two equivalent fractions for 1/3

The first five terms in the sequence generated by the explicit formula [tex]y_n[/tex] = -5n - 5 are: -10, -15, -20, -25, -30.

To generate the first five terms in the sequence using the explicit formula [tex]y_n[/tex]  = -5n - 5,

we substitute the values of n from 1 to 5 into the formula.

For n = 1:

[tex]y_1[/tex]= -5(1) - 5 = -10

For n = 2:

[tex]y_2[/tex] = -5(2) - 5 = -15

For n = 3:

[tex]y_3[/tex] = -5(3) - 5 = -20

For n = 4:

[tex]y_4[/tex] = -5(4) - 5 = -25

For n = 5:

[tex]y_5[/tex] = -5(5) - 5 = -30

Therefore, the first five terms in the sequence generated by the explicit formula [tex]y_n[/tex] = -5n - 5 are:

-10, -15, -20, -25, -30.

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Answer:

The determinant of an identity matrix is always 1.

Step-by-step explanation:

Given : An identity matrix.

We have to find the determinant of an identity matrix.

Consider an identity matrix,

Identity matrix is a matrix having entry one in its diagonal and  rest all entries are zero.

Let us consider a 2 × 2 identity matrix,

[tex]I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]

We know determinant of a  2 × 2 matrix

[tex]I=\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]

is given by

D = ad - bc

Thus, here a = 1 , b = 0 , c= 0 d= 1

Thus, D = 1 - 0 = 1

Thus, The determinant of an identity matrix is always 1.

To find out which is bigger, we calculate 40% of 210 and 1/4 of 320. 40% of 210 is greater than 1/4 of 320.

To find out which is bigger, 40% of 210 or 1/4 of 320, we need to calculate both values.

First, 40% of 210 can be calculated by multiplying 210 by 0.4. This gives us 84.

Next, 1/4 of 320 can be calculated by dividing 320 by 4. This gives us 80.

Therefore, 40% of 210 is greater than 1/4 of 320.

Final answer:

To find the product of (-2x^2)^3 and -3x, first calculate the cube of -2x^2 (-8x^6), then multiply it by -3x to obtain 24x^7.

Explanation:

The student has asked to find the product of two expressions, (-2x^2)^3 and -3x. To solve this, we first calculate the cube of -2x^2, which is -8x^6, then we multiply this result by -3x to find the final product.

So, let's perform these two steps:

Cube of -2x^2: (-2x^2)^3 = (-2)^3 × (x^2)^3 = -8 × x^6 = -8x^6

Multiplication by -3x: -8x^6 × -3x = 24x^7

Therefore, the product is 24x^7.

The method of pay that results in the most earnings is the second method of pay

In order to determine which method of pay would result in the most earnings ,  the value of each method would be determined

Value of the first option

6% commission on all sales = 6% x  $73,620.

0.06 x  $73,620. = $4,417.20

Value of the second option

Monthly salary of $3,000 plus 2% commission on all sales =  $3,000 + (2% x  $73,620)

$3,000 + (0.02% x  $73,620)

= $3000 + $1472.40

= $4472.40

Value of the third option

Graduated commission of 4% on the first $50,000 in sales and 9% on anything over that.

= (4% x $50,000) + (9% x $23,620)

= $2000 + $2125.80

= $4125.80

Value of the fourth option

Graduated commission of 5% on the first $35,000 in sales and 7% on anything over that.

= (5% x$35,000) + (7% x $38,620)

= $1750 + $2703.40

= $4,453.40

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Answer: The answer saying YES, is WRONG, the CORRECT ANSWER IS NO.

Answer:

The answer is no

0.45^2-4(-.005)(125)=2.7025

so no it do not exceed

Step-by-step explanation:

Using the simple interest formula, an investment of $480 at a 7% annual interest rate will earn $67.20 in simple interest after 2 years.

Finding Simple Interest on an Investment

To calculate the simple interest earned after 2 years on a $480 investment at a 7% annual interest rate, you can use the simple interest formula: Interest = Principal times Rate times Time.

The principal (P) is the initial amount of money, which in this case is $480. The rate (R) is the annual interest rate expressed as a decimal, so 7% becomes 0.07. The time (T) is the number of years the money is invested or borrowed, which is 2 years in this scenario.

Using the simple interest formula:

Interest = 480 times 0.07 times 2

Interest = 33.6 times 2

Interest = $67.20

Therefore, an investment of $480 at a 7% annual interest rate will earn $67.20 in simple interest after 2 years.

Answer:

870 calories Option D.

Step-by-step explanation:

A bag of chips contains calories per serving = 145

If each bag contains servings = 3

so total calories per bag = 3 × 145

                                         = 435

Now we have to calculate the total servings in 2 bags.

Number of calories in 1 bag = 435

Therefore, number of calories in 2 bags = 435 × 2

                                                                   = 870 calories

Option D. 870 calories is the answer.

To predict the number of votes for Nuncio for class president, multiply 3/4 (or 0.75) by the total number of students (340), resulting in a prediction that 255 students would vote for Nuncio.

To predict how many of the 340 students in the school would vote for Nuncio for class president, we need to understand the proportion that we got from the survey. Since 3 out of 4 students said they would vote for Nuncio, this is the same as 75% or 0.75 when expressed as a decimal.

We then apply this proportion to the total number of students in the school:

Convert the fraction 3/4 to a decimal: 3 ÷ 4 = 0.75.

Multiply the total number of students by the decimal: 340 students × 0.75 = 255 students.

Therefore, we predict that 255 of the 340 students would vote for Nuncio for class president.

Trade discounts are not fixed; they are true to vary based on several factors including order volume, buyer-seller relationships, and industry norms. They are a dynamic component of economic transactions within the complex trade environment and are influenced by market interactions and broader economic principles.

The statement "Amounts of trade discounts are not fixed" is true. Trade discounts can vary greatly and are typically influenced by a variety of factors including the volume of the goods ordered, the relationship between the buyer and seller, and the industry standards.

For instance, when businesses deliver larger lots, volume discounts may be offered, which reflect the lower costs of providing goods in bulk rather than differences in willingness to pay. This variation in trade discounts ensures that each transaction is adjusted to meet the precise needs of both the buyer and seller, depending on the specific circumstances of the trade.

Moreover, the trade environment is complex and the interactions between buyers and sellers determine the gains from trade in an economy. These interactions depend on market structure, negotiation possibilities, and the mode of sale, such as retail or auction.

Consequently, trade discounts are part of a dynamic economic system where various elements such as free trade agreements, industry adjustments, transaction costs, and the unmeasured benefits of competition and product variety all play a role in shaping the final outcome.

By setting up a system of linear equations and solving for x and y, we find that the cost of a dress is $8 and the cost of a belt is $4.

To find the cost of a dress and a belt, we can set up a system of linear equations using the information given. Let x denote the cost of a dress and y denote the cost of a belt. We then have two equations:

Subtract equation (2) from equation (1) to eliminate y:

5x + 2y - (3x + 2y) = $48 - $32

2x = $16

Now we can solve for x:

x = $16 / 2

x = $8

Now that we know the cost of a dress (x), we can substitute this value into equation (2) to find the cost of a belt (y):

3(8) + 2y = $32

24 + 2y = $32

2y = $32 - $24

2y = $8

y = $8 / 2

y = $4

Therefore, the cost of a dress is $8 and the cost of a belt is $4.

the real answer is 5.79, the other person had had miscalculation

The resulting acceleration of the object is approximately [tex]\( 1.127 \, \text{m/s}^2 \).[/tex]

To find the resulting acceleration of an object when a force is applied to it, you can use Newton's second law of motion, which states:

F = ma

Given that the force F = 7.1 Newtons and the mass m = 6.3 kg, we can rearrange the formula to solve for acceleration:

[tex]\[ a = \frac{F}{m} \]Substitute the given values:\[ a = \frac{7.1 \, \text{N}}{6.3 \, \text{kg}} \]Now, divide to find the acceleration:\[ a = \frac{7.1}{6.3} \, \text{m/s}^2 \]\[ a = 1.127 \, \text{m/s}^2 \][/tex]

So, the resulting acceleration of the object is approximately [tex]\( 1.127 \, \text{m/s}^2 \).[/tex]

Complete question:

An object with a mass of 6.3 kg has a force of 7.1 Newtons applied to it. What is the resulting acceleration of the object?​

Answer:

The correct option is 4.

Step-by-step explanation:

The relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F is defined by the given equation.

[tex]F=\frac{9}{5}C+32[/tex]

We need to find the formula for C.

Subtract 32 from both the sides.

[tex]F-32=\frac{9}{5}C+32-32[/tex]

[tex]F-32=\frac{9}{5}C[/tex]

Multiply both sides by 5.

[tex]5(F-32)=9C[/tex]

Divide both sides by 9.

[tex]\frac{5(F-32)}{9}=\frac{9C}{9}[/tex]

[tex]\frac{5}{9}(F-32)=C[/tex]

The formula for C is [tex]C=\frac{5}{9}(F-32)[/tex].

Therefore the correct option is 4.

Answer:

1626 divided by 12 is written as [tex]\frac{271}{2}=135\frac{1}{2}[/tex]

Step-by-step explanation:

To find : What is 1626 divided by 12 as a mixed number ?

Solution :

Writing 1626 divided by 12 in a fraction from,

[tex]\frac{1626}{12}[/tex]

Writing fraction in simpler form by reducing with common factors,

[tex]\frac{1626}{12}=\frac{2\times 3\times 271}{2\times 2\times 3}[/tex]

[tex]\frac{1626}{12}=\frac{271}{2}[/tex]

Writing [tex]\frac{271}{2}[/tex] in mixed fraction by dividing 271 by 2,

[tex]271=135\times 2+1[/tex]

i.e. [tex]\frac{271}{2}=135\frac{1}{2}[/tex]

Therefore, 1626 divided by 12 is written as [tex]\frac{271}{2}=135\frac{1}{2}[/tex]