please help me with this problem ​

Explanation:

Recall that the general point-slope form is \(y - y_1 = m(x - x_1)\) where m is the slope and \((x_1, y_1)\) is the point the line goes through. We see that the 2 and the m match up, so m = 2 is the slope.

Side note: We can rewrite that given equation into y - (-5) = 2(x - (-1)) to see that the line goes through the point (-1, -5)

Answer:

C: 2

Step-by-step explanation:

y + 5 = 2x + 2 (distribute 2)

y = 2x -3 (subtract 5 from both sides)

2x means: slope times x

Answer:

1/10

Step-by-step explanation:

1/2 * 1/5

Multiply the numerators

1*1 = 1

Multiply the denominators

2*5 =10

Numerator over denominator

1/10

Answer:

1/10

Step-by-step explanation:

multiply the numerators and denominators separately

1×1/2×5

any expression multiplied by 1 remains the same

1/2×5

2×5=10

1×1=1

1/10

Alvarez received $200,000 which is 40% of the profit.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it. Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

Given

Profit $500000

Alvarez owns 40% of the business.

Percentage

500000 × 40%

200000

Alvarez received $200,000 which is 40% of the profit.

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To maintain the height and width proportion of a shape while dragging, you would typically hold down the Shift key on your keyboard.

When you select and drag a shape, holding down the Shift key constrains the proportions of the shape and ensures that the height and width change proportionally.

This technique is commonly used in graphic design and image editing software, as well as in various drawing and design applications. By holding down the Shift key while dragging a shape, you can prevent it from being distorted or skewed, preserving its original aspect ratio.

This feature is especially useful when you want to maintain the shape's original proportions or when you need consistency in the size and dimensions of multiple shapes. It helps ensure that the height and width remain in the same ratio as the original shape, regardless of how you adjust its size.

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Answer:

5.024

Step-by-step explanation:

Answer:

5.024

Step-by-step explanation:

a) 0 kg of sugar is in the tank at the beginning., b) ds/dt = 0.08-(S/1120)*4, c) 0.32 kg of sugar is in the tank after 1 minute., d) 2.59 kg of sugar is in the tank after 84 minutes.

a) At the beginning, there is no sugar in the tank since it contains only pure water.

b) Let S(t) be the amount of sugar in the tank at time t (in minutes). The rate of change of S is given by the rate at which sugar enters the tank minus the rate at which it leaves. Since the solution enters at a rate of 4 L/min, and contains 0.08 kg of sugar per liter, the rate at which sugar enters is 0.08 kg/L * 4 L/min = 0.32 kg/min. Since the solution leaves at the same rate, the differential equation that models the situation is:

dS/dt = 0.32 - (S/1120) * 4

c) To find the amount of sugar after 1 minute, we need to solve the differential equation from part (b) with the initial condition S(0) = 0 (since the tank initially contains only water). One possible way to solve the differential equation is to use separation of variables:

dS/dt + (4/1120) S = 0.32

Multiplying both sides by dt and dividing by (0.32 - (4/1120) S), we get:

(1/S) dS = (4/0.32 - (1120/4)) dt

Integrating both sides from t = 0 to t = 1 and from S = 0 to S = S(1), we get:

ln(S(1)) - ln(0) = (1.25 - 280) * 1

S(1) = \(e^{0.25} * 1120\) ≈ 300.92 kg

Therefore, after 1 minute, there is approximately 300.92 kg of sugar in the tank.

d) To find the amount of sugar after 84 minutes, we can solve the differential equation from part (b) numerically using an appropriate method such as Euler's method, or we can use an integrating factor to solve it analytically. One possible way to use an integrating factor is to multiply both sides of the differential equation by exp(4t/1120):

exp(4t/1120) dS/dt + (S/280) exp(4t/1120) = 0.32 exp(4t/1120)

This can be written as:

d/dt [S exp(4t/1120)] = 0.32 exp(4t/1120)

Integrating both sides from t = 0 to t = 84, we get:

[S(84) exp(4/1120 * 84)] - [S(0) exp(4/1120 * 0)] = ∫(0 to 84) 0.32 exp(4t/1120) dt

Since S(0) = 0 and exp(4/1120 * 84) is a constant, we can simplify this to:

S(84) = (1/exp(4/1120 * 84)) ∫(0 to 84) 0.32 exp(4t/1120) dt

Using integration by substitution with u = 4t/1120, we get:

S(84) = (1/exp(4/1120 * 84)) * (1120/4) * (0.32/4) * [exp(4/1120 * 84) - 1]

S(84) ≈ 301.53 kg

Therefore, after 84 minutes, there is approximately 301.53 kg of sugar in the tank.

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The complete question is:

A tank contains 1120 L of pure water. At a rate of 4 L/min, a solution that contains 0.08 kilogramme of sugar per litre enters the tank. At the same rate that it drains from the tank, the solution is mixed.

a) How much sugar is in the tank when it first starts?

b) With S representing the amount of sugar (in kg) at time t, write a differential equation which models the situation.

c) After 1 minute, calculate the sugar content (in kilogramme).

d) After 84 minutes, calculate the sugar content (in kg).

Answer:

15.17

Step-by-step explanation:

Create a table with the place values for the first and second factors down the left and the top and bottom, respectively.

What is the box method?

Multiplication using the box method: Create a table with the place values of the first and second factors down the left and the top and bottom, respectively. Second step: multiply the place values and add the results to the table. Step 3: Add up all of the table's rows. Step 4: Add the sums of these rows.

Placing the first word in the first box and the last term in the last box is the first step in utilizing the box technique to factor a trinomial. Multiply the first and last boxes after that. Identify the first and last boxes' products, which together make up the middle word. Put these words in the remaining spaces.

Here's how you can use the box method to distribute and simplify the expression:

( -5x - 2 ) ( 5x + 4 )

⇒-5x -2

⇒5x 4

⇒-25x^2 -10x + 20x - 8

⇒-25x^2 + 10x - 8

So the simplified expression is:

-25x^2 + 10x - 8.

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The probability that a randomly selected student used acrylic paint given that the student chose to create a portrait is 3/5 or 60%.

To find the probability that a randomly selected student used acrylic paint given that the student chose to create a portrait, you can use the conditional probability formula:

P(Acrylic Paint | Portrait) = P(Acrylic Paint and Portrait) / P(Portrait)

From the given data:

- There were 3 students who used acrylic paint and created a portrait.
- There were a total of 5 students who created a portrait (3 with acrylic paint and 2 with oil paint).

So, the probability calculation would be:

P(Acrylic Paint | Portrait) = (3/5) / (5/5) = 3/5

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Answer:

B

Step-by-step explanation:

Say the point below point B is point C.

AB belongs to triangle ABC.

To find hypotunuse AB, we need BC and AC so that we can use pythagorean thereom.

BC is already given --> 1.

AC is a diagonal of the rectangular prisms's base.

We already have 2 sides for the triangle that the base diagonal belong's to.

AC^2 = 4^2 + 6^2

AC^2 = 16 + 36 = 52

AC = √52

Now we have AC ad BC. We can find AB using pythagorean thereom.

AC^2 + BC^2 = AB^2

(√52)^2 + (1)^2 = AB^2

52 + 1 = AB^2

AB^2 = 53

AB = √53

option B

The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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1. The measure of AC = 8.4

2. The measure of AC' = 6

3. The measure of C'B' = 12.6

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.

Given:

Segment B'C' is parallel to segment BC.

A line splits a triangle's sides in the same proportion if it runs parallel to one side and crosses the other sides at two different spots.

Then,

10/4 = 6/x

x = 2.4

The measure of AC = 2.4

And,

14/8.4 = 21/y

y = 12.6

The measure of C'B' = 12.6

Therefore, all the required values are given above.

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Answer:

-128

Step-by-step explanation:

Given, f(x)=2x

3

−21x

2

+36x−20

∴f

′

(x)=6x

2

−42x+36

When f(x) is a maximum or a minimum, f

′

(x)=0

Hence, 6x

2

−42x+36=0

x

2

−7x+6=0

x

2

−6x−x+6=0

x(x−6)−1(x−6)=0

(x−6)(x−1)=0

x=1,6

Again f

′′

(x)=12x−42

=6(2x−7)

Now, when x=1,f

′′

(x)=−30 ....[negative]

And when x=6,f

′′

(x)=30 ....[positive]

Hence, f(x) is maximum for x=1 and minimum for x=6.

The maximum and minimum values of f(x) are

f(1)=2(1)

3

−21(1)

2

+36(1)−20

=2−21+36−20=−3

f(6)=2(6)

2

−21(6)

2

+36(6)−20

=432−756+216−20=−128

Therefore, probability solution is estimating this likelihood without additional data or analysis is inappropriate correct response is option a.

The main goal of the mathematical branch known as statistical inference is to estimate the likelihood that a statement is accurate or that a particular event will take place. Any number among 0 and 1, where 1 typically denotes confidence and 0 typically denotes possibility, can be used to symbolise chance. A probability diagram illustrates the likelihood that a particular occurrence will take place.

Here,

Because of the skewed demographic distribution, the right response is (a).

We could use the normally distributed to compute probabilities because the length of adult American ladybirds is distributed normally with a known standard deviation. The normal distribution may not, however, correctly depict the distribution of ladybird lengths in the population due to the skewed population distribution.

Furthermore, even if the difference between the actual community mean and the assumed mean of 1 cm is tiny, the given size of the population of 440000 could result in a statistically significant outcome.

However, because the assumption of normality may not hold true, this does not imply that we can accurately determine the likelihood of a random ladybird in Raleigh being larger than 1.5 centimetres.

Therefore, estimating this likelihood without additional data or analysis is inappropriate.

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Answer:

So what is the question?

Step-by-step explanation:

Brooklyn can drive her car  127 miles for every 5 gallons of gas

     y = 127      x = 5

     y  = (127 / 5) miles   for every one gallon x

    y  = 25.4x

d) about 39.07% of the chicks weigh between 196 and 317.

To answer these questions, we can use the provided five-number summary and apply the concepts of quartiles and percentiles.

a. To find the percentage of chicks weighing more than 196, we need to calculate the percentage above the first quartile (Q1). The first quartile (Q1) represents the 25th percentile, meaning 25% of the chicks weigh less than or equal to Q1.

The percentage of chicks weighing more than 196 is therefore:

100% - 25% = 75%

Therefore, about 75% of the chicks weigh more than 196.

b. Similarly, to find the percentage of chicks weighing more than 263, we need to calculate the percentage above the median. The median represents the 50th percentile, so 50% of the chicks weigh less than or equal to the median.

The percentage of chicks weighing more than 263 is:

100% - 50% = 50%

Therefore, about 50% of the chicks weigh more than 263.

c. To find the percentage of chicks weighing more than 317, we need to calculate the percentage above the third quartile (Q3). The third quartile (Q3) represents the 75th percentile, meaning 75% of the chicks weigh less than or equal to Q3.

The percentage of chicks weighing more than 317 is:

100% - 75% = 25%

Therefore, about 25% of the chicks weigh more than 317.

d. To find the percentage of chicks weighing between 196 and 317, we need to calculate the percentage between the first quartile (Q1) and the third quartile (Q3). The difference between the first quartile and the third quartile represents the interquartile range (IQR).

The percentage of chicks weighing between 196 and 317 is the percentage within the IQR:

Q3 - Q1 = 315 - 197 = 118

Percentage within the IQR = (118 / (Max - Min)) * 100

                           = (118 / (410 - 108)) * 100

                           = (118 / 302) * 100

                           ≈ 39.07%

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Answer:

Step-by-step explanation:

The sum of suplementary angles is allways 180°

so:

x  -   the other angle

3x  - three times the other angle

180°- x  - one angle

180° - x + 184° = 3x

   364° = 4x

     x = 91°

180°- x = 180° - 91° = 89°

Answer:algebra ok

Step-by-step explanation:

Answer:

8 rides $39 cost

Step-by-step explanation:

i just did it

For the quadrilateral ABCD the statement which proves that this quadrilateral is not a rectangle is (a) The slope of CD is "(-5-1)/(-5-5) = 3/5", and the "slope of DA is [3-(-5)]/[-3-(-5)] = 8/2", these "two-segments" are not perpendicular , so the shape is not a rectangle;

The coordinates of the "four-vertices" of the quadrilateral ABCD are :

A(-3,3), B(2,6), C(5, 1), D(-5,-5);

To prove whether the quadrilateral is a rectangle or not, we need to show that its adjacent sides are perpendicular and its diagonals are congruent.

In this question, we are given the coordinates of the four vertices of the quadrilateral.

To determine if it's a rectangle, we use the slope formula to find the slopes of the sides of the quadrilateral. If slopes of adjacent sides are "negative-reciprocals" of each other, then they are perpendicular. If the slopes of the diagonals are equal, then they are congruent.

Using the given coordinates, we find that the slope of CD is = (-5-1)/(-5-5) = 3/5, and

The slope of DA is = [3-(-5)]/[-3-(-5)] = 8/2. These two slopes are not negative reciprocals of each other, so CD and DA are not perpendicular.

So, the quadrilateral is not a rectangle.

Therefore, the correct option is (a).

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The given question is incomplete, the complete question is

The coordinates of the "four-vertices" of the quadrilateral ABCD are :

A(-3,3), B(2,6), C(5, 1), D(-5,-5);

Which statement proves whether or not this quadrilateral is a rectangle?

(a) The slope of CD is (-5-1)/(-5-5) = 3/5, and the slope of DA is 3-(-5)/-3-(-5)=8/2, these two segments are not perpendicular , so the shape is not a rectangle;

(b) The slope of AB is (6-3)/(2-(-3) = 3/5, and slope of BC is (6-1)/(2-5) = -5/3, these two segments are perpendicular , so the shape is a rectangle;

(c) The slope of BC is (6-1)/(2-5) = -5/3, and slope of CD is (-5-1)/(-5-5) = 3/5, these two segments are not perpendicular, so the shape is not a rectangle;

(d) The slope of AB is (6-3)/(2-(-3) = 3/5, and slope of CD is (-5-1)/(-5-5) = 3/5, these two segments are perpendicular , so the shape is a rectangle;

The area of the composite shape is 84 square units, which is the sum of the areas of the two rectangles (10x4 and 8x3) and the triangle (base 8 and height 5).

The area of the composite shape is equal to the sum of the areas of the two rectangles and the triangle. We can find the area of each shape using the formula for area:

Area of a rectangle = length × width

Area of a triangle = (base × height) / 2

Given measurements of the shapes:

The first rectangle has a length of 10 units and a width of 4 units, so its area is 10 × 4 = 40 square units.

The second rectangle has a length of 8 units and a width of 3 units, so its area is 8 × 3 = 24 square units.

The triangle has a base of 8 units and a height of 5 units, so its area is (8 × 5) / 2 = 20 square units.

To find the total area of the composite shape, we can add up the areas of each shape:

Total area = area of rectangle 1 + area of rectangle 2 + area of triangle

Total area = 40 + 24 + 20

Total area = 84 square units

Therefore, the area of the composite shape is 84 square units.

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The probability that the proportion of overweight or obese children in the sample will be greater than 0.57 is less than 50%.

The first paragraph summarizes the answer, stating that the probability is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.

In the second paragraph, we can explain the reasoning behind this conclusion. The Central Limit Theorem states that for a large sample size, the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution. In this case, the sample was taken in a way that meets the conditions for using the Central Limit Theorem.

Since the population proportion of overweight or obese children is 0.60, any sample proportion below this value is more likely to occur. Therefore, the probability of obtaining a sample proportion greater than 0.57 would be less than 50%. This is because the resulting z-score, which measures how many standard deviations the sample proportion is away from the population proportion, would be negative.

To summarize, the probability of the proportion of overweight or obese children in the sample being greater than 0.57 is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.

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Answer:

f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)

Step-by-step explanation:

We can find the function f(x) by integrating f'(x) with respect to x:

â«f'(x) dx = â«(2/(x^3) + 4e^x + 5) dx

f(x) = -1/x^2 + 4e^x + 5x + C

To find the constant C, we can use the given initial conditions:

f(-1) = 1 = -1/(-1)^2 + 4e^(-1) - 5 + C

C = 1 + 1/1 - 4e^(-1)

f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)

Therefore, the function f(x) is:

f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)

Answer:

Step-by-step explanation:

Column 2 = Column 1 * Column 3

Answer:

6 < x

Step-by-step explanation:

4(3x + 2) <5(3x - 2)

Distribute

12x +8 < 15x -10

Subtract 12 x from each side

12x +8-12x < 15x-12x -10

8 < 3x - 10

Add 10 to each side

8+10 < 3x-10+10

18 < 3x

Divide by 3

18/3 < 3x/3

6 < x