Find the product (8×+9y) (8×-9y)

One way to solve a system of 3 equations with 3 variables is to use Gaussian elimination or Gauss-Jordan elimination method.

Gaussian elimination method:

The steps for Gaussian elimination are as follows:

Gauss-Jordan elimination method is similar to Gaussian elimination, however in the final step, it converts the matrix into a Reduced Row Echelon Form (RREF) which leads to more easily solving the system of equations.

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Answer:

C

Step-by-step explanation:

The value of f(4) - g(-5) if function  f(x) = 3 / 2x + 2 and g(x) = 2x² - 3 is -39.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.

Given:

f(x) = 3 / 2x + 2 and g(x) = 2x² - 3

Calculate the value of f(4) and g(-5) as shown below,

f(4) = 3 / 2 × 4 + 2

f(4) = 12 / 2 + 2

f(4) = 6 + 2

f(4) = 8

g(-5) = 2 × (-5)² - 3

g(-5) = 2 × 25 - 3

g(-5) = 50 - 3

g(-5) = 47

Now, calculate the value of f(4) - g(-5) as shown below,

f(4) - g(-5) = 8 - 47

f(4) - g(-5) = -39

Thus, the value of f(4) - g(-5) is -39.

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On using the distribution method the value could be  [tex]e ^ {t^{2}[/tex]/ 2

What is the Gamma Distribution  ?

A distribution which is described as two parameters – shape parameter and inverse scale parameter, having continuous probability distributions.

Given,

Z be a standard normal random variable: i. E. , Z ∼ N(0, 1).

Using the distribution method, find the pdf of U = Z 2.

And Using result from previous part, show that pdf of U follows a special case of Gamma distribution and also of χ 2 distribution.

Suppose e Z ∼ N (0, 1),  then

mZ (t) = 1√2πetxe−x2/2dx

= et2/21/√2π

[tex]e ^ {-(x-t)^{2} /2[/tex] dx

= [tex]e ^ {t^{2}[/tex]/ 2

hence, on using the distribution method the value could be [tex]e ^ {t^{2}[/tex]/ 2

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The percent increase is 50%.

The percentage increase in a quantity is the rate of difference in the old and new value to the old value, express in percentage.

i.e percentage increase = (old value - new value)/ old value

If the new quantity were be have decreased, then the percentage decrease can also be determined.

Considering the given question, the percentage increase can be determined by;

old quantity = 8

new quantity = 4

So that,

percentage increase = (old value - new value)/ old value

                                   = (8 - 4)/ 8 *100%

                                   = 4/ 8 * 100%

percentage increase = 50%

The percent increase is 50%.

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By dividing we can get proper fraction is 9/10.We can find answer by dividing two fractions.

A proper fraction is a fraction which has its numerator value less than the denominator. For example, ⅔, 6/7, 8/9, etc. are proper fractions.. We simplify fractions because it is always to work or calculate when the fractions are in the simplest form.

To divide a fraction with a whole number  we multiply the given whole number with the denominator of the fraction. Here, 8/5 ÷ 5 = 8/5 × 1/5 = 8/25. Therefore, 8/5 ÷ 5 = 8/25. Because multiplication is easier than division and because division by itself does not always produce whole numbers.

Now we get

1/2 divide 5/9

1/2 * 9/5

9/5

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The variable for the equation 2n - 3 =7 is 5.

What is variable ?

A variable is a symbol used to denote a mathematical object in mathematics. Any number, vector, matrix, function, function argument, set, or set element can be represented by a variable.

A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem. Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.

An amount that can fluctuate depending on the mathematical issue is referred to as a variable. The generic letters x, y, and z are frequently employed in mathematical expressions and equations. A variable, then, is a symbol denoting a number whose value is unknown.

Then variable is n

Variable is an alphabet that depend on number.

Then the variable there is n

And the coefficient of the variable is 2

The coefficient is the number behind a variable

And the value of the variable is

2n-3=7

Add 3 to both sides

2n-3+3=7+3

2n=10

Divide both side by 2

2n/2=10/2

n=5

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The standard deviation equation ( 1 + 6.8)% × 93000 > 202800

What is standard deviation?

Your dataset's standard deviation serves as a gauge of its degree of variability. It displays the typical difference between each outcome and the mean.

                            While a high standard deviation indicates that values are frequently distant from the mean, a low standard deviation indicates that values are typically grouped close to the mean.

( 1 + 6.8)% × 93000

= 202800

Then we get n ≈ 12,

the equation ( 1 + 6.8)% × 93000 > 202800

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If Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1) then the scale factor used is 1/3

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller.

Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1).

A(−3, −3)---->A(−3/3, −3/3)---->A′(−1, −1)

B(3, 3)---->B(3/3, 3/3)---->B′(1, 1)

C(0, 1)---->C(0/3, 1/3)---->B′(0, 1/3)

Hence, the scale factor used is 1/3.

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On solving the provided question, we cans ay that - the value of the each unit in this time will be from unitary method is 85.

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

value of the 20 unit is 1700

value of the each unit will be 1700/20 = 85

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The completed blanks in the statement are underlined as follows

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

A mathematical expression

The mathematical expression is given as

2x⁴ + 53x⁵ - 2 + x⁶

The standard form

To do this, we rearrange the expression from the highest power to the least

So, we have the following representation

x⁶ + 53x⁵ + 2x⁴  - 2

The degree

This is the highest power in the expression

So, the degree is 6

The leading coefficient

This is the coefficient of the term that has highest power of x

So, the leading coefficient is 1

The name of the expression

The expression has 4 terms

So, the name is a polynomial

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If the total number of minutes used and text messages sent last month was 561 , then the number of minutes she use is  207 minutes .

The total number of minutes used and text messages is = 561 ;

the cost for per minute cost is = 8 cents ;

the cost for per text message is = 5 cents ;

Bella's total bill amount is = $34.26 = 3426 cents

let the number of minutes used be = x minutes ; and

let the number of text messages be = y ;

So ,According to the question ,

the equations representing the situations are ,

[tex]x+y=561[/tex]  and [tex]8x+5y=3426[/tex]

Substituting the values of [tex]y=561-x[/tex] in the equation [tex]8x+5y=3426[/tex] ,

we get ;

[tex]8x + 5(561-x)= 3426[/tex]

On solving ,

we get ; x = 207 minutes ;

So , the number of text messages (y) = [tex]561-207[/tex]

= 354 text messages.

Therefore , the number of minutes is = 207 minutes .

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It will take a time of n/60m minutes for the jetski to cover n metres at the same speed.

Speed = distance/ time

Speed = m/s

For the distance of n meters.

distance = speed * time

n = m/s*time

n = m /s* time

Time = n(m/sec)

Time = n/m * sec

Time = n/60m min

Thus, it will take  n/60m minutes for the jetski to cover n metres at the same speed.

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Answer:

Which ratio forms a probation with 18/30

=20/35

=50/90

=36/46

=60/100

Step-by-step explanation:

a. The number of 2-inch thick slices that Mei can cut from the 12-inch loaf of bread is 6.

b. The inches of bread that would be left over is zero.

The information given an be solved by Illustratingnut with an expression. This is simply used to show the relationship between the variables that are provided or the data given regarding an information.

Since Mei needs to cut a 12-inch loaf of bread into slices that are inch thick, the number of 2-inch thick slices that Mei can cut from the 12-inch loaf of bread is:

= 12 / 2

= 6

There'll be no left over

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Answer:

The area of the shaded region is, [tex]24mm^{2}[/tex]

Step-by-step explanation:

First we have to calculate the area of ΔABC and ΔXYZ.

Area of ΔABC = [tex]\frac{1}2}[/tex]×[tex]Base[/tex]×[tex]Height[/tex]

Area of ΔABC = [tex]\frac{1}{2}[/tex]×[tex]5mm[/tex]×[tex]12mm[/tex]

Area of ΔABC =[tex]30mm^{2}[/tex]

and,

Area of ΔXYZ = [tex]\frac{1}{2}[/tex]×[tex]Base[/tex]×[tex]Height[/tex]

Area of ΔXYZ = [tex]\frac{1}{2} X3mmX4mm[/tex]

Area of ΔXYZ = [tex]6mm^{2}[/tex]

Now we have to calculate the area of the shaded region.

Area of the shaded region = Area of ΔABC - Area of ΔXYZ

Area of the shaded region = [tex]30mm^{2} - 6mm^{2}[/tex]

Area of the shaded region = [tex]24mm^{2}[/tex]

Therefore, the area of the shaded region is, [tex]24mm^{2}[/tex]

The polynomial's zero is 2 since the value of k = -2 is  [tex]3x^{2}[/tex]  +4x+2k . A polynomial is an equation that combines variables, constants .

Using just the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables, a polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients. Using addition, subtraction, multiplication, and division of numbers, a polynomial is an equation that combines variables, constants, and exponents (No division operation by a variable).

given

−2 is a zero of f(x)=[tex]3x^{2}[/tex]+4x+2k

f(−2)=0

∴[tex]3(-2)^{2}[/tex] +4(−2)+2k=0

=>12−8+2k=0

=>2k=−4

=>k=−2

The polynomial's zero is 2 since the value of k = -2 is  [tex]3x^{2}[/tex]  +4x+2k .

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this is a question of arithmetic and the solution is as follows,

The expression 8x + 12y represents the sum of harry and mike’s total monthly wages.

Generally the equation for the  The Distributive property is mathematically given as,

a x (b +c) = a x b+ b x c.

Where

8x+12y

Therefore,

= 4 x 2x + 4 x 3x

= 4 x( 2x + 3x)

= 4( 2x + 3x)

Arithmetic

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division.

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Answer:

1. 4x3<7×3

12×2<21×2

24×4<42×4

96×9<168×9

864<1512

2. 11+3>-2+3

14+3>1+3

17_4>4-4

13>0

3. -2/leg-2

-18/leg-18

4. -4<8

0<2

So Dylan needs 1.375 liters of water more for his experiment.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

To find out how much more water Dylan needs, we can subtract the amount of water he currently has from the amount of water he needs for the experiment.

2.5 - 1.125 = 1.375 liters

So Dylan needs 1.375 liters of water more.

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Answer:

AC = PF

Step-by-step explanation:

Answer:

D) 7.5%

Step-by-step explanation:

We can solve this through guessing and checking, or we can do this mathematically. We will try both approaches.

Mathematically:

We know that to get the extra $30 if we have $100, is a 30% interest. Now, since we have 4x 100, and these numbers are inversely proportional, we will need to divide 30 by 4. Doing this gives us 30/4 = 7.5, so the answer is 7.5%.

Guess and Check:

This way is a bit slower, but we will go through each answer and find how much money we would get from them. So, we would take our percent, change it to a number of that percent, considering we are taking it from 100, and multiply it by 4 since we have $400. We will get each of these respectively:

A) 3% = 3 * 4 = $12

B) 4.5% = 4.5 * 4 = $18

C) 6% = 6 * 4 = $24

D) 7.5% = 7.5 * 4 = $30

As you can see, D) gives us that extra $30, so the answer is D) 7.5%.

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The F-ratio is a measure used in statistical tests, specifically in ANOVA (Analysis of Variance) to test for differences between means of multiple groups.

a) On average, what value is expected for the F-ratio if the null hypothesis is true?

The answer is a. 1. If the null hypothesis is true, it means that there is no significant difference between the means of the groups being compared. Under this assumption, the F-ratio is expected to have a value close to 1, as the variance between the groups is not significantly different from the variance within the groups.

b) On average, what value is expected for the F-ratio if the null hypothesis is false?

The answer is d. Much greater than 1.00. If the null hypothesis is false, it means that there is a significant difference between the means of the groups being compared. Under this assumption, the F-ratio is expected to have a value much greater than 1, as the variance between the groups is significantly larger than the variance within the groups.

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In answering the question, we discovered that a sample size of 20 was required in order to reach this conclusion.

The sample size is the number of observations used to estimate a certain population. The population was used to determine the sample size.

The act of promoting a product to increase sales is known as advertising. Based on the scenario given, the advertisement is misleading for the following reasons:

For this finding to be reliable, a sample size of 20 samples is rather small. Although the company was aware that the fertilizer treatment might get rid of weeds in approximately 2 weeks, customers said it would take 4 weeks for all of the weeds to die.

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There are 7 white cars, 16 blue cars,  14 red cars and 5 silver cars.

Two or more expressions with an Equal sign is called as Equation.

Let w represents white cars

b represent blue carr

r represents red cars

s represents silver cars

There were three times more silver colour cars than red cars

3s=r...(1)

There were 2 more blue cars than red and silver cars together

b+2=r+s..(2)

There were twice more white cars than red.

2w=r..(3)

42 cars altogether in the parking lot.

w+b+r+s=42

After solving the above equation we get

s=5, b=16, w=7 and r=14

Hence, there are 7 white cars, there are 16 blue cars, there are 14 red cars and 5 silver cars.

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Answer: To determine the correct statement, you need to find a pattern in the values of D(t). You can do this by finding the difference between consecutive values of D(t).

The difference between -60 and 0 is 60.

The difference between 0 and 10 is 10.

The difference between 10 and 90 is 80.

The difference between 90 and 100 is 10.

The difference between 100 and 130 is 30.

The difference between 130 and 150 is 20.

The pattern that emerges is that the difference between consecutive values of D(t) is always 25. This means that the correct statement is "The function is D(t)=25t−60". The correct answer is therefore d.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.change minutes to hours,45 minutes is [tex]\frac{3}{4}[/tex] hours

2.then use 390÷    [tex]\frac{3}{4}[/tex]=390·[tex]\frac{4}{3}[/tex]=130·4=520 nautical per hour