Given that log 2 = a and log 3 = b, express the following in terms of a and b:
a) log 72

The value of the scalars a = 3 , and b = -1  .

In the question ,

it is given that

u = (1, −1, 3, 5) and v = (2, 1, 0, −3)

and the equation au + bv = (1, −4, 9, 18)

Substituting the first value of u that is u=1 and substituting the first value of v that is v=2 ,

we get a+2b=1     ....(i)

Now , Substituting the second value of u that is u= -1 and substituting the second value of v that is v=1 ,

we get -a+b= -4      ...(ii)

Solving the equations (i) and (ii)

Adding both the equations we get

a-a+2b+b=1-4

3b= -3

b= -1

a+2b=1

put b= -1

a+2(-1)=1

a-2=1

a=3.

Therefore , the value of the scalars a = 3 , and b = -1  .

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Climate change is altering the approach to sustainability and sustainable development as a result in the disruption of the economy of the countries which are affected.

This is referred to as the long-term shifts in temperatures and weather patterns and are influenced by factors such as greenhouse gas emissions, solar cycle etc which affects the different factors.

Climate change will make people become poor due to the unfavorable working environment being it causes and therefore brings about a disruption in the economy as there will be a shift in focus which makes it the correct choice.

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Answer:

9812.29

Step-by-step explanation:

Using the compound interest formula,

[tex]8500 \left(1+\frac{0.024}{4} \right)^{(6)(4)} \approx 9812.29[/tex]

Based on the calculations using the given points, the slope in this situation is equal to 5.

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

Slope = (30 - 10)/6 - 2)

Slope = 20/4

Slope = 5.

In conclusion, the slope of the line that passes through the given points is equal to 5.

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The volume of house built by David for cat is 64 ft³.

Firstly representing the mentioned statement about volume as mathematical expression. Exponent is the power of variable or constant. So, volume = x³, where x is the edge length.

As the edge length of house of car is given, we will keep the value in formula to find the volume of house.

V = 4³

Taking cube of the value on Right Hand Side of the equation

V = 4×4×4

Performing multiplication on Right Hand Side of the equation

V = 64 ft³

Thus, the volume of the house of cat is 64 ft³.

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Question 1

Using scientific notation, we know a=2, b=4, c=1, and d=3. So,

[tex]\frac{a}{2}+\frac{b}{4}+\frac{c}{8}+\frac{d}{16}=1+1+\frac{1}{8}+\frac{3}{16}=37/16[/tex]

Question 2

[tex]a+13b=3(3a-b)\\\\a+13b=9a-3b\\\\16b=8a\\\\a=2b\\\\\therefore \frac{a^3}{b^3}=\frac{(2b)^3}{b^3}=\frac{8b^3}{b^3}=8[/tex]

optionsWe want to obtain an expression equivalent to 8 using these symbols and numbers.

The option that exactly matches this is,

That is because,

7 divided by 7 is 1.

1 squared is still one, and;

1 added to 7 is 8.

So one answer is option D.

We also have another answer.

Which is;

That's because 7 squared is 49, and 7 + 49 is 56.

56 divided by 7 is 8.

So our answers are option C and option D

Answer:

acxdddhdhxhhh sax skskskkkkkddffffffrrkel sssddjeeeeerrjrrjtjjj

Answer:

74.52

Step-by-step explanation:

[tex]P(10)=0.018(10)^3-0.294(10)^2+3.074(10)+55.180 \\ \\ =74.52[/tex]

Bring the variable to the left and the remaining values to the right to define the value of x. If m/8 = 86° and m/4 = (4x + 2)° then value of  x = 21.

Any of the algebraic expressions, including addition, subtraction, multiplication, and division, should be used. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.

Let the m/8 = 86° and m/4 = (4x + 2)°

m ∠4 = m ∠8 (Corresponding angles are equal)

To estimate the value of x

4x + 2 = 86

Substracting both sides of the equation by 2, we get

4x + 2 - 2 = 86 - 2

simplifying the above equation,

4x = 86 - 2

4x = 84

Dividing both sides of the equation by 4, we get

4x / 4 = 84 / 4

x = 21

Therefore, the value of x = 21.

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Answer: The function g because the graphs of f and g are symmetrical about the line y=x.

Answer:

A. The function g because the graphs of f and g are symmetrical about the line y=x.

Step-by-step explanation:

Answer:

0.00908 is the answer...

Given:

To graph the given polynomial function, we can plug in any values of x to find values of h(x). The graph is shown below:

We also note that the x-intercept is the point on the x-axis, while the y-intercept is the point on the y-axis. Hence,

x-intercepts: (1,0), (-2,0)

y-intercept: (0,-4)

Tt can also be noted that (x − 1) occurs 3 times while (x+2) occurs 2 times. Hence, x=1 has a multiplicity 3, while x=-2 has a multiplicity 2.

aased on the graph, the end behavior would be:

Solution

Given

The standard form of the straight line is given by 5y - 2x = 20 .

Ax + By = C is the standard form for two-variable linear equations.

We know that when a straight line passes through (a,b) with slope m then the equation of the line is given by:

y - b = m ( x - a )

putting the values in the respective places we get:

y - 2 = 2/5 × ( x + 5 )

or, 5y - 10 = 2x + 10

or , 5y - 2x = 20

Hence the standard form of the straight line is given by

5y - 2x = 20 .

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Your best option is to simply choose six distinct numbers, in any sequence. You would win if those six numbers matched the six that the lottery officials chose (again, in any sequence).

The likelihood of selecting the correct six numbers is one in

[tex]\frac{23}{6}[/tex] = [tex]\frac{23}{6(23-6)}[/tex] = [tex]\frac{23.22.21.20.19.18}{1.2.3.4.5.6}[/tex] = 100974

Therefore, 100946/100947, or a probability of losing, is very near to 1.

The total of your payouts multiplied by the probability that each scenario will occur is the anticipated value of the game. which is

(50,000) [tex]\frac{1}{100947}[/tex] + (-1) [tex]\frac{100946}{100947}[/tex] = [tex]\frac{50000-100946}{100947}[/tex] = -0.5046

You will typically break even if its value is 0. You should play the game if it is more than zero because you will typically win, and you shouldn't play it if it is less than zero because you will typically lose. The payoff is decently substantial for this, however the typical player loses just over 70 cents per round. Almost every player loses a complete dollar.

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Answer:

distribute the 4 to the k and -15 so you get 4=4k-60 then add the 60 to the other 4 so its 64=4k then divide 4 to 64 and your answer is 16

Step-by-step explanation:

[tex]4=4k-60\\4k-60=4\\4k=4+60\\4k=64\\\frac{4k}{4} =\frac{64}{4} \\k=16[/tex]

As solved above k=16

Answer: [tex]f(-4)=-19, g(3)=-29[/tex]

Step-by-step explanation:

[tex]f(-4)=4(-4)-3=-19\\\\g(3)=-3(3)^2 -2=-29[/tex]

Answer:

Step-by-step explanation:

59+ 43.6

43.6=44.0

59+44

59+43.6

=103.0

Equation is 5y = 3x + 8.

Slope is the inclination of a line with respect to the horizontal is measured numerically. The slope of any line, ray, or line segment in analytical geometry is defined as the ratio of the vertical to the horizontal distance between any two points on the line, ray, or segment. The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.

Given Data

line that passes through the point (1, -1) &

is parallel to the graph of y = 3/5x + 2

y = mx + c

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

m = [tex]\frac{3}{5}[/tex]

Equating points,

-1 = [tex]\frac{3}{5}[/tex](1) + c

-1 = [tex]\frac{3}{5}[/tex] + c

-1 - [tex]\frac{3}{5}[/tex] = c

[tex]\frac{-5-3}{5}[/tex] = c

[tex]\frac{-8}{5}[/tex]

Equation-

y = [tex]\frac{3}{5}[/tex]x + [tex]\frac{8}{5}[/tex]

5y = 3x + 8

Equation is 5y = 3x + 8.

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The effective annual yield if the interest is compounded daily is 10.5155 %.

The annual interest rate or rate of return that an investor is entitled to over a particular time period is known as effective annual yield.

​In the case of daily, there are 360 days in a year.

Therefore, making n = 360.

Therefore, the effective annual yield if the interest of 10% is compounded daily when r = 10 % and n = 360 will be:

Y = ( 1 + r/n )ⁿ - 1

Y = ( 1 + 0.1 / 360 )³⁶⁰ - 1

Y = ( 1 + 0.000277 )³⁶⁰ - 1

y = 1.105155 - 1

Y = 0.105155

However, since it is in decimal form, we must first multiply it by 100 before adding the symbol "%" after the last digit of the value.

Therefore,

Y = 0.105155 × 100%

Y = 10.5155 %

Therefore, the effective Annual Yield is 10.5155 %

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A numeral exists a sign, combination of symbols, or figure that represents a number.

142 in base 5 means [tex]$1\left(5^2\right)+4\left(5^1\right)+2\left(5^0\right)[/tex] = 25 + 20 + 2 = 47

11011 in base 2 means [tex]$1\left(2^4\right)+1\left(2^3\right)+0\left(2^2\right)+1\left(2^1\right)+1\left(2^0\right)[/tex]= 27π

39 T in base 12 means [tex]$3\left(12^2\right)+9\left(12^1\right)+10\left(12^0\right)[/tex] = 550

A numeral is a sign, combination of symbols, or figure that represents a number. It can be a mathematical numbering system.

A numeral's value is determined by the number it represents. All modern numbers cannot be represented by all number systems; Roman numerals, for instance, do not have a zero. A numeral system should, in theory, be able to: Represent a useful set of numbers (e.g. all integers, or rational numbers).

The correct answer is as follows:

142 in base 5 means [tex]$1\left(5^2\right)+4\left(5^1\right)+2\left(5^0\right)[/tex] = 25 + 20 + 2 = 47

11011 in base 2 means [tex]$1\left(2^4\right)+1\left(2^3\right)+0\left(2^2\right)+1\left(2^1\right)+1\left(2^0\right)[/tex]= 27π

39 T in base 12 means [tex]$3\left(12^2\right)+9\left(12^1\right)+10\left(12^0\right)[/tex] = 550

The complete question is:

Write each of the following numerals in base 10. For base​ twelve, T and E represent the face values ten and​ eleven, respectively.

Write each of the following numerals in base 10. For base​ twelve, T and E represent the face values ten and​eleven, respectively.

a. 142five

b. 11011two

c. 39Ttwelth

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In the given triangle we have :

Base line with angle A, and the Hypotenuse of angle A

Since the ratio of Base to the hypotenuse is the Cosine trignometric ratio:

Answer : Cosine

Probability of randomly selecting two members who currently hold positions of chairman and ranking member and reassigning them to their current positions from a committee of 14 members is (1 /182).

As given,

Total members in the committee=14

Number of members serve as chairman and ranking member=2

Total number of ways to assigned new position

=¹⁴P₂

=(14!) / (14-2)!

=(14 × 13 × 12!) / 12!

=14 ×13

=182

Each member is equally likely to serve in any of positions.

Each position there is only one way to reassign position.

Probability of randomly selecting two members = 1 /182

Therefore, probability of randomly selecting two members who currently hold positions of chairman and ranking member and reassigning them to their current positions from a committee of 14 members is (1 /182).

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Answer:420

Step-by-step explanation: multiply 300 times 4% =12. Then multiply 12 times 10=120. Then add 300 and 120=420

Answer:

  987

Step-by-step explanation:

You want to determine a three-digit combination based on clues about which digits are right and/or correctly placed.

This tells you one of digits 1, 2, or 7 is correct and correctly placed.

Clue 2 tells you that digit is not 1. Clue 4 tells you that digit is not 2.

  7 is correctly placed as the 3rd digit

We already know that 1 is not the correct digit. This means 3 must be the first digit, or 8 must be the first or second digit.

We already know that 7 is a correct digit, properly placed as the 3rd digit. Since 1 is not a correct digit, 9 must be a correct digit, properly placed as the 1st digit.

  9 is correctly placed as the 1st digit

Combining this fact with Clue 2 means ...

  8 is correctly placed as the 2nd digit

The combination is 987.

__

Check

Clues 4 and 5 are consistent with this combination.

The given graph shown in the image is a function, Option b is correct.

Given that,
A graph is shown, and we have to determine whether the graph shown is a function or not.

The function which is in format f(x) =a^x  where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

here,
The graph shows of a curve representing an exponential function,

There is why the graph shown is a function, and also the graph is continuous and as well as differentiable.

Thus, the given graph shown in the image is a function, Option b is correct.

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[tex]\sin^2 x=1-\cos^2 x \\ \\ \cos^2 x=1-\sin^2 x[/tex]