Lesson 1. 12

At an ocean depth of 10 meters, a buoy bobs up and then down 6 meters from the ocean's depth.

Ten seconds pass from the time the buoy is at its highest point to when it is at its lowest point.

Assume at x= O the buoy is at normal ocean depth.

Find the following:

Period =

Equation of the mideline:

Amplitude =

Maximum =

Minimum =

The domain of the function y = √ x is x ≥ 0.

The domain of a function is the set of all input values for which the function is defined. The square root function, represented by √, is only defined for non-negative real numbers. This is because the square root of any negative number is not a real number, it becomes an imaginary number. Therefore, the domain of √ x is the set of all real numbers greater than or equal to zero.

This means that any input value less than zero would result in an undefined output for the square root function. In this case, since the square root is the only function, the domain of the function y = √ x is x ≥ 0. This means that the function can only take non-negative real numbers as input and will output a non-negative number.

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Consequently, it would take polynomials roughly 690,64 years for the disintegrations to disappear.

A polynomial is a mathematical statement made up of coefficients and uncertainty that exclusively uses additions, subtractions, multiplications, and positive integer powers of variables. A single indeterminate x polynomial is represented by the expression x2 4x + 7. A polynomial is an expression in mathematics that consists of variables (sometimes referred to as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression made up of coefficients and variables. The only operations that an expression can contain are addition, subtraction, multiplication, and non-negative integer exponents. These expressions are known as polynomials.

The formula for this is Activity = decay constant x atoms.

1238 = 2.64 x 1010 times the decay constant

decay constant is equal to 4.76 x 10-8 min-1.

Currently, the disintegrations are being slowed to 809 disintegrations per minute.

Ln(809) = Ln(2.64 x 1010) - Ln(4.76 x 10-8 x t)

t=3.63x108min = 690.64y

Consequently, it would take roughly 690,64 years for the disintegrations to disappear.

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The age of your uncle is modeled by:

y = 2 + 3*x

Evaluating it, we can see that when you are 12 years old, your uncle will be 38 years old.

Let's define the variables: y as your uncle's age and x as your age.

Here we know that your uncle is 2 years older than 3 times your age, so we can write the linear equation:

y = 2 + 3*x

This is the equation we needed to find.

b) If you are 12 years old, then we can write x = 12 in the equation above, then we will get:

y = 2 + 3*12

y = 2 + 36

y = 38

That's the age of your uncle.

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The solution of the expression 3x² - 4 = 0 is x = ±2/√3.

The term expression in math is defined as a sentence with a minimum of two numbers or variables and at least one math operation

Here we have the expression 3x² - 4 = 0.

Now, we have to solve this one by using the following steps:

First we have to add 4 to both sides of the equation, then we get the expression as,

=> 3x² = 4

Now, we have to Divide each term by 3 and simplify, then we get

=> x² = 4/3

Then we have to take the specified root of both sides of the equation to eliminate the exponent on the left side,

=> x = √4/3

When we simplify this one further, then we get

=> x = ±2/√3.

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The minimum value of the given quadratic equation is 31/8. Solved using graph method to find a minimum value that is c - b^2/4a.

By graphing the equation and locating the minimum point on the graph, you may visually determine the minimum value. The graph's vertex will have the lowest y-value. When you have a graphing calculator that can perform the majority of the work for you, this is very simple.

A graph makes it simple to determine the minimum value of a quadratic equation. One can use the graph to identify the minimum point of the quadratic equation and to find the minimum value in a visual way. If the quadratic equation is written as [tex]y= ax^2 + b*x + c[/tex]one can follow the equation that says the minimum value is min = c- (b^2/4a) to obtain the minimum value of the quadratic equation.

Given Quadratic equation is y = 2x^2 + 3x + 5

a = 2 , b =3 ,c = 5.

Minimum value  = c - (b^2/4a)

= 5 - 9/8

=31/8.

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Answer: Triangle ABC is a right triangle, because it satisfies the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

c^2 = a^2 + b^2

25^2 = 17^2 + 21^2

625 = 289 + 441

625 = 730

Since it is a right triangle, angle A is the angle opposite side a, which is the side that is the length of 17.

A right triangle also has one angle which is always 90 degree, that is the angle opposite the hypotenuse, so the remaining angle is A, which is 90- angle C, which is

90 - 42.3 = 47.7 degree.

Therefore the measure of angle A is 47.7°

So the correct answer is C. 42.3°

Step-by-step explanation:

The degree of the polynomial [tex]5x^{3} + 4x^{2} + 7x[/tex]  is 3 , that means it is a third degree polynomial called as cubic polynomial  .

What is Degree Of Polynomial ?

The degree of the polynomial is defined as  the highest power of the polynomial expression. But, if the polynomial has multiple variables, the degree of polynomial can be found by adding the powers of the different variables  in the polynomial expression.

For Example : the degree of polynomial ⇒  [tex]9x^{2} + 7x + 2[/tex] is  2 .

The polynomial is given as : [tex]5x^{3} + 4x^{2} + 7x[/tex] , we have to find the degree ,

So , we can see that the the term having the highest power of the given polynomial is [tex]5x^{3}[/tex] , and the degree is 3 .

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We can conclude from answering the above question that the first two patterns of the matrix  form a sequence in the third from top with the numbers 4-2-6.

A matrix is a set of numbers arranged in rows and columns. learns about the elements and dimensions of matrices and introduces them for the first time. A rectangular grid of numbers in rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. Its single row and 1 n row matrix order are the reasons behind its name. A = [1 2 4 5] is a row matrix of order 1 by 4, for instance. P = [-4 -21 -17] of order 1-by-cubic is another illustration of a row matrix.

We can conclude from answering the above question that the first two patterns of the matrix  form a sequence in the third from top with the numbers 4-2-6.

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Answer: #18 is (1/2,0)

#19 (0,-1)

#20 5

#21 8√2 or 11.313708498985

Step-by-step explanation:

Answer:

R = 144400000/59 [this is a fraction]

Answer: A

Step-by-step explanation:

Based on the graph, we know that it is decreasing if it is going down from left to right.

A: correct

Looking at choice A, it says the interval is from -4<x<-3. This means we have to find x=-4 and x=-3. On the graph, that interval is going down from left to right, so it is decreasing.

B: incorrect

Looking at choice B, it says the interval is from -2<x<0. This means we have to find x=-2 and x=0. On the graph, that interval is going up from left to right, so it is increasing.

C: incorrect

Looking at choice C, it says the interval is from 0<x<2. This means we have to find x=0 and x=2. On the graph, that interval is going up from left to right, so it is increasing.

D: incorrect

Since we have identified A as decreasing, then none of the above can't be the answer.

Therefore, A is the correct answer.

The difference between the two polynomials (9x²+8x) - (2x²+3x) is:

7x² + 5x.

Polynomial:

A polynomial is a type of algebraic expression where the exponents of all variables must be integers. The exponent of each polynomial variable must be a non-negative integer. A polynomial consists of a constant and a variable, but you cannot divide a polynomial by a variable.

Example: Express the polynomial 5 + 2x + x2 in standard form.

To express the above polynomial in standard form, first check the degree of the polynomial.

The degree of the given polynomial is two. Write an expression involving the degree of the polynomial.

There is a term with variable exponent less than 2, i.e.1, then write it down.

Finally, we write a term with the variable exponent 0 as the constant term.

According to the Question:

Given polynomials is:

(9x²+8x) - (2x²+3x)

First, multiply the negative sign in the second polynomial

i.e., (9x²+8x) - (2x²+3x)

= 9x²+8x - 2x²-3x

Now, evaluate those terms who have same variables

=  9x²  - 2x² +8x-3x

= 7x² + 5x

Hence, the difference between polynomials are: 7x² + 5x.

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Altogether, the recipe uses 1/2 cup of flour and 1/8 cup of sugar.

Altogether in math refers to the sum of two or more numbers or values. It is a way of combining two or more items to obtain a total. In math, the term "altogether" is used to denote the sum of all the individual items, as opposed to all of them considered as one. For example, the sum of the numbers 2, 4, and 6 is 12, which is the "altogether" in math.

To calculate this, we must convert the fractions into decimals and then add them together.

The 1/3 cup of flour can be converted to 0.33 cup, and the 1/8 cup of sugar can be converted to 0.125 cup.

When added together, they equal 0.455 cup, or 1/2 cup. Therefore, the recipe uses a total of 1/2 cup of flour and 1/8 cup of sugar.

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In order to calculate how many postcards he sold, multiply €0.30 by (45.9 + 42) to get €97.20.

Multiplication, division, addition, and subtraction are all possible in mathematics. Expression, number, and mathematical operator are the components of a mathematical expression (such as addition, subtraction, multiplication, or division, etc.). Expressions and phrases can be contrasted. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For instance, the phrase 4m + 5 consists of the terms 4m and 5, as well as the provided expression's variable m, all of which are separated by the arithmetic sign +.

given

A stationer sells 17 magazines for €2.70 each, for a total of €45.9; 28 newspapers cost €1.50 each,

for a total of €42; and

x postcards, for a total of €0.30x,

for a total of €97.20.

In order to calculate how many postcards he sold, multiply €0.30 by (45.9 + 42) to get €97.20.

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Answer:

a.  The total cost of fixing the drain is $198

b. The plumber spend 13 hours fixing the drain

Step-by-step explanation:

We know the equation is

C=25h+73

C = the total cost

h = the number of hours

Let's solve question a by putting 5 in for h

C=25(5)+73

C = 125 + 73

C = $198

So, the total cost of fixing the drain is $198

Let's solve question b by butting 398 in for c

398=25h+73

325 = 25h

h = 13 hours

So, the plumber spend 13 hours fixing the drain

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Parallel programming can improve the performance of an application over sequential programming in certain cases, but it is not a guarantee.

Parallel programming allows for the use of multiple processors or cores to perform tasks simultaneously, which can improve the overall speed of an application. However, parallel programming can also introduce complexity and overhead, which can decrease performance. The potential for improved performance depends on the specific application and the design of the parallel implementation. Some applications may not benefit from parallel programming because they are not computationally intensive or because their data is not easily divided into parallelizable tasks. Additionally, the performance improvement also depends on the number of cores and the communication costs between them.

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C). The highest amount their liability coverage will provide is  $400,000

This is because most standard liability policies will provide up to $300,000 for bodily injury and $100,000 for property damage, but the policyholder may be able to purchase additional coverage for higher limits if they need it. The exact amount of coverage will depend on the policy the policyholder purchased.

Liability insurance is a component of the general insurance system of risk financing that protects the purchaser from the risks of liabilities imposed by lawsuits and similar claims, as well as the insured if the purchaser is sued for claims covered by the insurance policy.

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Answer:

x = 6

Step-by-step explanation:

x:(x + 3) = 2:3

[tex] \frac{ \\ x}{x + 3} = \frac{2}{3} [/tex]

cross multiply

3x = 2(x + 3)

3x = 2x + 6

subtract (2x) from both sides

3x – 2x = 2x – 2x + 6

x = +6

x = 6

Answer:

Step-by-step explanation:

A unit rate means a rate for one of something. You should write it as a ratio with a denominator of one.

For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate

IT's  0.80 per serving i think

The range and the IQR of the weights are 3.3 pounds and 0.95 pounds respectivly.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

The value that, when a dataset is arranged, falls exactly in the center is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, there are different processes to take when calculating the median.

The term "standard deviation" (or "[tex]\sigma[/tex]") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

a) the range is the difference between the highest and lowest value:

range =7.5-4.15 =3.3 pounds

the IQR is the difference between the third and first quartile

IQR= Q₃ -Q₁ =6.55 - 5.6 = 0.95 Pounds

b) Skewed because the mean and median are not the same value.

c) All values will be multiplied by 16

Mean: 96 ounce

Standard deviation: 10.4 ounce

Quartiles: 89.6 ounce and 104.8 ounce

Median:99.2 ounce

IQR: 15.2 ounce

Range: 52.8 ounce

d) The mean,quartiles and median increase by 30,the result remain unchanged:

Mean: 126 ounce

Standard deviation: 10.4 ounce

Quartiles: 119.6 ounce and 134.8 ounce

Median:129.2 ounce

IQR: 15.2 ounce

Range: 52.8 ounce

e)  The median, quartiles and IQR might not changed,because they are unaffected by an outlier.

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If her monthly payment is P3,000 and interest is compounded semi-annually at 9%, the cost of the TV set comes to P17,545.08.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest.

In finance and economics, compound interest is common.

In contrast to simple interest, which does not compound since past interest is not added to the principal for the current period, compound interest allows interest to build over time.

The interest per period multiplied by the number of periods in a year yields the simple annual interest rate.

According to our question-

9% = 0.09 / 2

=0.045 + 1 =1.045^(1/6)

=1.00736312 - 1 x 12 x 100

=8.836%

PV=0;

PMT=3000;

R=0.08836/12; N=6; PV

=PMT*(((1 + R)^N - 1)*((1 + R)^-N)* R^-1)

PV==17,545.08

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Therefore , the solution of the given problem of algorithm comes out to be solution of the non solvable and solvable problems cannot be solved.

A method for performing calculations or solving problems is known as an algorithm. Algorithms act as a thorough set of instructions that step-by-step direct hardware- or software-based processes through a series of planned activities. In every aspect of IT area, algorithms are utilized regularly.

Here,

Two different kinds of issues arise in TOC: - Problems that can be and can't be computed When something is "computable" (or "solvable"),

it means that it can be solved using an algorithm or a set of steps.

No method exists that can produce an output that is either "true" or "false," hence this problem is non-computable (or unsolvable).

Therefore , the solution of the given problem of algorithm comes out to be solution of the non solvable and solvable problems cannot be solved.

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Answer:

4

Step-by-step explanation:

Half means 1/2

Half of 8

= 1/2 x 8

= 8/2

= 4

Hence, half of 8 is 4.

Answer: 4

Step-by-step explanation:4 + 4 is 8 half of 4 is eight.

An example of x-intercept is (3,0).

Here x=3 is the x-intercept in this line.

By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.

We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.

The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.

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The standard form of linear function y = - (1 / 2) · x + 6 is (1 / 12) · x + (1 / 6) · y = 1.

In this question we find a linear function in slope-intercept form:

y = m · x + b

Where:

From which we must obtain the linear function in standard form:

a · x + b · y = c

Where:

We can derive the standard form of the linear equation by algebra properties:

y = m · x + b

(1 / b) · y = (m / b) · x + 1

- (m / b) · x + (1 / b) · y = 1

If we know that m = - 1 / 2 and b = 6, then the equation of the line in standard form is:

- [(- 1 / 2) / 6] · x + (1 / 6) · y = 1

(1 / 12) · x + (1 / 6) · y = 1

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Answer: 13.6 grams per egg.

Step-by-step explanation:

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]2(x-2)^2=8(7+y)\hspace{5em}\stackrel{\textit{quick switcheroo}}{2(y-2)^2=8(7+x)} \\\\\\ (y-2)^2=\cfrac{8(7+x)}{2}\implies (y-2)^2=4(7+x)\implies (y-2)^2=28+4x \\\\\\ y-2=\pm\sqrt{28+4x}\implies \boxed{y=2\pm\sqrt{28+4x}}\qquad \impliedby f^{-1}(x)[/tex]

Answer:

C. ∠1 and ∠3 are vertical angles and congruent.

The total number of pizzas consumed by the 10 members of the club is 2.5 and 3.5 pizzas remain, as Mr. Cam bought 6 pizzas and each of the 10 members ate 1/4 of a pizza.

Mr. Cam bought 6 pizzas for the club and each of the 10 members ate 1/4 of the pizza. To find out how many pizzas were eaten, we can use the formula:

Number of members x Pizza per member = Total Pizzas Consumed

In this case, we can substitute the given values in the formula:

10 members x 1/4 pizza/member = 10/4 = 2.5 pizzas

This means 2.5 pizzas were consumed by the members. Since Mr. Cam bought 6 pizzas and 2.5 pizzas were eaten, the total number of pizzas remaining is 6 - 2.5 = 3.5 pizzas.

This equation works because it uses the concept of the unitary method, where we find the total number of pizzas consumed by multiplying the number of members by the number of pizzas each member ate. This way we can find the total amount of pizza consumed.

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