Write an inequality to express the relationship between -2 and -5.

Answer:

Pi/4

Step-by-step explanation:

first we have to figure out what cos of 7pi/4 is. Using the unit circle, we know that it is equal to root2/2. Cos to the negative 1 is basically just finding the radian value that matches the value in the parenthesis. This means we have to find the corresponding radian to root2/2. Using the unit circle, we find this to be pi/4

Accοrding tο the given questiοn the equatiοn will be written as 2x = 28.

In its simplest fοrm in algebra, the definitiοn οf an equatiοn is a mathematical statement which shοws that twο mathematical expressiοns are equal. Fοr example, 7x + 5 = 19 is an equatiοn in which 7x + 5 and 19 are twο expressiοns separated by an "equals" sign. It cοnsists a variable, cοnstant term and signs.

Let, Andre has x tοys.

Camerοn has twice as many cars as Andre.

As Andre has x tοys then Camerοn has 2x tοys.

Given that Camerοn has 28 tοy cars.

Tο make an equatiοn we need tο equate the cοnditiοns.

Sο, accοrding tο the questiοn ,2x=28

Hence, the equatiοn is 2x=28.

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According to the question as a fraction squared the value we will get at the end is 9/25.

A fraction is a numerical representation of part of a whole. It is written as a ratio of two numbers, separated by a slash (/). The top number in the fraction, known as the numerator, represents the number of equal parts of the whole, while the bottom number, known as the denominator, represents the total number of parts in the whole. For example, a fraction of "1/4" means that one of the four equal parts of the whole is being represented. Fractions are used to represent ratios and can also be used to represent parts of a whole.

This is because 3/5 can be rewritten as the fraction 6/10, and the square of this fraction is (6/10)² = (6/10)(6/10) = 36/100
= 9/25.

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Answer:

171 ft squared

Step-by-step explanation:

Answer: We can use the formula for compound interest to find the future value of the $2,000 gift:

FV = PV * (1 + r/n)^(n*t)

where PV is the present value of the gift, r is the annual interest rate, n is the number of compounding periods per year, t is the number of years, and FV is the future value.

In this case, PV = $2,000, r = 0.07 (7%), n = 4 (quarterly compounding), and t = 17. Substituting into the formula, we get:

FV = $2,000 * (1 + 0.07/4)^(4*17)

Simplifying, we get:

FV = $2,000 * (1.0175)^68

Using a calculator, we get:

FV = $6,186.22 (rounded to two decimal places)

Therefore, the $2,000 gift will be worth approximately $6,186.22 in 17 years if it is invested at 7% and compounded quarterly.

Step-by-step explanation:

Answer: To solve 18 ÷ 8 using the algorithm, we can follow these steps:

- Write 18.00 above the division bar.

- Write 8 to the left of the division bar.

- Divide 8 into the first digit of 18 (which is 1) and write the result (0) above the division bar, and write the remainder (1) below the digit 1.

- Bring down the next digit (8) and write it next to the remainder (1) to get 18.

- Divide 8 into 18 and write the result (2) above the division bar, and write the remainder (2) below the digit 18.

- Since we have no more digits to bring down, we have our final answer: 18 ÷ 8 = 2 with a remainder of 2.

So, using the algorithm, we find that 18 ÷ 8 is equal to 2 with a remainder of 2.

Step-by-step explanation:

The function C(k) that models the amount Liana will pay for using k kilowatt hours of electricity in one month is: [tex]C(k) = 0.0682k - 8.32.[/tex]

We must find the function C(k) that models the amount Liana will pay in one month for using k kilowatt-hours of electricity.

The ordered pair for November and September is now (550,45.83) and (1250,93.57), respectively. The function will be linear because she pays the same amount for each kilowatt-hour of electricity.

So, the model equation can be written as:

[tex](C(k) - 93.75) / (93.75 - 45.83) = (k - 1250) / (1250 - 550)\\(C(k) - 93.57) / 47.74 = (k -1250) / 700\\C(k) - 93.57 = 0.0682k - 85.25\\C(k) = 0.0682k - 85.25 + 93.57 \\C(k) = 0.0682k - 8.32.[/tex]

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Evaluated the numerical expression [tex](3^2)^{\tfrac13[/tex], we get result = [tex]\sqrt[3]{9}[/tex]

Every aspect οf οur daily lives is related tο numbers, frοm the number οf laps we have dοne οn the track tο the number οf hοurs we slept at night.

In mathematics, a number can be even οr οdd, prime οr cοmpοsite, decimal, fractiοn, ratiοnal οr irratiοnal, natural οr integer, real οr integer, ratiοnal οr irratiοnal, οr any cοmbinatiοn thereοf.

Given:

[tex](3^2)^{\tfrac13[/tex]

Evaluating

[tex](9)^{\tfrac13[/tex]

= [tex]\sqrt[3]{9}[/tex]

Thus, Evaluated the numerical expression [tex](3^2)^{\tfrac13[/tex], we get result = [tex]\sqrt[3]{9}[/tex]

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The solution to the system of equations is (-2, -6).

What are system of equations ?
A system of equations is a set of two or more equations that are to be solved simultaneously. Each equation in the system represents a relationship between variables, and the solution to the system is the set of values for the variables that satisfies all of the equations in the system.

For example, consider the following system of equations:

x + y = 5

2x - y = 3

According to the question:

To find the solution to the system of equations, we need to find the point where the two lines intersect. We can do this by setting the two equations equal to each other:

3x = x - 4

Subtracting x from both sides, we get:

2x = -4

Dividing both sides by 2, we get:

x = -2

Now that we know that x = -2, we can substitute this value into either of the equations to find y. Using the first equation, we get:

y = 3(-2) = -6

Therefore, the solution to the system of equations is (-2, -6).

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Answer:

-1

Step-by-step explanation:

((-9-11)/(-4))/ (−7^2 + (11 x 2^2)) can be simplified as follows:

((-9-11)/(-4))/ (−7^2 + (11 x 2^2))

= (-20 / -4) / (-49 + 44)

= (5) / (-5)

= -1

Therefore, ((-9-11)/(-4))/ (−7^2 + (11 x 2^2)) simplifies to -1

Five times a number less sum twelve as equal to two times the number multiplied by twelve. There are twelve.

The result or solution we obtain from adding two or more integers is known as the SUM. Addends are the figures that are combined. In the example above, the sum of the addends, 6, and 4, is 10. Below is another illustration: Thus, we may argue that 8 plus 5 equals 13, or 8 plus 5 equals 13.

Prepare: We'll find x.

Spread out the 2 initially on a left side of this equation:

2x plus 24 = 5x - 12

After that, shift all of the x terms to a left and each of the constant terms towards the right:

2x - 5x = -12 - 24

-3x = -36

In order to find x, divide both sides by -3.

x = 12

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In contrast, if the loan period is extended, the total amount owed is expressions spread out across more instalments, allowing the monthly payment to be cheaper.

In mathematics, you can double, divide, add, or subtract something. The following is an expression: Expression, numerical value, and math operator A mathematical expression is made up of numbers, parameters, and functions. Opposing sentences and expressions are possible. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and a mathematical action between them. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical sign +.

Assuming all other factors remain constant in the loan payment formula, the monthly payment rises when the principal amount or interest rate rises and falls when the loan period lengthens. This is due to the fact that the formula computes the fixed amount required to pay off the loan in full, including interest, over a set number of installments. If the principle or interest rate is higher, the total amount owing increases, and the monthly payment must be higher to pay off the loan in the same length of time. In contrast, if the loan period is extended, the total amount owed is spread out across more instalments, allowing the monthly payment to be cheaper.

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After answering the given query, we can state that In this case, %Y = 0, equation so this would not be a component in inducing inflation.

An equation is a mathematical assertion that establishes the equality of two expressions that are joined together by the equals symbol ('='). For example, 2x – 5 equals 13. Expressions like 2x-5 and 13 are examples. The letter '=' connects the two phrases. A mathematical formula is called an equation if it contains two algebraic expressions on either side of the equal symbol (=). It shows how the right and left algorithms are equivalent to one another. Any calculation will result in L.H.S. = R.H.S. (left side = right side).

The quantity theory of money, which asserts that the price level (P) is inversely proportional to real GDP and directly proportional to the money supply (M) and velocity of money (V), is represented by the equation%M +%V %P +%Y. (Y)

Therefore, for there to be inflation (%P > 0), there must also be a rise in the velocity of money (V) (%V > 0). This indicates that money is exchanging hands more frequently, which causes consumers to spend more money and rates to rise.

Alternatively, if the money supply stays constant and the velocity of money increases, a rise in real GDP (Y) would also cause an increase in the price level. In this case, %Y = 0, so this would not be a component in inducing inflation.

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Answer:

94

Step-by-step explanation:

The domain of the function f(x) is the set of all real numbers.

For any function y = f(x), we define the domain as the set of the possible inputs of the function, this would be the set of the possible x-values.

We usually assume that the domain is the set of all real numbers and then we remove the problematic points, these are the values of x that make a denominator equal to zero, or that give a negative argument for a square root for example.

In this particular case we have a polynomial function:

f(x)=-x^4+2x^2-x-2

Notice that there is no denominator, no square root, no logarithm, then there are no problematic points. This function works fine for all real numbers, then the domain is the set of all real numbers.

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Answer:

Domain = (−∞,∞),{x|x∈R}

Range = (−∞,0.05617288],{y|y≤0.05617288}

Answer: The equation that best represents the phrase "What numbers on the number line are 2 units away from?" is:

O |x-2|=2

This equation represents the absolute value of the difference between x and 2 being equal to 2, which means that x can be 2 units away from either side of the point 2 on the number line.

Step-by-step explanation:

The probability of pulling out 2 red marbles at random from the jar is approximately 0.0741 or about 7.41%.

A combination is a choice of things without respect to order, whereas a permutation is an arrangement of objects in a certain order in probability and combinatorics. In other terms, a combination is an unordered selection of things from a set, but a permutation is an ordered arrangement of a collection of objects.

Given that, a jar containing 8 red marbles and 20 blue marbles.

The total number of marbles are:

8 + 20 = 28.

To choose 2 marbles out of 8 red marbles we have:

C(8,2) = 8! / (2! * (8-2)!) = 28

Similarly, the total number of ways to choose 2 marbles out of 28 is:

C(28,2) = 28! / (2! * (28-2)!) = 378

The probability of choosing 2 red marbles from the jar is:

P(2 red marbles) = 28 / 378 = 0.0741

Hence, the probability of pulling out 2 red marbles at random from the jar is approximately 0.0741 or about 7.41%.

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Answer:

Step-by-step explanation:

the magnitude of ∠DGF= ∠BAD (alternate angles)

∴the magnitude of ∠DGF=40°

∠ FDG=∠ADB(VERTICALLY OPP. ANGLES)

∠FDG= 180-(90+40)

          = 50°

by using the Pythagoras' theorem

FD²+2²= 4²

FD²= 12

FD= 2√3

There are 12 possible οutcοmes.

A tree  diagram will visualise all 12 choices at one place.

The first choice is Dοοr 1, Curtain 1 & second choice is  Dοοr 1, Curtain 2.

A tree diagram is a visual tοοl that can help tο οrganize all the pοssible οutcοmes οf a randοm event, such as chοοsing a dοοr and a curtain behind the dοοr.

Here,

3 doors and 4 curtains behind them

i.e. [tex]^3C_1 \times ^4C_1[/tex]

= 3 × 4

= 12

Hence there are 12 possible οutcοmes

The tree diagram wοuld have three branches, οne fοr each dοοr, and each branch wοuld have fοur sub-branches, οne fοr each curtain behind the dοοr. The end pοints οf the branches wοuld represent all the pοssible οutcοmes οf the game.

The first chοice is tο chοοse οne οf the three dοοrs.

The secοnd chοice is tο chοοse οne οf the fοur curtains behind the chοsen dοοr.

Pοssible οutcοmes οf the tree diagram cοuld be as fοllοws:

Dοοr 1, Curtain 1

Dοοr 1, Curtain 2

Dοοr 1, Curtain 3

Dοοr 1, Curtain 4

Dοοr 2, Curtain 1

Dοοr 2, Curtain 2

Dοοr 2, Curtain 3

Dοοr 2, Curtain 4

Dοοr 3, Curtain 1

Dοοr 3, Curtain 2

Dοοr 3, Curtain 3

Dοοr 3, Curtain 4

Each οf these οutcοmes is equally likely, assuming that the player has nο infοrmatiοn abοut what is behind each curtain.

Tree diagram is given below in attachment

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The solution for each of the ordered pair for the the system of equations is found.

Part a: y = 3x+5 ; (-6, -13), (1,8)-  (solution) ; (-4,1), (0, -5)- (not a solution).

Part b: -9x + 3y=15 : (-6, -13), (-6, -13) - (solution); (-4,1), (0, -5) - (not a solution).

Part a: y = 3x+5

(-6, -13)

put x = -6

y = 3(-6)+5 = -13 (solution)

(-4,1)

y = 3(-4)+5 = -7 (not a solution)

(0, -5)

y = 3(0)+5 = 5 (not a solution)

(1,8)

y = 3(1)+5 = -8 (solution)

Part b: -9x + 3y=15

Put each values and check;

(-6, -13)

-9(-6) + 3(-13) = 15

15 = 15  (solution)

(-4,1)

-9(-4) + 3(-1) = 15

33 ≠ 15  (not a solution)

(0, -5)

-9(0) + 3(--5) = 15

-8 ≠ 15  (not a solution)

(1,8)

-9(1) + 3(8) = 15

15 = 15  (solution)

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When you round 19995 to the nearest ten, you look at the digit in the tens place, which is 9. Since 9 is greater than or equal to 5, you round up the digit in the thousands place to the next higher number, which is 20000.

Therefore, 19995 rounded to the nearest ten is 20000.

Answer:

The error is $2.44.

The length of x, given the similar triangles, can be found to be 1 cm.

To find the length of x, you should find the scale factor by which the larger figure was derived from the smaller triangle.

You can do this by using the length of two corresponding sides in the two triangles. We can use the corresponding sides of 6 cm and 1. 5 cm.

The scale factor then is:

= 6 / 1. 5

= 4

The length of x would be the found by using the scale factor and the corresponding length of 4 cm which is then:

= 4 / 4

= 1 cm

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The total surface area of the cuboid is 148 cm².

What is the total surface area of the cuboid?

Surface area is the total area on the surface of a three-dimensional shape. To find the surface area of a cuboid that has 6 rectangular faces, add the areas of all 6 faces. Or, you can label the length (l), width (w), and height (h) of the cuboid and use the formula: surface area (SA)=2lw+2lh+2hw.

The total surface area of a cuboid is the sum of the areas of its six faces.

In this case, the cuboid has dimensions of 5 cm, 4 cm, and 6 cm.

The area of the top and bottom faces (which are identical) is:

5 cm x 6 cm = 30 cm²

The area of the front and back faces (which are identical) is:

4 cm x 6 cm = 24 cm²

The area of the left and right faces (which are identical) is:

4 cm x 5 cm = 20 cm²

Therefore, the total surface area of the cuboid is:

30 cm² + 30 cm² + 24 cm² + 24 cm² + 20 cm² + 20 cm² = 148 cm²

Therefore, the total surface area of the cuboid is 148 cm².

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The predicted values of y might not be accurate if any of the x-values lie outside of the range of x-values used to calculate the regression line.

One variable (the independent variable) is used to forecast the other variable in linear regression, a statistical technique for examining the relationship between two variables (the dependent variable). In linear regression, the connection between the variables is represented by a line (or curve) fitted to the data points. The regression line is the name assigned to this line, and it is used to forecast values of the dependent variable based on the independent variable.

given

To determine the regression line's equation:

Determine the r-value, or correlation coefficient, between the x and y numbers.

To determine the slope (b) of the regression line, use the numbers from steps 1-3: b = r * (s y / s x).

Calculate the regression line's y-intercept (a) using the numbers from steps 1-4: a = mean(y) - b * mean (x).

The regression line's equation is: y = a Plus bx.

The predicted value of y is meaningful if the x-value is within the range of x-values used to compute the regression line.

The projected value of y is affected if the x-value is outside of that range.

For instance, if the regression line's equation is y = 3.2 + 0.6x, then:

(a) Y = 6.4 when x = 5 victories (predicted earned run average).

(b) If y = 9.2 and x = 10 triumphs (predicted earned run average).

(c) If y = 14.6 and x = 19 triumphs (predicted earned run average).

(d) With 15 victories, x, y = 11.2 (predicted earned run average).

The predicted values of y might not be accurate if any of the x-values lie outside of the range of x-values used to calculate the regression line.

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The students' reasoning is flawed as adding 2 numbers doesn't necessarily result in 101.

What is reasoning?

Mathematical reasoning is the act of applying logical and critical thinking to a mathematical problem in order to determine the best approach to take (and, just as essential, the approach to avoid taking) in order to arrive at a solution.

The student's reasoning is flawed because there is no reason to expect that the sum of the two values should be 101.

The problem asks for the percentage of students who chose option A and the percentage of students who chose option B, which are two independent values that do not necessarily add up to 100 or any other fixed number.

In fact, it is possible for both percentages to be less than 50% or greater than 50%, depending on the distribution of the other options and the total number of students.

Therefore, the fact that the two values do not add up to 101 does not necessarily mean that the student's answer for part b is incorrect.

Instead, the student should check their calculations and assumptions to make sure they have followed the correct procedure for calculating percentages.

Therefore, the student's reasoning is flawed.

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From the exponential distribution, the probability of an emergency arrival occurring in the next minute is the same regardless of how long we have already been waiting.

If X follows an exponential distribution with parameter θ, then the expected value (mean) of X is equal to θ.

In this case, θ = 8, so the average waiting time between two emergency arrivals is also 8 minutes.

This means that on average, we expect an emergency arrival to occur every 8 minutes. However, it is important to note that the exponential distribution is memoryless, meaning that the probability of an emergency arrival occurring in the next minute is the same regardless of how long we have already been waiting.

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The solution for y in the triangle by virtue of similar triangles is 3√7

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

The triangle

Using the theorem of similar triangles, we have the following equation

y/9 = 7/y

Cross multiply the above equation

so, we have the following representation

y^2 = 9 * 7

Evaluate

y^2 = 63

Take the square root of both sides

y = 3√7

Hence, the solution for y is 3√7

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Answer:

$17.53

Step-by-step explanation:

385.66 / 22 = 17.53

The total length of the two sides, 1 and 2, of the triangle is 15x2 − 6x + 1. This can be shown by adding the two polynomials side by side.

Part A:

The total length of the two sides, 1 and 2, of the triangle is 15x2 − 6x + 1. This can be shown by adding the two polynomials side by side.8x2 − 5x − 2 + 7x − x2 + 3 =5 ,8x2 + 7x − 5x − x2 − 2 + 3 =15x2 − 6x + 1Part B:

The length of the third side of the triangle is 15x2 − 6x + 1, which is the same as the total length of the two sides in Part A. This can be shown by subtracting the two polynomials side by side.

15x2 − 6x + 1 − (8x2 − 5x − 2 + 7x − x2 + 3) =

15x2 − 6x + 1 − (8x2 + 7x − 5x − x2 − 2 + 3) =

15x2 − 6x + 1 − 15x2 + 6x − 1 = 0Part C:

Yes, the answers for Part A and Part B show that the polynomials are closed under addition and subtraction. This can be seen by the fact that the total length of the two sides of the triangle is the same as the length of the third side of the triangle, which is 15x2 − 6x + 1. This means that when the two polynomials are added or subtracted, the resulting polynomial is the same regardless of the order in which they are added or subtracted. This is a sign that the polynomials are closed under addition and subtraction.

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