A ball is launched from a 682.276 meter tall platform. the equation for the ball's height h at time t seconds after launch is h(t) = -4.9t^2 + 682.276, where h is in meters. what is the maximum height the ball achieves before landing?

The difference between these two values will give us the mass of solid sugar that came out of solution upon cooling to 20°C.

(a) To determine how much sugar will dissolve in 1000 g of water at 80°C, we need to find the point on the sugar-water phase diagram that corresponds to these conditions. At this point, the curve separating the liquid and solid phases (called the solubility curve) indicates the maximum amount of sugar that can be dissolved in the water at that temperature.

Once we have identified this point, we can read off the corresponding sugar concentration in the liquid phase. This will give us the maximum amount of sugar that can be dissolved in 1000 g of water at 80°C.

(b) When the saturated liquid solution in part (a) is cooled to 20°C, some of the sugar will precipitate as a solid. This means that the composition of the remaining liquid phase will be different from its composition at 80°C.

To determine the new composition, we need to find the point on the phase diagram that corresponds to 20°C and the sugar concentration we found in part (a). This point will lie on the solubility curve, which separates the liquid and solid phases at 20°C.

Once we have identified this point, we can read off the corresponding sugar concentration in the liquid phase. This will give us the composition of the saturated liquid solution at 20°C.

(c) The amount of solid sugar that comes out of solution upon cooling to 20°C can be calculated using the mass balance equation:

mass of solid sugar + mass of dissolved sugar = total mass of sugar

At 80°C, we found the maximum amount of sugar that can be dissolved in 1000 g of water. We can use this value to calculate the mass of dissolved sugar at 80°C. Then, at 20°C, we can use the composition we found in part (b) to calculate the mass of dissolved sugar in the saturated liquid solution.

The difference between these two values will give us the mass of solid sugar that came out of solution upon cooling to 20°C.

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(1). Gaussian elimination with partial pivoting and express the upper triangular matrix U as U=M3P3M2P2M1P1A

where Mi and Pi, i=1,2,3 are the elementary matrices and the permutation matrices that implement Gaussian elimination with partial pivoting.

Given that the matrix A is:A=  3 -2  4  2  6 -5 12  4  6  1 -8  5 -3  3  4  6We need to find the P T LU factorization of A using Gaussian elimination with partial pivoting.

Now we shall apply Gaussian elimination with partial pivoting:

First step: Swap R2 and R5 to get a pivot of greater magnitude in the 2nd row.    

P1AP1^T=⎣⎡​3−2  4  2  6 12  4 −5⎦⎤​⇔P1=⎣⎡​1  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0⎦⎤​

Second step:

Make the entries below the 2nd row 0 using R3, R4 and R5.  

M1P1A=⎣⎡​3−2  4  2  6 12  4 −5⎦⎤​⇔M1=⎣⎡​1  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0⎦⎤​    

M1P1A=⎣⎡​3−2  4  2  6 12  4 −5⎦⎤​    

M1P1A=⎣⎡​3−2  4  2  6 12  4 −5⎦⎤​⇔R3=R3-2*R1,  R4=R4-2*R2,  R5=R5+2*R2    

P1M1A=M2P2M1P1A=⎣⎡​3−2  4  2  6 12  4 −5⎦⎤​⇔P2=⎣⎡​1  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0⎦⎤​

Third step: Make the entries below the 3rd row 0 using R4 and R5.      

M2P2M1P1A=⎣⎡​3−2  4  2  6 12  4 −5⎦⎤​⇔M2=⎣⎡​1  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0⎦⎤​      

M2P2M1P1A=⎣⎡​3−2  4  2  6 12  4 −5⎦⎤​      

M2P2M1P1A=⎣⎡​3−2  4  2  6 12  4 −5⎦⎤​⇔R4=R4-3*R1,  R5=R5+4*R1      

P2M2P1A=M3P3M2P2M1P1A=U=⎣⎡​3−2  4  2  6 12  4 −5⎦⎤​⇔P3=⎣⎡​1  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0⎦⎤​P3M3P2M1A=U=⎣⎡​3−2  4  2  6 12  4 −5⎦⎤​

Thus the upper triangular matrix U=M3P3M2P2M1P1A is given by: U=⎣⎡​3 -2  4  2  0  3 -1  6  0  0  1 -1  0  0  0  8⎦⎤​

(2). Use the result of Part (1) to express A as A=P TLU and determine P and L.

The lower triangular matrix L is obtained by replacing the upper diagonal entries of the matrix M3P3M2P2M1P1A with 0 and adding 1s along the main diagonal.

L=⎣⎡​1  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0⎦⎤​

The permutation matrix P is given by P=P3P2P1=⎣⎡​0  1  0  0  0  0  0  1  0  0  0  0  1  0  0  0⎦⎤​

Thus, A can be written as A=P TLU=⎣⎡​0  1  0  0  0  0  0  1  0  0  0  0  1  0  0  0⎦⎤​

⎣⎡​1  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0⎦⎤​⎣⎡​3 -2  4  2  0  3 -1  6  0  0  1 -1  0  0  0  8⎦⎤​

Therefore, the P T LU factorization of A is given by

P T=⎣⎡​0  1  0  0  0  0  0  1  0  0  0  0  1  0  0  0⎦⎤​

L=⎣⎡​1  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0⎦⎤​

U=⎣⎡​3 -2  4  2  0  3 -1  6  0  0  1 -1  0  0  0  8⎦⎤​

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Answer:

The answer is 13.6

a^2+b^2=c^2

so 13^2+4^=c^2

169+16=c^2

square root of 185 is 13.6

so the answer is 13.6 or 14 if you round

Answer:

w

Step-by-step explanation:

Answer:

There would be 950 cm of thread left on the reel

Step-by-step explanation:

Here in this question, we are interested in knowing the amount of thread left on the reel.

To answer this question properly, we shall need to be consistent in using our units.

Thus, we need to convert the length of thread on the reel to cm.

Mathematically;

100cm = 1 m

let x cm = 15.25 m

x = 15.25 * 100 = 1525 m

Since 575 cm has been used for a project, the amount of thread in cm left on the reel will be;

1525 cm - 575 cm = 950 cm

Answer:

yo congratulations on finishing 10th grade (congratulate me on finishing 8th)

hamood spelled backwards is doomah so...um...

also do u mean 7/2/21..bc 6/2/21 is like in June and we're in July

The area of the shape that is the combination of rectangle and trapezoid will be 71 square inches.

The quantity area demonstrates the amount of a sector on a planar or hemispherical cup. Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.

The shape is a combination of a rectangle and a trapezoid.

The area is the summation of the area of the rectangle and the area of the trapezoid. Then we have

Area = Area of the rectangle + Area of the trapezoid

Area = 5 x 9 + (1/2) x (4 + 9) x 4

Area = 45 + 26

Area = 71 square inches

The area of the shape that is the combination of rectangle and trapezoid will be 71 square inches.

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The missing graph is given below.

Part A:

Based on the medians, the plants in Group A grew less on average, as compared to the plants in Group B.

Part B:

The range and IQR are greater in Group B as compared to Group A, so there is less variability in the growth of plants in Group B.

A box and whisker plot displays a "box" with its left edge at Q₁, right edge at Q₃, "center" at Q₂ (the median), and "whiskers" at the maximum and minimum.

Given:

Caleb is comparing the growth of plants using two different fertilizers.

The box-and-whisker plot is given.

From the diagram, we can clearly see that the median of A is less than the median of B.

Part A:

Based on the medians, the plants in Group A grew less on average, as compared to the plants in Group B.

Part B:

The range and IQR are greater in Group B as compared to Group A, so there is less variability in the growth of plants in Group B.

Therefore, the blanked words are given above.

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Answer:

78

Step-by-step explanation:

The area of the rhombus is  49√6. Option B

The formula for calculating the area of a rhombus is expressed as;

Area = pq/2

Where;

p and q are the diagonals of the rhombus

From the diagram shown, let's determine the value of p

Using the trigonometric identity;

Tan θ = opposite/adjacent

Substitute the values into the formula, we have;

tan 60 = p/7

Find the value of tan 60 and then substitute

√3 = p/7

cross multiply

p = 7√3

But;

Area = 7√3 × 7√3/2

Area = 49√6

Hence, the value is 49√6

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In the given definitions, there are several difficulties and violations of the rules for definition by genus and difference. These include ambiguity, lack of specificity, and the inclusion of irrelevant information.

The rules being violated include the requirement for clear and concise definitions, inclusion of essential characteristics, and avoiding irrelevant or subjective statements.

12. The definition of a raincoat as an outer garment of plastic that repels water is too broad. It lacks specificity regarding the material and construction of the raincoat, as not all raincoats are made of plastic. Additionally, the use of "outer garment" is subjective and does not provide a clear distinction from other types of clothing.

13. The definition of a hazard as anything that is dangerous is too broad and subjective. It fails to provide a specific category or characteristics that define what qualifies as a hazard. The definition should include specific criteria or conditions that identify a hazard, such as the potential to cause harm or risk to safety.

14. The definition of sneezing as emitting wind audibly by the nose is too narrow and lacks clarity. It excludes other aspects of sneezing, such as the involuntary reflex and the expulsion of air through the mouth. The definition should encompass the essential characteristics of sneezing, including the reflexive nature and expulsion of air to clear the nasal passages.

15. The definition of a bore as a person who talks when you want him to listen is subjective and relies on personal preference. It does not provide objective criteria or essential characteristics to define a bore. A more appropriate definition would focus on the tendency to dominate conversations or disregard the interest or input of others.

In conclusion, these definitions violate the rules for definition by genus and difference by lacking specificity, including irrelevant information, and relying on subjective or ambiguous criteria. Clear and concise definitions should be based on essential characteristics and avoid personal opinions or subjective judgments.

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The correct value of approximately 19 payments are required to settle the loan.

To determine the number of payments required to settle the loan, we need to calculate the loan balance and divide it by the payment amount.

First, let's calculate the loan balance. The down payment made by General Computers Inc. is 30% of $61,000, which is $18,300. This means the loan amount is the remaining balance:

Loan amount = Purchase price - Down payment

= $61,000 - $18,300

= $42,700

Next, let's calculate the interest rate per period. The given interest rate is 3.50% compounded semi-annually. Since the payments are made quarterly, we need to adjust the interest rate accordingly. The semi-annual interest rate is:

Semi-annual interest rate = Annual interest rate / Number of compounding periods per year

= 3.50% / 2

= 0.035 / 2

= 0.0175

Now, let's calculate the loan balance after each payment. We'll use the formula for the future value of an ordinary annuity to calculate the loan balance at the end of each quarter:

Loan balance after each payment = Loan amount * (1 + Semi-annual interest rate)^(-Number of payments)

In this case, the loan amount is $42,700 and the payment amount is $2,250.53.

Let's calculate the number of payments required to settle the loan by iteratively subtracting the payment amount from the loan balance until the loan balance becomes zero:

Loan balance after payment 1 = $42,700 * \((1 + 0.0175)^(-1)\)

Loan balance after payment 2 = (Loan balance after payment 1 - Payment amount) * \((1 + 0.0175)^(-1)\)

Loan balance after payment 3 = (Loan balance after payment 2 - Payment amount) *\((1 + 0.0175)^(-1)\)

...Loan balance after payment n = (Loan balance after payment n-1 - Payment amount) *\((1 + 0.0175)^(-1)\)

We continue this calculation until the loan balance becomes zero.

Using this iterative calculation, we find that it takes approximately 19 payments to settle the loan.

Therefore, approximately 19 payments are required to settle the loan.

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Answer:

110degrees

Step-by-step explanation:

Complete question

Q4: If x and y are two supplementary angles whereas m<x=70 then find the m<y.

The sum of two supplementary angles is 180degrees, hence;

m<x + m<y = 180

70 + m<y = 180

m<y = 180 - 70

m<y = 110degrees

Hence the measure of ,=m<y is 110degrees

Answer:

square root of 125

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below :)

After 8 hours, there are approximately 76.052 milligrams of medication remaining in Rory's bloodstream.

To solve this problem, we can use the concept of exponential decay, where the amount of medication decreases at a constant rate proportional to the amount present at that time.

Given that the medication is halved every 13 hours, we can determine the decay constant (k) using the formula:

k = ln(0.5) / 13

where ln represents the natural logarithm.

Now, let's calculate the decay constant:

k = ln(0.5) / 13

≈ -0.05314 (rounded to five decimal places)

The equation representing the amount of medication (M) in Rory's bloodstream at any given time (t) is:

\(M(t) = M_o \times e^{(kt)\)

where M₀ is the initial amount of medication (150 milligrams).

After 8 hours (t = 8), we can calculate the amount of medication remaining in Rory's bloodstream:

\(M(8) = 150 \times e^{(-0.05314 \times 8)\)

M(8) ≈ 76.052 milligrams (rounded to three decimal places)

Therefore, after 8 hours, there are approximately 76.052 milligrams of medication remaining in Rory's bloodstream.

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To rewrite the expression 18a^3b + 9ab^2 using a common factor, we can factor out the common factor from both terms. In this case, the common factor is 9ab.

Taking out the common factor, we have:

18a^3b + 9ab^2 = 9ab(2a^2 + b)

So, the expression 18a^3b + 9ab^2 can be simplified as 9ab(2a^2 + b) by factoring out the common factor 9ab.

This process is known as factoring out the greatest common factor (GCF). By factoring out the GCF, we simplify the expression and make it more manageable and easier to work with.

Factoring out the GCF is a useful technique in algebra to simplify expressions and solve equations. It helps in identifying common factors and allows us to rearrange terms more easily.

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P (HR/caught) ≈ 0.44

Probability is a measure of the likelihood of an event to occur.  Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

Dependent Events:

Two events are said to be Dependent when the outcome of the first event influences the outcome of the second event.

The probability of occurrence of A and B is given by the formula:

P(A and B) = P(A) · P(B|A).

Where A and B are dependent events

Given,

Probability of choosing High road by the runner

P(HR) = 0.8

Probability of choosing Low road by the runner

P(LR) = 0.2

Probability of runner to be caught on

Probability to be caught on HR

P(HR ∩ caught) = 0.01 × 0.8

Probability to be caught on LR

P(LR ∩ caught) = 0.05 × 0.2

Probability of being caught P(caught) = 0.01 × 0.8 + 0.05 × 0.2

Probability that runner took the high road, given that he was caught:

P (HR/caught) = P(HR ∩ caught) / P(caught)

P (HR/caught) = 0.01 × 0.8 / 0.01 × 0.8 + 0.05 × 0.2

P (HR/caught) = 0.008/0.008 + 0.01

P (HR/caught) ≈ 0.44

Hence, probability of the runner choosing high road while being caught:

P (HR/caught) ≈ 0.44

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The value of x which is the length of the base of the triangle in the question is; 29 meters

A triangle is a three sided polygon, with three interior angles.

Please find attached the possible diagram in the figure, (created with MS Word), which is a question from a mathematics textbook posted on the internet

The diagram indicates that the altitude or height of the triangle = 8 meters

The specified area of the triangle is; A = 261 square meters

The base length of the triangle = x

The formula for the area of a triangle, A, is; A = (1/2) ×Base length × Height

Therefore;

A = 261 m² = (1/2) × x × 18 m

x = 261 m² ÷ ((1/2) × 18 m) = 29 m

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The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

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

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Step-by-step explanation:

the answer to your problem is m= -5/2

Answer:

-2.5

Step-by-step explanation:

The slope formula \(\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\) tells us the formula for any slope with 2 given points. We have to plug in the numbers from our 2 ordered pairs to get \(\frac{-4 - 1}{2 - 0}\), which simplifies to \(\frac{-5}{2}\) and can be written as -2.5

The slope of this equation is -2.5

Answer:

\(\large\boxed{\tt x = 2}\)

Step-by-step explanation:

\(\textsf{We are asked to solve for x in the given equation.}\)

\(\textsf{We should know that x is cubed, meaning that it's multiplied by itself 3 times.}\)

\(\textsf{We should isolate x on the left side of the equation, then find x by cubic rooting}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{How is this possible?}}\)

\(\textsf{To isolate variables, we use Properties of Equality to prove that expressions}\)

\(\textsf{are still equal once a constant has changed both sides of the equation. A Cubic}\)

\(\textsf{Root is exactly like a square root, but it's square rooting the term twice instead}\)

\(\textsf{of once.}\)

\(\large\underline{\textsf{For our problem;}}\)

\(\textsf{We should use the Subtraction Property of Equality to isolate x, then cubic root}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{Solving;}}\)

\(\textsf{Subtract 1 from both sides of the equation keeping in mind the Subtraction}\)

\(\textsf{Property of Equality;}/tex]

\(\tt \not{1} - \not{1} - x^{3} = 9 - 1\)

\(\tt - x^{3} = 8\)

\(\textsf{Because x}^{3} \ \textsf{is negative, we should exponentiate both sides of the equation by}\)

\(\textsf{the reciprocal of 3, which is} \ \tt \frac{1}{3} .\)

\(\tt (- x^{3})^{\frac{1}{3}} = 8^{\frac{1}{3}}\)

\(\underline{\textsf{Evaluate;}}\)

\(\tt (- x^{3})^{\frac{1}{3}} \rightarrow -x^{3 \times \frac{1}{3} } \rightarrow \boxed{\tt -x}\)

\(\textsf{*Note;}\)

\(\boxed{\tt A^{\frac{1}{C}} = \sqrt[\tt C]{\tt A}}\)

\(\tt 8^{\frac{1}{3}} \rightarrow \sqrt[3]{8} \rightarrow 2^{1} \rightarrow \boxed{\tt 2}\)

\(\underline{\textsf{We should have;}}\)

\(\tt -x=2\)

\(\textsf{Use the Division Property of Equality to divide each side of the equation by -1;}\)

\(\large\boxed{\tt x = 2}\)

Main Answer:The correct answer would be C)0.79.  

Supporting Question and Answer:

How is the coefficient of determination related to the correlation coefficient?

The coefficient of determination measures the proportion of the variance in the dependent variable that can be explained by the independent variable(s). It ranges from 0 to 1, where 0 indicates no relationship and 1 indicates a perfect fit.

Since the coefficient of determination is the square of the correlation coefficient, squaring the correlation coefficient (r) will give us the value of r².

Body of the Solution:The coefficient of determination, denoted as R^2, is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). It ranges between 0 and 1.

The relationship between the coefficient of determination (R^2) and the correlation coefficient (r) is given by the equation:

R^2 = r^2

Given that r = 0.89, we can find the value of R^2:

R^2 = (0.89)^2

= 0.7921

So, the coefficient of determination (R^2) equals 0.7921, which is approximately 0.79.

Final Answer:Therefore,the coefficient of determination (R^2) equals 0.7921, which is approximately 0.79.

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The coefficient of determination (R^2) equals 0.7921, which is approximately 0.79.

The coefficient of determination measures the proportion of the variance in the dependent variable that can be explained by the independent variable(s). It ranges from 0 to 1, where 0 indicates no relationship and 1 indicates a perfect fit.

Since the coefficient of determination is the square of the correlation coefficient, squaring the correlation coefficient (r) will give us the value of r².

The coefficient of determination, denoted as R^2, is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). It ranges between 0 and 1.

The relationship between the coefficient of determination (R^2) and the correlation coefficient (r) is given by the equation:

R^2 = r^2

Given that r = 0.89, we can find the value of R^2:

R^2 = (0.89)^2

= 0.7921

So, the coefficient of determination (R^2) equals 0.7921, which is approximately 0.79.

Therefore, the coefficient of determination (R^2) equals 0.7921, which is approximately 0.79.

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The formula for the area of a circle A = πr^2, where A is the area, π is the mathematical constant pi, and r is the radius.

In this case, the radius So, the area of the tabletop is:

A = πr^2

A = (22/7) x (5/2)^2

A = (22/7) x (25/4)

A = 550/28 radius is given as 2 1/2 feet, or 5/2 feet in fractional form.

A = 19 11/28 square feet

Therefore, the area of Melba's tabletop is approximately 19 11/28 square feet

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Answer:

7x-26

Step-by-step explanation:

Answer:

f(x - 4) = 7x - 26

Step-by-step explanation:

Since the original equation was f(x) = 7x + 2, then to solve the following equation, you need to use the substitution method in relation to the added number (-4). So, if f(x - 4), you would now substitute the (x - 4), in place of the previous (x). Therefore the new problem would be f(x - 4) = 7(x - 4) + 2; after distributing, you would get 7x - 28 + 2. Then further simplifying, this would be 7x - 26, after doing -28 + 2. Finally, the answer would be f(x - 4) = 7x -26.

Answer: stop being a brat

Step-by-step explanation:

The answer is:

5/4

Work/explanation:

Let's work out the slope of the line.

The equation is in y = mx + b form where m = slope; b = y intercept.

Similarly, in y=5/4x - 7/4, the slope is 5/4.