Use the distance and slope formula to prove that qaudlateal ABCD IS A PARLLAGRAM

The total volume of the original mixture is 4 liters.

Given that:

A mixture of 50% alcohol and 50% water has 4 liters of water added to it. It is now 25% alcohol.

Let 'x' be the amount of water and alcohol. Then we have

x / (x + x + 4) = 0.25

x/(x + 2) = 0.5

2x = x + 2

x = 2

The total volume of the original mixture is calculated as,

Total volume = x + x

Total volume = 2 + 2

Total volume = 4 liters

The total volume of the original mixture is 4 liters.

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In the right triangle, the value of x is approximately 64°

From the question, we are to set up an equation for x and then solve for the value of x.

To determine the value of x, we will use SOH CAH TOA

sin (angle) = Opposite / Hypotenuse

cos (angle) = Adjacent / Hypotenuse

tan (angle) = Opposite / Adjacent

In the given diagram,

x is the included angle

Adjacent = 12

Opposite = 25

Thus,

We can write that

tan (x) = 25/12

tan (x) = 2.0833

x = tan⁻¹ (2.0833)

x = 64.3586

x ≈ 64° (to the nearest degree)

Hence,

The value of x is approximately 64°

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The volume of the figure created is 98 cubic units.

Given that:

A triangle with coordinates (0,0), (0, 7), and (6,0) is rotated 360 degrees about the x-axis.

A cone is formed when a triangle rotates. Then the volume created is calculated as,

V = 1/3 x 7² x 6

V = 49 x 2

V = 98 cubic units

The volume is 98 cubic units.

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A graph of this function d = 45t is shown in the image below.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

d = kt

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 45/1 = 90/45

Constant of proportionality, k = 45.

Therefore, the required linear equation or function is given by;

d = kt

d = 45t

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The summation of the given expression is as follows:

17.) = 5

18.) = 1

19.) = 1/2

For question 17.)

The summation of 2k+3 when K= 1

= 2(1)+3

= 2+3

= 5

For question 18.)

The summation of (3/2)^k where k = 0 would be = 1

For question 19.)

The summation of 1/2^k+1 where k = 0

= 1/2^0+1

=1/2^1

=1/2

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The equations of the circles in standard form, obtained from the coordinates of the center and the points on the circle are;

5) (x + 16)² + (y + 16)² = 3²

6) (x - 15)² + (y + 7)² = 8

7) (x + 6)² + (y + 2)² = 6²

8) (x + 9)² + (y + 3)² = 89

The standard form of the equation of a circle is; (x - h)² + (y - h)² = r²

Where;

(h, k) = The coordinates of the center of the circle

5) The center of the circle is (-16, -16)

The coordinates of a point on the circle is (-13, -16)

Therefore; r² = (-13 - (-16))² = 3²

The equation of the circle in standard form is therefore;

(x - (-16))² + (y - (-16))² = 3²

(x + 16)² + (y + 16)² = 3²

6) The coordinates of the center of the circle = (15, -7)

The coordinate of a point on the circle = (17, -5)

r² = (17 - 15)² + (-5 - (-7))² = 8

The equation is; (x - 15)² + (x - (-7))² = 8

(x - 15)² + (x + 7)² = 8

7) The coordinates of the center = (-6, -2)

The coordinate of a point on the circle = (-12, -2)

The square of the radius is therefore; r² = (-6 - (-12))² = 6²

(x - (-6))² + (y - (-2))² = 6²

(x + 6)² + (y + 2)² = 6²

8) The coordinates of the center is; (-9, -3)

The point on the circle is; (-1, -8)

The square of the radius is; r² = (-1 - (-9))² + (-8 - (-3))² = 89

The equation of the circle is therefore; (x - (-9))² + (y - (-3))² = 89

(x + 9)² + (y + 3)² = 89

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Answer: Yes

Step-by-step explanation:

Yes because the angles are both 120 degree's

(I'm not sure if this is right but btw I love your pfp :))

The 99.5% confidence interval for the mean reduction in cholesterol is 0.922 < μ < 0.978.

To construct a 99.5% confidence interval for the mean reduction in total cholesterol, we can use the formula CI = x ± Z*(σ/√n).

Substituting the given values, we get:

CI = 0.95 ± 2.807*(0.18/√318)

CI = 0.95 ± 2.807*0.01009389877

CI = 0.95 ± 0.02833357384

CI = 0.95 + 0.0283 or 0.95-  0.0283

CI = 0.9783 or 0.9217

This means we are 99.5% confident that the true population mean reduction in total cholesterol lies within this interval.

Full question "A sample of 318 patients between the ages of 38 and 82 were given a combination of drugs ezetimibe and simvastatin. They achieved a mean reduction in total cholesterol of 0.95 millimole per liter. Assume the population standard deviation is = 0.18. Construct a 99.5% confidence interval for the mean reduction in total cholesterol in patients who take this combination of drug"

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Answer: 226

Step-by-step explanation:

The angle is half of the arc angle

so mDGF is 2 times as big as the angle

mDGF=113*2

mDGF=226

A price-setter company will use more: cost-plus pricing methods

A company endowed with the capability to set their own market prices is likely to resort to various pricing approaches, such as cost-plus, target costing, and target pricing methods.

However, targeting pricing proves to be the most preferable scheme of these since it involves establishing the desired selling price based on estimated market value before factoring in acceptable expenses to procure an adequate profit margin.

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A price-setter company, which has considerable market power, is more likely to use cost-plus pricing methods. This method ascertains the price of a product by determining the cost of production and then adding a certain amount for profit. Hence, this strategy ensures that the company covers all costs and makes a profit on each sale.

A price-setter company, which has significant market power, is likely to use more cost-plus pricing methods. In a cost-plus pricing method, the company sets the price of a product by determining the cost of production and then adding a specific amount or percentage as profit. This pricing strategy is straightforward and ensures that all costs are covered and a profit is made on each sale. It offers stability and predictability, which is desirable for a price-setter company with substantial control over the market.

On the other hand, target costing and target pricing methods involve setting a price first and then figuring out how to meet that price with production. These methodologies are typically used in more competitive industries, where companies don't have as much power to set their own prices.

However, a price-setter company, assuming it's not in a perfectly competitive market, has the power to set the price without having to intensely consider competitors' prices or customers' price sensitivity, therefore, it may use cost-plus pricing methods more.

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Answer:

Step-by-step explanation:

If the large Jar is $4.10 for 540g

and  small jar  $2.81 for 360 g

You need to show how much it cost for 1 g,so you can compare how much it cost per gram. You would divide the total cost by the grams to see how much it is for 1 g.

Large jar.   $4.10/540 = $.0076  for 1 gram

Small Jar.   $2.81/360 =$.0078 for 1 gram

Because the large jar is cheaper to buy per gram, the large jar is the best value for the money.

Answer:

rectangular pyramid has 8 edges

Answer:

y = [tex]\frac{-3}{8}[/tex]x - [tex]\frac{57}{8}[/tex]

Step-by-step explanation:

a perpendicular slope is the opposite reciprocal.  The slope will be [tex]\frac{-3}{8}[/tex]

Two write the equation, you need the slope and the y-intercept.  We have the slope ([tex]\frac{-3}{8}[/tex]).  We know need to find the y-intercept.

We will use the m or slope of [tex]\frac{-3}{8}[/tex], x value of -3 from the point (-3,-6)and the y value of -6 from the point (-3,-6)

y = mx + b

-6 = [tex]\frac{-3}{8}[/tex]([tex]\frac{-3}{1)}[/tex]) + b

-6 = [tex]\frac{9}{8}[/tex] + b  Subtract [tex]\frac{9}{8}[/tex] from both sides

[tex]\frac{-6}{1 }[/tex] - [tex]\frac{9}{8}[/tex] = [tex]\frac{9}{8}[/tex] - [tex]\frac{9}{8}[/tex] + b  Use the common denominator of 8

[tex]\frac{-48}{8}[/tex] - [tex]\frac{9}{8}[/tex] = b

[tex]\frac{-57}{8}[/tex] = b

y = [tex]\frac{-3}{8}[/tex]x - [tex]\frac{57}{8}[/tex]

The bearing of the airport from the plane is 245°

The bearing of a point from a location is given by the angle in degrees of rotation from the Northern direction of the location to the direction of the location of the point

The given bearing of the plane from the airport = 65°

Therefore, the direction of the plane from the Northern direction of the airport = 65°

From the Northern direction of the plane, the bearing of the airport = 245°

Hence, the bearing of the airport from the plane is 245°

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The machine's purchasing cost is $309,210.

The acquisition cost of the machine is the total cost incurred by the firm to purchase and put the machine into service.

To determine the acquisition cost of the machine, we need to add up all the costs listed in the question.

Invoice price = $299,000

Applicable sales tax = $2,100

Freight paid = $1,160

Cost of insurance coverage = $1,025

Installation costs = $1,900

Testing and adjusting costs = $1,375

Repair of damages caused by the firm's employees = $1,450

Prepaid maintenance contract = $1,200

Total acquisition cost = Invoice price + Sales tax + Freight paid + Cost of insurance coverage + Installation costs + Testing and adjusting costs + Repair of damages caused by the firm's employees + Prepaid maintenance contract

Total acquisition cost = $299,000 + $2,100 + $1,160 + $1,025 + $1,900 + $1,375 + $1,450 + $1,200

Total acquisition cost = $309,210

Therefore, the acquisition cost of the machine is $309,210.

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The difference between the median test score in the morning and the afternoon is 12.5

From the question, we are to determine the difference between the median test score in the morning and the afternoon.

From the given diagram, we have box plots.

From the given box plots, we will determine the median test score in the morning and the median test score in the afternoon.

The median test score in the morning = 87.5

The median test score in the afternoon = 75

Thus,

The difference between the median test score in the morning and the afternoon =

Median test score in the morning - Median test score in the afternoon

The difference between the median test score in the morning and the afternoon = 87.5 - 75

The difference between the median test score in the morning and the afternoon = 12.5

Hence,

The difference is 12.5

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A reflection transformation on a coordinate plane changes the figure over a line called the line of reflection. This line acts as a reflect and the picture created by the change could be a reflect picture of the first figure.

b. In case a figure is reflected over the x-axis, the x-coordinates of all the focuses within the figure will stay the same, but the y-coordinates will be increased by -1. So, in the event that a point on the initial figure has arranges (x,y), its picture after reflecting over the x-axis will have arranges (x,-y).

c. In case a figure is reflected over the y-axis, the y-coordinates of all the points within the figure will remain the same, but the x-coordinates will be copy by -1. So, in case a point on the first figure has push (x,y), its image   after reflecting over the y-axis will have arranges (-x,y).

Therefore, d. To reflect a triangle over the y-axis, we need to know the  the mirror image  of each point with regard to the y-axis. One way to do usually to increase the x-coordinate of each point by -1 and also keeping the y-coordinate the same.

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See text below

2. Reflections:

Transformations Review

a. How would you describe what this transformation looks like when performed on a coordinate plane?

b. If your figure was reflected across the x-axis, how would that affect the figure's coordinates?

c. If your figure was reflected across the y-axis, how would that affect the figure's coordinates?

d. On the coordinate plane: First, plot a triangle. Then, reflect your triangle over the y-axis and draw the result:

The true population proportion of people with kids is between 0.0565 and 0.1835.

We are given that;

Number of people= 100

Percent= 95%

Now,

To construct a 95% confidence interval for the true population proportion of people with kids. Here are the steps to do so:

Find the sample proportion p. This is the ratio of the number of successes (people with kids) to the sample size. In this case, p = 12 / 100 = 0.12.

Find the z-value that corresponds to the 95% confidence level. You can use a table or a calculator to find this value. The z-value for a 95% confidence level is 1.96.

Find the standard error of the sample proportion. This is the standard deviation of the sampling distribution of p. You can use the formula √p (1-p) / n to find this value. In this case, the standard error is √0.12 (1-0.12) / 100 = 0.0324.

Plug these values into the formula for the confidence interval and simplify. You get:

Confidence interval = 0.12 +/- 1.96*0.0324 Confidence interval = 0.12 +/- 0.0635 Confidence interval = [0.0565, 0.1835]

Therefore, by proportions the answer will be 0.0565 and 0.1835.

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The fraction in factored form is determined as  (x - 8)(x + 10) / (x - 10)(x + 8).

The quotient of the division is calculated as follows;

( x² - 3x - 40 )/ (x² + 8x - 20) ÷ (x² + 13x + 40)/(x² + 12x + 20)

Factorize each of the expressions;

x² - 3x - 40

= x² + 5x - 8x - 40

= x(x + 5) - 8(x + 5)

= (x + 5)(x - 8)

x² + 8x - 20

= x² + 2x - 10x - 20

= x(x + 2) - 10(x + 2)

= (x + 2)(x - 10)

x² + 13x + 40

=  x² + 5x + 8x + 40

= x(x + 5) + 8(x + 5)

= (x + 5)(x + 8)

x² + 12x + 20

=  x² + 2x + 10x + 20

= x(x + 2) + 10(x + 2)

= (x + 2)(x + 10)

The fraction in factored form is written as;

(x + 5)(x - 8)/(x + 2)(x - 10) ÷ (x + 5)(x + 8)/(x + 2)(x + 10)

(x + 5)(x - 8)/(x + 2)(x - 10)  x  (x + 2)(x + 10)/(x + 5)(x + 8)

= (x - 8)(x + 10) / (x - 10)(x + 8)

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The percentage of adults who eat more than 10.4 ounces of chicken in one sitting is 2.5%. The correct option is A.

We know that the distribution is approximately normal with a mean of 8 ounces and a standard deviation of 1.2 ounces. We want to find the percentage of adults that eat more than 10.4 ounces of chicken in one sitting.

To solve this problem, we can use the standard normal distribution table or a calculator with the normal distribution function.

Using the calculator, we can standardize the value 10.4 using the formula:

[tex]z = \dfrac{(x - \mu)} { \sigma}[/tex]

where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, we have:

[tex]z = \dfrac{(10.4 - 8) }{1.2} = 2[/tex]

We can then use the calculator to find the percentage of the distribution that lies above the z-score of 2. This is approximately 2.5%.

Therefore, the answer is A. 2.5%.

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Part(2),

The volume of the snowcone is larger than the volume of the paper cup, the snowcone will overflow when it melts.

Part(3),

The difference in price per cubic inch is $0.0128/in³.

Part(4),

The volume of the cylinder with a radius of 8 inches and a height of 6 inches.

Part(2)

The volume of a cone is given by the formula V = (1/3)πr²h,

where r is the radius and h is the height. The volume of the snowcone is therefore V = (1/3)π(4 cm)²(12 cm) = 201.06 cubic cm.

V = (1/3)π(3 cm)²(12 cm) = 113.1 cubic cm.

Since the volume of the snowcone is larger than the volume of the paper cup, the snowcone will overflow when it melts.

Part(3)

To compare the cost per cubic inch of the two sizes of cereal boxes, we need to calculate the volume of each box and divide the cost by the volume.

The volume of the family-sized box is V = 3 in x 9 in x 12 in = 324 cubic inches.

The cost per cubic inch is therefore $6/324 in³ = $0.0185/in³.

The volume of the regular-sized box is V = 2 in x 8 in x 9 in = 144 cubic inches. The cost per cubic inch is, therefore, $4.50/144 in³ = $0.0313/in³.

The difference in price per cubic inch is $0.0313/in³ - $0.0185/in³ = $0.0128/in³.

Part(3)

The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.

For the cylinder with a radius of 6 inches and a height of 8 inches, the volume is V = π(6 in)²(8 in) = 904.78 cubic inches.

For the cylinder with a radius of 8 inches and a height of 6 inches, the volume is V = π(8 in)²(6 in) = 1206.37 cubic inches.

Therefore, the volume of the cylinder with a radius of 8 inches and a height of 6 inches.

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The distributive property of multiplication can be used to calculate the sum of the difference between the multiples of the variables expression as follows;

[tex]\sum\limits_{i = 1}^{124} (29\cdot a_i - 13 \cdot b_i)[/tex] = -30

The distributive property states that multiplying the difference between addend by a value produces a result which is equivalent to the multiplication of each addend individually and finding the difference from the resulting values.

The distributive property of multiplication indicates that we get;

Where; [tex]\sum\limits_{i=1}^{124} a_i = -10[/tex], and [tex]\sum\limits_{i=1}^{124} b_i = -20[/tex]

[tex]\sum\limits_{i=1}^{124} (29\cdot a_i - 13\cdot b_i) = 29 \times \sum\limits_{i=1}^{124} a_i - 13 \times \sum\limits_{i=1}^{124} b_i = 29 \times (-20) - 13 \times (-10))[/tex]

29 × (-10) - 13 × (-20) = -30

Therefore;

[tex]\sum\limits_{i=1}^{124} (29\cdot a_i - 13\cdot b_i) =-30[/tex]

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Answer: 2 2/3+ 8

Step-by-step explanation: it goes 2 under the ten

Answer:

See provided explanation

Step-by-step explanation:

Slope=change in y/change in x

General equation for a line: y=mx+b

You know that the slope(m) is 8/3, and the y-intercept is 8. So your graph will intersect the y axis at the point (0,8). from there, use slope=rise/run to graph the remaining points. Starting at (0,8), move 8 up and 3 right, this is your next point. Do the same in the other direction, starting at (0,8) move down 8 and left 3 points. Doing this will get you the points (-3,0) and (3,16). repeat this process until you have enough points to form a line. I attatched a picture of what the graph should look like.

A feasible solution to minimizing turbidity value is through the use of an iterative technique, entailing either gradient descent method or simulated annealing method.

The stopping criterion for this approach would be at 0.1 percent.  It involves sequentially determining water turbidity dependent on the coagulant dosages used in adjustment procedures based on preceding calculated values.

By further implementing this process until the specified percentage average is met, ease and accuracy in assessing turbidity levels are achievable.

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The simplified expression is 120x³ + 120x².

To simplify the expression 5x(2x+2)12x, we can use the distributive property of multiplication over addition and simplify the resulting terms.

First, we distribute 5x to the expression (2x+2), which gives us:

5x(2x+2) = 10x² + 10x

Next, we can multiply the result by 12x:

12x(10x² + 10x) = 120x³ + 120x²

Therefore, the simplified expression is 120x³ + 120x².

We can see that the original expression was a multiplication of three factors, and we used the distributive property to simplify it by expanding and multiplying the resulting terms. The final expression has a common factor of 120x², which we can factor out to get 120x²(x+1).

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Answer:

Length= 43.98 cm

Step-by-step explanation:

Circumference=2πr

r=7cm

C=2π(7)

C=43.98 cm

circumference is equal to the length of ribbon along the outside of the circular object

If the graphs of the linear equations in a system are parallel: A. There is no solution.

The general form for the equation of a line is:

y = mx + c

where:

m is slope

c is y-intercept

Usually, for two equations to have a solution, they must intersect each other.

However, If the graphs of the two equations are parallel lines, then there will be no solution, and the system is called an inconsistent system because the two lines will never intersect each other.

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The solutions to the expressions are (m-8)² = m² - 16m + 64 and 2m²-16m + m²-8m+161 = 3m²- 24m + 161

From the question, we have the following parameters that can be used in our computation:

(m-8)²

Expand

So, we have

m² - 16m + 64

Next, we have

2m²-16m + m²-8m+161

Evaluate the like terms

3m²- 24m + 161

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The probability that her Internet service is not broken for five days in a row is given by P ( A ) = 0.0102

Given data ,

Let the probability that the internet connection is lost = 60 %

Now , We may utilize the probability of independent occurrences occurring sequentially to determine the likelihood that her Internet service won't be down for five days in a row. We may add the probability for five days as the occurrences of her Internet service being down or up on each day are independent.

The likelihood of her Internet service remaining operational for one day is 0.40.

Her chances of having uninterrupted Internet access for five days are equal to (0.40)⁵

P ( A ) =  (0.40)⁶ is about equivalent to 0.0102

Hence , the probability of Ashley's Internet service remaining up for five consecutive days is around 0.0102 or 1.02%

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