theorems can be applied to every triangle in the provided pair:

1) SSS

2) SAS

3)SAS

4) SSS

5) SAS

6) SAS

1) We can observe from the that;

FY ≅ CW

FP ≅ CM

YP ≅ MW

This proves the Side-Side-Side (SSS) congruency theorem, which states that the three corresponding sides of the two triangles are congruent.

2) We can observe from the picture that;

CBD and BCA are congruent because they both have alternate interior angles. Thus;

CBD and BCA

We can also see that

EB ≅ EC

DB ≅ CA

Inferring from the fact that two corresponding sides and an angle of the two triangles are congruent

Using the Side-Angle-Side (SAS) congruency theorem, construct BED and AEC.

3) The image demonstrates that;

SVU and SVT

The shared sides provide using the reflexive property;

SV ≅ SV

VT ≅ VU

Inferring from the fact that two corresponding sides and an angle of the two triangles are congruent

Side-Angle-Side (SAS) congruency theory is used by VSU and VST.

4) The picture shows what;

MN ≅ QP

MQ ≅ NP

The shared sides provide using the reflexive property;

NQ ≅ NQ

This implies that the three corresponding sides of the two triangles are congruent, which, according to the Side-Side-Side (SSS) congruency theorem, means that QNM QNP.

5) The image demonstrates that;

GL ≅ HL

GJ ≅ HK

JLG and HLK are incongruent angles in the vertical direction;

JLG and HLK

Inferring from the fact that two corresponding sides and an angle of the two triangles are congruent

employing the Side-Angle-Side (SAS) congruency theorem, QNM and QNP.

6) From the triangles provided, we note that;

XZY and XZW (They both form a straight angle of 90 degrees.)

The shared side is congruent to itself using reflexive property, therefore;

XZ ≅ XZ

Also;

ZW ≅ ZY

Inferring from the fact that two corresponding sides and an angle of the two triangles are congruent

Using the Side-Angle-Side (SAS) congruency theorem, XYZ = XWZ.

To Learn more About congruence theorems refer To:

brainly.com/question/3168048

#SPJ1

Complete question:

The work done by stretching the spring to the given distance is:

[tex]W=\frac{kx_{0} }{3}[/tex]

The given parameters:

Applied force on the spring = F

Extension of the spring, = x₀

The work done by stretching the spring to the given distance is calculated as follows:

[tex]W=\int\limits^b_a {F} \, dx[/tex]

Where:

F - Force.

W- Work.

x- Distance.

If we know that F=k.x², then the work of the nonlinear spring is:

[tex]W=\int\limits^b_a {F} \, dx \\W=\int\limits^b_a {kx^2} \, dx \\W=k\int\limits^b_a {x^2} \, dx \\\\W=k[\frac{x^3}{3}]\\\\W=k[\frac{x_b-x_a}{3} ]\\\\W=k[\frac{x_o-0}{3} ][/tex]      

W=kx₀/3

Thus, the work done by stretching the spring to the given distance is: W=kx₀/3

To know more about the work done:

https://brainly.com/question/20709938

#SPJ4

Answer: Net (of a shape)

Step-by-step explanation:

Answer:

Step-by-step explanation:

no need for step by step its called a net

The coordinate of the point that partitions the given line in the ratio 2:1 is; (-8, 0)

If the coordinates are given as;

P (x₁ , y₁) and Q (x₂ , y₂) and the partition of the line segment is divided internally in the ratio m : n, then its coordinate ( x, y) given by :

( x ,y ) = [(mx₂ + nx₁)/ ( m + n), (my₂ + ny₁)/ ( m + n)]

We are given the coordinates as  ( − 8 , 10 )to ( − 8 , − 5 ) and if it is partitioned in the ratio 2: 1, the coordinates of the points of partition are;

(x, y) =  [(2(-8) + 1(-8))/ (2 + 1), (2(-5) + 1(10))/ (2 + 1)]

(x, y) = (-24/3), (0/3)

(x, y) = (-8, 0)

Read more about Partitioning line segments at; https://brainly.com/question/17374569

#SPJ1

Answer:

307,8

Step-by-step explanation:

The area of a circle is 3.14 times the radius squared, and the radius is the diameter divided by 2. Hence the area is 307.8

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{- \cfrac{4}{3}}(x-\stackrel{x_1}{3}) \implies y +7= -\cfrac{4}{3} (x -3) \\\\\\ y+7=-\cfrac{4}{3}x+4\implies {\Large \begin{array}{llll} y=-\cfrac{4}{3}x-3 \end{array}}[/tex]

The correlation coefficient for this data-set is given as follows:

r = 0.43.

The coefficient is obtained inserting the points in a data-set in a correlation coefficient calculator.

The points for the data-set in this problem are given as follows:

(1,2), (4,3), (3,4), (1,1), (4,2), (6,2), (2,1), (6,2), (2,1).

Inserting these points into a correlation coefficient calculator, the correlation coefficient for this data-set is given as follows:

r = 0.43.

Meaning that the correct option is given by the third option.

More can be learned about correlation coefficients at brainly.com/question/16355498

#SPJ1

To reach the speed of light, the spaceship will take 3.1 × 10⁷ seconds. The result is obtained by using the formula for acceleration.

Acceleration is the rate of change in velocity of an object with respect to time. It can be expressed as

[tex]a = \frac{\Delta v}{\Delta t}[/tex]

Where

If we were in a spaceship with an acceleration of g, determine the time we reach the speed of light!

We have

To find the time so that we can reach the speed of light, we use the formula for acceleration.

[tex]a = \frac{\Delta v}{\Delta t}[/tex]

[tex]g = \frac{c - 0}{\Delta t}[/tex]

[tex]9.8 = \frac{3 \times 10^{8}}{\Delta t}[/tex]

[tex]\Delta t = \frac{3 \times 10^{8}}{9.8}[/tex]

Δt = 0.306 × 10⁸

Δt = 3.1 × 10⁷ s

Hence, the spaceship will take 3.1 × 10⁷ seconds to reach the speed of light.

Learn more about acceleration here:

brainly.com/question/30365491

#SPJ4

Answer:

A

Step-by-step Explanation:

Every $1 decrease in price corresponds to a 0.8 increase in the number of pairs of jeans sold.

So, if [tex]x[/tex] pairs of jeans are sold, the revenue in dollars is [tex](175-x)(40+0.8x)[/tex].

The roots of this function are [tex]x=175[/tex] and [tex]x=-50[/tex]. The maximum is achieved halfway between these roots at [tex]x=62.5[/tex].

When 62.5 pairs of jeans are sold, the price is $112.50.

The store should discount the price to $112.50 to maximize its revenue

Discount is a deduction from the usual cost of something, typically given for prompt or advance payment or to a special category of buyers.

From the above question, every $1 decrease in price corresponds to a 0.8 increase in the number of pairs of jeans sold.

So, if  pairs of jeans are sold, the revenue in dollars is (175 - x)(40 + 0.8x)

The roots of this function are x = 175 and x = -50. The maximum is achieved halfway between these roots at x = 62.50.

Therefore, When 62.5 pairs of jeans are sold, the price is $112.50.

More can be learnt about discounts at

brainly.com/question/7459025

#SPJ1

the simplified expression is 2x9/4.19, which can be written as A/B, where A = 2x9 and B = 4.19. Therefore, the value of A is 18 and the value of B is 4.

To simplify the expression V4219, first divide it into two separate terms by breaking the number 4219 into 4 and 2119.

Now, we need to simplify the terms 4 and 2119 separately.

To simplify the term 4, we need to divide it by 4, which gives us 1.

To simplify the term 2119, we need to divide it by 19, which gives us 2x9.

Hence, the simplified expression is 2x9/4.19, which can be written as A/B, where A = 2x9 and B = 4.19. Therefore, the value of A is 18 and the value of B is 4.

Learn more about expression here

https://brainly.com/question/14083225

#SPJ4

Answer:

6 votes

Step-by-step explanation:

Answer:

y ≥ -x -7

Step-by-step explanation:

The inequality is greater than or equal to because it is above the line and it is a solid line.

The slope is -1.  If you select a point on the line, you go down one unit and one unit to the right to get back on the line.  The slope is the rise over the run.  -1/1 = -1

The y intercept is where the graph crosses the y axis (0,-7) So the y intercept is -7

The probabilities of adults who drinks only coffee , both/ coffee ,soda and doesn't drink any are 5% , 65% and 35%.

Let A be the event that an adult consumes coffee.

Let B be the event that an adult consumes carbonated soda.

Given probabilities of the events.

P (A) = 0.4

P (B) = 0.6

P(A∩B) = 0.35

(a). P(A)  - P(A∩B) = 0.4 - 0.35

                             = 0.05 OR 5 %

(b). P(AUB) = P (A) + P (B) - P(A∩B)

                   = 0.4 + 0.6 - 0.35

                   = 0.65 OR 65%

(c). The given case represents compliment of the event when the adult consumes at least one of the drink. According to probability axiom, the probability is given by:

P ((AUB)') = 1 - P (AUB) = 1-0.65 = 0.35

Therefore,

P ((AUB)') = 0.35 or 35 %.

Learn more about Probability here :

https://brainly.com/question/30034780

#SPJ4

The shingles are in the 6th row is 110 using arithmetic process.

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The study of numbers and the operations on those numbers, which are relevant to all other branches of mathematics, is the focus of a branch of mathematics known as arithmetic operations. It includes addition, subtraction, multiplication, and division as its fundamental operations.

Given that A = 75 and d = 7, n = 6

A₆ = A + (n-1)d

A₆ = 75 + (6-1)7

A₆ = 75 + 5 * 7

A₆ = 75 + 35

A₆ = 110

To learn more about arithmetic process visit:

brainly.com/question/14340818

#SPJ1

Answer:

33

Step-by-step explanation:

it starts with 75 and decreases by 7 for each row. on the 6th row youll be at 33!

STARTS AT 75

row one: 68

row two: 61

row three:54

row four: 47

row five: 40

row six: 33

Answer:

5 (less than sign) 2

Step-by-step explanation:

Answer:

5n-20

Step-by-step explanation:

Product means multiply and so the product of 5 and n is 5n. To decrease this value by 20 , means to subtract 20 from it hence: 5n - 20 is algebraic expression for the statement

Answer:

To find the ordered pairs that are solutions to the equation X+2y=8, we need to isolate the variable y on one side of the equation.

We can start by subtracting X from both sides:

X+2y = 8

X+2y-X = 8-X

2y = 8-X

Now we can divide both sides by 2:

y = (8-X)/2

So the ordered pairs (X, y) that are solutions to the equation X+2y=8 are the ones that satisfy the equation y = (8-X)/2.

We can substitute any value of x into the equation and find the corresponding y value.

For example, if we take X= 4, we can find the corresponding y value:

y = (8-4)/2 = 4/2 = 2.

so (4,2) is a solution to the equation X+2y=8.

We can also plot the equation on a Cartesian plane and find the points where the equation is true, those are the solutions.

Alternatively, we can solve the equation for X and find the solutions for y.

X = 8-2y

So the ordered pairs (X, y) that are solutions to the equation X+2y=8 are the ones that satisfy the equation X = 8-2y

We can substitute any value of y into the equation and find the corresponding X value.

For example, if we take y= 2, we can find the corresponding X value:

X = 8-2(2) = 8-4 = 4.

so (4,2) is a solution to the equation X+2y=8.

In this case, any value of X and y that satisfies the equations y = (8-X)/2 or X = 8-2y are solutions to the equation X+2y=8