Which term describes gross pay that is calculated based on the number of hours an employee has worked?

Answer:

Addition property of equality  that justifies this statement if p=q then p+s=q+s

Step-by-step explanation:

Addition property of equality states that you add the same number to both sides of an equation.

For example

If a = b then;

a+c = b+c

As per the statement:

if p=q

then;

p+s=q+s

⇒Addition property of equality justifies this statement.

Answer: Carbon occurs as a solid, liquid, and gas.

Carbon is found everywhere.

Carbon is versatile and easily combines with other elements.

Carbon bonds with other elements to form macromolecules.

We are given the equation:

sin θ = 3 / 4

To find for the value of θ, simply compute using the calculator:

θ = sin^-1 (3 / 4)

θ = 48.60° = θ1

To find for the other value, subtract the answer from 180°, so:

θ2 = 180° - 48.60°

θ2 = 131.40°

So the angles are 48.60° and 131.40°

The angles θ for which sin(θ) equals 3/4 between 0° and 180° are approximately 48.6° and 131.4°.

The student's question relates to the topic of trigonometry. Specifically, finding the angles θ for which the sine equals 3/4. To answer this, in the first quadrant, we can use the arcsin function to get θ = arcsin(3/4). Using a calculator, θ ≈ 48.6°. In the second quadrant, the sine is still positive, so θ = 180° - arcsin(3/4) ≈ 131.4°. Thus, the solution is 48.6°, 131.4°. It's worth noting that using a calculator's arcsin function usually gives a result in the first quadrant (0° - 90°) so we have to calculate the second quadrant angle ourselves.

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The expression that represents the phrase 'one third the sum of 12 and a number' is B.) 1/3(12+x).

To represent the phrase "one third the sum of 12 and a number", we can break it down into two parts:

1. The sum of 12 and a number

2. One third of that sum

The expression for the sum of 12 and a number is (12 + x). Then, one third of that sum is [tex]\(\frac{1}{3}(12 + x)\).[/tex]

So, the correct expression is:

[tex]B.) \(\frac{1}{3}(12 + x)\)[/tex]

Answer:

Step-by-step explanation:

2400 × 0.15 = 360

2400 - 360 = 2040

2040 × 1/8 = 255 kg of Cement

2040 × 2/8 = 510 kg of Sand

2040 × 5/8 = 1275 kg of Stone

To check if it is right

255 + 510 + 1275 = 2040 kg

1 cubic meter of concrete the weight of water is 360 Kg, the weight of cement is 255 Kg, the weight of sand is 510 Kg and the weight of stone is 1275 Kg and this can be determine by forming the linear equation in one variable.

Given :

The weight of the water in the concrete will be:

[tex]= 2400\times \dfrac{15}{100}[/tex]

= 360 Kg

Let x be the weight in Kg. Then the combine weight of stone, cement and sand will be:

[tex]8x = 2400 - 360[/tex]

8x = 2040

x = 255 Kg

Then the weight of the cement will be = 255 Kg.

The weight of the sand will be = [tex]\rm 255\times 2 = 510\; Kg[/tex].

The weight of the stone will be = [tex]\rm 255\times 5 = 1275\; Kg[/tex].

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Final answer:

The original equation, after multiplication and simplification, results in -10x^2y^2 - 16y^2 + 8x^-1y^3. This process demonstrates the use of the distributive property and exponent rules in algebra.

Explanation:

The question requires us to multiply -2x-3y by (5yx5+8xy-4y2x2). Proceed by applying the distributive property, which involves multiplying each term inside the parentheses by -2x-3y. Here are the steps:

Multiply -2x-3y by 5yx5 to get -10x2y2.

Multiply -2x-3y by 8xy to get -16y2.

Multiply -2x-3y by -4y2x2 to get 8x-1y3.

Therefore, the final result of the multiplication is -10x2y2 - 16y2 + 8x-1y3.

The result is [tex]\[ -10yx^2 - 16y^2x^{-2} + 8x^{-1}y^3 \][/tex].

To multiply [tex]\(-2x^{-3} y\) by \(5yx^5 + 8xy - 4y^2x^2\)[/tex], we distribute [tex]\(-2x^{-3} y\)[/tex] to each term inside the parentheses.

[tex]\[ -2x^{-3} y (5yx^5) + (-2x^{-3} y)(8xy) + (-2x^{-3} y)(-4y^2x^2) \][/tex]

Simplify each term:

[tex]\[ = -10yx^2 + (-16)x^{-2}y^2x + 8x^{-1}y^3 \][/tex]

[tex]\[ = -10yx^2 - \frac{16y^2}{x^2} + 8x^{-1}y^3 \][/tex]

[tex]\[ = -10yx^2 - 16y^2x^{-2} + 8x^{-1}y^3 \][/tex]

Thus, the final result of the multiplication is [tex]\[ -10yx^2 - 16y^2x^{-2} + 8x^{-1}y^3 \][/tex].

This expression cannot be further simplified, as it represents the result of multiplying each term in the first expression by each term in the second expression and then combining like terms.

Therefore, the correct option is B. [tex]\[ -10yx^2 - 16y^2x^{-2} + 8x^{-1}y^3 \][/tex].

Complete Question:

To graph the inequality y ≤ 1 - 3x, we can start by graphing the equation y = 1 - 3x. The graph should be a solid line passing through the y-axis at 1 and the x-axis at 1/3. The shaded region below the line represents the solution set.

The given inequality is y ≤ 1 - 3x. To graph this inequality, we can start by graphing the equation y = 1 - 3x. This equation represents a line with a y-intercept of 1 and a slope of -3. We can plot the y-intercept at (0, 1) and use the slope to find additional points on the line.

For example, if we increase x by 1, y will decrease by 3. So, when x = 1, y = -2. By connecting these points and extending the line, we can have a line passing through the y-axis at 1 and the x-axis at 1/3.

To graph the inequality y ≤ 1 - 3x, we shade the region below the line because any point in this region will satisfy the inequality.

Therefore, the graph should be a solid line with arrows at both ends, passing through the y-axis at 1 and the x-axis at 1/3, and the region below the line shaded.

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Answer:

B) −4

Step-by-step explanation:

A) f(x) = 15x + 25; f(6) = 115

Answer:

less than -3 and greater than 5

Step-by-step explanation:

The correct transformation that preserves the size and shape of an object, resulting in congruent images, is an isometric transformation. Examples include translation, rotation, and reflection, all of which maintain the object's proportions and dimensions.

A transformation that preserves the size and shape of an object's original image, such that the image is congruent to the pre-image, is known as an isometric transformation. This transformation includes operations like translation (a shift from one place to another), rotation (turning around a center), and reflection (flipping over a line). All these transformations keep the object's dimensions and proportions unchanged. The key property of isometric transformations is that they maintain congruency and preserve distances and angles.

An example of an isometric transformation is when a square is rotated 90 degrees around its center. The square's shape and size remain the same, even though its orientation has changed. This contrasts with dilation, which changes the size of the object, and affine transformations, which can alter both shape and size, such as through stretching or skewing. The correct answer to the student's question is B. isometric.

Answer:

The inequality would be r/7 ≤ 18 and the solution would be r ≤ 126

Step-by-step explanation:

We start by writing the inequality

r/7 ≤ 18

We know to use division between r and 7 since it asks for the quotient and we know to use a ≤ sign since it says "is no more than"

To solve, simply multiply both sides by 7

r ≤ 126

The inequality will be r/7 ≤ 18

Since it's a quotient, we'll need to divide the expression and this will be:

= r/7 ≤ 18

Now the value of r will be gotten thus:

r/7 ≤ 18

Cross multiply.

r ≤ 18 × 7

r ≤ 126

Therefore, this mean that the value of r will be 126 or numbers lower than 126

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1. Independent probability of A and B occurring together (drawing a red queen): [tex]\( \frac{1}{26} \)[/tex]

2. Conditional probability of A given B (drawing a red card given that a queen was drawn): [tex]\( \frac{1}{2} \)[/tex]

- Independent probability: This is the probability of two events occurring together, assuming that one event's occurrence does not affect the other. Mathematically, if A and B are independent events, then [tex]\( P(A \cap B) = P(A) \times P(B) \).[/tex]

- Conditional probability: This is the probability of an event occurring given that another event has already occurred. Mathematically, if A and B are events with[tex]\( P(B) > 0 \)[/tex], then the conditional probability of A given B is [tex]\( P(A|B) = \frac{P(A \cap B)}{P(B)} \).[/tex]

Let's illustrate these concepts with an example:

Suppose we have a deck of cards (52 cards total), and we're interested in two events:

A: Drawing a red card

B: Drawing a queen

First, let's find the independent probabilities:

1. Probability of A (drawing a red card):

  - There are 26 red cards out of 52 total cards, so [tex]\( P(A) = \frac{26}{52} = \frac{1}{2} \).[/tex]

2. Probability of B (drawing a queen):

  - There are 4 queens out of 52 total cards, so[tex]\( P(B) = \frac{4}{52} = \frac{1}{13} \).[/tex]

Now, let's find the probability of both events occurring together (A and B):

3. Probability of A and B (drawing a red queen):

  - There are 2 red queens (hearts and diamonds) out of 52 total cards, so [tex]\( P(A \cap B) = \frac{2}{52} = \frac{1}{26} \).[/tex]

For independent events,[tex]\( P(A \cap B) = P(A) \times P(B) \):[/tex]

[tex]\[ \frac{1}{26} = \frac{1}{2} \times \frac{1}{13} \][/tex]

Now, let's find the conditional probability of A given B:

[tex]\[ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{1}{26}}{\frac{1}{13}} = \frac{1}{2} \][/tex]

1. Independent probability of A and B occurring together (drawing a red queen): [tex]\( \frac{1}{26} \)[/tex]

2. Conditional probability of A given B (drawing a red card given that a queen was drawn): [tex]\( \frac{1}{2} \)[/tex]

In summary, we first calculated the independent probabilities of A and B, then found the probability of A and B occurring together, and finally calculated the conditional probability of A given B using the given formulas and calculations.v

complete question

how can you interpret the independent or conditional probability of two events

-1 +4y < 31

 add 1 to each side:

4y < 32

divide both sides by 4

y<32/4

y<8

The concept referred to in the question is the 'confidence interval', which represents the estimated range that will contain the parameter in the event of obtaining a large quantity of different samples of size n. The denoted term '____' is the standard error (SE), which describes the standard deviation of these sample means distribution. As the number of samples increases, according to the central limit theorem, these sample sums or means tend towards a normal distribution.

The portion of the question, 'The​ _______ represents the expected proportion of intervals that will contain the parameter if a large number of different samples of size n is obtained...' refers to the confidence interval. The confidence interval is a range of values, derived from statistical analysis, that is likely to contain the parameter of interest. For instance, a 0.95 confidence interval stands for a 95% probability that the population parameter will fall within this range.

The second fill-in-the-blank part of the question, 'it is denoted​ _______.' refers to the standard error. The standard error denoted as SE or rarely s.e., represents the standard deviation of the sampling distribution of the mean or in simpler words, it highlights how much our sample mean might differ from the actual population mean.

As the number of different samples (n) gets larger, the sampling distribution of the sum, ΣX, or the mean, X, tends towards the normal distribution, according to the central limit theorem. This feature is harnessed in diverse areas such as probability theory and statistics.

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