How to find the inverse of the matrix Question number 19

The equivalent expression will be;

⇒ ''negative one eighteenth times x plus 3''

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''Sixth times the quantity 4 times x plus 18 end quantity minus 13 over 18 times x''

Now,

Since, The algebraic expression is,

''One sixth times the quantity 4 times x plus 18 end quantity minus 13 over 18 times x''

Hence, The mathematical expression is,

⇒ 1/6 (4x + 18) - 13/18x

⇒ 4/6x + 3 - 13/18x

⇒ 12/18x - 13/18x + 3

⇒ - 1/18x + 3

Thus, The equivalent expression is,

''negative one eighteenth times x plus 3''

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Answer:

Explanation:

Given the below polynomials expression;

The 1st step to solving the above is to clear the brackets while minding the signs as shown below;

The 2nd step is to group like terms;

Let's go ahead and evaluate;

Answer:

5/27

Step-by-step explanation:

3/9 x 5/9

= ( 3 x 5 )/( 9 x 9 )

9 can be splitted as 3 x 3

= ( 3 x 5 )/( 3 x 3 x 9 )

= 5/( 3 x 9 )

= 5/27

Answer:

[tex]\frac{5x}{27}[/tex]

Step-by-step explanation:

Cancel the number 3/9 = 1/3

= 1/3 x 5/9

Apply the function rule

1 · x · 5

3 · 9

Multiply the numbers 1 · 5 = 5

[tex]\frac{5x}{3 }[/tex]· [tex]9[/tex]

Now just Multiply the numbers: 3 · 9 = 27

= [tex]\frac{5x}{27}[/tex]

The initial flat rate that bike rental service charges is $19.70

The additonal charges per hour is $5.60.

Let x be the number of hour.

The equation formed is

The y-intercept is determined by substituting x=0.

Hence the y -intercept is 19.70 dollar.

We need to translate into an inequality the following problem:

What number divided by five is more than 6?

Let's call k the number we are looking for. Then, that "number divided by five" can be translated as:

Now, "more than" is represented using the symbol ">" (with the opened end turned to the greater amount.

Thus, since the above expression "is more than 6", this can be translated as:

Answer

In this scenario, there are only 2 possible outcomes. It is either the answer is correct or wrong.Since the outcomes are independent, it means that it is binomial probability. We would apply the binomial distribution formula which is expressed as

P(x) = nCx * p^x * q^(n - x)

where

n is the sample size

x is the number of successes

p is the probability of success

q = 1 - p = probability of failure

From the information given,

p = 1/4 = 0.25

q = 1 - 1/4 = 3/4 = 0.75

n = 12

x = 5

We want to find P(x = 5)

P(x = 5) = 12C5 * 0.25^5 * 0.75^(12 - 5)

P(x = 5) = 0.103

The probability that among 12 test subjects, exactly 5 answers are correct is 0.103

l

Now we graph the piecewise defined function:

We know that

• Gonna owns 5/6 of the section of land.

• She plants peanuts on 2/3 of her land.

We have to find 2/3 of 5/6, let's multiply these fractions.

We have to round 32020.20 to the nearest tenth.

In this case, the number is expressed with decimals up to the hundred (2 decimals).

As the decimals in the hundreds is 0, we don't even need to round it, as we can ignore this and write the number as:

In this case, the decimal is in the tenths without the need of rounding.

Answer: 32020.2

You have the following expression:

10x⁴(10x)⁻²

in order to simplify the previous expression proceed as follow:

10x⁴(10x)⁻² = 10x⁴/(10x)² = 10x⁴/10²x²

by simplifying the previous fraction, you obtain:

10x⁴/10²x² = 10⁻¹x²

where you have taken into account that the quotient between factors with different exponents, is equal to the same factor powered to the difference of the exponents:

Hence, the answer is:

10⁻¹x²

In order to solve the given expression follow these steps:

1. Take the square roots on both sides in order to get rid of the power on the left side:

√(x-5)² = ±√3

x - 5 = ±√3

2. add 5 on both sides:

x-5 + 5 = 5 ±√3

x = 5 ±√3

Then, the solution is x = 5 ±√3

Answer:

A. The set is {-1, 0, 1, 2, 3, 4, 5, 6}

Explanation:

Note the following;

*When we use parentheses or open brackets, ( ), in an interval notation, it signifies that those points are excluded in the set.

*When we use closed or square brackets, [ ], in an interval notation, it signifies that those points are inclusive in the set.

*The union symbol (U) is used to join two intervals together.

Given the interval notation, (−2,4) ∪ [−1,6], since there -2 and 4 are in parentheses, it means that they are not included in the set while -1 and 6 are included in the set since they are in square brackets. So the members of the set can be represented in a graph as;

Answer:

Explanation:

Here, we want to solve and graph the compound inequaqlity

We start by solving the sides, one at a time

For the second part, we have:

Now, let us write the solution in compound from:

Finally, we proceed to plot the graph as follows:

Step-by-step explanation + Answer:

x = 1st job

y = 2nd job

x + y = 22......x = 22 - y

7x + 8.25y = 171.50

7(22 - y ) + 8.25y = 171.50

154 - 7y + 8.25y = 171.50

-7y + 8.25y = 171.50 - 154

1.25y = 17.50

y = 17.50 / 1.25

y = 14 <== 14 hrs at the 8.25 per hr job

x + y = 22

x + 14 = 22

x = 22 - 14

x = 8 <=== 8 hrs at the 7 per hr job

Natural numbers are the non-negative integers

So we will put inside its circle all the positive integers and zero

Let us find them using the 1st picture

there are 0 and square root 36 because its value is 6

Whole numbers are positive numbers only

So we can put 0 in a natural circle and 6 in the whole part and 12/4 because it equals 3

Integers are positive and negative whole numbers

We have -8 and - square root 25 because it equals -5

So put -8 and - square root 25 in the integer circle

Rational numbers are all numbers can but in the form of the fraction

So we will choose the number with decimal or fraction

6.2, -1/2, 2.21 on the rational part

The rest of the numbers are irrational numbers

Put them in the part of irrational numbers

342 peanuts were divided equally into 6 small bags. "p" represents the total number of peanuts

To determine how many peanuts go in each bag, you have to divide the total amount of peanuts by the number of bags:

The variable of this example is the number of peanuts, and the constant is the number of bags.

So, the statements that apply are:

- The operation is a division

- 342 divided by 6 equals 57

-Each bag will have 57 peanuts.

-To evaluate, substitute 342 for the variable.

-Write the division expression as a fraction,

Given, the fraction of children, C=5/8.

The fraction of adults, A=3/8.

Therefore 5/8 is more than 3/8 is given by,

Therefore, 5/8 is more than 3/8 by 66.67%.

In each of the figures, there are 8 boxes. In the first figure showing the fraction of children, two boxes are shaded more than the figure for adults. In the second figure for the fraction of adults, only 3 boxed are shaded.

So, the % by which 5/8 is more than 3/8 can be found as

5/8 is 5 parts of 8. 3/8 is 3 parts of 8. So, if the total number of people is 8, five people are children and three people are adults.

So, number of children is 2 more than the number of adults, whose number is 3.

Therefore, the fraction for number of children more than the adults with respect to the number of adults is 2/3. In percentage,

So, 5/8 is more than 3/8 by 66.67%.

Given

Solution

From the problem, the population increases by 100 each year.

a constant increase of 100 means that the slope of a line is 100.

Slope is the same as constant increase or rate of increase.

The equation of the line with a slope is :

where m is the slope and b is the initital population.

Since we dont have an initital population, b = 0.

The equation will be :

It is stated also that P represents the population that has increased. So y will be p.

and t represent the number of years. So x will be t.

That will be :

ANSWER :

The equation is p = 100t

Given:

When planning a cruise:

you have a choice of 2 destinations: Cozumel (C) or Jamaica (J)

and a choice of 3 types of rooms: balcony (B), inside view (I), or ocean view (O)

and a choice of 2 types of excursions: water sports (W) or horseback riding (H)

We will list the sample space in regard to the vacations

First, we will draw the tree diagram

The tree diagram will be as shown in the following figure:

So, there are 12 outcomes you could pick from.

The sample space will be as follows:

CBW, CBH, CIW, CIH, COW, COH

JBW, JBH, JIW, JIH, JOW, JOH

A store pays $62 and they mark up the price by 0.4 of the price:

a) given equation is,

b) the given equation is

From the problem, we have a triangle with base of 15 cm and a height of 18 cm.

The area of the triangle is :

where b = base and h = height.

Using the formula above, the area will be :

The answer is 135 cm^2

The explanation goes as contained below.

The shape is a cube and for a cube all sides are equal,

from the question the Area of just one side is :

The linear equation that passes through (15, 40) and (41, 61) is:

y = (21/26)*x + 725/26

A general line is written as:

y = m*x + c

Where m is the slope and c is the intercept of the y-axis.

If the linear equation passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:

slope = (y₂ - y₁)/(x₂ - x₁)

In this case the line passes through (15, 40) and (41, 61), then the slope is:

m = (61 - 40)/(41 - 15) = 21/26

Then the line is:

y = (21/26)*x + c

To find the value of c we can replace the values of one of the poitns, if we use the first one we will get:

40 = (21/26)*15 + c

40 = 315/26 + c

40 - 315/26

725/26 = c

The linear equation is.

y = (21/26)*x + 725/26

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Given: Beth and Bryce sign on a $205,000 mortgage at a 5% annual interest rate for 30 years. This results in a monthly payment of $1100.48.

Required: To find the amount of interest she paid in month 1 and the amount toward reducing the balance.

Explanation: The monthly payment gets divided into two parts- One goes into the loan repayment and the other for the loan's interest.

The interest payment is based on the interest rate, which is 5%.

The monthly interest is:

The amount that goes towards reducing her balance is:

Final Answer: Interest in month 1 = $854.17

Their balance is reduced by $246.31

The compound interest model is given by the following expression:

Where a is the principal (initial amount), r is the interest rate in decimal form, n is the number of times compounded in a year and x is the number of years.

a) In this case, $4 are invested at 1% interest rate, then a = 4, r = 0.01 (1%) and n = 4 (compounded quarterly) and the above equation can be rewritten to get a model that led us to calculate the value of your shares over the time like this:

b) By replacing 0 for x, we can determine the y-intercept of the model, like this:

The result of raising any number to 0 is 1, then we get:

Then, the y-intercept if this model is 4 and it represents the initial amount invested ($4)

c) By replacing 10 for x, we get:

Then, after 10 years the estimated value of the shares will be $4.42

d) for a $4 stock with 2% interest compounded semiannually the model changes, we can write it like this:

By replacing 10 for x, we get:

As you can see, after 10 years the estimated value of the shares will be $4.88, which is greater than the previous penny stock investment, you would have shared better.

To answer this question, we can use the standard normal distribution to find the asked percentiles. We will need the z-scores to find the values for them.

The z-scores are given by the formula:

Where

• x is the raw value (the one we need to find here)

• μ is the population's mean. In this case, μ = 1.75 Mgal.

• σ is the population's standard deviation. In this case, σ = 2.82 Mgal.

The 86th percentile represents the value for which 86% of the cases are less than this value, and, therefore, 14% are above this value.

Then we can find it, if we know the value for which, z, in the standard normal table, represents the cumulative probability (0.86) for the distribution. If we consult the table, we have:

Therefore, the value for z is, approximately, z = 1.08, and we can use this value to find the value for x (the 86th percentile, in this case):

Therefore, the 86th percentile, if we round the value to two decimal places, is, approximately, x = 4.80.

We can apply the same procedure as before. Then we have:

Then we have:

If we round the result to two decimal places, we have that the 28th percentile is x = 0.11 (approximately).

The third quartile is equivalent to the 75% percentile. Then we can use the same process as before to find the value of z that represents it as follows:

And we can apply the same formula as before:

If we round this value to two decimal places, we have x = 3.65 (approximately).

Solution:

Given:

Let the cost of each daylily be d

Let the cost of each shrub be s

Generating the system of equations;

Equation (2) multiplied by 2;

Substituting the value of d into equation (2);

Therefore, the cost of one daylily is $2 and the cost of one shrub is $5.