Trigonometric ratios can be used with any type of triangle.
O
True
O
False

The number of cans Tara collected is 35.

Mrs. Kenney's class is holding a canned food drive for Thanksgiving. Tara collected 10 more cans than Phil. Laurie collected twice as many cans as Tara.  They collected 130 cans altogether.

Therefore, let's find the number of cans Tara collected.

Hence, using equation,

let

x = number of cans Phil collected

Number of cans Tara collected = x + 10

Number of cans Laurie collected = 2(x + 10) = 2x + 20

Therefore,

x + x + 10 + 2x + 20 = 130

4x + 30 = 130

4x = 130 - 30

4x = 100

x = 100 / 4

x = 25

Hence, Tara collected 25 + 10 = 35 cans.

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Answer:

False. The center of a semisimple Lie algebra is usually not trivial.

Step-by-step explanation:

The center of a semisimple Lie algebra is the set of elements of the Lie algebra that commute with all other elements in the algebra. In most cases, the center of a semisimple Lie algebra is not trivial, meaning it contains at least one non-zero element. For example, the center of the simple Lie algebra sl(2,C) contains the two-dimensional Lie algebra spanned by the scalar matrices I and -I. The center of the Lie algebra so(5,C) is spanned by the five-dimensional Lie algebra spanned by the matrices diag(1,1,1,-1,-1). These examples demonstrate that the center of a semisimple Lie algebra is usually not trivial.

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Answer:

7 hours

Step-by-step explanation-35/-5=7

a. [tex]6x+11=55[/tex]

Subtract 11 from both sides:

[tex]6x+11-11=55-11[/tex]

[tex]6x=44[/tex]

Divide both sides by 6:

[tex]\dfrac{6x}{6} =\dfrac{44}{6}[/tex]

[tex]x=7.333333[/tex]

___________________________

b. [tex]-3x-18=39[/tex]

Add 18 to both sides:

[tex]-3x-18+18=39+18[/tex]

[tex]-3x=57[/tex]

Divide both sides by -3:

[tex]\dfrac{-3x}{-3} =\dfrac{57}{-3}[/tex]

[tex]x=-19[/tex]

___________________________

c. [tex]2x-14=-28[/tex]

Add 14 to both sides:

[tex]2x-14+14=-28+14[/tex]

[tex]2x=-14[/tex]

Divide both sides by 2:

[tex]\dfrac{2x}{2} =\dfrac{-14}{2}[/tex]

[tex]x=-7[/tex]

___________________________

d. [tex]7x+9=58[/tex]

Subtract 9 from both sides:

[tex]7x+9-9=58-9[/tex]

[tex]7x=49[/tex]

Divide both sides by 7:

[tex]\dfrac{7x}{7} =\dfrac{49}{7}[/tex]

[tex]x=7[/tex]

___________________________

Only option d had a solution of x = 7.

Answer:

In standard form the equation would be

6x -9y = 54

Step-by-step explanation:

Let x = 0

-9y = 54  Divide both sides by -9

y = -6

(0,-6)

Let y = 0

6x = 54  Divide both sides by 6

x = 9

(9,0)

Answer:

use the Pythagoras theorem

Step-by-step explanation:

x²+(2x)²=x²+4x²=5x²

square root of 5x²= (square root of 5)x

The relationship between the quantity of firemen and the amount of damage brought on by a fire is, in fact, created by a third party. Thus, choice A is the best one.

Firefighter

A fireman is a first responder and rescuer who has received significant training in firefighting. They are primarily responsible for putting out dangerous flames that endanger life, property, and the environment as well as for rescuing humans and, in some circumstances, animals from perilous situations.

The third aspect

The numbers that divide 3 in three equal parts with no remainders are known as its factors. As is well known, the earliest odd prime number is three. The three components and their pair can be expressed in both good and negative ways. For illustration, the pair factor of 3 is shown.

It is true to say that a third party is to blame for the correlation between the number of firefighters and the amount of damage a fire causes. So, option A is the best choice.

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The factors of 3 are the numbers that split it into three equal pieces with no remainders. The oldest odd prime number is three, as is common knowledge. The three elements and their paired expressions have both positive and negative connotations. The pair factor of three is displayed as an illustration.

It is accurate to say that there is a third party at fault for the association between the quantity of firefighters and the scope of a fire. As a result, option A is the best one.

If you isolated x in the second equation to use the substitution method. -3y + 12 expression we substitute into the first equation.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.

The substitution method has three straightforward steps, which are listed below:

2x + y = 8

-x - 3y = -12

__________

-3y + 12

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The equation of the line that represents the straight line in the graph will be y = (3/2)x.

An association between various factors brings about a straight model when a diagram is shown. The variable will have a level of one.

The straight condition is given as,

y = mx + c

Where m is the incline of the line and c is the y-block of the line.

From the figure, the line is passing through the origin. Then we have

y = mx + c

0 = m (0) + c

c = 0

Then the equation of the line is written as,

y = mx

From the figure, the line also passes through points (4, 6). Then we have

6 = 4m

m = 3/2

Then the equation of the line is given as,

y = (3/2)x

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The SUV will be $5,299.13 worth than the car 5 years after their model years.

What is the meaning of rounded to the nearest cent?

Look at the number to the right of the whole cents when rounding money to the closest cent. In this instance, it is 9. Increase the cents by one if the figure is five or above. The cents should remain the same if the number is four or less. Given that 9 is more than 5, $3.299 equals $3.30.

Given that,

The value of a car can be predicted by using the function

f(x)=12,000(0.89)^x

Where x years from its model year.

To find the current value of the car, put x = 0 in the model equation:

f(0)=12,000(0.89)^0

f(0) = 12,000.

To find the value of the car after 5 years, put x = 5 in the model equation:

f(5)=12,000(0.89)^5

f(5) = 6700.871

The difference of the value of car is 12,000 - 6700.871 = $5299.129 = $5299.13 (rounded to the nearest cent)

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Answer: The value of x-[tex]\sqrt{x}[/tex]= 2

Step-by-step explanation: [tex]x^{2}[/tex] - 16[tex]\sqrt{x}[/tex]

Let [tex]u= \sqrt{x}[/tex], then

[tex]u^{2} = x\\^u{4} =x^{2}[/tex]

substituting these into the original equation

[tex]u^{4} -16u -12 =0[/tex]

This factor is easy as -

[tex](u^{2} -2u -2) (u^{2} +2u +6) =0[/tex]

[tex]u^{2} -2u -2=0\\[/tex]

Salaried employees get paid more for additional hours worked but they must keep up with their responsibilities and complete necessary tasks even if that means working extra hours. The correct option is A

Salaried employees can be defined as someone who receives a fixed amount of pay salary regardless of how many hours they work each weeks. Salaried employees enjoy the security of steady paychecks and they tend to pull in higher overall income than hourly worker.

Therefore the correct option is A Salaried employees get paid more for additional hours worked.

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The value of the integral [tex]\int\limits^2_0 {f(x)} \, dx[/tex] is 5. The value of the integral [tex]\int\limits^5_2 {f(x)} \, dx[/tex] is 0. The value of the integral [tex]\int\limits^8_0 {f(x)} \, dx[/tex] is 25.

The definite integral of a function over a limit represents the area under the curve bounded by the limit as given in integration.

The integral represents the area under the curve.

(a) [tex]\int\limits^2_0 {f(x)} \, dx[/tex] = area of the triangle with base 2 and height 5.

Area = (1/2)2 x 5 = 5 units square

(b) [tex]\int\limits^5_2 {f(x)} \, dx[/tex] = area under the triangle with base 1 and height 5 - area above the triangle with base 1 and height 5 = 0

(c) [tex]\int\limits^8_0 {f(x)} \, dx=\int\limits^2_0 {f(x)} \, dx+\int\limits^4_2 {f(x)} \, dx+\int\limits^8_4 {f(x)} \, dx[/tex]

⇒ 5 + 0 + 4 x 5 = 25 units sqaure.

Hence "integral [tex]\int\limits^2_0 {f(x)} \, dx[/tex] is 5. Integral [tex]\int\limits^5_2 {f(x)} \, dx[/tex] is 0. The value of the integral [tex]\int\limits^8_0 {f(x)} \, dx[/tex] is 25".

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Both the methods can be used to solve a mixed fraction including a whole number and a fraction or solving the difference of a whole number and a fraction.

Mixed fractions are type of fractions which involve a whole number and a fraction. This is of the form a [tex]\frac{b}{c}[/tex]. This is actually a + [tex]\frac{b}{c}[/tex].

You can use either methods when solving a whole number and a fraction.

Let us take a whole number 3 and a fraction [tex]\frac{2}{10}[/tex] for instance.

First Method :

Solve it by cross multiplication.

Let the denominator of the whole number 3 be 1.

[tex]\frac{3}{1}[/tex] ± [tex]\frac{2}{10}[/tex] = [(3 × 10) ± (2 × 1)] / (1 × 10) = [30 ± 2] / 10

If the question is for adding, we get, [tex]\frac{3}{1}[/tex] + [tex]\frac{2}{10}[/tex] = (30 + 2) / 10 = 32/10

If the question is finding difference, we get, [tex]\frac{3}{1}[/tex] - [tex]\frac{2}{10}[/tex] = (30 - 2) / 10 = 28/10

Second Method :

Again let the denominator of the whole number be 1.

Find the LCD (Least Common Denominator) of 1 and 10.

This is 10.

So we have to make the denominator of [tex]\frac{3}{1}[/tex] to 10.

Multiply both numerator and denominator with 10, we get 30/10.

A normal multiplication of fractions, if the denominator is same add or subtract the numerators let the denominator be as such.

Now add or subtract [tex]\frac{30}{10}[/tex] ± [tex]\frac{2}{10}[/tex] = (30 ± 2) / 10.

Hence both the methods can be used.

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The solution for f(-2) in the function f(x) = x² + 3 is 7

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

f(x) = x 2 +3

To make the equation legible, we need to rewrite it

So, we have the following representation

f(x) = x² + 3

Also from the question, we have

f(-2)

This means that the value of x is -2, and we calculate f(x) when x = -2

Substitute the known values in the above equation, so, we have the following representation

f(-2) = x² + 3

So, we have the following equation

f(-2) = (-2)² + 3

Evaluate

f(-2) = 7

Hence, the solution is 7

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The probability of getting 3 successes is 0.00463 Or 0.46%.

In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment). The binomial probability is [tex]P(x) = ^nC_xp^xq^{n-x}[/tex] if the likelihood of success on a given trial is p.

Given, A fair die is rolled three times. Getting a 4 is considered 'success', while all other outcomes are 'failures'.

So, The probability(p) of getting a 4 on a die is (1/6), and hence the probability of failure(q) = 1 - 1/6 = 5/6.

Also given, n = 3.

Therefore, The probability of getting 3 successes is,

[tex]P(x = 3) = ^3C_0(1/6)^3\times(5/6)^0[/tex].

[tex]P(x = 3) = 1\times\frac{1}{216}\times1[/tex]

[tex]P(x = 3) = \frac{1}{216}[/tex].

So, the probability of 3 successes is 1/216.

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The 99% confidence interval for the mean wage of all judges is given as follows:

($61.5, $68.5).

We have the standard deviation only for the sample, hence the t-distribution is used to obtain the confidence interval.

The equation that defines the bounds of the confidence interval is given as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 25 - 1 = 24 df, is t = 2.797

The remaining parameters are given as follows:

[tex]\overline{x} = 65, s = 6.25, n = 25[/tex]

Hence the lower bound of the interval is calculated as follows:

65 - 2.797 x 6.25/5 = $61.5.

The upper bound of the interval is of:

65 - 2.797 x 6.25/5 = $68.5.

The problem asks for the 99% confidence interval for the mean wage of all judges.

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Answer:

To find the number of integral solutions for x in the given inequality, we can first solve the inequality to find the range of values that x can take on. To do this, we need to isolate the x term on one side of the inequality, so let's start by subtracting 9 from both sides of the inequality:

-69 ≤ 7x + 9 ≤ 49

-9 ≤ 7x ≤ 40

Next, we can divide both sides of the inequality by 7 to isolate the x term:

-9/7 ≤ x ≤ 40/7

The result of this calculation is a range of values for x, but we are looking for the number of integral solutions, which means we need to find the number of whole numbers that x can take on within this range. In this case, we can see that the range of possible values for x is from -1 to 5, and there are 5 whole numbers within this range (-1, 0, 1, 2, 3, 4, 5), so there are 5 integral solutions for x in this inequality.

In general, to find the number of integral solutions for x in an inequality of the form a ≤ bx + c ≤ d, where a, b, c, and d are constants, you can follow these steps:

1.Solve the inequality to isolate the x term on one side, by subtracting c from both sides and then dividing both sides by b. This will give you the range of possible values for x.

2.Count the number of whole numbers within this range to find the number of integral solutions for x.

Step-by-step explanation:

The number of badges that can be cut from a piece of card, which is 20 centimeters by 30 centimeters, is 21.

A region's size on a plane or curved surface is expressed by a measurement known as an area. Unlike the area of a plane region or plane area, which refers to the area of a shape or planar lamina, surface area describes the area of an open surface or the boundary of a three-dimensional object.

Given:

A sheet of the card is 20 centimeters by 30 centimeters,

The diameter of a badge, d = 60 mm or 6 cm,

Calculate the area of the sheet as shown below,

[tex]Area = length \times width[/tex]

Area = 20 × 30 = 600 cm²

Calculate the area of the badge as shown below,

[tex]Area = \pi d^2 / 4[/tex]

Area = 3.14 × 6² / 4

Area = 28.26 cm²

To calculate the number of badges[tex]No\ of\ badges = Area\ of \ sheet / Area \ of badge[/tex], use the formula given below,

Number of badges = 600 cm² / 28.26 cm²

Number of badges = 21.23 or 21

Therefore, the number of badges that can be cut from a piece of card, which is 20 centimeters by 30 centimeters, is 21.

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As Silas says Frotastic is a better deal. Because at Frotastic we get 1 ounce at $0.48

The ounce is derived from the Ancient Roman uncia, which was equal to one-twelfth (1/12) of a Roman pound and weighed around 27.35 grams, or 0.967 of an Avoirdupois ounce (libra). This originally meant "unit" because it originates from the Latin uno ('one'). The word "uncia" was borrowed twice: once into Old English as "ynsan" or "yndsan" from an unrecorded Vulgar Latin version that palatalized the "c" before the I to become the present English word "inch."

Here at Fromazing, 1 ounce of Frozen Yougurt costs $0.50 per ounce

whereas at Frotastic  5oz = $2.40

1oz = 2.40/5

= 0.48$

8oz = $3.84

1oz = 3.84/8

= $0.48

11 oz = $5.28

10z = 5.28/11

=$0.48

similar case for 14 oz = $6.72

1oz = 6.72/11

=$0.48

Therefore Frotastic is a better deal as Silas said

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The solution of the mixed number as a whole number is 11.4.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

A mixed number is the combination of a whole number and a proper fraction. It usually denotes a number between two whole numbers.

The given fraction is 11(⁴/₁₀). The mixed number can be simplified as below,

E = 11(⁴/₁₀)

E = 114 / 10

E = 11.4

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The solution to the system of linear equations is where they intersect which is at (- 0.5, 1.5).

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

From the graph of two lines in the coordinate system, every square box has a side length of 1 unit.

Now, The solution of the system is the point at which these two lines intersect.

By, Observing the graph we conclude that at (- 0.5, 1.5) they intersect and it is the solution of these two linear equations.

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Answer:

-6°

Step-by-step explanation:

26.4 - 32.4 = -6

Subtract the absolute values of the both number and give the sign of the larger absolute value.

32.4 - 26.4 = 6

The sign will be negative because -32.4 has a larger absolute value (farther from zero) than 26.4

Answer:

- 6°F.

Step-by-step explanation:

  26.4

-  32.4

= -6.0

The temperature at midnight:

-6°F.

If the correlation coefficient is 0.4, the total variation in salary can be explained by gender is 16%.

A statistical concept known as the correlation coefficient aids in establishing a relationship between expected and actual values gained through statistical experimentation. The estimated correlation coefficient's value explains how well the expected and actual values match.

Correlation Value of the coefficient is always between -1 and +1. If the correlation coefficient value is positive, the two variables have a similar and same relationship. Otherwise, it shows how the two variables are different.

If the correlation coefficient (R) =  0.4

Coefficient of determination (R²) = (0.4)²

Coefficient of determination (R²) = 0.16

So that, the total variation in salary can be explained by gender is 16%.

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The required equation of the line passing through (-8, 1) and parallel to x - 4y = 4 is y = 1/4x + 1.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Slope of the given line x - 4y = 4
y = 1/4x - 1
m = 1/4

The slope of the parallel lines is always equal

Now,
Equation of the parallel line passing through the point (-8, 1) is given as,
y - y₁ = m (x - x₁)
y -1 = 1/4(x + 8)
y = 1/4x + 1

Thus, y = 1/4x + 1 is the needed equation for the line passing through (-8, 1) and parallel to x - 4y = 4.

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1) curl = del x

2) grad(div ) = del(div )

3) div(curl(grad )) = div(curl(grad))

What is Scalar field and Vector field?

1) The curl of a vector field is a vector field that describes the local rotational motion of the field. It is defined as the cross product of the del operator (a vector operator that operates on scalar and vector fields) and the vector field:

    curl = del x

2) The gradient of the divergence of a vector field is a scalar field that describes the local rate of change of the divergence of the field. It is defined as the del operator applied to the divergence of the field:

   grad(div ) = del(div ).

3) The divergence of the curl of the gradient of a scalar field is a scalar field that describes the local rate of change of the curl of the gradient of the field. It is defined as the divergence of the curl of the gradient of the field:

   div(curl(grad )) = div(curl(grad)).

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The radius of the full-sized pool is 2 times larger than the radius of the kiddie pool.

By using the expression to approximate the radius of a circle, we want to compare the radius of the two pools.

The expression for the radius of a circle is:

R = √(A/3)

Where A is the area of said circle.

The circular kiddie swimming pool has an area of 28ft^2, we just replace that in the above expression to get:

R =  √(28 ft^2/3) = 3 ft

The full-sized pool has an area of 113 ft^2, then its radius is:

R' = √(113 ft^2/3) = 6 ft

To see how much greater is the radius of the full-sized pool than the radius of the kiddie pool, we just take the quotient:

R'/R = 6ft/3ft

= 2

Hence, the radius of the full-sized pool is 2 times larger than the radius of the kiddie pool.

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Answer:

the eqn given by the function is y=9---(1)

given point is(-3,9)=(X,y)

we know,

y=mx

mx=9 [from 1]

or,m(-3)=9 [from point]

or,m=9/-3

:.m=-3

hence, slope=-3

In order to determine the school that was given the fewest laptops, sort numerically in ascending order (second option)

A numeric data is a dataset that is made up of numbers. An example of a numeric data is the age of students in a class. The best colours of students in a class is not an example of numeric data.

The data that contains information on the number of laptops that was given to a school would be numeric. For example, a school can recieve 100 laptops while another school would receive 10 laptops.

In order to sort a numeric data in ascending order, it means that the smallest numbers would be arranged first.

For example consider this data set 2, 5 100, 1000, 4, 90. In order to arrange in ascending order, this would be the order of the numbers: 2, 4, 5, 90, 100, 1000.

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