If x = 3 (y + 2) minus 1 what is the value of w in terms of x and y?
w = StartFraction x minus 3 y Over 3 EndFraction
w = StartFraction x minus 3 y + 1 Over 3 EndFraction
w = x minus 3 y + 1
w = StartFraction x + 1 Over 9 y EndFraction

The resulting polynomials are listed below:

Herein we find two cases of addition of polynomials and the two cases of subtraction of polynomials. Each operation must be done by taking algebra properties into account. Complete procedures are shown below:

Addition - Case 1

(a - 5) + (2 · a - 3)              Given

(a + 2 · a) + [- 5 + (- 3)]       Associative and commutative properties

3 · a - 8                              Distributive property / Definitions of addition and subtraction

Addition - Case 2

(5 · t² - 6 · s · t + 8 · t - 3) + (7 · t² + 8 · s · t - 2 · t + 9) + (3 · t² + 2 · s · t + 5 · t + 5)                                         Given

(5 · t² + 7 · t² + 3 · t²) + (- 6 · s · t + 8 · s · t + 2 · s · t) + (8 · t - 2 · t + 5 · t) + (- 3 + 9 + 5)                                   Associative and commutative properties

15 · t² + 4 · s · t + 11 · t + 11       Distributive properties / Definitions of addition and subtraction / Result

Subtraction - Case 1

(10 · m - 2 · n - 1) - (5 · m - 2 · n + 2)          Given

(10 · m - 5 · m) + (- 2 · n + 2 · n) + (- 1 - 2)   Commutative and associative properties / (- a) · (- b) = a · b / (- a) · b = - a · b

5 · m - 3                                                      Distributive property / Cancellative property / Definition of addition and subtraction / Modulative property / Result

Subtraction - Case 2

(- 5 · x³ + 3 · x² + 6 · x) - (3 · x³ + 9 · x² + 4 · x)              Given

(- 5 · x³ - 3 · x³) + (3 · x² + 9 · x²) + ( 6 · x + 4 · x)           Commutative and associative properties / (- a) · (- b) = a · b / (- a) · b = - a · b

- 8 · x³ + 12 · x² + 10 · x                                                  Distributive property / Definition of addition and subtraction / Result

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For solve the equation there are following prpperties are used

Step -1 Distributive properties,

Step - 2 Subtraction,

Step - 3 Addition, and

Step - 4 Division.

The distributive property of multiplication , simplify expressions wherein multiply a number by a sum or difference. According to this property, the product of a sum or difference of a number is equal to the sum or difference of the products.

Given equation -

-2(5x + 8) = 14 + 6x

The equation was solved using the following steps.

Step 1: -10x - 16 = 14 + 6x

Step 2: -10x - 6x - 16 = 14 = -16x -16 = 14

Step 3: -16x = 30

Step 4: x = -30 / 16

Step 5: x = -15/8.

Complete the statements with the process used to achieve steps 1-4.

Step 1 - here we are using distributive properties

            -10x -16 = 14 + 6x

            distribute -2 in the parenthesis to 5x and 8

Step 2 - by subtraction method

           -16x - 16 = 14

            subtraction of -6x

Step 3 - Aply addition

           -16x = 30

            Addition of 16

Step 4 - Division

           x = -30/16

          division of -16

            x = -15 / 8

Hence , Step- 1, 2, 3, and 4 are distributive properties, subtraction, addition, and division respectively.

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We need to know about arranging numbers in an ascending order to solve the problem. The numbers arranged in ascending order is 73156, 75136, 84945, 85105, 91504, 93405, 94054.

There are two ways to arrange numbers- ascending order and descending order. Ascending order is the method of arranging numbers from lowest to highest and descending order is the method of arranging numbers from highest to lowest. To arrange 5-digit numbers in an ascending order we will need to know how to find the lowest number first. For 5-digit number we will be checking the first two digits of the number first that will tell us the numbers in tens of thousands, after we find the smallest tens of thousand in the list we follow the same process to  find the consecutive numbers. If two numbers have same first two digits then we chcek the hundreds and so on. For the given question the numbers arranged in ascending order will be

73156, 75136, 84945, 85105, 91504, 93405, 94054

Therefore we found the ascending order arrangement of the 5-digit numbers which is 73156, 75136, 84945, 85105, 91504, 93405, 94054.

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Answer:

x = -1, PR = 38.

Step-by-step explanation:

As Q is the midpoint of PR

PQ = QR

6x + 25 = 16 - 3x

9x = -9

x = -1.

PR

= 6x + 25 + 16 - 3x

= 6(-1) + 25 + 16 - 3(-1)

= -6 + 25 + 16 + 3

= 38.

Answer: D. 10 5/6

Step-by-step explanation: K12 UNIT TEST

The standard equation of each ellipse is ( 2,1)

Let a=x^2

       b=y^2

And 2h=xy coefficient of term

Then the second degree equation represent an ellips hyperbola as

ab-h^2>= or <0

Here ab-h^2=225>0

The equation can be written as

(x+2)^2/9+(y-1)^2/25=1

Center c of the elips is (-2,1)

A

a=5

b=3

axis x=-2

e=✓a^2-5^2/5

 =2✓14/5

As

S=S`

Cs=Cs`=✓14

ellipse=(2,1+√14) (2,1,√-14)

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The equal piles of chart paper that she can make such that each pile has only one color is 6.

It should be noted that from the information, the craft teacher has 12 sheets of blue chart paper and 18 sheets of red chart paper.

In this case, the highest common factor between the numbers is 6

Therefore, the piles of chart paper that she can make such that each pile has only one color is 6.

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By using the concept of weighted averages, the weighted average of the given values is equal to 7.35.

Weighted average is a kind of average in which each element has an specific weight in contrast with uniform average, where each element has the same weight. In this problem we have three values associated to three distinct weights, whose weighted average is:

x = 0.75 · 7 + 0.15 · 8 + 0.10 · 9

x = 7.35

By using the concept of weighted averages, the weighted average of the given values is equal to 7.35.

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leslie uses the scaling factor as 1 m actual size of soccer field is 1.89 mm in drawing.

What is scaling ?

It is the technique to resize drawing with comparing to actual size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles.

It is given that, leslie drew a scale drawing of soccer field. in real life, the soccer field is 99 meters long. it is 187 millimeters long in the drawing.

Now, corelating the scale given which means for 99m of actual side of the soccer field scale is 187 mm. Now, the scaling factor is calculated by dividing 99 m with 187 mm.

99 m actual size of soccer field = 187 mm in drawing

1 m actual size of soccer field = (187/ 99) mm in drawing = 1.89 mm in drawing

Therefore, leslie uses the scaling factor as 1 m actual size of soccer field is 1.89 mm in drawing.

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The scale she used for the length of the park in real to her drawing is 529:1.

Ratio is comparison of two or more similar units written in simplest form.

According to the given question leslie drew a drawing of a city park. in real life, the soccer field is 99 meters long. it is 187 millimetres long in the drawing.

We have to find the scale she used in her drawing.

We know 1 meter is 1000 millimetre.

∴ 99 meters is 99000 millimetres.

We know a:b can be written as a/b.

So the scale ratio of the length in real life to her drawing is

99000/187.

529/1 approx.

Which is 529:1.

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Answer:

Step-by-step explanation:

8:12

24:36

[tex]Let$p_1$ - true proportion of California residents who reported insufficient rest or sleep during the preceding 30 days$p_2$ - true proportion of Oregon residents who reported insufficient rest or sleep during the preceding 30 days$\hat{p}_1$ - sample proportion of California residents who reported insufficient rest or sleep during the preceding 30 days $=0.08$$\hat{q}_1=1-\hat{p}_1=1-0.08=0.92$$n_1$ - sample size of CA residents $=11,545$[/tex][tex]$\hat{p}_2$ - sample proportion of Oregon residents who reported insufficient rest or sleep during the preceding 30 days $=0.088$$\hat{q}_2=1-\hat{p}_2=1-0.088=0.912$$n_2$ - sample size of OR residents $=4,691$The $95 \%$ Confidence Interval for $\left(p_1-p_2\right)$ is given by,$$[/tex][tex]\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{p_1 q_1}{n_1}+\frac{p_2 q_2}{n_2}}$$if $p_1$ and $p_2$ are unknown we use$$\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{\hat{p}_1 \hat{q}_1}{n_1}+\frac{\hat{p}_2 \hat{q}_2}{n_2}}$$where $Z^*=Z_{\frac{\alpha}{2}}=Z_{0.0250}$[/tex][tex]Plugging in, we get$$\begin{aligned}\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{\hat{p}_1 \hat{q}_1}{n_1}+\frac{\hat{p}_2 \hat{q}_2}{n_2}} \\(0.08-0.088) & \pm 1.96 \sqrt{\frac{0.08(0.92)}{11545}+\frac{0.088(0.912)}{4691}} \\&-0.008 \pm 0.009498026 \\&(-0.017498026,0.001498026) \\& \approx(-0.0175,0.0015)\end{aligned}$$[/tex][tex]a) For the Hypothesis Test we have,- i) State the hypotheses.$$\begin{aligned}&H_0: p_1-p_2=0 \\&H_1: p_1-p_2 \neq 0\end{aligned}$$[/tex]

A hypothesis test examines a suggested mathematical model to see if a sample of data contains enough evidence to disprove the null hypothesis.

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smaller x value (x, y)=(-15,-8)

larger x value (x, y)=(+15,-8)

[tex]\sqrt{x^{2} + y^{2} } = 17[/tex]

[tex]x^{2} +y^{2} = 289[/tex]

y= -8

[tex]x^{2} =289-64[/tex]

[tex]x^{2} =225[/tex]

x= ±15

The points are (15, -8) and (-15, -8)

Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). Mathematics, scientists, and engineers frequently employ a variety of coordinate systems. The positions of points in 2D or 3D are defined by two or three straight-line axes known as cartesian coordinates, sometimes known as rectangular coordinates. All scales are linear, which means that they are all graduated in uniform-sized increments. The positions of points in 2D are defined by a different coordinate system called semilog coordinates. The other scale is logarithmic while the first is linear.

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Answer:

y = - 2(x - 3)² + 4

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (3, 4 ) , then

y = a(x - 3)² + 4

to find a substitute (1, - 4 ) into the equation

- 4 = a(1 - 3)² + 4 ( subtract 4 from both sides )

- 8 = a(- 2)² = 4a ( divide both sides by 4 )

- 2 = a

y = - 2(x - 3)² + 4 ← equation in vertex form

It is the stratified random sampling technique that was used by the school administrator.

Sampling methods are defined as how we choose members for study purposes from the population.When a person is not randomly selected which maybe it be biased somehow,  the data may not be representative of the population. Stratified random sample, In this sampling, the population chosen is split first into groups ., the overall sample consists of some members from every group, and those members are chosen randomly from every group, this sampling guarantees that members from each group will be represented in the sample.

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'

8,468 written in scientific notation is 8.47 x 10³.

Scientific notation is used to compress large numbers in smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

For example:

• The number : 1 x 10² is equivalent to 100

• The number 1 x 10³ is equivalent to 1000

8,468 becomes 8.47 x 10³

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Answer:

Please see the picture below.

Step-by-step explanation:

Answer:

7x+6

Product means multiplication

and we'll use X for "number"

and add 6

so 7x+6

The required equation model as of the given condition is 6 + 7×x.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.

Here,
Let the number be x,
6 is added to the product of 7 and a number.
= 6 + 7 × x

Thus, the required equation model as of the given condition is 6 + 7 × x.

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B is the y- intercept of the equation B = 28 - 7t, where B is the percentage of the battery.

What is a linear graph?

Linear graphs are straight line graphs to represent the relationship between two quantities. This graph helps in depicting a result in single straight lines. There is no use of curves, dots, bars, etc., and a straight line is denoted by the term linear. Let's represent the given example in the form of a data table.

Given equation,

B = 28 - 7t

B represents the battery percentage of the phone.

t represents time,

According to the equation, with passing of time the percentage of the battery drops.

28 is the highest amount of battery present at 0 time hours.

With passage of time the battery decreases.

So, in t = 1 hr,

battery, B = 28 - 7*1 = 28 -7 = 21%

similarly, t = 4 hrs,

B = 28 -7*4 = 28 -28 = 0%

The battery completely drains and becomes 0%

Therefore, B is the y- intercept of the equation B = 28 - 7t, where B is the percentage of the battery.

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Answer:

15

Step-by-step explanation:

Change x to the declared value: [tex]5|6-9|[/tex]

Subtract: [tex]5|6-9| = 5|-3|[/tex]

NOTE: remember that little minus big = negative of big minus little.

i.e.: 6-9 = -(9-6) = -(3) = -3

Evaluate the Absolute Value: [tex]5|-3| = 5(3)[/tex]

NOTE: remember that the absolute value of a number = the number's distance from 0 (always a positive number).

i.e.: |-2| = 2; |5| = 5

Multiply: [tex]5(3) = 15[/tex]

Answer:

0.16 for one egg. 1.90 for a dozen.

Step-by-step explanation:

For 24 eggs it is 3.79 dollars, so to find the price of one egg we just divide 3.79 by 24, which is 0.16.

There are 12 eggs in a dozen, and it's 3.79 for 24 eggs, so I can divide it by 2 to get to a dozen, so 3.79/2 = 1.90

Answer:

.16 per egg

1.90 for a dozen

Step-by-step explanation:

Take the total cost and divide by the number of eggs to find the cost for one egg

3.79/24 =.157916667

Since this is money we round to the nearest cent

.16

The cost per one egg is .16 or 16 cents

Multiply this by 12 to get the cost of 12 eggs

3.79/24  * 12 =1.895

This will round to 1.90

(Do not use the rounded answer to find the cost of a dozen eggs, because it will be higher.  We need to use the exact answer when calculating)

As per standard deviation criteria for outliers,  26.3 mm is the maximum thickness for which the statistician would need to examine the machine's configuration.

What is the standard deviation?

The numbers that do not lie within two standard deviations of the mean are considered outliers by the two-standard deviation criteria for outliers.

If the mean is 23.5 mm and the standard deviation is 1.4 mm

Next, the highest thickness needs to be checked: mean Plus 2 (standard deviation)

= 23.5 + (2 *1.4)

= 26.3 mm

Therefore, 26.3 mm is the maximum thickness for which the statistician would need to examine the machine's configuration.

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Answer: the answer to your question is 16 and 24

Using it's concept, the probabilities are given as follows:

A. 1/4.

B. 11/16.

C. 0.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, the number of marbles is given by:

7 + 5 + 4 = 16.

Then:

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The value of v in the equation is as follows:

Solve two thirds times v plus 6 equals one third times v minus 2.

Therefore, the equation is as follows:

2 / 3 × v + 6  = 1 / 3 × v - 2

2 / 3v + 6 = 1 / 3 v - 2

add 2 to both sides of the equation

2 / 3v + 6 = 1 / 3 v - 2

2 / 3v + 6 + 2 = 1 / 3 v - 2 + 2

2 / 3v + 8 = 1 / 3 v

subtract 2 / 3 v from both sides

2 / 3v + 8 = 1 / 3 v

2 / 3v - 2 / 3 v + 8 = 1 / 3 v  - 2 / 3 v

8 = 1v - 2v / 3

cross multiply

24 = - v

v = - 24

Therefore, v  = -24

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Answer:

watashiwa ana men toire ne duse ka

fipinjin desu

The drug company uses the Pre experimental design to test a new weight reduction medication.

Experimental Design:

Experimental design refers to how participants are allocated to the different groups in an experiment. Types of design include repeated measures, independent groups, and matched pairs designs.

Basically, there are 3 major types of experimental designs.

They are,

Given,

A drug company wanted to test a new weight reduction medication.

The researchers identified 500 adults from the age of 30 to 40 and randomly assigned them to two groups.

The first group received the medication and the second group received a placebo.

After 6 weeks the percentage of each group who lost more than five pounds was recorded and compared.

Here we need to find in which experimental design is used.

Here, they used the Pre-Experimental design concept,

In the Pre-Experimental concept,

They used the static group comparison method,

Basically, the process of static group comparison method is,

In a static-group comparison study, 2 or more groups are placed under observation, where only one of the groups is subjected to some treatment while the other groups are held static. All the groups are post-tested, and the observed differences between the groups are assumed to be a result of the treatment.

Therefore, in this experiment they used the Pre-Experimental design.

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Answer:

The measure of B is 56 degrees.

Answer:

y = 1/2x - 5

or x - 2y = 10

Step-by-step explanation:

x - 2y = 2

2y = x - 2

y = 1/2x - 1

If two lines are parallel, their slopes are equal

so m = 1/2, y = -3, x = 4

y = mx + b

-3 = 1/2(4) + b

-3 = 2 + b

b = -5

so y = 1/2x - 5

or 2y = x - 10

x - 2y = 10