8.5 x 10[2] my assignment is about exponents

Given:

The trigonometric function is given as,

The objective is to simplify the expression.

Explanation:

The given expression can be written as,

Now, consider the algebraic identity,

Then, the equation (1) can be written using the algebraic identity as,

Consider the Pythagorean identity,

Then, equation (2) can be written as,

Hence, the simplified expression is sec²x + tan²x.

Using simultaneous equation, the solution to the system of linear equations are 1223 $10 tickets, 1332 $20 tickets, and 763 $30 tickets were sold.

Let's solve the problem step by step.

Let:

x = number of $10 tickets sold

y = number of $20 tickets sold

z = number of $30 tickets sold

From the given information, we can form the following equations:

Equation 1: x + y + z = 3318 (Total number of tickets sold)

Equation 2: y = x + 109 (109 more $20 tickets than $10 tickets were sold)

Equation 3: 10x + 20y + 30z = 61760 (Total sales from ticket sales)

We can use these three equations to solve for the values of x, y, and z.

First, let's substitute Equation 2 into Equation 1:

x + (x + 109) + z = 3318

2x + 109 + z = 3318

2x + z = 3209 (Equation 4)

Now, let's substitute the value of y from Equation 2 into Equation 3:

10x + 20(x + 109) + 30z = 61760

10x + 20x + 2180 + 30z = 61760

30x + 30z = 59580

x + z = 1986 (Equation 5)

We now have a system of equations (Equations 4 and 5) with two variables (x and z). We can solve this system to find the values of x and z.

Multiplying Equation 4 by 30, and Equation 5 by 2, we get:

60x + 30z = 96270 (Equation 6)

2x + 2z = 3972 (Equation 7)

Now, subtract Equation 7 from Equation 6:

(60x + 30z) - (2x + 2z) = 96270 - 3972

58x + 28z = 92298

Simplifying, we have:

29x + 14z = 46149 (Equation 8)

Now, we can solve Equations 5 and 8 simultaneously:

x + z = 1986 (Equation 5)

29x + 14z = 46149 (Equation 8)

Multiplying Equation 5 by 14, and Equation 8 by 1, we get:

14x + 14z = 27804 (Equation 9)

29x + 14z = 46149 (Equation 8)

Now, subtract Equation 9 from Equation 8:

(29x + 14z) - (14x + 14z) = 46149 - 27804

15x = 18345

Divide both sides of the equation by 15:

x = 18345 / 15

x = 1223

Substituting the value of x into Equation 5, we can find z:

1223 + z = 1986

z = 1986 - 1223

z = 763

Now that we have the values of x and z, we can substitute them back into Equation 1 to find y:

1223 + y + 763 = 3318

y + 1986 = 3318

y = 3318 - 1986

y = 1332

Therefore, the solution to the problem is:

x = 1223 (number of $10 tickets sold)

y = 1332 (number of $20 tickets sold)

z = 763 (number of $30 tickets sold)

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Answer:

87% decrease (rounded to nearest whole percent)  

Step-by-step explanation:

Change = 360,000 - 46,000

              = 314,000

Percent of change = \(\frac{314,000}{360,000}\) × 100%

                               = 87% (rounded to nearest whole percent)

Answer:

y = 5

Step-by-step explanation:

The angle formed is a right angle which has a measure of 90 degrees. This means that the sum of the two angles is 90 degrees. Using this information we can set up an equation and solve for y

Set up equation

7y + 8 + 8y + 7 = 90

==> combine like terms

15y + 15 = 90

==> subtract 15 from both sides

15y = 75

==> divide both sides by 15

y = 5

A linear function is defined as y = mx + b, in which m is the slope and b is the y-intercept.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

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Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)

Simplifying the equation:

\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)

\(\qquad\quad\implies 0.1x = 21\)

\(\qquad\qquad\implies \bold{x = 210}\)

\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Answer:

Step-by-step explanation:

Typically yes you need to know

Mean

Median

Mode

and Range

Mean = average, add all numbers then divide by how many

Median = midpoint, middle number.  Be sure to list numbers from small to large if there are 2 middle numbers (this happens when there are an even amount), take the average of the 2 middle numbers

Mode = numbers that occurs the most in the list of numbers

Range = This is the largest number minus the smallest number.  

We are given the following function:

If we want to stretch a graph vertical we must multiply the function by the factor we want to stretch it:

Therefore, if we want to stretch the given function by a factor of 4 we must multiply the given function by 4:

To shrink the function horizontally we must do the following change:

Therefore, the new function must be:

Simplifying we get:

Now, we graph both functions. We get:

The blue graph represents the original function, and the green graph represent the modified function

Answer:

8x(4) = 64

8x = 16

h = 2 inches

The number that will go in between 0.438 and 44% in the thousandth place is 9 and the number is

This is found by converting all the given number to decimal

0.438

the thousandth place has number 8

44% = 0.440

The thousandth place has number 0

4/9 = 0.44444

this is greater than the two numbers and hence cannot go in between them

9/20 = 0.45

this is greater than the two numbers and hence cannot go in between them

checking the two numbers 0.438 and 0.440 the number that can go in between them is 0.439

9 in thousandth place is 0.009

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a. the amount of liquid in the tank:  5580 liters

b. The amount of liquid should be added  to fill the tank 100% capacity : 450 liters

We have been given a right circular conical tank.

h = 4 m and r = 1.20 m

We know that the formula for the volume of cone is,

V = πr²h/3

The volume of the tank would be,

V = (π × r² × h)/3

V = (π × 1.20² × 4)/3

V = 18.09/3

V = 6.03 m³

Let h1 be the height of liquid level in the tank and  V1 be the volume of the liquid in the tank.

h1 = 3.70 m

V1 = (π × r² × h1)/3

V1 = (π × 1.20² × 3.70)/3

V1 = 16.74 / 3

V1 = 5.58 m³

V1 = 5580 liters

The amount of liquid need to added to fill the tank 100% of capacity.

V2 = V - V1

V2 = 6.03 m³ - 5.58 m³

V2 = 0.45 m³

V2 = 450 liters

Therefore, a. the amount of liquid in the tank:  5580 liters

b. The amount of liquid should be added  to fill the tank 100% capacity : 450 liters

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Answer: i= -6

Step-by-step explanation:

first, you want to separate the constants(Normal numbers that do NOT have i or a letter attached to them, in this case the 3 and the 8) from the -2i. To do this, you have to combine like terms first

3+8=11

Now you must subtract 11 from both sides of the equation,

11-11=0

23-11=12

you should be left with just -2i on one side, and 12 on the other side.

You now want i (the variable) by itself, so divide by the number attached to it (in this case, -2) do this for both sides.

-2i/-2= i

12/-2=-6

you are now left with your variable (i) equaling -6

The value of m + n is given as follows:

A. 18.

The exponential expression for this problem is defined as follows:

\((x^5y^6)^{\frac{1}{5}}(x^3y^4}^{\frac{1}{4}}\)

Applying the power of power rule, we have that the exponents are given as follows:

Then the values of m and n are given as follows:

m = 7, n = 11.

Thus the sum is given as follows:

m + n = 7 + 11 = 18.

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The solution by substituting 15 for b in the Original equation. The answer is true.

The steps needed to solve the equation b + 6 = 21 are:

Subtract 6 from both sides of the equation: b + 6 - 6 = 21 - 6, which simplifies to b = 15.

Check the solution by substituting 15 for b in the original equation: 15 + 6 = 21, which is true.

Therefore, the correct steps to solve the equation are:

Subtract 6 from both sides of the equation. The answer is b = 15

the solution by substituting 15 for b in the original equation. The answer is true.

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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B. box and whisker plot

A boxplot—sometimes called a box and whisker plot—is a dense display that aims to provide lots of context for any given dataset. The chart visually represents several summary metrics in a single view: minimum: the smallest value maximum: the largest value

Ann made money from illegal gambling in 2019 in $2,197,890

As per the details provided in the above question are as follow,

Consider the income obtained from Extortion is x.

While the income obtained from the illegal gusting is y

Now in 2019

x + y = $3956202

\(y=x+\frac{x \times 25}{100}\\y=\frac{5}{4} x\)

Substitute the value of  \($x=\frac{4}{5} y$\) in above equation we get,

\(\frac{4}{5} y+y & =3,956,202 \\\\\frac{9}{5} y & =3956202 \\\\y & =\frac{5}{9} \times 3956202\)

y = $2197890

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The reason that justifies the second statement "Angle L is congruent to angle T" is:

In a parallelogram, opposite angles are congruent.

Option C is the correct answer.

A parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

Parallelogram LENS and parallelogram NGTH

Now,

Parallelogram LENS:

∠L = ∠N _____(1)

Opposite angles are equal.

Parallelogram NGTH:

∠N = ∠T ______(2)

Opposite angles are equal.

Now,

∠ENS = ∠GNH

Vertical angles are equal.

So,

From (1) and (2).

∠L = ∠T

Angle L is congruent to angle T

Thus,

Angle L is congruent to angle T

[ In a parallelogram, opposite angles are congruent ].

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money

shopping

dividing

Based on the information given regarding the statistics, the observational unit in the list is B. The individual games.

An observation unit is also called a statistical unit and it is the entity on which information is received and statistics are compiled when collecting statistical data.

From the given problem, the information is collected for the two teams, therefore the observational unit in the list is the individual games.

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Answer:

So in this question you want the average because both of y'all are working together. To take the average you want to multiply 2x3=6/2=3

3 hours if y'all work together!

Step-by-step explanation:

Answer:

love

salvation

Step-by-step explanation:

Answer:

Hey!

Step-by-step explanation:

If A and B are sets, then the relative complement of A in B, also termed the set difference of B and A, is the set of elements in B but not in A.

Two Angles are Supplementary when they add up to 180 degrees. These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°: Notice that together they make a straight angle.

The value of the given summation is:

\(\sum (29a_i - 13b_i) ]= -30\)

Here we know that the sums are:

\(\sum a_i = -10\\\\\sum b_i = -20\)

And we want to find the value of the sum:

\(\sum (29a_i - 13b_i)\)

First we can distribute the sum to get:

\(\sum 29a_i + \sum - 13b_i\)

And take the coefficients out of the sum:

\(29\sum a_i -13\sum b_i\)

Now replace the known values:

\(29\sum a_i -13\sum b_i = 29*-10 - 13*-20 = -290 + 260 = -30\)

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Answer:

Is this a question? A recipe? Or a challenge?

Step-by-step explanation:

Actual time is much longer than the 50-year timeframe suggested by the speaker.

How to verify the statement?

This claim is based on the assumption that the rate of pollution reduction from each factory remains constant at 80%, and the number of factories increases by 3% per annum.

To verify this claim, we can use the following formula to calculate the expected total pollution after n years:

Total pollution after n years = \(Present \: pollution \: level x (1 + 0.03)^n \times (1 - 0.8)^n\)

Here, the first factor represents the increase in pollution due to the growth in the number of factories, and the second factor represents the reduction in pollution due to the 80% reduction in pollution from each factory.

We can set the expected total pollution after n years equal to the present pollution level and solve for n:

\(Present \: pollution \: level = Present \: pollution \: level \times (1 + 0.03)^n \times (1 - 0.8)^n\)

Simplifying this equation, we get:

\(1 = 1.03^n \times 0.2^n\)

Taking the logarithm of both sides of the equation, we get,

\(n \times log(1.03) + n \times log(0.2) = 0 \\ n \times (log(1.03) + log(0.2)) = 0 \\ n = \frac{0} { (log(1.03) + log(0.2))} \\ n = 271.56\)

Therefore, according to this calculation, it would take approximately 272 years for the total annual pollution to return to its present level if the number of factories in the country increases by 3% per annum, and they all immediately reduce the amount of pollution they produce by 80%. This is much longer than the 50-year timeframe suggested by the speaker.

It is important to note that this calculation assumes that the pollution reduction from each factory remains constant at 80% and does not take into account any other factors that may affect pollution levels, such as changes in technology or regulations. Therefore, this should be considered as a rough estimate and not as an exact prediction.

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Correct question is "A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. Verify the statement. (use logarithm)"

The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :

The equation of the linear relationship in slope-intercept form is y = 2x - 8. Option A is the correct answer.

To determine the equation of the linear relationship in slope-intercept form based on the table, we need to find the slope and y-intercept.

By observing the table, we can calculate the slope by selecting any two points. Let's choose the points (0, -8) and (4, 0).

Slope (m) = (change in y) / (change in x)

= (0 - (-8)) / (4 - 0)

= 8 / 4

= 2

Now that we have the slope, we can find the y-intercept by substituting the values of one point and the slope into the equation y = mx + b and solving for b.

Using the point (0, -8):

-8 = 2(0) + b

b = -8

Therefore, the equation of the linear relationship in slope-intercept form is: y = 2x - 8. Option A is the correct answer.

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Answer:

b=12

Step-by-step explanation:

Answer:

y = -5/2x

Step-by-step explanation:

Perpendicular = opposite sign and reciprocal slope

-5/2x

y = -5/2x