is -2/3 a natural number​

The evaluation of each expression is 3/2 , 1/2.

What is logarithms:

Logarithms are the other way of writing the exponents. A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation. For example, if 102 = 100 then log10 100 = 2.

Hence, we can conclude that,

Log b x = n  or   bn = x

Where b is the base of the logarithmic function.

This can be read as “Logarithm of x to the base b is equal to n”.

In this article, we are going to learn the definition of logarithms, two types of logarithms such as common logarithm and natural logarithm, and different properties of logarithms with many solved examples.

What is properties of logarithms:

Properties of logarithms functions are used to solve logarithm problems. We have learned many properties in basic math's such as commutative, associative and distributive, which are applicable for algebra. In the case of logarithmic functions, there are basically five properties.

This are as follows:

The product property

The quotient property

Power rule

Change of base rule

Reciprocal rule

Now,

3log₉ 3 = [(9)^x]^3 = 3

[(3^2)^x]^3 = 3

x = 3/2

Second part,

1/4 log₉ 81

= 1/2

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Answer: 13.7

Step-by-step explanation:

First you do 16.6 - 2 = 14.6 then you subtract 0.9 from 14.6, your equation would be 14.6 - 0.9 = 13.7

Hope This Helps!

Answer:

13.7

Step-by-step explanation:

Igor has not been skiing in 10 years. however, when he gets on his skis, his body remembers exactly how to ski. the kind of memory that makes it possible for him to remember how to ski is procedural.

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The projectile motion equation [tex]h(t) = - g \cdot {t}^{2} + v_{0}\cdot {t} + h_{0}[/tex], gives;

First part;

Second part;

Third part;

The quadratic equation that represents the projectile motion can be presented as follows;

[tex]h(t) = - g \cdot {t}^{2} + v_{0}\cdot {t} + h_{0}[/tex]

g = 16 ft./s² or 9 m/ s²

First part;

When

[tex] v_{0} = 0 \: and \: h_{0} = 100 \: ft.[/tex]

We have;

h(t) = -16•t² + 100

When the object hits the ground, we have;

h(t) = 0, which gives;

0 = -16•t² + 100

Therefore;

16•t² = 100

t² = 100 ÷ 16 = 25/4

t = √(25/4) = 5/2 = 2.5

Second part;

The direction in which the object is thrown = Upwards

Initial height of the object, [tex] h_{0} = 6 \: ft[/tex]

Initial speed of the object, [tex] h_{0} = 30 \: ft/sec[/tex]

The equation of the projectile motion is therefore;

h(t) = -16•t² + 30•t + 6

Which gives;

When the object is at its starting height of 6 feet, h(t) = 6, which gives;

6 = -16•t² + 30•t + 6

-16•t² + 30•t = 0

A solution to the above equation is t = 0

The other solution is found as follows;

-16•t² + 30•t = 0

-16•t + 30 = 0

30 = 16•t

t = 30/16 = 1.875

Third part;

When the object hits the ground, we have;

h(t) = 0, which gives;

0 = -16•t² + 30•t + 6

Which gives;

t ≈ 2.06

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The expression is written as 2 × 10 =  2 x 10^ 1  = 20

The index form of a number  can be defined as that number written as an exponential expression.

It is also said to be a single number that is  raised to another number.

Given the expression;

2x _____ = 2 x 10^ 1 = ______

Note that a number raised to the power 1 is that same number, so we have;

2 × 10

2 x 10^1 = 2 × 10

2 × 10  = 20

Thus, we have the expression to be written as 2 × 10 =  2 x 10^ 1  = 20

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The expression is f(y) = 80y.

We have a school canteen.

We have to write down an expression for the cost in pence of y cups of tea.

A function in mathematics is a relation involving two variables, such that one variable is dependent on the other for its value.

According to the question -

Number of cups of tea = y

Cost of one cup = 80 pence.

Therefore, the function representing the cost in pence of y cups of tea =

f(y) = 80y

Hence, the expression is 80y.

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Person B recovers their investment in a shorter amount of time.

In order to determine the recovery time, divide the total cost of college by the salary that is earned after graduating from college.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

Recovery time = cost of college / salary after college

Recovery time for person A  = $45,000 / $33,000 = 1.36

Recovery time for person B  = $30,000 / $37,000 = 0.81

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Line m passes through the point value of k is -1/3.

Now let us find the slope of the equation using the slope equation of line:

y = mx + b,

From the given slope let’s find y,

y-7= -3/2(x+4)

y-7= -3/2x - 6

y= -3/2x + 1

=-1 / (-3/2)

=2/3

As these two lines are perpendicular the product of the slopes is -1.

m= 2/3 , y=-1

Line m is given as  y=2/3 x +b

As the line m passes through the points

(-1, 4) and (5, k)

X=4,

To find b

-1 = 2/3 * 4+b

-1=8/3+b

b=-11/3

By substituting all the values in the formula we get value of k,

Line m : y=2/3*-11/3

When x=5

k=y=2/3*5-11/3

=10/3-11/3

=-1/3

K = -1/3

A perpendicular is a straight line that makes an angle of 90° with any other line. 90° is also known as a right angle and is marked through a little square among two perpendicular lines.

Hence, the value of k is -1/3. The two lines intersect at a right angle, and hence, are stated to be perpendicular to each other.

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Answer: k=8

Step-by-step explanation:

To find the value of k in the equation y-7=-3/2(x+4), we need to determine the slope of the line given by this equation.  

First, let's rewrite the equation in slope-intercept form (y = mx + b),

where m is the slope and b is the y-intercept:  

y - 7 = -3/2(x + 4) y - 7 = -3/2x - 6 y = -3/2x - 6 + 7 y = -3/2x + 1  

Comparing this equation with the general slope-intercept form, we can see that the slope (m) is -3/2.  

Since the line y - 7 = -3/2(x + 4) is perpendicular to line m, we know that the slopes of the two lines are negative reciprocals of each other.  

The negative reciprocal of -3/2 is 2/3.  

Therefore, the slope of line m is 2/3.

We know that line m passes through the points (-1, 4) and (5, k). Using the slope-intercept form, we can write the equation of line m as:

y = 2/3x + b  Substituting the coordinates (-1, 4) into the equation,

we can solve for the y-intercept (b):  4 = 2/3(-1) + b 4 = -2/3 + b 4 + 2/3 = b 12/3 + 2/3 = b 14/3 = b  Therefore, the equation of line m is:  y = 2/3x + 14/3  Substituting the x-coordinate 5 and solving for k:  k = 2/3(5) + 14/3 k = 10/3 + 14/3 k = 24/3 k = 8  Hence, the value of k is 8.

The Harmonic Mean for the length of strings 3/4 and 3/5 is 2/3 .

Harmonic mean for 2 numbers "a" and "b" is denoted by

[tex]HM=\frac{2}{\frac{1}{a} +\frac{1}{b} }[/tex].

In the given question ;

Given that ;

the length of the first string is 3/4

Length of the second string is  3/5.

Substituting the values in the formula of harmonic mean

we get,

HM=[tex]\frac{2}{\frac{1}{\frac{3}{4} }+\frac{1}{\frac{3}{5} } }[/tex]

[tex]=\frac{2}{\frac{4}{3} +\frac{5}{3} }[/tex]

Taking LCM of denominator as 3 and solving further we get ;

[tex]=\frac{2}{\frac{5+4}{3} }\\ \\ =\frac{2}{\frac{9}{3} }[/tex]

Rewriting the complex fraction

=2*(3/9)

=6/9

On further simplifying we get ;

=2/3

Therefore , the Harmonic Mean for the length of strings 3/4 and 3/5 is 2/3 .

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The sum of the polynomials is [tex]\bold{4.5t^3 + 12.3t^2-132t+24}[/tex].

Given polynomials are:

[tex]1.3t^3+t^2-42t+8\\ 1.3t^3+t^2-6t+8 \\1.9t^3+8.4t^2-42t \\1.9t^2-42t+8[/tex]

To find the sum of the polynomials, add the coefficients of the terms of same degree in each polynomials. That is add the terms containing [tex]t^3[/tex] , then terms of [tex]t^2[/tex], then terms of t and finally the constant terms of the polynomials.

So we get, [tex](1.3t^3+t^2-42t+8)+(1.3t^3+t^2-6t+8 )+(1.9t^3+8.4t^2-42t )+(1.9t^2-42t+8)\\ = (1.3+1.3+1.9)t^3+(1+1+8.4+1.9)t^2+(-42-6-42-42)t+(8+8+8)\\=\bold{4.5t^3 + 12.3t^2-132t+24}[/tex]

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Answer:

in image

Step-by-step explanation:

The total asset is $4750

The worth of the car is valued at the worth of  has $4000 and you he have a baseball card collection valued at $750.

The capital is also know as the equity which means the net worth.

Liabilities are everything a business owes, now and in the future.

Assets are everything a business owns. Assets may be current or fixed assets

Therefore,

Total Assets - Total Liabilities = Capital

Where

Base ball card collection = $750

Total assets = ?

Capital = $4000

Hence,

Total Assets  =  $4000 + $750

Total Assets  = $4750

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Answer:

Step-by-step explanation:

=the highest common factor is [tex]3b^{3}[/tex]

therefore you can divide each and every term of the expression and take it out of the brackets.

[tex]=3b^{3} (3+8)\\=3bx^{3} (11)[/tex]

Although I still see no use of factorising because there are only like times that is what I put on table. Please ask if you have questions

The mean of the probability distribution is 21.35 and the variance of the probability distribution is 51.3275

Given the probability distribution with values of x and corresponding P(x). We need to find the values of [tex]x^2[/tex], x P(x), [tex]x^2[/tex] P(x) to calculate mean and variance.

x       P(x)          [tex]x^2[/tex]      x P(x)      [tex]x^2[/tex] P(x)

7       0.10         49       0.7         4.9

14     0.20        196      2.8         39.2

21     0.25         441     5.25       110.25

28     0.45        784     12.6       352.8

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

∑x P(x) = 21.35

∑[tex]x^2[/tex] P(x) = 507.15

Mean = ∑x P(x) = 21.35

and variance = ∑[tex]x^2[/tex] P(x) - [tex](\sum x\ P(x) )^2[/tex] = 507.15 - 455.8225 = 51.3275

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The required number of combinations is 24.

Given that,
To make an outcome tree to show all possible combinations. you have three pairs of shorts four shirts, flip-flops, and sneakers.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,

                                       flip flops                  
         short 1                    short 2                    short 3
Shirt 1                shirt 2                      shirts 3                  shirts 4
Number of combinations = 12
                                         
                                       sneakers
         short 1                    short 2                    short 3
Shirt 1                shirt 2                      shirts 3                  shirts 4
Number of combinations = 12

Total number of combination = 12 + 12 = 24

Thus, the required number of combinations is 24.

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Answer:

3.36

Step-by-step explanation:

→ How much is a dozen

12

→ Multiply by 14

168

→ Divide by 50

168 ÷ 50 = 3.36

The domain, range and  x-intercept of the given function are (-∞,∞), (-∞,∞) and (1,0) respectively.

Given the function in the question;

g(x) = −4x + 4

The domain of the expression is all real numbers except where the expression is undefined.

For -4x + 4, there is no real numbers that makes the expression undefined.

Hence, domain is (-∞,∞).

Also, the range is the set of all valid y-values.

The range is (-∞,∞).

For the x-intercept, substitute 0 in place of y or g(x) in the given function and solve for x.

g(x) = −4x + 4

0 = −4x + 4

4x = 4

x = 4/4

x = 1

Hence, the x-intercept in point form is (1,0)

Therefore, the domain, range and  x-intercept of the given function are (-∞,∞), (-∞,∞) and (1,0) respectively.

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The force on one of the ends due to hydrostatic pressure is 332.8lb.

How is a hydrostatic pressure produced?

The force on one of the ends due to hydrostatic pressure is 332.8lb

Data;

Density = 62.4 lb/ft^3

length = 4ft

radius = 2ft

Force Due to Pressure

The force due to hydrostatic pressure can be calculated as

From the attached diagram

F = Pressure * area

density = 62.4 lb/ft³

depth of water = 2- y

pressure  = ( 2- y ) ( 62.4)

                = 124.8 - 62.4

We can proceed as

x² + ( y - 2)² = 2²

x² = 4 - ( y - 2)²

x = ± √4y - y²

this implies that

2x = 2 √4y - y²

The area is given as

δA = ( 2x) * δy

δA = 2√4y - y² δy

The force would be given by

δF = ( 2- y ) ( 62.4) (2 √ 4y - y²)δy

The total force is given by

F = [tex]\int\limits^2_0 {( 2 - y)} \, (62.4) ( 2\sqrt{4y - y^{2} } dy[/tex]

F = 124.8 [tex]\int\limits^2_0 {( 2-y)} \,( \sqrt{4y - y^{2} } dy[/tex]

F = 124.8 [tex][ -\frac{1}{3} y( y- 4 ) ( \sqrt{4y - y^{2} }[/tex]

F = 124.8 [tex][ -\frac{1}{3} (2) ( 2-4) \sqrt{4(2) - 2^{2} }[/tex]

F = 332.8lb

The force on one of the ends due to hydrostatic pressure is 332.8lb

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The distance between pair of parallel lines with the  following equation

y=2x+3 y=2x-7 [tex]2{\sqrt 5}[/tex] units

​

Parallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.

The fundamental characteristics listed below make it simple to recognize parallel lines.

The slope of a line which is perpendicular to both the lines will be [tex]-\frac{1}{2}[/tex].

Check what are the y-intercept of any one of the two lines & write the equation of the perpendicular line through it.

The y-intercept of line y = 2x-7 is (0, -7).

So, the equation of any line with slope [tex]-\frac{1}{2}[/tex] and a y-intercept of −7 is

y = [tex]-\frac{1}{2}x-7[/tex]

The perpendicular intersects or meets the line y = 2x -7 at (0,-7).

Now, to find the point of intersection of the perpendicular & the other line, solve the two equations.

Solve for x:

                    2x + 3 =    [tex]-\frac{1}{2}x-7[/tex]

                          [tex]\frac{5}{2} x[/tex] = -10                                        (combine them like terms)

                            x = -4                                         (multiply each side by 2\5)              

Find y:

               y = [tex]-\frac{1}{2}.(-4)-7[/tex]

                  = -5

so, the point is (-4,-5).

Now using the Distance Formula, find the distance between the points (-4,-5) and (0,−7).

​

[tex]{\displaystyle d={\sqrt {\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}}[/tex]

  [tex]={\sqrt {\left(0-(-4\right)^{2}+\left(-7-(-5\right))^{2}}}[/tex]

  [tex]={\sqrt {4^2 +(-2)^2}}[/tex]

  [tex]=2{\sqrt 5}[/tex]

​

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​

The value in the missing place is 10 after plugging the value of F = 0.833; the answer is 10.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

0.83 = F

0.83 is a repeating decimal

Multiply by 10 on both sides:

10x0.83 = Fx10

8.33 = ? F

Plug F = 0.833

8.33 = ? (0.833)

? = 0.833/0.833

? = 10

8.33 = (10) F

Thus, the value in the missing place is 10 after plugging the value of F = 0.833; the answer is 10.

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Answer:2.5

Step-by-step explanation:

5/2=2.5

LM is the perpendicular bisector, median, and altitude of Δ JKL.

Since Δ JLM ≅ ΔKLM, we can prove JM ≅ MK and [tex]\angle[/tex] LMJ ≅ [tex]\angle[/tex] LMK. Since [tex]\angle[/tex] LMJ ≅ [tex]\angle[/tex] LMK and they are a linear pair, then we know they are right angles and LM ⊥ JK.

CPCTC is an abbreviation for "corresponding parts of congruent triangles are congruent," and it states that if two or more triangles are congruent, their corresponding angles and sides are also congruent.

CPCTC is frequently used at or near the end of a proof in which the student is asked to demonstrate that two angles or two sides are congruent. It means that if two triangles are proven to be congruent, the three pairs of sides that correspond must also be congruent, as must the three pairs of angles that correspond.

Since Δ JLM ≅ ΔKLM, we can prove JM ≅ MK and [tex]\angle[/tex] LMJ ≅ [tex]\angle[/tex] LMK. Since [tex]\angle[/tex] LMJ ≅ [tex]\angle[/tex] LMK and they are a linear pair, then we know they are right angles and LM ⊥ JK.

Therefore, we know that JM ≅ MK by CPCTC, making M the midpoint of JK. Therefore, LM is the perpendicular bisector, median, and altitude of ΔJKL.

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Answer:

The recipe with 14 cups of tomatoes requires more tomatoes. This is because it needs 10 cups more of tomatoes than the recipe with 4 cups.

The sequence can be expressed by the formula: v(n) = 5000 . (3/4)ⁿ⁻¹. Helium left at the start of the 10th day is 375.42 cm³

1st day:

Helium is filled with 5000 cm³ of helium.

We can write v(1) = 5000 cm³

2nd day:

The balloon losses 1/4 of helium volume. In other word, the remaining volume of helium is:

(1 - 1/4) = 3/4 of its initial volume.

We can write:

v(2) = 3/4 . 5000 = 3750  cm³

We can continue this process:

v(3) = 3/4 . 3750 = 2812.5

Notice that each day remaining volume of helium forms a geometric sequence, with v(1) = 5000 and a common ratio (r) = 3/4.

Recall the formula for the nth term of a geometric sequence:

v(n) = v(1) . rⁿ⁻¹

To find the explicit formula, substitute v(1) = 5000 and (r) = 3/4:

v(n) = 5000 . (3/4)ⁿ⁻¹

Tenth day means n = 10. Substitute these parameters into the formula:

v(10) = 5000 . (3/4)¹⁰⁻¹

v(10) = 5000 . (3/4)⁹

        = 375.42 cm³

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The eighth term of the given geometric sequence is:  [tex]\frac{3}{2048}[/tex]

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: 24, -6, 3/2, ...

Here, [tex]\frac{-6}{24}=\frac{\frac{3}{2}}{-6} = \frac{1}{-4}[/tex]

Thus, for the given geometric progression, a₁ = 24, and r = -1/ 4.

The nth term of a geometric progression is given by: [tex]a_n=a_1(r^{n-1})[/tex]

For n = 8, a₈ = 24 ( -1/4) ⁷

=> a₈ = [tex]\frac{6}{(-4)^6} = \frac{6}{64\times64}[/tex] = [tex]\frac{3}{2048}[/tex]

Hence, The eighth term of the given geometric sequence is:  [tex]\frac{3}{2048}[/tex].

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The model for the total number of people in the US Labor force is T = -0.0054t² + 0.087t + 13.559 .

In the given question

the number of men "M" in the US labor force is modelled by the equation ,

M = 0.0016t² + 0.315t + 19.467   ...(i)

and

the number of women "W" in the US labor force is modelled by the equation ,

W= 0.007t² - 0.228t + 5.908   ...(ii)

Let "T" denoted the model for total number of people in the US Labor force.

The total number of people in the US Labor force = Number of Men + Number of Women in US Labor force.

Adding equation (i) and (ii) we get ,

T = (0.0016t² + 0.315t + 19.467) + (0.007t² - 0.228t + 5.908)

Adding the like terms we get ,

T = (0.0016-0.007)t² + (0.315-0.228)t + (19.467-5.908)

T = -0.0054t² + 0.087t + 13.559

Therefore , the total number of people in the US Labor force is modeled by the equation T = -0.0054t² + 0.087t + 13.559  .

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Answer:

kribble

Step-by-step explanation:

Answer: rftyguhjiomnbvfdswertyio

Step-by-step explanation:

pyploliguatd

The total number of penalty kicks is 9+ 2y where the penalties made is x and the penalties missed is y

The given parameters are:

Leroy made 9 more penalty kicks than he missed

Represent the penalties made with x and the penalties missed with y

So, we have

x = 9 + y

The total number of penalty kicks is then calculated as

Total = x + y

This gives

Total = 9 + y + y

Evaluate

Total = 9+ 2y

Hence, the total number of penalty kicks is 9+ 2y where the penalties made is x and the penalties missed is y

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The width of the lake on the scale drawing is 30 cm.

Based on the given conditions, formulate 1500*2/100

Cross out the common factor: 15*2 = 30

Get the result as 30 cm

An object is enlarged in a scale drawing. An expansion increases or decreases the size of an object by multiplying each of its lengths by a scale factor. Typically, a ratio is used to describe the scale of a drawing. a representation of a real thing with correct sizes that have been scaled back or blown up slightly (called the scale). The scale is represented by the length in the drawing, a colon (":"), and then the actual length that corresponds to it.

Hence, the width of the lake on the scale drawing is 30 cm.

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