what is the slope of the line passing through (13,-2) and (3,-2)

Answer:

The remainder is -1

The binomial is not a factor of the polynomial

Step-by-step explanation:

In the algebraic division, there are 4 terms

The remainder theorem:

Let us use it to solve the question

∵ The dividend is x² - 2

∴ f(x) = x² - 2

∵ The divisor is x - 1

∴ (x - h) = (x - 1)

∴ h = 1

Let us find f(1)

∵ f(1) = (1)² - 2 = 1 - 2 = -1

∴ f(1) = -1

∴ The remainder is -1

∵ f(1) ≠ 0

∴ x - 1 is not a factor of x² - 2

∴ The binomial is not a factor of the polynomial

Answer:

(0, 9)

Step-by-step explanation:

The y-intercept is the point when x = 0. By looking at the graph, when x = 0, y = 9. Therefore, the y-intercept of the line is (0, 9).

Estimate each product then write whether the estimate is greater than or less than the actual product.

= 3027 chairs are there.

There are 325 rows of 9 chairs in the theater.

There are 102 chairs in the balcony.

The total number of chairs there are in the theater and balcony is equal to 3027 chairs.

According to the question;

There are 325 rows in the theater.

Each row contains 9 chairs.

Additionally, there are 102 chairs in the balcony.

In essence, the number of chairs in the theater is;

= 325 × 9

= 2925 chairs.

Additionally, there are 102 chairs in the balcony;

In essence, the total number of chairs is;

= 2925 + 102

= 3027 chairs.

Hence the answer is, = 3027 chairs are there.

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To rotate a point (x, y) 90 degrees clockwise about the origin, we can swap the x and y coordinates and change the sign of the new x coordinate.

For quadrilateral ABCD, let's denote the coordinates of points A, B, C, and D as (x₁, y₁), (x₂, y₂), (x₃, y₃), and (x₄, y₄) respectively.

To find the coordinates of the rotated quadrilateral A'B'C'D', we apply the rotation transformation to each point:

A' = (y₁, -x₁)

B' = (y₂, -x₂)

C' = (y₃, -x₃)

D' = (y₄, -x₄)

In other words, we swap the x and y coordinates of each point and change the sign of the new x coordinate. These new coordinates represent the rotated points of the quadrilateral.

It's important to note that this rotation assumes the origin as the center of rotation. If a different center of rotation is specified, the transformation will be different.

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Answer:

£4290

Step-by-step explanation:

£5500 x (1.00-0.22)

the x (1.00-0.22) is showing we are decreasing by 22%

can also be written like

(£5500x1) - (£5500x0.22)

The decision rule for rejecting the null hypothesis is:

If the calculated t-value is greater than 1.708, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

To determine the decision rule for rejecting the null hypothesis, we need to perform a hypothesis test based on the given information. Let's set up the null and alternative hypotheses:

Null Hypothesis (H0): The mean pressure of the valve is 5.8 pounds/square inch.

Alternative Hypothesis (H1): The mean pressure of the valve is greater than 5.8 pounds/square inch (the valve performs above specifications).

We'll conduct a one-sample t-test since we have the sample mean, sample standard deviation, and sample size.

Given:

Sample mean (\(x^-\)) = 6.1 pounds/square inch

Sample standard deviation (s) = 0.9

Sample size (n) = 26

Level of significance (α) = 0.05 (corresponds to a 5% significance level)

To determine the decision rule, we need to find the critical t-value or the critical region for rejection. Since the alternative hypothesis is one-tailed (the mean pressure is expected to be greater than 5.8), we'll find the critical t-value for the upper tail.

Using the t-distribution table or a t-distribution calculator with (n-1) degrees of freedom (df = 26 - 1 = 25) and the significance level α = 0.05, we find the critical t-value.

The critical t-value at a 5% significance level for the upper tail is approximately 1.708.

Therefore, the decision rule for rejecting the null hypothesis is:

If the calculated t-value is greater than 1.708, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

In summary, the decision rule for rejecting the null hypothesis is: Reject H0 if the calculated t-value is greater than 1.708.

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The law of conservation of energy and momentum can be used to construct the equation that connects the initial release height of block x (hx) and the speed of the two-block system following the collision (v s).

Block x's initial kinetic energy (0.5 * m x * v x2) and potential energy (m x * g * hx) are both equal to the total kinetic energy of both blocks after the collision (0.5 * (m x + m y) * v s).

Combining everything, we get the following equation:

m x * g * hx + 0.5 * m x * v x2 = 0.5 * (m x + m y) * v s2.

where g is the acceleration brought on by gravity, v x is the starting speed of block x, and m x and m y are the masses of blocks x and y.

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Answer:

-7(x+2)

Step-by-step explanation:

-3(2x+5)-(x-1)

↦ -6x+(-15)-x+1

↦-6x-x-15+1

↦7x-14

↦2(x-7)

If the contribution margin from the order is greater than the additional fixed expenses, accepting the special order can result in an increase in operating income.

When evaluating a special sales order, the first step is to calculate the revenue from the order. This is typically based on the selling price and the quantity of units to be sold. Then, the variable expenses directly associated with fulfilling the order, such as direct materials, direct labor, and variable manufacturing overhead, are deducted from the revenue to determine the contribution margin.

Next, the additional fixed expenses that would be incurred if the special order is accepted need to be considered. These expenses are typically costs that are directly related to the production or fulfillment of the order and are not already included in the existing fixed expenses.

To assess the impact of the special order on operating income, the increase (or decrease) in operating income is calculated by subtracting the additional fixed expenses from the contribution margin. If the result is positive, it indicates that accepting the special order would lead to an increase in operating income.

In the given scenario, it is mentioned that Cotton has excess capacity to manufacture the special order. If the incremental analysis shows that the special order would result in a positive increase in operating income, it would be beneficial for Cotton to accept the special sales order.

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Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

\(x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6\)

What is the solution to the equation 98 g = 150 98 g = 150. 98 98 g = 150 minus 98. t = 52. 98 g = 150. 98 minus 98 g = 150 minus 98. t = 52. 98 g = 150. 98 98 g = 150 98. t = 52. 98 g = 150. 98 minus 98 g = 150 98. t = 148.the equation 98 g = 150 is g = 1.53.

To solve for g, we need to isolate it on one side of the equation. We can do this by dividing both sides by 98.

98 g = 150

98 g/98 = 150/98

g = 1.53

Therefore, the solution to the equation is g = 1.53.

Conclusion: The solution to the equation 98 g = 150 is g = 1.53.
Main Answer: The correct equation to solve is 98g = 150. To find the solution, we need to isolate g by dividing both sides of the equation by 98.


1. Start with the given equation: 98g = 150
2. To isolate g, divide both sides by 98: g = 150 / 98

The solution to the equation 98g = 150 is g ≈ 1.53 (rounded to two decimal places).

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The number of calories per cup of popcorn is 28 oz and the number of calories per ounce of soda is 14 oz.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let the number of calories per cup of popcorn be x and the number of calories per ounce of soda be y.

Roselle has 3 cups of popcorn and 6 oz of soda for a total of 162 calories.

3x+6y=162 ------(I)

Carmel has 1 cup of popcorn and 11 oz of soda for a total of 162 calories.

x+11y=182

x=182-11y------(II)

Substitute equation (II) in equation (I), we have

3(182-11y)+6y=162

546-33y+6y=162

546-162-27y=0

384-27y=0

384=27y

y=384/27

y=14

Substitute y=14 in equation (II), we get

x=182-11(14)

x=28

Therefore, the number of calories per cup of popcorn is 28 oz and the number of calories per ounce of soda is 14 oz.

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"Your question is incomplete, probably the complete question/missing part is:"

Roselle has 3 cups of popcorn and 6 oz of soda for a total of 162 calories. Carmel has 1 cup of popcorn and 11 oz of soda for a total of 182 calories. Determine the number of calories per cup of popcorn and per ounce of soda

Answer:

$7.54 is the right answer

Answer:

The answer should be $7.54

Step-by-step explanation:

120.67 ÷ 16 = 7.54

120.67 Being the pay for 16 hours

16 being the number of hours

The probability of selecting exactly three clubs from a standard deck is 0.088. Where n = 5; p = 0.25; q = 0.75; and x = 3 . It is calculated by using binomial probability.

The binomial probability formula is

P(X = x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾ = \(\frac{n!}{(n-x)!x!} p^xq^{(n-x)}\)

Where n is the number of trials, p i is the probability of success, and q is the probability of failure.

And q = 1 - p

It is given that, a card is selected from a standard deck and replaced.

This experiment has repeated a total of five times. i.e., trials n = 5

So, the probability of success is p = 1/4 = 0.25

(Since one card is to be selected from the five trials where each time the card is replaced)

Then, the probability of failure is q = 1 - 0.25 = 0.75

And it is given that we need to find the probability of selecting exactly three clubs. So, the required random variable is x = 3.

Then, using the binomial probability formula, we get

P(X = x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾

⇒ P(X = 3) = ⁵C₃ p³q⁽⁵⁻³⁾ = ⁵C₃(0.25)³(0.75)² = 0.0878

On rounding off, we get the required probability as 0.088.

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Answer:d

Step-by-step explanation:

Permutations for each word can be calculated by considering the number of unique letters in it and taking factorial of it.

a) Inverary: There are 8 letters in the name "Inverary" (I, N, V, E, R, A, R, Y), so there are 8! (8 factorial) permutations of all the letters in the name. This equals 40320 permutations.

b) Beamsville: There are 9 letters in the name "Beamsville" (B, E, A, M, S, V, I, L, E), so there are 9! (9 factorial) permutations of all the letters in the name. This equals 362880 permutations.

c) Mattawa: There are 7 letters in the name "Mattawa" (M, A, T, T, A, W, A), so there are 7! (7 factorial) permutations of all the letters in the name. This equals 5040 permutations.

d) Penetanguishene: There are 14 letters in the name "Penetanguishene" (P, E, N, E, T, A, N, G, U, I, S, H, E, N), so there are 14! (14 factorial) permutations of all the letters in the name. This equals 87178291200 permutations.

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Answer:

x = 4

Step-by-step explanation:

Given

\(\frac{7+2x}{3}\) = 5 ( multiply both sides by 3 to clear the fraction )

7 + 2x = 15 ( subtract 7 from both sides )

2x = 8 ( divide both sides by 2 )

x = 4

A random variable is said to be continuous if it is measured over an interval. Option b. "is measured over an interval" correctly describes a continuous random variable.

A continuous random variable can take on any value within a given interval, including decimal values. It represents measurements that can be infinitely divided and can take on an uncountable number of values. Examples of continuous random variables include the height of individuals, the time it takes to complete a task, or the temperature of a room. These variables are not restricted to specific discrete values and can vary continuously.

On the other hand, discrete random variables (options a, c, and d) can only take on a countable number of distinct values. Discrete random variables represent outcomes that are distinct and separate, such as the number of students in a class, the number of cars passing by, or the number of heads obtained when flipping a coin.

These variables do not have decimal values and cannot be measured over a continuous range.

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Answer:0.4 10*8

Step-by-step explanation:

Alex can paint 4.5 dollhouses with one can of paint.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

The total number of dollhouses paint by Alex in 2 cans = 9

To find number dollhouses paint by 1 cans, use ratio property,

2 cans = 9 dollhouses

1 can = 9/2 dollhouses

1 can = 4.5 dollhouses

4.5 dollhouses can be paint with each can of paint.

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Answer:

A) Amanda will pay $47.5

B) 0.5

C) $120

Step-by-step explanation:

A) From the graph given, at 45 miles, the total cost of rentage = $142.50

She now splits this cost with 2 of her friends. Thus each of them will pay;

Amount = 142.5/3 = $47.5

So,Amanda will pay $47.5

B) To find the slope, we will pick two points on the graph and use their respective coordinates to find the slope.

Coordinates we pick are;

(0, 120) and (50, 145)

Thus, slope; m = (y2 - y1)/(x2 - x1)

m = (145 - 120)/(50 - 0)

m = 25/50

m = 0.5

C) The equation for the graph will now be; y = mx + c

Where m is slope and c is y - intercept.

Thus;

y = 0.5x + 120

Coincidentally, c = 120 will be the fixed price of the truck while 0.5x will be the variable cost depending on how many miles are driven.

Thus renting for a day is simply the fixed cost of $120

Answer:

Step-by-step explanation:

Cost is 1200 rupees

Desired gain is 1/3, which is:

Selling price is:

Marked price is x, and 1600 is the discounted price by 20%:

The necessary preprocessor directive to enable the use of functions like sqrt and sin

#include <math.h>

Generally, A preprocessor directive is a command that is processed by the preprocessor in a programming language before the actual compilation of the source code begins.

Preprocessor directives are used to give instructions to the preprocessor, which is a program that performs text substitution on

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Answer: The order of rotational symmetry of a shape is the number of times it can be rotated around a full circle and still look the same. If the triangle is rotated a full 360°, it never looks the same except when it arrives back at its original starting position.

Step-by-step explanation:

The order of rotational symmetry of this drawing is 4.

Each point in a figure is transformed into a rotation by rotating it a certain amount of degrees around another point.

As this is not a regular octagon, the appearance after a 45° rotation is different:

It must be rotated 90 degrees before it appears the same.

As a result, it maintains its appearance following rotations of 90, 180, 270, and 360 degrees, when it returns to its initial position.

As a result, the rotational symmetry order is 4.

The image is given in the image below.

Therefore, the order of symmetry is 4.

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The complete question:

What is the order of rotational symmetry of this drawing?

The drawing image is given in the image below.

Answer:

60-69

Step-by-step explanation:

Answer:

61 miles

Step-by-step explanation:

Since the distance Mia travels is constant, we can find the distance travelled over four days by multiplying 15 1/4 by 4:

(15 1/4) * 4 = 61

Thus, Mia travels 61 miles in 4 days

Answer: 4,700

Step-by-step explanation: 678 is above 650, meaning it is closer to 700 than it is 600

so rounding this makes it 4,700

unless you meant it as a decimal which 4.678 would result in 4.68 since the 8 before 7 would round up the 7 to an 8 making it 4.68

Hope this helps ^_^

Answer:

It's 4,700.

Step-by-step explanation:

When rounding to the nearest hundred, we use the following rules:

1) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

2) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.

3) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.