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The exact value of the logarithmic expression 12 · ㏒₃ [z⁷ / (y⁵ · t²)] is equivalent by logarithm properties to -711 / 5.

In this question we must determine the exact value of a logarithmic expression by means of logarithm properties, which are described below:

Logarithm of a product

㏒ (a · b) = ㏒ a + ㏒ b

Logarithm of a division

㏒ (a / b) = ㏒ a - ㏒ b

Logarithm of a power

㏒ aⁿ = n · ㏒ a

Now we proceed to determine the exact value of the expression:

12 · ㏒₃ [z⁷ / (y⁵ · t²)]

12 · [㏒₃ z⁷ - ㏒₃ (y⁵ · t²)]

12 · (㏒₃ z⁷ - ㏒₃ y⁵ - ㏒₃ t²)

12 · (7 · ㏒₃ z - 5 · ㏒₃ y - 2 · ㏒₃ t)

12 · (7 · 7.74 - 5 · 11.03 - 2 · 5.44)

-711 / 5

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When t=2+√110/4, the ball will be 50 feet  height above the ocean.

Height is the measurement of someone or something from the top to toe or the base to head.height always refers to something is mesured either its high or low.

As per the given question

Because h=-16t^2+64t+96

So when h = 50

It means -16t^2+64t+96 =50

-16t^2+64+46=0

8t^2-32t-23=0

{∆=b^2-4ac,x= -b+√∆/2a}

So, ∆=(-32)^-4×8×(-23)=1760>0

So t =2- √110/4 <0

Thus tha answer is t = 2+√110/4

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Answer:

The width of the parking is 69 meters

Step-by-step explanation:

Rectangle area = L*W

6279 = 91*W

Widht = 6279/91

W = 69 m

The line parallel to the given line 2x+2y=-12 is also -1.

Define slope.

Slope of a line refers to the measure of the steepness and the direction of a line.

Illustrate y= m x+ c.

y = mx + c refers to an equation of a line having a gradient of m and a y-intercept of c. This equation is often referred to as the slope-intercept form of the equation of a line.

We know that,

The general equation of a line is y=m x+ c,

where m = slope and b = y-intercept, c is a constant

Now, the equation of the given line is,

2x+2y=-12

⇒x + y=-6

Now expressing the equation in the form of y=m x+ c

So, y=-6-x

Further, on rearranging we get y= (-1) x-6

                                                   y = mx + c

So, according to the equation,on comparing we get

m=-1 and c=-6

On comparing, the slope of the given line is -1.

Since, 'The slopes of two parallel line is always equal'.

Thus, the line parallel to the given line is also -1.

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Answer: 2x + 2y = -1

Step-by-step explanation:

Answer:  d/ 30x +200 <= 1400

Step-by-step explanation:

It can't be the first two answers because the truck can only hold 1400

So it must be < or = 1400

It says that she loaded computers for 200 pounds and x number of books, 30 pounds each.

So the equation is 30x + 200 <=1400

The graph for the linear equation y = -2x + 5 is plotted and shown in the image attached below.

If we are given an equation of a line that is expressed in slope-intercept form as y = mx + b, it means that the graph will have a slope = rise / run = the value of m, while it would cut across the y-axis at b, that is the y-intercept.

Given the equation in slope-intercept form as y = -2x + 5, it means that the graph will have a slope that has a ratio of the rise to the run as -2, while the line will intercept the y-axis at y = 5.

Therefore, the graph in the image attached below shows the equation, y = -2x + 5.

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Using the formula of simple interest, the time period it takes to double the principal is approximately 14.29 years

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

The formula is given as

S.I = P(1 + rt)

Substituting the values into the simple interest formula

S.I = 1000(1 + 0.07 * t)

However, we are to calculate the time it takes to double the money

2000 = 1000(1 + 0.07 * t)

2 = 1 + 0.07t

0.07t = 2 - 1

t = 1 / 0.07

t = 14.29 years

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The students that prefer science than Maths are 27

From the question, we have the following parameters that can be used in our computation:

Math = 24

Science = 33

Total proportion = 100

The additional number of students that prefer science than Maths is calculated as

Additional = (Science - Maths)/Total proportion * Number of students

So, we have

Additional = (33 - 24)/100 * 300

Evaluate

Additional = 27

Hence, the number of students is 27

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The decibel level of the noise from a motorcycle with intensity 10⁻² watts per square inch (W/in²) is equal to 50 dB.

In Science, sound intensity can be defined as a measure of the power of a sound wave per unit area. This ultimately implies that, sound intensity is a quantity that is typically be used for measuring the energy of sound and its unit of measurement is Watts per square meter (W/m²) or .

Mathematically, sound intensity level or decibel level can be calculated by using this formula:

[tex]\beta = 10 log(\frac{I}{I_{ref}} )[/tex]

Note: The reference value of sound intensity is equal to 1.0 × 10⁻¹² watts per square inch (W/in²).

Since the intensity of the noise from this motorcycle is 10⁻² W/in², the decibel level (in dB) would be calculated as follows:

Decibel level, β = 10 × log(10⁻²/10⁻¹²)

Decibel level, β = 10 × log(10¹⁰)

Decibel level, β = 10 × 10

Decibel level, β = 100 dB.

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The system of linear equations have no solution

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.

In the problem, given the system of linear equations are

y = 4/5x - 3 ...eq(i)

y = 4/5x + 1 ...eq(ii)

a) Since there are two unknown variables(x, y) the number of solutions expected is 2.

b)

From equation (i)

y = 4/5x - 3

Put eq(i) into equ(ii)

4/5x - 3 = 4/5x + 1

0 = 4

There's no solution for x and y

In the calculation, there's no solution for both x and y because the variables in both equation are equal to one another and hence cancel out.

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Answer: 60

Step-by-step explanation:

The square root of 144 is 12.

12 = x/5

You multiply 5 on BOTH sides (make sure when you do something to one side you do it to the other)

60 = x

Answer:

D) = (x - 6 )(x - 6)

Step-by-step explanation:

x^2 - 12x + 36

= x^2 -6x -6x + 36

= x(x - 6) -6(x - 6)

= (x - 6 )(x - 6)

Answer:

[tex]\boxed{\tt (x-6)(x-6)}[/tex]

Step-by-step explanation:

To factor x²−12x+36 we need to find two numbers that add together to get -12 and multiply together to get 36:-

Let's try -6 and -6:-

[tex]\tt -6+-6 = -12[/tex]

[tex]\tt -6\times -6 = 36[/tex]

[tex]\tt (x-6)(x-6)[/tex]

_________________

Hope this helps!

Have a nice day!

Answer:

1.2 minutes

Step-by-step explanation:

Kelsey moves 1/3 length per minute. The sidewalk moves 1/2 length per minute. Walking on the sidewalk, Kelsey moves (1/3+1/2) = 5/6 lengths per minute, or 6/5 minutes per length.

So  it takes Kelsey 1 1/5 minutes to walk the length on the moving sidewalk.

Answer:

3,2,4

The fastest restaurant for service is the second choice.                                                   It takes 2 minutes to service each customer.

Step-by-step explanation:

27/9 = 3 minutes per customer

8/4 = 2 minutes per customer

32/8 = 4 minutes per customer

Answer: y = 1/12x

Step-by-step explanation:

(24, 2)

(12, 1)

find slope (y2 - y1) / (x2 - x1)

2 - 1 / 24 - 12

1 / 12

find y intercept

y = mx + b

1 = 1/12(12) + b

1 = 1 + b

b = 0

y = 1/12x + 0

y = 1/12x

Answer:

58 teams

Step-by-step explanation:

This is a division problem. There are a total of 1043 players and there is a max number of 18 members per team. 1043 divided by 18 = 57 and a remainder. Because there is a remainder you add one more team for the remaining members.

Answer: 57.9

Step-by-step explanation:

Based on the given conditions, formulate: 1043 / 18

Evaluate the equation/expression: 57.9444

get the result: 57.9444

After rounding: 57.9

Answer: 57.9

The equation to model the cost 'y' based on the number of movies streamed 'x' would be 14 = 2x and 20 = 6x.

What is a linear equation in one variable?

The linear equation in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

For the first case:

If 2 movies are streamed, the cost is $14 per month

So the cost = number of movies * cost per movie

            y = 2*x

           14 = 2x

For the second case:

If 6 movies are streamed, the cost is $20 per month

So the cost = number of movies * cost per movie

            y = 6*x

           20 = 6x

Hence the equation to model the cost 'y' based on the number of movies streamed 'x' would be 14 = 2x and 20 = 6x.

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Both have a domain of [tex][0, \infty)[/tex] which in other words, is the set of nonnegative real numbers. I recommend using a graphing calculator to verify both of these functions have the same domain.

The reason for this is because we need to avoid negative numbers under the square root. So it leads us to [tex]\text{x} \ge 0[/tex]

Answer: 200384X 403 or 496 X 404

Step-by-step explanation: hope this helped

Triangles MNO and QPO are congruent.

It is given that

O is the midpoint of NP,

NP is perpendicular to MN, and

NP is perpendicular to PQ.

Therefore, Triangles MNO and QPO are congruent.

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Answer:

5/ Slope is 0

6/ Slope is 4/1

7/ Slope is -4/2 = -2

8/ Slope is undefined

Step-by-step explanation:

5/ Slope is 0 when it goes straight to the right

6/ We see that the y goes up 4, x over 1, so the slope is 4/1

7/ We see that the y goes down by 4, and x over by 2, so the slope is -2

8/ Slope is undefined when it goes straight up!

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The scale factor of the transformation is 1.5

From the question, we have the following parameters that can be used in our computation:

Point T (6,2) T’ (9,3)

Also, see attachment for the missing graph in the question

This means that

The scale factor of the transformation = T'/T

Substitute the known values in the above equation, so, we have the following representation

Scale factor = (9, 3)/(6, 2)

Evaluate

Scale factor = 1.5

Hence, the scale factor is 1.5

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The two solutions for the system of equations:

y = x^2+ 5x - 3

y - x = 2

Are:

(-5, -7) and (1, -1)

Here we have the following system of equations:

y = x^2+ 5x - 3

y - x = 2

We can replace the first equation into the second one to get:

(x^2+ 5x - 3) - x = 2

x^2 + 4x - 3 = 2

x^2 + 4x - 3 - 2 = 0

x^2 + 4x - 5  = 0

Using the quadratic formula, we will get the solutions:

[tex]x = \frac{-4 \pm \sqrt{4^2 - 4*1*-5} }{2} \\\\x = \frac{-4 \pm 6}{2}[/tex]

The two solutions are:

x = (-4 - 6)/2 = -5

x = (-4 + 6)/2 = 1

To find the values of y, we can evaluate the linear equation:

when x = -5

y - (-5) = -2

y + 5 = -2

y = -2 - 5 = -7

So one solution is (-5, -7)

when x = 1

y - 1 = -2

y = -2 + 1 = -1

The other solution is (1, -1)

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Answer:

11, 13, 17, and 19!

Step-by-step explanation:

Answer:

11, 13,17 and 19

Step-by-step explanation:

prome numbers are natural numbers that are greater than 1 and not a product of two natural numbers eg 2×5 =10 so it's not a prime number 2×6 or 3×4 =12 it's not also a prime number e.t.c

Answer: c.

Step-by-step explanation:

I used rounding: 3 is closer to 2 3/5 than 2 and 5 * 3 is 15, so the answer is about 15.

Answer:47/50

Step-by-step explanation:

47+3=50

47 adult tickets sold

47/50

The probability that a student chosen at random studies physics and chemistry or both is  35/41 = 0.85

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

The formula for probability states that the possibility of an event happening, or P(E), equals the ratio of the number of favorable outcomes to the number of total outcomes. Mathematically, it looks like this: P(E) = favorable outcomes/total outcomes.

The Venn diagram shows:

There are 2 students studying both biology and physics.

Six students study biology and chemistry together.

There are 4 students who study physics and chemistry.

There are 5 students who just study physics.

There are 7 students who just study biology.

There are 8 students who just study chemistry.

There are 6 students that study none.

As a result, there are a total of 41 students, which is equal to 2 + 6 + 4 + 5 + 7 + 8 + 3 + 6 students.

There are 21 students who study chemistry, which is equal to 8 + 6 + 3 + 4 students.

The number of students that studies physics is = 14

The number of students that studies chemistry is =  21

Probability  = number of favorable outcomes / total number of outcomes

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Using division we know that (D) 2700÷9=300 is the basic fact using which John will get t know how many seeds will be planted in a row.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.

The other operations are multiplication, addition, and subtraction.

In mathematics, the division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed.

For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

The division sign, "," or occasionally "/," is used in computer code.

So, we know that: Total seeds are 2700 and the total rows are 9

If there are the same amount of seeds in each row.

Following that, the number of seeds will be put in each row.

= (Total seeds) ÷ (Total rows)

= 2700÷9

= 300

Therefore, using division we know that (D) 2700÷9=300 is the basic fact using which John will get t know how many seeds will be planted in a row.

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Correct question:

John has 2,700 seeds of corn to plant in 9 rows on his farm. Each row will have the same number of seeds. Part A

Which basic fact can John use to find out how many seeds will be planted in each row?

A. 9÷3=3

B. 27÷9=4

C. 27÷9=3

D. 2700÷9=300

The hypothesis is A prism base that are regular polygons

Conclusion: It is a regular prism

If-then form: If a prism has bases that are regular polygons, then it is a regular prism

An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion.

As indicated, this is p → q. Read this: if p, then q. If the hypothesis is correct but the conclusion is untrue, a conditional statement is false.

The conditional statement is of two parts the hypothesis which is p and the conclusion which is q

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