The equation shows the relationship between a planet’s orbital period, t, and the planet’s mean distance from the sun, a, in astronomical units, au. If the orbital period of planet y is twice the orbital period of planet x, by what factor is the mean distance increased?.

Answer:

5

Step-by-step explanation:

diameter = 4 so radius =2

open up the cylinder so its top & bottom circle's circumference = 2πr =4π

top & bottom circle's area = πr² = 4π each, 8π for both

total surface = 28π

so lateral surface = 28π - 8π = 20π

so 20π = 4π* height

so height is 5

Correlation does not imply causation. It only says the two factors are related somehow - not that change in one affects the others directly. For example, the sales of ice-cream and sales of air conditioners may both go up during the summer season. Hence, they are correlated but one is not the cause of the other.

b. √60 is equivalent to 60^1/2

60^1/2 represents the square root of 60. The square root of a number is a value that when multiplied by itself, gives the original number. So in this case, √60 * √60 = 60. Therefore, the equivalent of 60^1/2 is √60.

Option a, 60/2 is not equivalent, because it is not the value that when multiplied by itself gives 60.

Option c, 1/60^2 is not equivalent, because it is not the value that when multiplied by itself gives 60.

Option d, 1/√60 is not equivalent, because it is not the value that when multiplied by itself gives 60.

It is important to note that 60^1/2 is not the same as (60^1)^1/2, the first one is finding the square root of 60 while the second one is finding the 1/2 power of 60 which is not the same thing.

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The solution of the division of 4 2/9 by the number 1 1/3 is

Mixed fractions are type of fractions which consist of a whole number part and a fractional part.

Mixed fractions are of the form a b/c where a is the whole number part and b/c is the fractional part.

The given fractions are 4 2/9 and 1 1/3.

First we have to change the mixed fraction into improper fraction.

4 2/9 = (4 × 9 + 2) / 9 = 38/9

1 1/3 = (1 × 3 + 1) / 3 = 4/3

Dividing these,

4 2/9 ÷ 1 1/3 = 38/9 ÷ 4/3

                     = (38/9) × (3/4)

                     = 38 / (3 × 4)

                     = 19/6

                     = 3 1/6

Hence the solution of the division of the mixed fractions given is 3 1/6.

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Answer:

−5y = 10 − 5x and −2y = 8 − 4x is x =2 and y = 0.

Step-by-step explanation:

Perpendicular drawn through point R on the given line segment PQ.

Constructed figure is attached.

Step of construction :

Constructed figure is attached.

Therefore, perpendicular line drawn through point R on line segment PQ using above steps of construction.

The above question is incomplete , the complete question is :

Draw any line segment PQ take any point R on it. Through R draw a perpendicular to PQ.

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Algebra Formulas for Class 8

Some essential 8th-class formulas related to Algebra are:

Algebraic Identities For Class 8

(a + b)2 = a2 + 2ab + b2

(a − b)2 = a2 − 2ab + b2

(a + b) (a – b) = a2 – b2

(x + a) (x + b) = x2 + (a + b)x + ab

(x + a) (x – b) = x2 + (a – b)x – ab

(x – a) (x + b) = x2 + (b – a)x – ab

(x – a) (x – b) = x2 – (a + b)x + ab

(a + b)3 = a3 + b3 + 3ab (a + b)

(a – b)3 = a3 – b3 – 3ab (a – b)

I tried my best!

Answer:

moon = 7

star = 4

Step-by-step explanation:

First equation:

moon + 1 = star + star

   7   + 1 = 4 + 4

Second Equation:

moon = 3 + star

    7 = 3 + 4

Hope this helps

Answer:

star =2

Step-by-step explanation:

m=moon s= star

m+1=s+s     you took the one form here

m=3+s         and added it here

now subtract the one which would be 2 so the star = 2

your moon is correct

Answer:

Step-by-step explanation: First we start by using the order of operations and do -2 + 16 which is 14. Then we do multiplication left to right, do 3 x 6 = 18x2 =36 +14 =50

if ΔEFG, e = 75 cm, m∠G=141° and m∠E=16° then length of g is 171.24 cm

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that ΔEFG, e = 75 cm, m∠G=141° and m∠E=16°

We need to find the length of g.

Because two angles are given, F = 180 – (141 +16 )

m∠F=180-157F=23

Now let us apply the sine rule

SinE/e=SinF/g

Sin16/75=sin23/g

g=171.24 cm

Hence, if ΔEFG, e = 75 cm, mm∠G=141° and mm∠E=16° then length of g is 171.24 cm

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A triangle can not have three sides whose lengths are 3.2 cm 5.3 cm 9.4 cm

We know that the triangle inequality theorem states that for any triangle the sum of any two sides of a triangle is greater than or equal to the third side.

Here, we have been given the three measurements.

Let a = 3.2 cm, b =  5.3 cm and c = 9.4 cm

Consider the sum of sides a and b,

a + b

= 3.2 + 5.3

= 8.5cm

< 9.4

= c

i.e., a + b < c

Acctording to triangle inequality theorem, a, b, c can not be the sides of triangle, as the sum of two sides that measure 3.2 cm and 5.3 cm is not greater than or equal to the third side which measures 9.4 cm

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Mid-point formula is used to determine the mid-point of a line segment. An example of the mid-point formula is discussed below.

What is the mid-point formula?

The centre of a line segment is known as the midpoint. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

The formula used to find this mid-point of the line is called the mid-point formula.

[tex](x_{m},y_{m} ) =(\frac{x_{1} +x_{2} }{2} ,\frac{y_{1} +y_{2} }{2})[/tex]

where, [tex](x_{m} ,y_{m})[/tex] = mid-point coordinates

            [tex](x_{1} ,y_{1})[/tex]   = first point coordinates

            [tex](x_{2} ,y_{2})[/tex]   = second point coordinates

An example of mid-point formula is given below.

Find the mid-point of a line whose end coordinates are (3,5) and (6,10).

From the question, we can write,

                [tex](x_{1} ,y_{1}) = (3,5)\\(x_{2} ,y_{2}) = (6,10)[/tex]

Then as discussed above, we can find the mid-point using the formula,

             [tex](x_{m},y_{m} ) =(\frac{x_{1} +x_{2} }{2} ,\frac{y_{1} +y_{2} }{2})[/tex]

                [tex]x_{m} = \frac{x_1 + x_2}{2} = \frac{3+6}{2} = 4.5[/tex]

                [tex]y_{m} = \frac{y_{1} + y_{2}}{2} = \frac{5+10}{2} = 7.5[/tex]

Therefore the mid-point of the given line found using the mid-point formula is (4.5, 7.5).

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The observed frequency of the cell is fewer than the expected frequency, according to a typical rule of thumb for interpreting the standardized residual: If the residual is less than -2. If the observed frequency is more than the expected frequency, it is greater than 2.

The meaning of a negative residual?

A negative residual indicates an excessively high anticipated value, and a positive residual indicates an excessively low expected value. A regression line's goal is to reduce the total amount of residuals.

A good residual value is what?

Check out the Car Lease Ratings section of our Lease Kit for a complete list of high-residual vehicle brands and models.

                A car is probably not a good lease deal if the lease-end residual value is less than 50% of the MSRP (for a 36-month lease). 55% to 65% of MSRP would be a nice residual.

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(12 - 7) is a Numerical expression.

An expression written having a variable in it is referred to as a variable expression. A numerical expression is an expression made up of numbers and operations.

Expressions that use numbers to perform operations are an example of a numerical expressions like 2(3 + 8). If there is at least one variable and one operation must be present in an algebraic expression such as 2(x + 8y) is an example of variable expression.

Here we have the expression (12 - 7)

As we can see there are only numerical values but there are no variables in the given equation, So the given expression is a Numerical expression

Therefore,

(12 - 7) is a Numerical expression.

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It is possible to construct a triangle whose sides are 15 cm 12 cm and 9 cm because the sum of two sides are greater than three sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 15 cm 12 cm and 9 cm.

The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.

To check this we firstly add the 15 and 12

15 + 12 > 9

27 > 9

Now we add 15 and 9

15 + 9 > 12

24 > 12

Now we add 12 and 9

12 + 9 > 15

21 > 15

It is possible to construct a triangle whose sides are 15 cm 12 cm and 9 cm because the sum of two sides are greater than three sides.

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Following the addition of both sides of the equation by 2/3, x is equivalent to 3/2(x-5)=-6.

An equation is a mathematical formula that joins two statements using the equal sign (=) to denote equality. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the terms 3x + 5 and 14 in the equation 3x + 5 = 14.

given

Add 2/3 to both sides of the equation.

(2/3(3/2⋅(x−5))=2/3⋅−6

Simplify the problem on both sides.

x − 5 = −4

Put all terms on the right side of the equation that don't contain x.

x = 1

Following the addition of both sides of the equation by 2/3, x is equivalent to 3/2(x-5)=-6.

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The scientific notation for the answer to 1.9×10⁷*3×10⁶ is 5.7×10¹³.

An exponent is a number or letter placed above and to the right of the base of a mathematical statement. It denotes that the base will be raised to a specific level of power. Exponents are classified into four types: positive, negative, zero, and rational. Positive exponents indicate how many times a base may be multiplied by itself. The number of times a number is multiplied by itself is referred to as its exponent. For instance, 2 to the third (written as 23) means: 2 x 2 x 2 = 8. 2 x 3 = 6 does not equal 23. Keep in mind that a number raised to the power of one is itself.

Here,

=1.9×10⁷*3×10⁶

=5.7×10⁽⁷⁺⁶⁾

=5.7×10¹³

The scientific notation for the result of 1.9×10⁷*3×10⁶ is 5.7×10¹³.

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Answer: 9 minutes

Step-by-step explanation:

12 x 3/4(.75) = 9

The predicted sales for week 6 is 740

In the case of linear regression using excel formula, we can find the intercept and the slope value for the regression model.

The equation of linear regression is similar to the slope formula what we have learned before in earlier classes such as linear equations in two variables.

Forecast[tex]$=\mathrm{A}+\mathrm{B}(\mathrm{x})$[/tex]

Where A is the intercept of the data, B is the slope, and X is the period.

Intercept [tex]=[/tex] INTERCEPT (Range Y, Range X)

The above data generates the equation.

Now the data corresponds to an intercept value of 698 and a slope of 8.

Therefore, for period [tex]$6, x=6$[/tex]

The equation [tex]$=698+(8 * 6)=746$[/tex]

The intermediate calculations are in the table below:

PERIODUNITSFORECAST

____________________

1            700      706

2           724       714

3           720       722

4           728       730

5                         738

6                         740

Therefore, the predicted sales for week 6 is 740.

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Answer: Try the answer A

One can create a triangle with the sides 3 cm, 5 cm and 7 cm.

We can check the possibility of constructing a triangle through side-side-side. It states that the sum of any two sides of triangle should be greater than third side of the triangle. Therefore, let us say 3 cm is side a, 5 cm is side b and 7 cm is side c.

Now, checking the rule.

Side a + side b > side c

3 + 5 > 7

Add the digits on left

8 > 7

Side b + side c > side a

5 + 7 > 8

Add the digits on left

12 > 8

side c + side a > side b

8 + 5 > 7

Add the digits on left

13 > 7

The side-side-side rule of triangle is followed in all the cases, and hence triangle formation is possible.

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Located in Ennis, Montana, Madison Valley Bank provides services to residents of Madison County and the surrounding region. Madison deposited $463 into a bank savings account with a 2% annual interest rate.

Although inflation doesn't stop, it does get better. We don't want it to completely end, in fact. The Federal Reserve, the US central bank tasked with reducing the rate of inflation through a series of interest rate hikes, has set a target of about 2%. As a result, albeit not by as much, prices will still increase. At an interest rate of 8% compounded semi-annually, a $1,000 investment made now will be worth $1,480.24 after five years.

Calculator for future inflation in the US: In 2025, $106.09 is expected to be the same as $100 in terms of purchasing power. Future inflation of 3% per year is used as the basis for this computation. A 3.00% future inflation rate is predicted. when $54,855.74 is the same as $30

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The coordinates of point G are (5, 6).

To find the coordinates of point G, we need to find the average of the x-coordinates and the average of the y-coordinates of points A and B.

Therefore, the coordinates of point G are (5, 6).

Key points:

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The length of bc is 8. The result is obtained by using the concept of conditions for similar triangles.

For two or more similar triangles, it has two conditions.

A right triangle abc with altitude bd drawn to hypotenuse ac has the length of sides as follow

Find the length of bc!

Observe the picture of triangles in the attachment! If we drawn a perpendicular line to the hypotenuse, we'll have three similar triangles.

The corresponding sides of the two triangles are

[tex]\frac{\overline{ac}}{\overline{bc}} = \frac{\overline{bc}}{\overline{dc}} = \frac{\overline{ab}}{\overline{bd}}[/tex]

The length of bc is

[tex]({\overline{bc})^{2} = \overline{ac} \times {\overline{dc}[/tex]

[tex]({\overline{bc})^{2} = 16 \times 4[/tex]

[tex]({\overline{bc})^{2} = 64[/tex]

[tex]{\overline{bc} = \sqrt{64}[/tex]

[tex]{\overline{bc} = 8[/tex]

Hence, the length side of bc on the right triangle is 8.

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Answer: -3

Step-by-step explanation:

The given equation is:

-2p-4 = 2

Let's add 4 to each side of the equation.

You'll get

-2p = 6

Now let's divide both sides by -2, and you get

p = -3

By fractions, 9/20 quarts of lemonade concentrate is needed to make lemonade for 24 people.

What are the names of fractions  numerical expression in mathematics known as a quotient, where a numerator and a denominator are split in half. Both are integers in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator of a proper fraction is less than the denominator.

Let x= the number of quarts of lemonade concentrate needed for 24 people. In this question " 20/3 quarts of water" was unnecessary information.

40x=24*(3/4)​

Cross products

x=24⋅ (3/4) ⋅ (1/40)= 9/20

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The exponent of 4 is called as a Biquadrate or fourth power of Exponent which is written as [tex]x^{4}[/tex] and read as number x raised to power 4 .

What is Exponent ?

The Exponent is defined as a method of expressing large numbers in terms of powers. which means, that exponent refers to how many times the number multiplied by itself.

The exponents of numbers are as follows :

(i) the exponent of 2 is called "Squared"  ,

(ii) the exponent of 3 is called "Cube" ;

(iii) the exponent of 4 is called "Biquadrate" .

Some Examples of "exponent of 4 " are : 2⁴ , 3⁴ .

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Answer: Zero or negative Zero

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

2a + 2 = 2

2a = 2 - 2

2a = 0

a = 0/2

a = 0

The probability of drawing a marble that is blue, and then, after replacing it, drawing a marble that’ green is 5/36.

In the given question, a jar of marble has 5 blue marble, 3 red marble, and 4 green marble.

We have to find the probability of drawing a marble that is blue, and then, after replacing it, drawing a marble that’ green.

Total number of marbles = 5 + 3 + 4

Total number of marbles = 12

The probability of choosing the blue marble = Number of Blue Marble/Total number of marble

The probability of choosing the blue marble = 5/12

Now replacing the marble blue and getting the green marble = Number of Green Marble/Total number of marble

Now replacing the marble blue and getting the green marble = 4/12

Now replacing the marble blue and getting the green marble = 1/3

The probability of getting blue marble then green marble = The probability of choosing the blue marble × The probability of choosing the green marble

The probability of getting blue marble then green marble = 5/12 × 1/3

The probability of getting blue marble then green marble = 5/36

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621 × 99 = 621 × 100 - 621 x 1

option b is correct.