rewrite the equation x^2+26x+164.5=0 in the form (x-p)^2=q​

The righting moment of the box-shaped barge is 14,515.2 Nm if she is heeled to an angle of 3°.

A box-shaped barge of 80 meters length and 8 meters breadth is floating at an even keel draft of 2.8 meters.

Her KG is 2.5 meters.

To calculate the righting moment if she is heeled to an angle of 3°, use the formula: RM = GZ x Displacement

Where, GZ = GM sin(θ)Displacement = Volume of water displaced × Density of water. Given, Length (l) = 80 meters

Breadth (b) = 8 meters, Draft (T) = 2.8 meters, KG = 2.5 meters, Angle of heel (θ) = 3°

Depth of the center of gravity (G) = T - KG = 2.8 - 2.5 = 0.3 meters.

The new center of buoyancy (B') moves to the new center of gravity (G').

GZ = GM sin(θ)= (BM - BG) sin(θ) = KB sin(θ)= T / 2 sin(θ) = 2.8 / 2 × sin 3°= 0.0756 meters

Displacement (D) = Volume of water displaced × Density of water= lb × bw × d × ρ= 80 × 8 × 0.3 × 1000= 192,000 kg

RM = GZ × Displacement= 0.0756 × 192,000= 14,515.2 Nm

Therefore, the righting moment of the box-shaped barge is 14,515.2 Nm if she is heeled to an angle of 3°.

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Answer:

Step-by-step explanation:

Use PEMDAS to determine order of operations.

P = Parentheses

E = Exponents

M/D = Multiplication/Division

A/S = Addition/Subtraction

The operation in the parentheses must be performed first, which is the addition of 6.1 + 12.

The next operation to perform is multiplication, which is 415 times (6.1 + 12).

The last operation to perform is the subtraction of 415 times (6.1 + 12) from 8.3.

6.1 + 12 = 18.1

8.3 - 415(18.1)

8.3 - 7511.5 = -7503.2

Answer:

The average height difference between randomly selected girls and boys is 5.5 inches. The standard deviation of the difference in height is about 4.18808 inches.

Step-by-step explanation:

Just subtract the girls' average from the boys' average to find the average difference between any girl and boy.

Calculate the variance from the given standard deviations (square the SD). Add the variances and find the square root of that sum. (SD = square root of Var).

The standard deviation is only able to be calculated when the two variables are independent.

The variances are added and not subtracted because finding a different average doesn't mean that the data that is being observed also has a different deviation (also there isn't really a situation where you would subtract the Var).

Between 1 and 1990, there are 2,475 integers for which the improper fraction (n^2 * 7) / (n * 4) is not in its lowest terms.

To determine when the fraction is not in lowest terms, we need to find values of n for which the numerator and denominator share a common factor greater than 1. Simplifying the fraction, we get (n * 7) / 4. For the fraction to be in lowest terms, n and 4 must be coprime, meaning they have no common factors other than 1. To find the values of n that violate this condition, we need to identify the multiples of 4 within the range 1 to 1990. There are 497 multiples of 4 in this range. However, since we are looking for values of n, we need to subtract 1 to exclude the multiple 0, yielding 496. Therefore, there are 496 values of n that do not satisfy the coprime condition. Subtracting this from the total number of integers in the range (1990 - 1 = 1989), we find that 1989 - 496 = 1493 integers yield the fraction in lowest terms. Finally, subtracting this number from the total number of integers (1990 - 1), we find that 1990 - 1493 = 497 integers give the fraction (n^2 * 7) / (n * 4) in lowest terms.

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Answer:

8x

Step-by-step explanation:

2x+2x+2x+2x

=8x if all the sides r 2x

Answer:

x+7

Step-by-step explanation:

Remove Parentheses

Collect like terms

Calculate

Answer: x+7

Step-by-step explanation: distribute the -2 first

3x - 2x + 8 - 1

simplify (combine like terms )

3x-2x= x

8-1= 7

x+7  

Hope this helps (^_^)

Answer:

\(-36c^{9}\)

Step-by-step explanation

\((-12)(c^{5} )(3)(C^{4})\)

\((-12)(3)(c^{5})(c^{4})\)

\((-12*3)(c^{4}*c^{5})\)

\((-12*3)(c^{4+5})\)

\(-36c^{9}\)

The expected value of a game represents the average amount of money that a player can expect to win or lose per game. The expected value of the game is $0.25.

Two heads: The probability of getting two heads is 1/4 (since the first coin can be either heads or tails, and the second coin must match). The player wins $1 in this case. Two tails: The probability of getting two tails is also 1/4. The player wins $1. Head and tail: The probability of getting a head and a tail is 1/2 (since the first coin can be either heads or tails and the second coin must be the opposite).

The player loses $1 in this case. To calculate the expected value, we multiply each outcome's probability by its corresponding monetary value and sum them up: (1/4 * $1) + (1/4 * $1) + (1/2 * -$1) = $0.25. Therefore, the expected value of the game is $0.25. On average, a player can expect to win $0.25 per game in the long run.

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(a)"If a person has no shirt (p), then they will not be served". (b)"No service, no shirt,". (c)"If a person has a shirt (p), then they will be served (q)." (d) "If a person is served (q), then they have a shirt (p)."

(a) To write the statement as a formal implication p⇒q, we identify the propositions p and q. In this case, p represents "a person has no shirt" and q represents "they will not be served." Therefore, the formal implication is p⇒q, which can be read as "If a person has no shirt, then they will not be served."

(b) The converse of the statement switches the positions of p and q. In this case, the converse is "No service, no shirt." This implies that if a person is not served (q), then they have no shirt (p).

(c) The inverse of the statement negates both p and q. The inverse of "No shirt, no service" is "If a person has a shirt, then they will be served." This means that if a person has a shirt (p), then they will be served (q).

(d) The contraposition of the statement switches and negates both p and q. The contraposition of "No shirt, no service" is "If a person is served, then they have a shirt." This implies that if a person is served (q), then they have a shirt (p).

In summary, the formal implication "No shirt, no service" (p⇒q) states that if a person has no shirt (p), they will not be served (q). The converse, inverse, and contraposition of the statement are "No service, no shirt," "If a person has a shirt, then they will be served," and "If a person is served, then they have a shirt," respectively.

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Answer: y = (1/3)*x - 5

Step-by-step explanation: Hope this helps!

Answer:

A. n = 1/63

B. k = 13/3

C. g = 5

D. w = 21/17

Step-by-step explanation:

A. 9n = 15/7 - 2

9n = 15-14/7

9n = 1/7

n = 1/7 ÷ 9

= 1/7 × 1/9

n = 1/63

B. 1/3 = k - 4

1/3 + 4 = k

1+12/3 = k

13 /3 = k

k = 13/3

C. g - 2/5g = 3

5g-2g/5 = 3

3/5g = 3

g = 3 ÷ 3/5

= 3 × 5/3

= 15/3

g = 5

D. 3/7w + 2w = 3

3w+14w/7 = 3

17/7w = 3

w = 3 ÷ 17/7

= 3 × 7/17

= 21/17

w = 21/17

Answer:

i think its D but i'm not very sure. try it

Step-by-step explanation:

The vendor sold 172 sodas and 58 hotdogs at the hockey game.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

let, the number of soda cans be 'x' and the number of hot dogs be 'y'.

So, From the given information x = 3y and the vendor sold a total of 232.

Therefore, x + y = 232.

3y + y = 232.

4y = 232.

y = 232/4.

y = 58.

So, He sold 58 hot dogs and 3×58 = 172 soda cans.

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Answer:

True

Step-by-step explanation:

The polynomial function is h(x)=\(\sqrt[3]{64x^{3} +27x^{6} }\). The degree of the polynomial is 6 and the leading coefficient is 27.

Given that,

The polynomial function is h(x)=\(\sqrt[3]{64x^{3} +27x^{6} }\)

We have to analyze the function to see if it is a polynomial function. State the degree and leading coefficient if the function is a polynomial.

The sum of one or more terms, each of which is either a number or a number multiplied by the independent variable and raised to a positive integer exponent, is known as a polynomial function.

The exponent of the variable, or zero if there is no variable, determines a term's degree.

The biggest term degree is the polynomial of the Function.

The Distributive Property is used to join terms having the same Degree.

Usually, terms are presented in order of decreasing Degree.

An nth degree polynomial function of x is often stated as follows:

F(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + aₙ₋₂xⁿ⁻² +... + a₁x + a₀

So,

h(x)=\(\sqrt[3]{64x^{3} +27x^{6} }\)

Therefore, the degree of the polynomial is 6 and the leading coefficient is 27.

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Answer:

Step-by-step explanation:

Reduce 88/80 to lowest terms

The simplest form of  

88

80

is  

11

10

.

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 88 and 80 is 8

Divide both the numerator and denominator by the GCD

88 ÷ 8

80 ÷ 8

Reduced fraction:  

11

10

Therefore, 88/80 simplified to lowest terms is 11/10.

MathStep (Works offline)

Download our mobile app and learn to work with fractions in your own time:

Android and iPhone/ iPad

Equivalent fractions: 176/160 44/40 264/240 440/400 616/560

More fractions: 176/80 88/160 264/80 88/240 89/80 88/8187/80 88/79

Fractions Simplifier

your answer is

9/36

The building has two rectangular shapes that want to be tiled and carpeted. Total cost for tiling and carpeting the office building is $1,747.08.

The area of a rectangular shape is given by:

Area = length x width

In this problem, there are two rectangular areas, one will be tiled and the other will be carpeted. The dimensions are:

Tiled area = 12' x 20' = 240  ft²

The cost of tiling is $0.99 per ft². Therefore,

Tiling cost = 240  ft² x $0.99/ft² = $237.6

Carpeted area = 14' x 18' = 252  ft²

The cost of carpeting is $5.99 per ft². Therefore,

Carpeting cost = 252  ft² x $5.99/ft² = $1,509.48

Total cost = tiling cost + carpeting cost

                = $237.6 + $1,509.48 = $1,747.08

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Answer:

Step-by-step explanation:

semi circle: pi(r^2)/ 2

r=3

AREA: 14.14

we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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The side length that is not the possible length of the third side of the triangle is 18 inches.

Two sides of a triangle measures 8 inches and 10 inches respectively . The possible length of the third sides of the triangle can be found using triangle inequality theorem.

According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.

Therefore, if the sides are a, b and c. The rules are as follows:

a + b > c

b + c > a

a + c > b

Hence,

8 + 10 > c

10 + c > 8

8 + c > 10

Therefore, using the triangle inequality theorem, the length that is not the third side of the triangle is 18 inches

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For the following linear system X1 + X2 1 X1 + (a − 1) x₂ = 2 ax1 + = ax2 a²x3 2a, the determinant is zero when a=1 and a=2. For all other values of a, the system will have unique solutions. Answer: a = 1 and a = 2.

Given system of linear equation,X1 + X2 = 1X1 + (a − 1)x₂ = 2ax1 + ax2 = a²x32a

We are supposed to find the values of 'a' such that the linear system has no solutions. The system can be written in the matrix form as:      [1 1 | 1]       [1 a-1 | 2a]       [a 1 | a²]

On finding the determinant of the matrix,

|A| = 1(a-1)2 - 1(2a) + 1(a2)                 = a2 - 2a + 1 - 2a + a -1                 = a2 - 3a + 2

This can be further factorized as (a-1)(a-2).

Therefore, the determinant is zero when a=1 and a=2. For all other values of a, the system will have unique solutions. Answer: a = 1 and a = 2.

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Answer:

0.125

Step-by-step explanation:

\( \frac{1}{2} \div 4\)

\( \frac{1}{2} \times \frac{1}{4} \)

\( \frac{1}{8} \: or \: 0.125\)

Answer:

0.125

Step-by-step explanation:

The polynomial within the numerator is 9x²+45x+54.

Given the denominator of the initial expression is \(\frac{?}{3x^2+15x+18}\) and also the rational expression simplifies to three.

A mathematical expression which will be rewritten to a rational fraction, an algebraic fraction specified both the numerator and therefore the denominator are polynomials. and a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Let's take the polynomial within the numerator is k.

So, rewrite the given expression as

\(\frac{k}{3x^2+15x+18}=3\)

or it also can be written as

\(\frac{k}{3x^2+15x+18}=\frac{3}{1}\)

Cross multiply either side as a×d=b×c where a=k, b=3x²+15x+18, c=3 and d=1 and acquire

k=3(3x²+15x+18)

Simplify the above expression,

k=9x²+45x+54

Hence, the polynomial within the numerator within the given expression \(\frac{?}{3x^2+15x+18}\) which is simplified to 3 is 9x²+45x+54.

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Answer:a

Step-by-step explanation:

ANSWER

ST = 4cm

EXPLANATION

We want to find the length of ST in triangle RST.

We are given that the two triangles are similar.

In similar triangles, the ratio of proportional sides of the two triangles are equal for all sides.

This means that:

Therefore, to find the length of ST, we can apply the last two proportions. That is:

That is the length of ST.

Answer:

8,377.58 \(mi^{3}\)

Step-by-step explanation:

To solve for the volume of a right circular cone like the one in the picture, you use \(\pi\)\(r^{2}\)\(\frac{h}{3}\).

Plug in the radius and height to get \(\pi\)\(20^{2}\)\(\frac{20}{3}\).

Then solve (and round to the nearest hundredth) and you should get 8,377.58.

Option B is correct. The anticipated and actual Metascore evaluations typically differ by only 7.8 points.

Given that,

We looked at the correlation between rotten tomatoes and metascore scores for a sample of 75 well-known films. A linear form with a strong positive relationship was visible in the scatterplot. Here are the outcomes of the stat crunch linear regression.

We have to find the number 7.8. What is this saying to us.

The average difference between Metascore and Rotten Tomatoes ratings is 7.8 points.

7.8 is the Estimate of error standard deviation. It is not Margin of error.

So, Option A is not correct.

The anticipated and actual Metascore evaluations typically differ by only 7.8 points.

The average error in predicted value and observed value is standard error.

So, Option B is correct.

On average the total variation in the predicted Metascore ratings is 7.8% of the total variation in the observed Metascore ratings.

It's not squared value.

So, Option C is not correct.

Therefore, Option B is correct. The anticipated and actual Metascore evaluations typically differ by only 7.8 points.

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The disparities between the actual and anticipated values in a regression model were referred to as residuals in the context Tufte provided.

American statistician Edward Rolf Tufte is a retired professor of political science, statistics, and computer science at Yale University.

Tufte talked about the idea of residuals. The discrepancies between the actual value and the projected value are known as residuals in statistics. Depending on whether the observed value is higher or lower than the projected value, they might be either positive or negative.

A model's residuals offer a gauge of how well it matches the data. According to him, residual plots are a great tool for seeing issues with the model fit and spotting outliers that might be skewing the results.

In contrast to relying exclusively on statistical tests, Tufte emphasised the significance of visually evaluating residuals since graphs can highlight patterns and correlations that may be missed in the numbers.

Overall, residuals are a key idea in statistics since they may be used to evaluate a model's reliability and point out its flaws.

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Answer:

1: D

2 (but actually 3) B

Step-by-step explanation:

Answer: x=-10

Step-by-step explanation:

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

4x+20=3x-6-2x-4

Next combine like terms: 4x-3x+2x=-20-6-4

                                           3x=-30

                                             x=- 10