The temperature in Anchorage,Alaska, dropped over four consecutive hours from 0 to -44F. If the temperature dropped the same amount each hour, how much did the temperature change each hour?

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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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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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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The value of y = 5 and CD = 4 cm in the segment.

The point D is the midpoint of a segment CF. CF = 2y-2 and CD = 3y - 11.

CD = (1/2) CF

3y - 11 = (1/2) (2y -2)   (multiply both sides by 2)

6y - 22 = 2y - 2

6y - 2y = -2 + 22

4y = 20

y = 5

Substitute with the value of y in the equation of CD, you get:

CD = 3y-11 = 3(5) - 11 = 15 - 11 = 4 cm

In geometric terms, a line segment is a section of a straight line that is bordered by two clearly defined end points and contains all of the points on the line that lie inside that segment. The Euclidean distance between two endpoints of a line segment provides the length of the segment.

Between two points of a line or curve. a portion of a plane or solid figure that is eliminated due to the intersection of a line, plane, or planes, particularly one that occurs between a chord and a circle's arc.

A line segment in geometry is bordered by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points.

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Answer: 25%

Step-by-step explanation:

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:

The measure of B is 56 degrees.

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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Answer:

Please see the picture below.

Step-by-step explanation:

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

The new balance in Jackie's account after 2 days will be -$27.50.

It should be noted that for each day that her checking account balance falls below zero, she is charged by the bank a fee of $7.50 per day.

Since her current balance in the account is –$12.50, the new balance after 2 days will be:

= -12.50 + (-7.50 × 2)

= -12.50 + -15

= -27.50

The balance is -27.50

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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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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.

[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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Answer:

f(x)=2x+1

Step-by-step explanation:

Use formula:

f(x)=a(x-h)+k

a=shrinking/stretching

h= horizontal translation

     left (+)

   right (-)

k= vertical translation

    left (-)

 right (+)

Answer: 16+d>20

d>4

Step-by-step explanation:

d=digs

16+d>20

16-16+d>20-16

d>4

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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Answer:

Step-by-step explanation:

6+4=10

10/2

answer =5

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:

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:

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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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

Answer:

3

Step-by-step explanation:

33 - 2[3(3 + 12) - (5 x 2)3] =

= 33 - 2[3(15) - (10)3]

= 33 - 2[45 - 30]

= 33 - 2[15]

= 33 - 30

= 3

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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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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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:

watashiwa ana men toire ne duse ka

fipinjin desu

Analyzing the given data, it cab be concluded that Option D, that is, mL3 = 126° is most likely being shown by the proof.  

It can be observed from the given diagram, angle 1 and angle 2 are complementary. By the definition of complementary angles, we get the sum of angle 1 and angle 2 equal to 90°.

=> mL1 + mL2 = 90°

The value of angle 1 is given as 36.

=> mL1 = 36⁰

Using the first observed condition and the value of angle 1, we can obtain the value of angle 2.

=> 36⁰ + mL2 = 90°

=> mL2 = 90 - 36 = 54°

Therefore, the value of angle 2 is obtained as 54°.

From the diagram given in the question, it can also be inferred that angle 2 and angle 3 form a linear pair. Using the linear pair theorem, we get the sum of angle 2 and angle 3 as 180°.

=> mL2 + mL3 = 180°

Previously, we have obtained the value of angle 2 as 54°.

Hence, by substituting the value of angle 2 in the above equation, we get,

54° + mL3 = 180°

=> mL3 = 180 - 54 = 126°

Therefore, By researching all the data and the results, we can conclude that all other options are discarded and the correct option is option D.

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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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