Non mutually exclusive events !

The expanded form of log y^10 is either 10 log y or 10 ln y

Assuming that the base of the logarithm is not specified, we can use the change of base formula to expand the logarithm:

log y^10 = log (y^10) / log (base)

Since the base is not specified, we can use any base we like. For example, we can use base 10 or base e (natural logarithm).

Using base 10:

log y^10 = log (y^10) / log 10

= 10 log y / 1

= 10 log y

Using natural logarithm:

log y^10 = log (y^10) / log e

= 10 log y / 1

= 10 ln y

Therefore, the expanded form of log y^10 is either 10 log y or 10 ln y, depending on the base used.

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The unearned interest and the payoff amount is $11,022.12 and $18,784.87 respectively

Given data ,

Kelly bought a new SUV for $28,000. She made a down payment of $11,000 and has monthly payments of $332.63 for 5 years.

She is able to pay off her loan at the end of 36 months.

Now , Total interest = (monthly payment x number of months) - loan amount

Total interest = ($332.63 x 60) - $17,000

Total interest = $19,957.80

Next, we need to calculate the interest that has already been paid over the first 36 months of the loan. We can use the formula:

Interest paid = (monthly payment x number of months) - (loan amount - down payment)

Interest paid = ($332.63 x 36) - ($28,000 - $11,000)

Interest paid = $8,935.68

The unearned interest is the difference between the total interest and the interest paid so far:

Unearned interest = total interest - interest paid

Unearned interest = $19,957.80 - $8,935.68

Unearned interest = $11,022.12

To find the payoff amount, we need to add the remaining principal balance to the unearned interest:

Payoff amount = remaining balance + unearned interest

To calculate the remaining balance, we can use the formula for the present value of an annuity:

Remaining balance = monthly payment x (1 - (1 + r)^-n) / r

Where r is the monthly interest rate and n is the number of remaining months. We can solve for r by using the total interest calculated earlier:

r = (Total interest / loan amount) / 12

r = ($19,957.80 / $17,000) / 12

r = 0.0986%

Using this interest rate and n = 24 (the remaining 24 months of the loan), we can calculate the remaining balance:

Remaining balance = $332.63 x (1 - (1 + 0.0986%)^-24) / 0.0986%

Remaining balance = $7,762.75

Payoff amount = $7,762.75 + $11,022.12

Payoff amount = $18,784.87

Hence , the interest is solved

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Answer:

the price of each lemon bought by Encik Halim is RM1.45.

Step-by-step explanation:

Encik Halim bought 108 lemons and packed them into packets of 3 lemons each. So he made a total of 108/3 = 36 packets.

Let's assume that the cost of each lemon bought by Encik Halim is x RM.

The total cost of 108 lemons would then be 108x RM.

Encik Halim sold each packet at a price of RM6.80, so the total revenue he earned from selling 36 packets would be 36 x RM6.80 = RM244.80.

We are told that Encik Halim made a profit of RM88.20 from the sale of these packets, so his total cost would be:

Total cost = Total revenue - Profit

Total cost = RM244.80 - RM88.20

Total cost = RM156.60

We know that Encik Halim bought 108 lemons, so we can write:

Total cost = Number of lemons bought x Cost per lemon

RM156.60 = 108x

Therefore, the cost per lemon bought by Encik Halim is:

x = RM156.60/108

x = RM1.45

So the price of each lemon bought by Encik Halim is RM1.45.

The median of this data set is equal to 9.

The mean of this data set is equal to 13.7.

The number of mode that this data set have is zero modes.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of data, we have;

Total, F(x) = 26+ 0 -1 + 33 + 2 + 31 + 10 + 21 + 7 + 8

Total, F(x) = 137

Mean = 137/10

Mean = 13.7.

Median = (8 + 10)/2

Median = 18/2

Median = 9.

In conclusion, the mode of the data set is non-existent or zero modes because all of the number have the same frequency.

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The graph of the function f(x)=−4.6|x+2|+7 is symmetric at x = -2

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

The function f(x)=−4.6|x+2|+7.

The function f(x)=−4.6|x+2|+7 is an absolute value function

An absolute value function is represented as

f(x) = a|x - h| + k

Where the line of symmetry is

x = h

Using the above as a guide, we have the following:

Line of symmetry: x = -2

Hence, the graph of the function is symmetric at x = -2

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The function shows that the chairs and sofas the manufacturer should produce to earn that profit is C. (6, 12) P= 1,260

The profit function is P = 50x + 80y.

In order to find the optimal production quantities that will maximize the profit function, we need to determine which vertex yields the highest profit.

From the given vertices, we can see that the profit at (0,0) is 0. The profit at (0,15) is 1,200, and the profit at (6,12) is 1,260.

Therefore, the manufacturer should produce 6 chairs and 12 sofas to earn a profit of 1,260.

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The expressions are written as;

h(t)+k(t) = 10t - 1

h(t)−k(t) = -2t + 1

Note that algebraic expressions are described as expressions that are made up of coefficients, variables, terms, constants and factors.

These expressions are made up of arithmetic operations, which includes;

From the information given, we have that;

h(t)=4t

k(t)=t+5t−1

To determine the value of h(t) + k(t), we have;

4t + t + 5t - 1

add the like terms, we get;

10t - 1

To determine h(t) = k(t)

4t- t - 5t + 1

add like terms

-2t + 1

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Answer:

t = time in years

p(t) = population at time t

[tex]p(t) = 500000( {1.043}^{t} )[/tex]

[tex]p(10) = 500000( {1.043}^{10}) = 761751 [/tex]

Answer: We can start by simplifying the cube root of 8:

³√8 = 2

Next, we can rewrite 5^-2 as 1/5^2:

1/5^2 x 2 = 1/25 x 2 = 2/25

So the answer, as a decimal, is 0.08 (or 0.08 rounded to two decimal places).

The probability that he passes Math and does not pass Physics is given as follows:

0.28 = 28%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The probabilities for each event is given as follows:

The events are independent, hence the probability that he passes Math and does not pass Physics is given by the multiplication of the probabilities of each event, as follows:

0.7 x 0.4 = 0.28 = 28%.

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The value of the product of -4  row one and row 3 is [90    -9     -1]

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or expression.

The given matrix is

[tex]\left[\begin{array}{ccc}1&2&1\\0&4&-2\\4&-1&6\end{array}\right] \left[\begin{array}{ccc}-5&\\3\\-8&\end{array}\right][/tex]

the product is given as

-4[1    2    1]  + [4    -1     3]

= [ -4 -8   -4]   +  [  4   -1    3]

= [90    -9     -1]

The sum of the product is [90    -9     -1]

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Therefore , the solution of the given problem of trigonometry comes out to be approximately 21.424 metres long when the sun is 35 degrees above the horizon.

Some people assert that the growth of astrophysics was influenced by the merging of various fields. Many metric problems can be solved or the result of a calculation can be ascertained with the use of exact mathematical techniques. Trigonometry is the study of the six basic geometric calculations from a scientific perspective. They go by many other names and acronyms, including sine, variance, direction, and others. (csc).

Here,

When the sun is at a 35° elevation angle and the structure is 15 metres tall, we want to determine the length of the shadow (on the next side).

Let x represent the desired shadow's length. Next, we have

=> tan 35° = 15/x

When we multiply both sides by x, we obtain:

=> x tan 35° = 15

By dividing both sides by 35° of tan, we obtain:

=> x = 15 / tan 35°

We may calculate the value of the tangent of 35 degrees using a calculator:

=> tan 35° ≈ 0.7002

Next, we have

=> 15x/0.702x=21.424 metres

Consequently, a building 15 metres high will create a shadow that is approximately 21.424 metres long when the sun is 35 degrees above the horizon.

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The calculated values of the actual lengths of the walls are AB = 144 ft, CD = 288 ft, EF = 528 ft and EF = 240 ft

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

Scale of blueprint = 1 in : 48 ft

This means that

Scale = 48 ft/1in

Calculating the actual lengths of the walls, we have

AB = 3in * 48 ft/1in

AB = 144 ft

CD = 6in * 48 ft/1in

CD = 288 ft

EF = 11in * 48 ft/1in

EF = 528 ft

FG = 5in * 48 ft/1in

EF = 240 ft

Hence, the actual lengths of the walls are AB = 144 ft, CD = 288 ft, EF = 528 ft and EF = 240 ft

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In a case whereby A solution has a total mass of 400 g. If the solvent has a mass of 236 g of the total mass, the strength of the drug  can be expressed as 41%.

From the question, the total mass =400 g

The solvent mass = 236 g

Then the mass of the drug = 400-236

= 164

Then the mass percentage of the drug can be calculated as 164/400 * 100

= 41%

Therefore, the strenght of the drug can be expressed as  41%

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Applying the triangle sum theorem, the measure of angle x is calculated as: m<x = 72 degrees.

In a triangle, when all of its interior angles are added together, the triangle sum theorem states that we will get a sum of 180 degrees.

Therefore, we have:

m<AHI = 63 degrees [based on the corresponding angles theorem]

Considering triangle AHI, applying the triangle sum theorem, we will have the following:

m<x + m<AHI + m<A = 180°

Substitute:

m<x + 63 + 45 = 180°

m<x + 108 = 180°

m<x = 180 - 108 [subtraction property of equality]

m<x = 72 degrees.

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The balanced equation of the hanger is 3z = 45 and the solution is z = 15

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

The hanger image

On the hanger image, we have the following

One side = z + z + z

The other side = 45

The expressions on either sides must be equal to have a balanced equation

So, we have

z + z + z = 45

Evaluate the like terms

3z = 45

Divide both sides of the equation by 3

z = 15

Hence, the balanced equation is 3z = 45 and the solution is z = 15

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An ordered pair that describes a point that should be removed from the graph so that the graph represents a function include the following: A. (1, 1).

In Mathematics and Geometry, a function can be defined as a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

Based on the graph shown below, we can reasonably infer and logically deduce that it does not represent a function because the input values (domain or independent values) are not uniquely mapped to the output values (range or dependent values);

3  → 1

1 → 1

In this context, we can reasonably infer and logically deduce that either (3, 1) or (1, 1) must be removed from the graph in order to represent a function.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Emma bought a brush for $1.75, a sketchbook for $7, and a paint set for $10.5.

B = 1/4 * S

S = 2/3 * P

B + S + P = 23.75 - 4.50

Emma spent 23.75 - 4.50 = $19.25 on the brush, sketchbook, and paint set.

Now we have the equation:

B + S + P = 19.25

Substitute the expressions from relationships 1 and 2 into the equation:

(1/4 * S) + S + (3/2 * S) = 19.25

Now combine the terms:

(1/4 * S) + (4/4 * S) + (6/4 * S) = 19.25

(11/4 * S) = 19.25

Now, to solve for S, multiply both sides of the equation by the reciprocal of the fraction (4/11):

S = (4/11) * 19.25

S = 7

The sketchbook cost $7. Now we can find the costs of the brush and the paint set using relationships 1 and 2:

B = 1/4 * S = 1/4 * 7 = 1.75

P = 3/2 * S = 3/2 * 7 = 10.5

Emma bought a brush for $1.75, a sketchbook for $7, and a paint set for $10.5.

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Complete question

Emma brought $23.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 /4 as much as the sketchbook, and the sketchbook cost 2/ 3 the cost of the paint set. Emma had $4.50 left over after buying these items. What is the total cost for each item

Step-by-step explanation:

Answer

The price of 6 DVDs, including sales tax = $62.87

Sales tax = $2.99

Required:

The cost of one DVD.

Explanation:

Step 1: Price of 6 DVDs excluding sales tax.

The price of 6 DVDs excluding sales tax = $62.87 - $2.99 = $59.88

Step 2: Use the Unitary Method:

According to the question,

6 DVDs price = $59.88

1 DVD price excluding sales tax = $ 59.88/6

The length of BC, to the nearest tenth of a centimeter, is calculated as: 12.6 centimeter.

Recall that two similar triangles will always have side lengths that are proportional in length. The triangles shown are similar to each other, therefore, the proportion below would be true:

AC/CE = BC/CD

Given the following:

AC = 7.2 units

CE = 2.4 units

CD = 4.2 units

BC = ?

Plug in the values:

7.2/2.4 = BC/4.2

Cross multiply:

BC = 7.2 * 4.2 / 2.4

BC = 12.6 cm

Thus, the length of side BC in the similar triangles shown is approximately 12.6 cm.

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Answer:

B) 50cm^2

Step-by-step explanation:

Answer:

(x, -1/2x + 5/2) or infinitely many solutions

Step-by-step explanation:

We can solve the system of equations using substitution.  We can start by isolating x in the first equation.  Then, we can plug in the entire equation made from isolating for x in the second equation, which will allow us to find y:

Isolating:

x = -2y + 5

Plugging in and solving for y:

4(-2y + 5) + 8y = 20

-8y + 20 + 8y = 20

20 = 20

We see that we get a constant equal to another constant.  Whenever you get this as a solution to a system of equations, this means that there are infinitely many solutions. We can express the general rule for the solution in coordinate form by isolating y in at least one of the equations:

y = -1/2x + 5/2

Thus, the general rule for the solution to the system of equations is

(x, -1/2x + 5/2), so you can either put this general rule as the answer or write solution = infinitely many solutions

You can see that there are infinitely many solutions by plugging in any number for x into the two equations and see that you get 5 for the equation and 20 for the second equation.  Let's try 4 for x and 0 for x:

4 for x in first equation:

4 + 2(-1/2(4) + 5/2) = 5

4 + 2(0.5) = 5

4 + 1 = 5

5 = 5

4 for x in the second equation

4(4) + 8(-1/2(4) + 5/2) = 20

16 + 8(0.5) = 20

16 +4 = 20

20 = 20

0 for x in the first equation:

0 + 2(-1/2(0) + 5/2) = 5

0 + 2(2.5) = 5

5 = 5

0 for x in the second equation:

4(0) + 8(-1/2(0) + 5/2) = 20

0 + 8(2.5) = 20

20 = 20

Based on the above, the width of the field is 62 meters.

Based on the question, Let's say that the width of the field is  denoted with 'w'.

Note that the formula for the perimeter (P) of a rectangle is:

P = 2(l + w)

where"

l = length

w =  width.

Fixing the values into the equation, it will be:

300 = 2(88 + w)

So, Divide both sides by 2:

150 = 88 + w

Subtract 88 from both sides:

w = 150 - 88

w = 62

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Se text below

The perimeter of a rectangular field is 300 m. If the length of the field is 88 , what is its width?

Answer:

6.92

Step-by-step explanation:

When ever there are also of decimal places you must at least write the first 2 only.

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The balance for the following month is $598.18.

The average daily balance for June is $184.89.

To calculate the interest for the month, multiply the average daily balance by the interest rate: $184.89 * 1.4% = $2.59.

To find the balance for the following month, add the initial balance, transactions, and interest, then subtract the payment: $352.12 + $331.89 + $81.58 + $30 + $2.59 - $200 = $598.18.

The balance for the following month is $598.18.

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f(x) = the total cost for detailing the car. x = the number of minutes it takes to detail the car. m = The cost per minute for the detailing in car. b = the flat fee for detailing the car.

An algebraic equation is said to be linear if the maximum power of the variable is 1. In other words, it is an equation that, when plotted on a coordinate plane, defines a straight line. A linear equation with a single variable has the general form:

ax + b = 0, where a and b are constants and x is the variable. A single value of x that causes the equation to be true is the answer to this equation.

The given situation can be expressed in the form f(x) = mx + b.

Where,

f(x) = the total cost for detailing the car.

x = the number of minutes it takes to detail the car.

m = The cost per minute for the detailing in car.

b = the flat fee for detailing the car.

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The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

From the question, we are to perform the given row operation on the given matrix

From the given information, the given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]

We are to carry out the operation

Add -4(row 1) to row 3

This means we should multiply row 1 by -4

-4 × [ 1     2    1   | -5

       -4   -8   -4  | 20

Now, we will add the result to row 3

4    -1     6  |  -8

-4   -8   -4  | 20

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

0    -9    2  |  12

Hence,

The resulting matrix becomes

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

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Answer:

B) There is no absolute max for y=f(x)

Step-by-step explanation:

There is no absolute max as the function increases infinitely

However there is an absolute minimum at x=0

The fraction of the square that is red is 1/6.

A fraction is a number that represents a part or parts of a whole. It consists of two numbers separated by a horizontal or diagonal line, with the number above the line (numerator) representing the part and the number below the line (denominator) representing the whole. For example, the fraction 3/4 represents three parts out of a whole that is divided into four equal parts.

A square divided into six equal parts has six equal sixths.

If Soo colors one of these equal parts red, then she has colored one-sixth of the square red.

Therefore, the fraction of the square that is red is 1/6.

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Ari will need 3.6 pound of seed.

We are Given that total number of pounds of grass seed needed

9

Let number of pounds of Bermuda seeds is x

Let number of pounds of Fescue seeds is y

Then sum of both gives equation:

x+y=9

y=9-x...(i)

Given that cost of 1 pound of Bermuda seed = $4.80

Then cost of x pound of Bermuda seed = $4.80x

The cost of 1 pound of Fescue seed = $3.50

Then cost of y pound of Fescue seed = $3.50y

The total cost will be 4.80x + 3.50y

Now combining all three parts, we get equation:

4.80x+3.50y=4.02 x 9

4.80x+3.50y=36.18...(ii)

4.80x+3.50y=36.18

4.80x+3.50(9-x)=36.18

4.80x+31.5-3.50x=36.18

4.80x-3.50x=36.18-31.5

1.3x=4.68

x=3.6

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