Your school roof is made of four trapezoids. Two of them have the bases of 14 m and 6 m respectively with the 8 m height. The remaining two have the bases of 12 m and 10 m with 6m height. How much roof material is needed to cover the roof?​

Answer: The solution of x is 2.5

Step-by-step explanation: hope it helps:)

Answer: \(x=\frac{5}{2}\)  

Step-by-step explanation:

Simplify the expression:

\(-2x+14+10x=34\)

\(\left(-2x+10x\right)+14=34\)

\(8x+14=34\)

Group all constants on the right side of the equation:

\(8x+14-14=34-14\)

\(8x=34-14\)

\(8x=20\)

Isolate the x:

\(\frac{8x}{8}=\frac{20}{8}\)

\(x=\frac{20}{8}\)

\(x=\frac{5\cdot 4}{2\cdot 4}\)

\(x=\frac{5}{2}\)

The \(CORRECT\)answer to this solution is: \(x=\frac{5}{2}\)

\(calderonj4588~:)\)

Answer:

68

Step-by-step explanation:

68 numbers from 1 to less than 69

Answer: i don't get it

Step-by-step explanation:

14) Notice that:

Therefore:

Now, we know that:

Then:

18) Notice that:

Therefore:

Answer:

Answer:

(Q.14) 13.65

(Q.18) .81

Step-by-step explanation:

(Q.14)

136.5/10

1365/10 * 1/10

1365/100

13.65

(Q.18)

8100/10000

8100*1/10000

81/100

.81

Finding the Equation

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:    

                                ⇒  y - 1 =  ³/₂ (x - (-2))  

                                      y - 1 =  ³/₂ (x + 2)

    we could also transform this into the slope-intercept form ( y = mx + c)  

                                  since   y - 1 =  ³/₂ (x + 2)  

                                        ⇒      y  =  ³/₂ x + 4

To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.

The 99% confidence interval for the mean grams of sugar μ = (2.7810, 3.6169), option A.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. So, it may be concluded that there is a 95% likelihood that the real value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.

The confidence interval for population mean is given by :-

\(\bar x \pm z_\alpha _/_2\frac{\sigma}{\sqrt{n} }\)

Given : Sample size : n= 51   ( >30 , that means its a large sample)

Sample mean : x = 3.2 grams

Standard deviation : σ = 1.1 grams

Significance level : 1 - 0.99 = 0.01

Critical value : \(z_\alpha _/_2 = \pm2.576\)

Now, the 99% confidence interval for the mean grams of sugar will be :-

= 3.2 ± (2.576) x 1.1/√51

= 3.2 ± 0.3967

= (2.7810, 3.5967)

Hence, the 99% confidence interval for the mean grams of sugar

μ = (2.7810, 3.6169).

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Answer:

third option: (x+3) / √x+2

Step-by-step explanation:

f(x) = √x+2           g(x) = (x² + 1) / x

(g·f)(x) = g(f(x)) = ((√x+2)² + 1) / √x+2

==> (x+2+1) / √x+2

==> (x+3) / √x+2

Hence the given statement is proved.

Given: ST || UV, ST = VU

we are asked to prove  STW = VUW

Statement(Reason)

ST || UV (Given)

Angle S = Angle V (Alternate interior angle)

Angle SWT = Angle VWU (Vertically opposite Angle)

ST = VU (Given)

Therefore, based on above, we can say that the triangle STW is congruent to VUW by AAS (i.e. Angle Angle Side congruency.

Hence the statement is proved bu angle angle side congruency.

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Answer:

the answer is 66°

Step-by-step explanation:

As it is given that triangle ABC is similar to triangle DEF so

< A = < D ( being corresponding angles of similar triangles)

3x + 18° = 4x + 2°

4x - 3x = 18° - 2°

x = 16°

So now

< A = 3 * 16° + 18° = 66°

The final answer is that the Hamming (8, 4) code transforms a word W of length four into a code word C of length eight using the given parity check equations.

The Hamming (8, 4) code is a form of error-correcting code that adds redundancy to a data word to detect and correct errors during transmission. In this code, a word W of length four is transformed into a code word C of length eight.

The transformation process involves adding four parity bits (c1, c2, c3, c4) to the original word W. Each parity bit is computed based on specific parity check equations. These equations ensure that the resulting code word C satisfies the desired properties for error detection and correction.

The parity check equations are:

c4 + w2 + w3 + w4 = 0

c3 + w1 + w3 + w4 = 0

c2 + w1 + w2 + w4 = 0

c1 + c2 + c3 + w1 + c4 + w2 + w3 + w4 = 0

These equations specify the relationships between the original word bits (w1, w2, w3, w4) and the added parity bits (c1, c2, c3, c4). By solving these equations, the values of the parity bits are determined.

The resulting codeword C is composed of the original word bits (w1, w2, w3, w4) and the computed parity bits (c1, c2, c3, c4). The eight bits in the code word C provide the necessary redundancy to detect and correct errors in the transmitted data.

Overall, the Hamming (8, 4) code ensures that the code word C maintains a specific relationship between its bits, enabling error detection and correction capabilities.

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Performing a Chi-Square test is a statistical tool used to determine if there is a significant difference between observed and expected data. The test helps to analyze categorical data by comparing observed frequencies to the expected frequencies. The p-value in a Chi-Square test refers to the probability of obtaining the observed results by chance alone.

If a p-value lower than 0.01 is obtained in a Chi-Square test, it means that the results are statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no significant difference between the observed and expected data. This means that the observed data is not due to chance alone, but rather to some other factor or factors.

The mean, or average, is not directly related to the Chi-Square test or the p-value. The Chi-Square test is specifically used to determine the significance of the observed data. However, the mean can be used as a measure of central tendency for continuous data, but it is not applicable to categorical data.

In conclusion, obtaining a p-value lower than 0.01 in a Chi-Square test means that there is strong evidence to reject the null hypothesis, and that the observed data is statistically significant.

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If circle has diameter lm and chord pq, lm = 20 cm, and pq = 16 cm, the length of RM is 10√2 centimeters.

In a circle, a diameter is a chord that passes through the center of the circle. Therefore, the point where the diameter and the chord intersect, in this case, point R, bisects the chord.

Since LM is a diameter, its length is twice the radius of the circle, which means LM = 2r. Thus, we can find the radius of the circle by dividing the diameter by 2: r = LM/2 = 20/2 = 10 cm.

Since point R bisects the chord PQ, RP = RQ = 8 cm (half of PQ). Thus, we need to find the length of RM. To do that, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, we have a right triangle RLM with RM as the hypotenuse, so we can use the Pythagorean theorem as follows:

RM² = RL² + LM²

RM² = (10)² + (10)²

RM² = 200

RM = √200 = 10√2 cm

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Complete question is:

Consider circle o with diameter lm and chord pq.

if lm = 20 cm, and pq = 16 cm, what is the length of rm, in centimeters?

Let the initial intensity be I, then,

Here, x is the proportionality constant and d is the distance.

When the seat is changed o one that is thrice as far from the

speakers, we have the new intensity as,

Therefore, the new intensity in terms of the original intensity can be written as,

Thus, the required fraction is 1/9.

To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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Taylor bought 5 cupcakes and 8 muffins from the bakery costing $22.00

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The slope intercept form of the linear equation is:

y = mx + b

where m is the slope and b is the initial value.

Let m represent the number of muffins and c represent the number of 2 cupcakes. Cupcakes cost $2.00 and muffins cost $1.50.

Taylor bought 13 cupcakes and muffins from the bakery, hence:

c + m = 13      (1)

Also, Taylor spent a total of $22.00, therefore:

2c + 1.5m = 22    (2)

From both equations:

c = 5, m = 8

Taylor bought 5 cupcakes and 8 muffins

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Answer: 96 cups

Step-by-step explanation: A gallon  holds 128 ounces there were 6 gallons used to make the punch. 128x6= 768 ounces

A cup holds 8 ounces so you would do 768/8 and that would give you 96 cups

The minimum stopping distance is 800 ft.

Part A: The minimum stopping distance for a driver going at the speed limit (40 mph) is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (40 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 800 ft.

Part B: For a driver going at 45 mph, the minimum stopping distance is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (45 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 925 ft, which is 15.6% greater than the stopping distance for the speed limit.

Part C: For a driver going at 50 mph, the minimum stopping distance is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (50 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 1250 ft, which is 56.3% greater than the stopping distance for the speed limit.

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the general solution of the given differential equation is:

y = [(1/3) x^3 + 2x^2 + 4x + C1] / |x^2 - 4|

To find the general solution of the given differential equation:

(x^2 - 4) dy/dx + 4y = (x + 2)^2

We can rearrange the equation to isolate the derivative term:

dy/dx = [(x + 2)^2 - 4y] / (x^2 - 4)

First, let's simplify the numerator:

[(x + 2)^2 - 4y] = (x^2 + 4x + 4) - 4y

= x^2 + 4x + 4 - 4y

= x^2 + 4x - 4y + 4

Now, substitute this simplified expression back into the differential equation:

dy/dx = (x^2 + 4x - 4y + 4) / (x^2 - 4)

This is a first-order linear homogeneous differential equation. To solve it, we can use the integrating factor method.

First, let's write the equation in the standard form: dy/dx + P(x)y = Q(x)

dy/dx + (4x / (x^2 - 4))y = (x^2 + 4x + 4) / (x^2 - 4)

The integrating factor is given by the exponential of the integral of P(x):

μ(x) = exp ∫ (4x / (x^2 - 4)) dx

To find the integral, we can use substitution. Let u = x^2 - 4, then du = 2x dx:

μ(x) = exp ∫ (2x dx) / (x^2 - 4)

= exp ∫ (du / u)

= exp(ln|u|)

= |u|

Substituting back u = x^2 - 4:

μ(x) = |x^2 - 4|

Now, multiply the entire differential equation by the integrating factor:

|x^2 - 4| dy/dx + (4x / (x^2 - 4)) |x^2 - 4|y = (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4)

The left side can be simplified using the product rule for differentiation:

d/dx [ |x^2 - 4|y ] = (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4)

Now, integrate both sides with respect to x:

∫ d/dx [ |x^2 - 4|y ] dx = ∫ (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4) dx

Integrating the left side gives:

|x^2 - 4|y = ∫ (x^2 + 4x + 4) dx

= (1/3) x^3 + 2x^2 + 4x + C1

where C1 is the constant of integration.

Finally, divide both sides by |x^2 - 4| to solve for y:

y = [(1/3) x^3 + 2x^2 + 4x + C1] / |x^2 - 4|

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Answer:

its 3 can i get the

crown pls

Step-by-step explanation:

The matching numbers are:

1) 0.0000225 = 2 x 10⁻⁵

2) 219,000 = 2 x 10⁵

3) 3,40,000 = 3 x 10⁶

4) 297,000 = 3 x 10⁵

5) 0.0000034 = 3 x 10⁻⁶

What are Exponents?

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.

We have to match the following terms :

1) 0.0000225 = 2 x 10⁻⁵
we can write 0.0000225 as
2.25 / 100000
or, 2.25 / 10⁵
then, 2.25 x 10⁻⁵

2) 219,000 =  2 x 10⁵
as the numbers after 2 are 5
therefore we write 10⁵

3) 3,40,000 = 3 x 10⁶
as the numbers after 3 are 6
therefore we write 10⁶

4) 297,000 = 3 x 10⁵
we round off 297 as 300
as the numbers after 3 are 5
therefore we write 10⁵

5) 0.0000034 = 3 x 10⁻⁶
we can write 0.0000034 as
3.4/ 1000000
or, 3.4 / 10⁶
then, 3.4x 10⁻⁶

Hence, the matching numbers are:
1) 0.0000225 = 2 x 10⁻⁵
2) 219,000 = 2 x 10⁵
3) 3,40,000 = 3 x 10⁶
4) 297,000 = 3 x 10⁵
5) 0.0000034 = 3 x 10⁻⁶

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The required quotient of the given expression 15a⁴b³/12a²b is 5a²b²/3.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

The expression is given in the question, as follows:

15a⁴b³/12a²b

Assume that the denominator does not equal zero.

As per the question, we have

15a⁴b³/12a²b

Cancel out the likewise terms in the above expression, and we get:

15a²b²/12

Reduce the fraction into the simplest form,

5a²b²/3

Therefore, the quotient of the given expression is 5a²b²/3.

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Answer:

\(\frac{1}{60}\)

Step-by-step explanation:

Problem:

 The possible values of x in the equation (60)x = 1;

Solution:

Such a problem like this in which the highest power of the unknown is 1 will have just one solution.

       60x  = 1

To solve this, we take the multiplicative inverse of 60;

   the multiplicative inverse of 60 = \(\frac{1}{60}\)

   Use this inverse to multiply both sides of the expression;

         \(\frac{1}{60}\) \(x\)  60x  = 1 x \(\frac{1}{60}\)

                   x  = \(\frac{1}{60}\)

Answer:

Step-by-step explanation:

\(\angle 2,\angle AEG, \angle GEB\)

The equation's answer is x = 7.5. 4x - 1 2 = x + 7.

x = 1 is the answer to the problem 3x + 2 = (2x + 13) 3.

a) To solve the equation 4x - 1 ÷ 2 = x + 7, we need to isolate the variable x. Let's follow the steps:

1: Distribute the division operation to the terms inside the parentheses.

  (4x - 1) ÷ 2 = x + 7

2: Divide both sides of the equation by 2 to isolate (4x - 1) on the left side.

  (4x - 1) ÷ 2 = x + 7

  4x - 1 = 2(x + 7)

3: Distribute 2 to terms inside the parentheses.

  4x - 1 = 2x + 14

4: Subtract 2x from both sides of the equation to isolate the x term on one side.

  4x - 1 - 2x = 2x + 14 - 2x

  2x - 1 = 14

5: Add 1 to both sides of the equation to isolate the x term.

  2x - 1 + 1 = 14 + 1

  2x = 15

6: Divide both sides of the equation by 2 to solve for x.

  (2x) ÷ 2 = 15 ÷ 2

  x = 7.5

Therefore, x = 7.5 is the solution to the equation 4x - 1 ÷ 2 = x + 7. However, note that this answer is not an integer, so it may not be valid for certain contexts.

b) To solve the equation 3x + 2 = (2x + 13) ÷ 3, we can follow these steps:

1: Distribute the division operation to the terms inside the parentheses.

  3x + 2 = (2x + 13) ÷ 3

2: Multiply both sides of the equation by 3 to remove the division operation.

  3(3x + 2) = 3((2x + 13) ÷ 3)

  9x + 6 = 2x + 13

3: Subtract 2x from both sides of the equation to isolate the x term.

  9x + 6 - 2x = 2x + 13 - 2x

  7x + 6 = 13

4: Subtract 6 from both sides of the equation.

  7x + 6 - 6 = 13 - 6

  7x = 7

5: Divide both sides of the equation by 7 to solve for x.

  (7x) ÷ 7 = 7 ÷ 7

  x = 1

Hence, x = 1 is the solution to the equation 3x + 2 = (2x + 13) ÷ 3.

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Answer:

9.5 ft

Step-by-step explanation:

Since it is a rectangle. The lengths are the same and the widths are the same.

12.4 + 12.4 = 24.8

43.8 - 24.8 = 19

19/2 = 9.5