use the rule “add 8” to find the cost of 6 T-shirts. Explain how you found your answer.

Answer:

i believe this is how you solve that problem... 2÷5×4

Answer:

See below.

Step-by-step explanation:

This is the correct formula for simple interest, but be careful with the numbers.

a = 6 000(1 + 0. 028t)

0.028 means 2.8% interest rate.

For 2.9% interest rate it should be

a = 6 000(1 + 0. 029t)

The effective interest rate for the specified account is 6.70%.

To find the effective interest rate, we can use the following formula:
Effective Interest Rate = (1 + Nominal Yield / Number of Compounding Periods) ^ Number of Compounding Periods - 1

In this case, the nominal yield is 6.5% and the number of compounding periods is 12 (since it is compounded monthly). Plugging these values into the formula, we get:

Effective Interest Rate = (1 + 0.065 / 12) ^ 12 - 1
Effective Interest Rate = (1.0054166666666667) ^ 12 - 1
Effective Interest Rate = 1.0670171619870418 - 1
Effective Interest Rate = 0.0670171619870418

Multiplying by 100 to convert to a percentage, we get:

Effective Interest Rate = 6.70%

Therefore, the effective interest rate for the specified account is 6.70%.

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a) Sin 2x = 2 tan x / 1 + tan^2 x is an identity.

b) Tan x + cot x = 2 csc 2x is an identity.

To verify that each equation is an identity, we will simplify both sides of the equation and show that they are equal.

For part a, we will use the double angle formula for sine and the Pythagorean identity.

sin 2x = 2 sin x cos x

2 tan x / 1 + tan^2 x = 2 sin x / cos x / 1 + sin^2 x / cos^2 x

= 2 sin x / cos x / cos^2 x / cos^2 x

= 2 sin x / cos x / 1 - sin^2 x

= 2 sin x / cos x / cos^2 x

= 2 sin x cos x

Therefore, sin 2x = 2 tan x / 1 + tan^2 x is an identity.

For part b, we will use the definitions of the trigonometric functions and the double angle formula for cosecant.

tan x + cot x = sin x / cos x + cos x / sin x

= (sin^2 x + cos^2 x) / (sin x cos x)

= 1 / (sin x cos x)

= 2 / (2 sin x cos x)

= 2 / sin 2x

= 2 csc 2x

Therefore, tan x + cot x = 2 csc 2x is an identity.

In conclusion, we have verified that both equations are identities.

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The magnitude of the resultant force  ||FR|| is 80.55 N.

The weight of the box is acting straight downward, perpendicular to the incline, so it does not affect the magnitude of the resultant force parallel to the incline. Therefore, we only need to consider the force of 150 N pushing the box up the incline.

Let's call the angle between the force of 150 N and the incline "theta". We can find theta by subtracting 58 degrees from 90 degrees (since the incline is at an angle of 58 degrees with respect to the horizontal). So:

theta = 90 degrees - 58 degrees

theta = 32 degrees

Now we can use trigonometry to find the component of the force of 150 N parallel to the incline. We'll use sine, since we know the hypotenuse (the force) and the opposite side (the component parallel to the incline):

sin(theta) = opposite/hypotenuse

sin(32 degrees) = ||FR||/150 N

Solving for ||FR||, we get:

||FR|| = 150 N * sin(32 degrees)

||FR|| ≈ 80.55 N

Therefore, the magnitude of the resultant force is approximately 80.55 N.

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The constant of variation k for this relationship is 4.

To find the constant of variation k for the given relationship, we can use the formula for direct and inverse variation:

k = (r * y^2) / √n

Where r is the variable that varies directly as the square root of n, and inversely as the square of y. To find the value of k, we can plug in the values of r, y, and n into the equation and solve for k.

For example, if r = 4, y = 2, and n = 16, we can plug these values into the equation to find k:

k = (4 * 2^2) / √16
k = (4 * 4) / 4
k = 16 / 4
k = 4

Therefore, the constant of variation k for this relationship is 4.

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It is true that the quotient of two integers will always result in a rational numbers, as the quotient of two integers is in fact a fraction.

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Answer:

a = 6

b = 5

c = -4

Step-by-step explanation:

(2x-1)(3x+4) = [tex]6x^{2}[/tex]+8x-3x-4 = [tex]6x^{2}[/tex]+5x-4

If the equation is [tex]ax^{2}[/tex]+bx+c, then the values of a, b, and c, are 6, 5, and -4 as it makes the equation true.

Answer:

Step-by-step explanation:

Given that, There are 16 songs that are put on the next CD.And there are 8.75 more songs.Also, 60% of the songs are removed. Based on the above information, the calculation is as follows:

16+(0.875 x 16)=17.4

17.4(0.60 x 17.4)= 181.656 = 182 :)

The equivalent expression is option D)  [tex]81/m^7.[/tex]

What is the equivalent expression?

In mathematics, an equivalent expression is one that has the same value or meaning as another expression, even though it may look different. In other words, two expressions are equivalent if they simplify to the same value or form.

To simplify the expression [tex](3m^{(-4)})^3 * (3m^5)[/tex], we need to apply the power of a power property of exponents, which states that [tex](a^b)^c = a^(b*c)[/tex].

Using this property, we can rewrite [tex](3m^{(-4)})^3[/tex] as [tex]3^3[/tex] * [tex](m^{(-4)})^3 = 27 * m^{(-12)[/tex]. Similarly, we can rewrite (3m⁵) as 3 * m⁵.

Substituting these values back into the original expression, we get:

[tex](3m^{(-4)})^3 * (3m^5) = 27 * m^{(-12)} * 3 * m^5[/tex]

[tex]= 81 * m^{(-12+5)[/tex]

[tex]= 81 * m^{(-7)[/tex]

Therefore, the equivalent expression is option D) [tex]81/m^7.[/tex]

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Answer:

x = 106 degrees

Step-by-step explanation:

we can create a triangle with angles x, 30, and 26+18.

that means x + 30 + (26 + 18) = 180.

move the constants to one side to get x = 180 - 30 - (26 + 18) = 106

Answer:

There would be no value to the laptop. If you’re looking for the actual value, it would be worth $-375.

Step-by-step explanation:

The value of the determinant of the coefficient matrixis 102.

A coefficient matrix in linear algebra is a matrix made up of the coefficients of the variables in a group of linear equations. In order to solve systems of linear equations, the matrix is used.

The value of the determinant of the coefficient matrix can be found by expanding the determinant along the second row. The coefficient matrix is:

| -3 0 -6 |
| 5 -2 3 |
| 2 -1 -7 |

Expanding the determinant along the second row, we get:

= 5(-1)³(-3(-7) - (-6)(-1)) - (-2)(-1)⁴((-3)(-7) - (-6)(2)) + 3(-1)⁵((-3)(-1) - (0)(2))
= 5(21 - 6) - (-2)(21 - 12) + 3(3 - 0)
= 5(15) - (-2)(9) + 3(3)
= 75 - (-18) + 9
= 75 + 18 + 9
= 102

Therefore, the value of the determinant of the coefficient matrix is 102.

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Answer: Im pretty sure its B

Step-by-step explanation:

Option A and C will be the correct answers based on the provided statement.

A right triangle's hypotenuse is its longest side, its "opposing" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To define the side of right triangles, we utilize specific terminology.

Congruence of the SAS Triangle According to the theorem, two triangles are said to be congruent to one another if they have a single pair of corresponding sides and an incorporated angle that are equal to one another.

The image shows two triangles that are congruent by the SAS Congruence Theorem.

As a result, the following claims satisfy the requirements for two triangles to be regarded as congruent to one another by the SAS Congruity Theorem:

A. the corresponding two sides and the included angle in both triangles are congruent.

C. A pair of two sides that are congruent with the equivalent two sides and angle in the opposite triangle and are parallel to an angle's ray.

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The amount of dog food consumed by five puppies every day as per given condition is equal to 0.65 pounds of food.

Total number of Julia dog Toby  puppies =  5

Dog food eats by each pup =  0.13 pounds every day

Total dog food consume by puppies in one day

= ( total number of puppies ) × ( Dog food eats by each pup every day )

Substitute the value to get the total consumed food,

⇒ Total dog food consume by puppies in one day

= ( 5 ) × ( 0.13 ) pounds of dog food

⇒ Total dog food consume by puppies in one day

= ( 0.65 ) pounds of dog food

Therefore, every day total dog food eat by puppies is equal to 0.65 pounds of food.

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Answer:

$9.50

Step-by-step explanation:

If there are 8 tickets and they all add up to $76, you have to divide 76 by 8 (the number of tickets)

The building's depression angle relative to the plane is found as  24.49°.

According to an aerial photographer who specializes in taking pictures of real estate properties.

The ideal shot should be taken at a height of around 406 feet and a distance of 891 feet from the structure.

Height h = 406 ft

Distance d =891 ft

The building's depression angle relative to the plane:

tan Ф = Height / Distance

tan Ф = 406 / 891

tan Ф = 0.455

Ф = 24.49°

Thus, the building's depression angle relative to the plane is found as  24.49°.

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If a = -3 when g = 9, the two values for a, which will make g equal 25 will be ± 9/5.

If G is inversely proportional to the square of A, then we can write the relationship as:
G = k/A^2 Where k is a constant.

We can use the given values of A and G to find the value of k:
9 = k/(-3)^2
9 = k/9
k = 81

Now we can use the value of k and the desired value of G to find the values of A:

25 = 81/A^2
A^2 = 81/25
A = ± √(81/25)
A = ± 9/5

So the two values of A that will make G equal 25 are 9/5 and -9/5.

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J is a maximal ideal.

1. To prove that A/J is a commutative ring with unity, note that the operations of addition and multiplication on A/J are well-defined and are commutative since they are inherited from the commutative ring A. Furthermore, the additive identity of A is the same as the additive identity of A/J, and therefore A/J has a unity.
2. Suppose first that J is a prime ideal of A. Then, if A/J is not an integral domain, there exist two nonzero elements x,y of A/J such that xy=0. This means that x and y are in the same coset of J in A. Thus, x-y is an element of J. Since J is prime, either x or y must be in J, which is a contradiction. Therefore, A/J is an integral domain. Conversely, if A/J is an integral domain, then the same argument can be reversed to show that J is a prime ideal.
3. If J is a maximal ideal of A, then A/J is a field by the fact proved in this chapter. Since a field is an integral domain, J is a prime ideal.
4. Suppose that A/J is a field. Then, for any ideal I of A, either I is contained in J or J is contained in I. This implies that J is a maximal ideal.

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Answer:

-7/8

Step-by-step explanation:

The two coordinates shown are (0,5) and (8,-2).

The slope formula is (y2-y1)/(x2-x1).

Using that, the slope of a line passing through both points is (-2-5)/(8-0).

That reduces to -7/8.

Answer:

-7/

Step-by-step explanation:

The proof is complete.

To prove that there exists a basis in vector space V that satisfies the condition of $W = \{0\}$, we will use the dimension theorem. The dimension theorem states that if $V$ is an $n$-dimensional vector space, then any subspace of $V$ has a dimension that is less than or equal to $n$. In this case, the given subspace $W$ has a dimension of $n-1$ and so it must be a subspace of $V$. Since the dimension of $W$ is less than the dimension of $V$, the dimension theorem states that there exists a basis in $V$ that satisfies the condition of $W = \{0\}$. Therefore, the proof is complete.

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The required slope of the line shown in the graph is 4/3, and the lines representing the rise and run are shown in the graph.

The slope of a line is a measure of how steeply the line is inclined with respect to the horizontal axis.

Here,

To calculate the slope of a line from the rise and run values, we use the formula:

slope = rise/run

In this case, rise = 6 and run = 4.5. Substituting these values into the formula, we get:

slope = 6 / 4.5

Simplifying the fraction by dividing both the numerator and denominator by 1.5,

slope = 4/3

Therefore, the slope of the line is 4/3.

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The equation that shows the relationship between the age of Danny and Terry is D = T - 6.

Let's represent Danny's age with the variable D and Terry's age with the variable T. We know that Danny is 22 years old, so we can write the equation D = 22.

We also know that Danny is 6 years younger than Terry, so we can write the equation D = T - 6. Now we can substitute the value of D from the first equation into the second equation to find the value of T.

D = T - 6

22 = T - 6

Add 6 to both sides of the equation:

22 + 6 = T

28 = T

So Terry is 28 years old.

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Answer:

Power – A power is an expression that represents repeated multiplication of the same number or variable, such as a raised to the power of n, denoted by aⁿ.

Base – The base is the number or variable that is raised to a power or exponent in a power expression.

Exponent – The exponent is the number that indicates how many times the base is to be multiplied by itself in a power expression.

Coefficient – The coefficient is the numerical factor of a term that contains a variable in an algebraic expression.

Exponential Form – The exponential form is a way of writing a number using a base and an exponent, such as aⁿ, where a is the base and n is the exponent.

Expanded Form – The expanded form is a way of writing an expression as the sum or difference of its individual terms, such as (a+b)² = a² + 2ab + b².

Standard Form – The standard form is a way of writing a number using digits, such as 1234 or 1.234 x 10³.

Exponent Laws – The exponent laws are a set of rules that describe how exponents can be manipulated in algebraic expressions, including the product law, quotient law, power law, and negative exponent law. These laws help simplify and solve equations involving exponents.

To solve this problem, we can use a system of equations. Let's call the number of main-floor seats x and the number of balcony seats y.
The first equation can be written as:
10x + 4y = 5800
The second equation can be written as:
0.3x + 0.5y = 1900

Now we can use the elimination method to solve for one of the variables. Let's multiply the second equation by -10 to eliminate the x variable:
-3x - 5y = -19000
Adding the two equations together gives us:
7x - y = 3900
Now we can use substitution to solve for one of the variables. Let's solve for y in the first equation:
y = (5800 - 10x)/4
And substitute this value into the second equation:
7x - (5800 - 10x)/4 = 3900
Multiplying both sides by 4 gives us:
28x - 5800 + 10x = 15600
Solving for x gives us:
38x = 21400
x = 563.16
And plugging this value back into the first equation to solve for y gives us:
y = (5800 - 10(563.16))/4
y = 609.21
So there are approximately 563 main-floor seats and 609 balcony seats.

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Using probability distribution, we can find that P(x=9) = 0.13

To determine the chance of each potential value that a random variable might have, a function known as the probability distribution is used. A discrete probability distribution can be defined using a probability distribution function and a probability mass function.

Both a probability density function and a probability distribution function can be used to define a continuous probability distribution. The geometric, Bernoulli, binomial, and Bernoulli distributions are examples of probability distributions.

Now in the given question,

P(3) = .04

P(6) = .62

P(12) = .21

Now,

p (3) + p (6) + p (9) + p (12) = 1

0.04 + 0.62 + p(9) + 0.21 = 1

p(9) = 0.13

Therefore, the value of P (9) = 0.13

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Answer:

Day 24 will be the day she'll reach $300

Step-by-step explanation:

Answer20th

Step-by-step explanation:

The number of cubes in the container is 8^(5) and the correct answers are 8^(5) and 8^(7)*8^(-2).

The total volume of the cubes in a container is 8^(7)  cubic centimetersand the volume of each individual cube is 8^(2) cubic centimeters. To find the number of cubes in the container, we need to divide the total volume by the volume of each individual cube.

This can be written as:

Number of cubes = 8^(7) / 8^(2)

Using the rule of exponents, when we divide two numbers with the same base, we can subtract their exponents. In this case, 7 - 2 = 5.

So the number of cubes in the container is:

Number of cubes = 8^(5)

Therefore, the correct answer is 8^(5).

The other option, 8^(7)*8^(-2), is also correct. This is because multiplying two numbers with the same base means we can add their exponents. In this case, 7 + (-2) = 5. So this also gives us the same answer, 8^(5).

In conclusion, the number of cubes in the container is 8^(5) and the correct answers are 8^(5) and 8^(7)*8^(-2).

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The simplified form of [tex](4x-3)(-5x^(2)+2x-4)[/tex] is: [tex]-20x^(3) + 23x^(2) - 22x + 12[/tex]

To multiply and simplify the given expression [tex](4x-3)(-5x^(2)+2x-4)[/tex], we can use the distributive property. This means we will multiply each term in the first parentheses by each term in the second parentheses and then combine like terms.

First, we will distribute the 4x to each term in the second parentheses:
[tex]4x * (-5x^(2)) = -20x^(3)4x * (2x) = 8x^(2)4x * (-4) = -16x[/tex]

Next, we will distribute the -3 to each term in the second parentheses:
[tex]-3 * (-5x^(2)) = 15x^(2)-3 * (2x) = -6x-3 * (-4) = 12[/tex]

Now we will combine all of the terms:
[tex]-20x^(3) + 8x^(2) - 16x + 15x^(2) - 6x + 12[/tex]

Finally, we will combine like terms:
[tex]-20x^(3) + 23x^(2) - 22x + 12[/tex]

So the simplified expression is:
[tex]-20x^(3) + 23x^(2) - 22x + 12[/tex]

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