(Scientific Notation LC)
Write 280,000,000 in scientific notation

x-7 is not a factor of [tex]x^{4}-3x^{3}+x^{2} +2x+1435[/tex].

In long division method, we divide  [tex]x^{4}-3x^{3}+x^{2} +2x+1435[/tex] by x-7

x-7 )  [tex]x^{4}-3x^{3}+x^{2} +2x+1435[/tex]  (  [tex]x^{3}-10x^{2} +71x-495[/tex]

        [tex]x^{4}+7x^{3}[/tex]

  -----------------------------

              [tex]-10x^{3}+x^{2} +2x+1435[/tex]

             [tex]-10x^{3}-70x^{2}[/tex]

          --------------------------

                        [tex]71x^{2} +2x+1435[/tex]

                        [tex]71x^{2} +497x[/tex]

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

                                  [tex]-495x+1435[/tex]

                                  [tex]-495x-3465[/tex]

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

                                                 [tex]4900[/tex]

As 4900 is a remainder, x-7 is not a factor.

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Answer:

Question 1: We need to know whether Angles P and N are congruent or not.

Question 2: Cannot be proven congruent

Question 3: AAS Congruence Theorem

Question 4: ASA Congruence Postulate

Step-by-step explanation:

Background info: The information (congruence lines on sides and angles) is read counterclockwise (starting from the very left to right).

Question 1: In order to prove the triangles congruent with the AAS, we need two pairs of congruent angles and one pair of congruent sides. We still need one more pair of congruent angles. Since the triangle is read counterclockwise, the angle to the left of the current congruent angle given needs to be given to us. This is angles P and N.

Question 2: For this answer, the triangles cannot be proven congruent because we are only given three congruent angle pairs. This means that it should be the "AAA" Theorem, however, it doesn's exist due to the fact that the triangles could still be two different sizes despite the fact that the angles are the same. In order to prove this congruent, we would need info on congruent sides.

Question 3: Reading the triangle left to right, we see a congruent angle pair (A), another congruent angle pair (A), and a congruent side pair (S). Putting this together, we get AAS.

Question 4: Reading the triangle left to right, we see an angle pair (A), a side pair (S), and an angle pair (A). Putting this together, we get ASA.

Hope this helps! (No guarantees it's 100% correct)

Answer: C or D(they appear the same, the answer is 5 hours)

Step-by-step explanation:

after 5 hours, train a has gone 5*50 miles, or 250 miles

after 5 hours, train b has gone 5*30 miles, or 150 miles

250miles + 150miles = 400 miles

The Z-score for a GPA of 2.98 is 1.60345

A Z-score is a numerical value or measurement that explains the relationship between a value of data and the mean of a group of values. It will be calculated in terms of standard deviations from the mean.

The formula to calculate the Z -score is given by

                     Z - score =  [tex]\frac{( \bar{x} -\mu) }{\sigma}[/tex]    

Where  [tex]\bar {x}[/tex]  = test value

μ = mean and σ = standard deviation

Here we have

GPAS at CCCOnline are normally distributed with a mean of 2.05 and a standard deviation of 0.58

⇒ mean μ = 2.05

⇒ Standard deviation σ = 0.58  

And we need to find the z-score for a GPA of 2.98

⇒  [tex]\bar {x}[/tex] = 2.98

From above observations

Z - score =  [tex]\frac{( 2.98 -2.05) }{0.58}[/tex]  

= [tex]\frac{( 0.93) }{0.58}[/tex]

= 1.60345  

Therefore,

The Z-score for a GPA of 2.98 is 1.60345

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Answer:

-3

Step-by-step explanation:

x= -18 + 15 = -3

Answer: 1/2

Step-by-step explanation:

I'm assuming this is rise over run. The rise is 1 and the run is 2.

Remember, [tex]\frac{rise}{run}[/tex]

Step-by-step explanation:

among other details this is the main thing about the standard form :

a polynomial in standard form is the sum of one or more terms; each term must be a monomial in standard form. also, the degrees of the terms should be decreasing as much as possible from left to right.

a monomial is the product of one or more factors: a constant coefficient and one factor for each variable in the expression. via exponent (e.g. 0) we control which variable is actually "showing", as any x⁰ = 1 and can therefore be omitted when writing as factor.

in other words :

e.g.

4x³ + 2x² + 5x + 1

2x + 3y + 7xy

are examples of the standard form.

in our case we have only x a variable. but we need to do all the squaring and multiplications and summing up to get the standard form.

that means

2(x - 1)² - 2 = ...

remember the priorities :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

2(x - 1)² - 2 = 2(x² - 2x + 1) - 2 =

= 2x² - 4x + 2 - 2 = 2x² - 4x

The unit rate of orange could be found by Sara and Daniel by ratio to be $1.50

If Sara's mother bought 8 large oranges for $12.00

Sara may have thought of it like if $12 is for 8 oranges the how much is for 1

12 : 8 then X : 1

12/8 then x/1

12/8 = x/1

x = $1.50

Daniel would have taken this method, if 8 oranges costs $12 then 1 orange would cost ?

8 oranges : $12 then 1 orange : ?

8 : 12 = 1 : ?

8/12 = 1/?

8 * ? = 1 * 12

? = 12/8

? = $1.5

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Answer:

27/256

Step-by-step explanation:

=(27)(1/4)(1)/(64)

=27/256

Answer: -1.631

Step-by-step explanation:

[tex]\log_{3} \frac{a}{3}=\log_{3} a-\log_{3} 3=-0.631-1=-1.631[/tex]

The graph of the function f(x) = x³ and g(x) = (x - 3)³ are related to each other that the function g(x) is shifted right to 3 points.

Function

Basically, function is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Given,

Here we need to find how the graph of g(x)=(x-3)³ related to the graph of f(x) = x³.

Here we have the two equations of the function that are,

f(x) = x³

g(x) = (x - 3)³

By looking at the given functions, we have identified that f(x) be the parent function:

And it can be written as,

=> f(x) = x³

And the first transformation is applied as,

f(x) → f(x) - 3

Now, the function f(x)  will shift right side by 3 units

Therefore, the function f(x) = x³ and g(x) = (x - 3)³ are related to each other that the function g(x) is shifted right to 3 points.

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The equation for the line parallel to the given line and passing through the given point is y = -4x + 5.

Given:

3y = -12x + 4 and point (1,1)

3y = -12x+4

divide by 3 on both sides

3y/3 = -12x/3 + 4/3

y = -4x + 4/3.

m = -4.

y = mx + c

substitute m and (1,1)

1 = -4*1 + c

1 = -4 + c

c = 1 + 4

c =5

substitute c and m value in y = mx+c

y = mx + c

y = -4x + 5.

Therefore the equation for the line parallel to the given line and passing through the given point is y = -4x + 5.

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The volume of the cuboid is 153000 [tex]cm^{3}[/tex];

What is the volume of the cuboid?

In general, the volume of a cuboid is equal to the area that it takes up in space. It is dependent upon the cuboid's three dimensions, or its length, breadth, and height. Due to the fact that all of a cuboid's faces are rectangular, the term "Solid Rectangle" is also referred to as a cuboid. All of the angles and the opposite faces of a cuboid in a rectangular cuboid are at right angles. A cuboid's volume is determined by the product of its length, breadth, and height. Cubic units are used to measure cuboids' volume.

The product of a cuboid's base area and height determines its volume. We can therefore write;

Cuboid volume equals base area times height [in cubic units].

The cuboid's base is shaped like a rectangle. As a result, a cuboid's base area is determined by multiplying its length by its breadth. Hence,

A cuboid's volume is equal to its length, width, and height in cubic units, or

A cuboid's volume is equal to l b h [in cubic units].

l = length, b = width, and h = height.

In the given question, we have;

Length = 30 cm;

Breadth = 60 cm;

Height = 85 cm;

And,

we know that:

The volume of the cuboid = lbh

The volume of the cuboid  = 30×60×85 [tex]cm^{3}[/tex]

The volume of the cuboid  = 1800 ×85 [tex]cm^{3}[/tex];

The volume of the cuboid  = 153000 [tex]cm^{3}[/tex];

Hence,

The volume of the cuboid  = 153000 [tex]cm^{3}[/tex];

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For each goody bag we need 3.4 cookies

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

We are given that there are 17 cookies that will be divided equally among 5 goody bags.

17 cookies = 5 goody bags.

For each goody bag.

Thus,

17/5 = 3.4 cookies.

Therefore, 3.4 cookies needed.

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Answer:

y = 15

Step-by-step explanation:

the triangle has congruent base angles of 50°

This means the triangle is isosceles with the 2 legs being congruent, so

3y - 10 = y + 20 ( subtract y from both sides )

2y - 10 = 20 ( add 10 to both sides )

2y = 30 ( divide both sides by 2 )

y = 15

The probability of winning the minimum award is [tex]\frac{^4C_3 . ^{53}C_1}{^{57}C_4} \times \frac{1}{47}[/tex].

The Player chooses 4 numbers from white balls numbered 1 to 59 and

1 number from gold ball numbered 1 to 47

He has to choose 3 correct numbers out of 4 numbers in the white ball

and 1 number from the gold balls.

He can do in [tex]^4C_3 . ^{53}C_1[/tex] and 1 way respectively.

So, the probability can be given by;

Probability = probability of choosing white ball * probability of choosing red ball

Probability = [tex]\frac{^4C_3 . ^{53}C_1}{^{57}C_4} \times \frac{1}{47}[/tex]

Thus, the probability of winning the minimum award when players pick four different numbers from 1 to 59 and one number from 1 to 47 and a player wins a minimum award of $225 by correctly matching three numbers drawn from the white balls (1 through 59) and matching the number on the gold ball (1 through 47) is [tex]\frac{^4C_3 . ^{53}C_1}{^{57}C_4} \times \frac{1}{47}[/tex].

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Answer:

4

Step-by-step explanation:

Welcome to Gboard clipboard, any text you copy will be saved here.

[tex]4(x)+4(-b)=x\\4x-4b=x\\4x-x=4b\\3x=4b\\\frac{3x}{3} =\frac{4b}{3} \\x=\frac{4b}{3}[/tex]

⇒They simply wanted you to simplify and make x the subject of the equation.

Answer:

Step-by-step explanation:

The are 6 possibilities for each dice, so the number of outcomes is:

Outcomes with the sum of 10:

Probability of getting 10 is 3 out of 36:

Applying the midsegment theorem:

a. x = 17; y = 2

b. Length of DF is: 20 units.

According to the midsegment theorem:

Length of GH = half the length of EF

Given the following:

GH = 1/2(EF)

Substitute:

x - 3 = 1/2(28)

x - 3 = 14

x - 3 + 3 = 14 + 3

x = 17

DH = HF

DH = y + 8

HF = x - 7

Therefore:

y + 8 = x - 7

Plug in the value of x

y + 8 = 17 - 7

y + 8 = 10

y = 10 - 8

y = 2

Length of DF = y + 8 + x - 7

Plug in the values of x and y:

Length of DF = 2 + 8 + 17 - 7

Length of DF = 20 units.

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Step-by-step explanation:

y = mx+ b

m is the slope = 5

you can get x,y from point (x,y); x=2, y=1

substitute all information we have to find b

1 = 5(2) + b

1 = 10 + b

1 - 10 = b

-9 = b

the function for line:

y = 5x - 9

The factors are mentioned in the table given below.

Number    Number of factors        prime or composite

12                    6                                      composite

20                   6                                      composite

21                    4                                       composite

31                    2                                      prime

43                   2                                        prime

Factors are those numbers which when divide the given number leaves zero as a remainder.

Factor of 12 = 1, 2 ,3, 4, 6 , 12

Factor of 20 = 1, 2 , 4,5,10 , 20

Factor of 21 = 1 ,3, 7, 21

Factor of 31 = 1, 31

Factor of 43 = 1, 43.

Prime number is a number which has only 2 factors that is number one(1) and the number itself.

Composite numbers which has more than 2 factors.

Therefore, the number of factors are mentioned in the table.

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Based on the residual plot, the linear model is appropriate as C. Yes, there is no clear pattern in the residual plot.

A continuous response variable is described as a function of one or more predictor variables in a linear model. They can assist you in comprehending and forecasting the behavior of complex systems, as well as analyzing experimental, financial, and biological data. Linear regression is a statistical technique for developing a linear model.

The residual plot depicts the difference between the observed and fitted response values. The ideal residual plot, also known as the null residual plot, depicts a random scatter of points forming a band.

In this case, no clear pattern was detected.

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Answer:

it seems like the person above me is correct.

Step-by-step explanation:

The materials travel faster on Belt One, considering the constants of the proportional relationships.

A proportional relationship is a linear function with intercept zero in which the output variable symbolized by y is given by the multiplication of the input variable symbolized by x and the constant of proportionality symbolized by k, according to the equation presented as follows:

y = kx

For each belt in this problem, the constant gives the velocity that the materials travel.

For Belt One, the relation is:

y = 157.1x.

Hence the velocity is of 157.1 inches per minute.

For Belt Two, the velocity is obtained as follows:

k = 125.6/2 = 62.8 inches per minute.

157.1 > 62.8, hence it travels faster on Belt One.

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Area of circle =  1764 pi in² in terms of pi .

area of circle = pi  r²

                      = 42 * 42 pi²

                      = 1764 pi in²

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If a nonagon has 9 sides. One angle of a regular nonagon measures (3w + 15)°. The value of w is: D. w = 42.

Given data:

Nonagon= 9 sides

Angle of a regular nonagon =(3w + 15)°

Value of w =?

Hence let find the value of w

Value of w = 3w + 15°

Value of w = 3(9) + 15°

Value of w = 27 + 15

Value of w = 42

Therefore the correct option is D.

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Answer: the answer is D. W=42

Step-by-step explanation:

Answer:

Measures of center generally tell us about the middle , or center of a distribution. They are the mean , the Mexican , and the mode. Each plays a useful role in statistics. The mean or arithmetic average , is calculated by adding all the data values and dividing by the number of values.

Answer:

Step-by-step explanation:

we cant see the problem or there answers