Write each expression as a single natural logarithm. ln 3+ ln 4

Answer: 4.9 years old

Step-by-step explanation: it’s the ages added up divided by the total (to find the average)

Answer:

hiya not sure of this is right but I would add all the dots up so with 3 add 3+3+3+3+3. because there is 5 dots do this with all of them and then divided by the amount of dots hope this helps

answer 4.9

Answer:almost everywhere.

Step-by-step explanation:

Simplifying the expression given in words gives - 256.08

Given data

the expression. negative 17 plus the quantity negative 2 and three tenths plus 8 and 12 hundredths end quantity divided by 6 all times 4 squared minus 8 and 6 tenths

rewriting the expression gives:

= ( -17 + ( -2 3/10 + 8 12/100 ) / 6) * 4^2 - 8 6/10

= ( -17 + ( -2.3 + 8.12 ) / 6) * 4^2 - 8.6

= ( -17 + ( 5.82 ) / 6 ) * 16 - 8.6

= ( -17 + ( 0.97 ) * 16 - 8.6

= ( -16.03 ) * 16 - 8.6

= -256.48 - 8.6

= -256.08

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Answer:

The polls were open for 9 hours on election day.

Step-by-step explanation:

10167 - 6504 = 3663

3663 / 407 = 9

Y= 120

Given :  

Function :

trigonometric function, in mathematics, one of six functions (sine [sin], cosine [cos], tangent [tan], cotangent [cot], secant [sec], and cosecant [csc]) that represent ratios of sides of right triangles. These six trigonometric functions in relation to a right triangle are displayed in the figure.

They are also known as circular functions since their values can be defined as ratios of the x and y coordinates (see coordinate system) of points on a circle of radius 1 that correspond to angles in standard positions. Trigonometry can be easily applied to surveying, engineering, and navigation problems in which one of a right triangle’s acute angles and the length of a side are known and the lengths of the other sides are to be found.

The fundamental trigonometric identity is sin2θ + cos2θ = 1, in which θ is an angle.

X = 8

Y = 12

f (x) = x*3/2

f(8) = 8*3/2 = 12

y = 12

hence proof  f(x)=x*3/2

x = 80

f(x) =x*3/2

f(80) = 80*3/ 2

y = 40 *3

y = 120

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The factoring of the expression 9 x²+48 x+64 is (3x+8)²

To solve this exercise, we have to follow the rules of factoring:

9 x²+48 x+64

1. Factor 48 from 48x:

9 x²+48 x+64

9 x²+(24+24) x+64

2. Apply the distributive property:

9 x² + 24x + 24x + 64

3. Groups the first two terms and the last two terms:

(9 x² + 24x) + 24x + 64

4. Factorize the greatest common denominator (GCM) of each group:

3x(3x + 8x) + 8(3x + 8)

5. Simplify the common term (3x + 8) with the distributive property:

(3x+8) (3x+8)

6. Rewriting as the square of a binomial, we get:

(3x+8)²

Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.

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Answer: 7

Step-by-step explanation: 42 divided by 6 is 7.

The true statements include:

B. The next time the clothing store will receive shipments of both jeans and dresses is in 24 days.

C. The next time the clothing store will receive shipments of both sweaters and dresses is in 40 days.

It should be noted the information is simply about factor. In this case, you've to look at the least common factors between the terms.

Therefore, the next time the clothing store will receive shipments of both jeans and dresses is in 24 days. This is because 6 and 8 has a LCM of 24.

Also, the next time the clothing store will receive shipments of both sweaters and dresses is in 40 days.

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Answer:

x=-20

Step-by-step explanation:

x-2=-22

x=-22+2=-20

Answer:

-20.

Step-by-step explanation:

X - 2 = -22

Add +2 to both sides I the equation, and we have :

X - 2 + 2 = -22 + 2

X + 0 = -20

.: X = -20

Evaluation of logarithm is [tex]log_{64}4 = \frac{1}{3}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .

where, a is the base of function or equation

           x define expression

Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms :

According to statement,

[tex]log_{64}4\\[/tex]

this equation can be written as

[tex]log_{2^6} 4 \\= > \frac{1}{6}log_24 \\\\ = > \frac{1}{6}log_2{2^2}\\\\= > \frac{1}{6}2log_2{2}\\\\= > \frac{1}{6}. 2 = \frac{1}{3}[/tex]

Thus solution for this equation is [tex]log_{64}4 = \frac{1}{3}[/tex]

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Given the recursive relation:

[tex]a_{n}=-4a_{n-1}[/tex]

[tex]a_{2}=-4a_{2-1} = -4a_{1} = - 4(10) = -40 \\ a_{3}=-4a_{3-1} = -4a_{2} = - 4( -4 0) = 160 \\ a_{4}=-4a_{4-1} = -4a_{3} = - 4(160) = -640[/tex]

Answer:

B or 5:8

Step-by-step explanation:

If you see in the question it says "The farmer observes that 5 chickens eat 8 apples." and thats your answer every 5 chickens eat 8 apples.

Answer:

7 books

Step-by-step explanation:

Since Leah spent $63 on books which cost 9$ each you would need to divide the 2.

63 / 9 would equal 7

After spending $63 and each book costs $9 Leah will be able to buy 7 books .

Given, that each book cost $9 .

Now when the total amount spend on books is $63 with each book costing $9 the total books bought can be given by the division equation.

Division fact:

The rules for multiplication and division are:

(1) positive × or ÷ positive = positive

(2) positive × or ÷ negative = negative

(3) negative × or ÷ negative = positive

Since Leah spent $63 on books which cost 9$,

= [tex]\frac{63}{9}[/tex]

= 7 books

Hence Leah can buy 7 books in total.

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Answer: The answer would be 4+1i

Step-by-step explanation:  First I multiplied -5 to within the parentheses and go -5-10i and then the 3 to get 9-12i. Then I simplified even further to get 4+1i.

Answer:

hope this will help you...

The radius of the circle whose circumference is 46mm comes out to be 7.32 mm

As we are been provided with that circumference of the circle is 46mm and we are told to find out the radius of the circle

The formula for circumference of circle = dπ where d is the diameter of the circle

Let us put the given values in the formula

           46 = d (3.14)

  46/3.14 = d

d= 14.64

The radius of the circle is half of the diameter of the circle which means r = d/2

The radius of the circle = 14.64/2 = 7.32mm

Hence, the radius of the circle whose circumference is 46mm comes out to be 7.32 mm

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Answer: I think Rick is 16 and jeff is 6

Answer:

a)  y = -441.105 + 0.2232x

b)  2043

Step-by-step explanation:

Correlation measures how closely two variables are linked.

If two variables are correlated, you can draw a line of best fit on the scatter plot.

Plot the points from the table where:

(See attached graph).

We can see that the points lie close to a straight line. Therefore, a line of best fit with a positive slope can be drawn, since the two variables are positively correlated.

Linear regression is a method for finding the equation of a line of best fit on a scatter plot.

The regression line of y on x:

[tex]y = a + bx[/tex]

where a = y-intercept and b = slope

We cannot find the y-intercept from inspection of the scatter plot (attached) since we would need to extend the x-axis to thousands of years.

Therefore, to find the regression equation, use a graphing calculator:

[tex]y=-441.105+0.2232x[/tex]

To find the approximate year the movie ticket price will reach $15, substitute y = 15 into the equation and solve for x:

[tex]\implies -441.105+0.2232x=15[/tex]

[tex]\implies 0.2232x=456.105[/tex]

[tex]\implies x=2043.481...[/tex]

Therefore, the approximate year the movie ticket price will reach $15 is during 2043.

Note:

For this problem, we have used the line of best fit (regression line) to predict a value of that is outside the range of the original data. When using values outside the range to predict corresponding values, this is called extrapolation. These predictions can be unreliable because there is no evidence that the relationship described by the regression line is true for all values of x. Therefore, caution should be applied in these cases.

Answer:

Maths: 70

English: 0

Music: 140

The rest remain the same

Science: 87.5

History: 52.5

Step-by-step explanation:

350/10 = 35

35 x 4 = 140

140/2 = 70

35 + 35 + 70 = 140

Answer: ITS B

Step-by-step explanation:

The smallest value is 8.

the largest value is 44.

the median is 20.

the first quartile(Q1) is 12.

the third quartile (Q3) is 24

it represents among 100 cars the smallest speed is equal to 8 mph when passing through a busy intersection.

it represents among 100 cars the biggest speed is equal to 44 mph when passing through a busy intersection.

it represents among 100 cars half of them, their speed is equal to or less than 20 mph when passing through a busy intersection.

it represents among 100 cars 25% of  them, their speed is equal to or less than 12 mph when passing through a busy intersection.

it represents among 100 cars half of them, their speed is equal to or less than 20 mph when passing through a busy intersection.

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The volume of crater is 0.0375 km³.

We are given the diameter of crater which is 1 kilometer. Now, the formula to be used for calculation of volume is -

d = 2∛(V÷0.3)

Keep the value of diameter in the formula to find the volume of crater -

1 = 2∛(V÷0.3)

Dividing both sides of the equation by the number 2

1/2 = (2∛(V÷0.3))/2

Solving the equation we get -

0.5 = ∛(V÷0.3)

Taking cube on both sides of the equation

0.5³ = (∛(V÷0.3))³

On solving we get

0.125 = V÷0.3

Shifting 0.3 to numerator on Left Hand Side of the equation

V = 0.125×3

Performing multiplication on Right Hand Side on the equation

V = 0.0375 km³

Hence, the volume of crater is 0.0375 km³.

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The value of f(8) is -4.

Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer.

For example, 4x + 5x - 1 is a polynomial.

We can consider the polynomial to be:

f(x) = x - 12 so that when we divided by x - 8 we get a remainder of -4.

i.e

(x - 12) / (x-8)

x - 8 ) x - 12 ( 1

          x - 8          [ (x - 8) x 1 = x - 8 ]

              -4           [ we change the sign of the coefficient ]

                            [ x - 8 becomes (-x + 8) ]              

                            [ x gets canceled and -12 + 8 = -4 ]

We see that the quotient is 1 and the remainder is -4.

Now,

We can  use this polynomial f(x) = x - 12.

f(8) = 8 - 12 = -4

We can also directly say that the value of f(8) is -4 because the remainder is given as -4.

Thus,

The value of f(8) is -4.

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Lisa can make 16 '3/4 lb' bags of pecans.

Given,

Amount of lbs of pecans Lisa gathered from her backyard = 12 lbs

Amount of lb bags of pecans Lisa going to make for gifts = 3/4 lb

We have to find the number of 3/4 lb bags of pecans Lisa can make:

That is,

Total number of 3/4 lb bags = (Amount gathered from backyard) ÷ (Amount of lb bags going to make for gifts)

= 12 ÷ 3/4

= 12 × 4/3

= 4 × 4

= 16

Therefore, Lisa can make 16 3/4 lb bags of pecans.

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The approximate length is 0.62 years or 225 days.

A year is the time it takes for a planet, moon, or other celestial body to make one orbit around the Sun. ( when we take our solar system as an example). In the case of other exoplanets, the celestial bodies, moon, and other planets orbit around the main star. The period of the moon's orbit around the earth is related to the moon.

The reference point is very important in determining the exact length of a year. The length is dependent upon the reference point used for the orbital movement.

Jupiter completes a Single orbit once every 4333 days, due to which one Jupiter year is equivalent to 11.86 earth years.

A year is the time it takes for a planet, moon, or other celestial body to make one orbit around the Sun. ( when we take our solar system as an example). In the case of other exoplanets, the celestial bodies, moon, and other planets orbit around the main star. The period of the moon's orbit around the earth is related to the moon.

The reference point is very important in determining the exact length of a year. The length is dependent upon the reference point used for the orbital movement.

The second, closest planet to our Sun, Venus, completes a Single orbit once every 224.7 days, due to which one Venus year is equivalent to 0.6152 earth years.

Now, if Venus is 0.72 AU away from Sun, then we can calculate the length of the planet's year.

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after subtracting and simplifying the expression ( 2 x⁴ + 5 x³ - 8 ) - ( 9 x ² - 8 x + 8 ), we get the result as 2 x⁴ + 5 x³ - 9 x² + 8 x - 16.

We are given an expression:

( 2 x⁴ + 5 x³ - 8 ) - ( 9 x ² - 8 x + 8 )

We need to subtract the expression and simplify the result.

We get that:

Subtracting the expression, we get that:

2 x⁴ + 5 x³ - 8 - 9 x ² + 8 x - 8

Simplifying the expression, we get that:

= 2 x⁴ + 5 x³ - 9 x² + 8 x - 16

Therefore, after subtracting and simplifying the expression ( 2 x⁴ + 5 x³ - 8 ) - ( 9 x ² - 8 x + 8 ), we get the result as 2 x⁴ + 5 x³ - 9 x² + 8 x - 16.

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The factorized expression of 5z + 3y - 15x + 9 is 5(z - 3x) + 3(y + 3)

The expression is given as

5z+3y-15x+9

Rewrite the above expression properly

So, we have

5z + 3y - 15x + 9

Regroup the expression, as follows

So, we have:

5z + 3y - 15x + 9 = 5z - 15x + 3y + 9

Factorize the expression, as follows

So, we have:

5z + 3y - 15x + 9 = 5(z - 3x) + 3(y + 3)

Hence, the factorized expression of 5z + 3y - 15x + 9 is 5(z - 3x) + 3(y + 3)

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Answer:

The explanation is the same as the previous question.

The minimum of the objective function, f, subject to the constraints is (10.3, 8.3)

Plugging in 5 points, the intersections of the bounds of the 5 constraints, yields the least solution, f = 7x + 4y.

(0,60) provides 240

(6,30) f= 42+120 = 162

(10.3,8.3) = 72.1+ 33.2 = 105.3

(48,2) = 336+ 8 = 344

(60,0) = 420

At the moment when the minimum f is approximately (10.3,8,3)

5x+y = 60 and x+6y = 60 intersect at that point. Multiply the first equation by 6 and take the second equation out to get 30x + 6y = 360.

x + 6y = 60

29x = 300

Rounding to 10.3, x = 300/29 = about 10.345

adjusted to 8.3, y = 60-5x = 60 - 5(10.345) = 60-51.724

10.3, 8.3 reduces the value of the function f = 7x+4y.

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