triangle abc with vertices at a(−1, −1), b(1, 1), c(0, 1) is dilated to create triangle a′b′c′ with vertices at a′(−3, −3), b′(3, 3), c′(0, 3). determine the scale factor used.

The evaluated integral is (7/4) (π - (3√3)/6) (rounded to an appropriate decimal approximation based on the given values of π and √3).

To evaluate the integral ∫∫(7/2 cos(x)) dV, where the region of integration is given by V: 1 ≤ c ≤ 2 and 0 ≤ x ≤ cos⁻¹(2c-1), we can reverse the order of integration.

Step 1: Write the integral with reversed order of integration:

∫∫(7/2 cos(x)) dc dx

Step 2: Determine the limits of integration for the reversed order. The variable c now varies from 1 to 2, and x varies from 0 to cos⁻¹(2c-1). Therefore, the integral becomes:

∫[1,2] ∫[0,cos⁻¹(2c-1)] (7/2 cos(x)) dx dc

Step 3: Integrate with respect to x first. The integral with respect to x is straightforward:

∫[1,2] [sin(x)] [0,cos⁻¹(2c-1)] (7/2) dc

Step 4: Evaluate the inner integral:

∫[1,2] [sin(cos⁻¹(2c-1))] (7/2) dc

Step 5: Simplify the inner integral using the trigonometric identity sin(cos⁻¹(u)) = √(1 - u²):

∫[1,2] [√(1 - (2c-1)²)] (7/2) dc

Step 6: Integrate with respect to c:

(7/2) ∫[1,2] [√(1 - (2c-1)²)] dc

Step 7: Evaluate the integral:

Using the trigonometric substitution u = sin(t), du = cos(t) dt, and the limits change to t: π/6 ≤ t ≤ π/2.

(7/4) ∫[π/6, π/2] [√(1 - sin²(t))] cos(t) dt

Step 8: Simplify the integrand:

(7/4) ∫[π/6, π/2] [cos²(t)] dt

Step 9: Apply the double-angle formula for cosine:

(7/4) ∫[π/6, π/2] [(1 + cos(2t))/2] dt

Step 10: Split the integral into two separate integrals:

(7/4) [∫[π/6, π/2] (1/2) dt + ∫[π/6, π/2] (cos(2t)/2) dt]

Step 11: Integrate each term separately:

(7/4) [(t/2) + (sin(2t)/4)] evaluated from π/6 to π/2

Step 12: Substitute the limits and simplify:

(7/4) [((π/2)/2 + (sin(2(π/2))/4) - ((π/6)/2) - (sin(2(π/6))/4)]

Step 13: Simplify further:

(7/4) [(π/4 + 0 - π/12 - (1/4)(√3/2))]

Step 14: Simplify and calculate the final value:

(7/4) [(π/4 - π/12 - (√3/8))]

= (7/4) [(3π - π - 3√3)/12]

= (7/4) [(2π - 3√3)/12]

= (7/4) (π - (3√3)/6)

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Answer:

v = -1/6

Step-by-step explanation:

Combine all like terms, getting 18v = -3. Then, divide both sides by 18 to get -3/18, or v = -1/6

Hopefully this helps- let me know if you have any questions!

Answer:

the each snack cost is 1

Step-by-step explanation:

Let us assume the each snack cost be x

So according to the question

The following equation would be applied

5x + 1 + 4 = 10

5x + 5 = 10

5x = 5

x = 1

hence, the each snack cost is 1

So the same would be considered and relevant too

Answer:

Step-by-step explanation:

5- There are 2 right-angled triangles and 1 equilateral triangle or you can just say triangles

6- area for a triangle is a=bh(1/2)

so 4×3=12(1/2)=6

and 4×3=12(1/2)=6

In both triangles, they're a=6

7- 4×6=24(1/2)=12

the top flag is a=12

8-12+6+6=24

9- the rectangular flag has an area of 24 since a=bh and the added areas of the triangles are 24. I conclude that these are two ways of finding the area of this rectangular flag.

hope this helps : )

Answer:

Lololololo9lolo9lkiujyhgdfbhjkifewkjuhgsdvcgfh

Step-by-step explanation:

Answer:

to present another's viewpoint

Answer:-

D, to analyze specific data i guess

Step-by-step explanation:

its83

(a+b)^2=a^2+2ab+b^2

x^2+(-9)2x-2=0

b^2=81

83+(-2)=81

The area under the standard normal distribution curve between z=0 and z=0.25 is 0.0987.

First cumulative probability = z = 0 and

Second cumulative probability = z = 0.25

The Standard Normal Distribution Table, often known as the Z-table, may be used to determine the area under the standard normal distribution curve between z=0 and z=0.25. The table shows the total likelihood (area) up to a specified z-value. The cumulative probability, which can be found by looking up the z-value of 0 in the table, is 0.5000. The cumulative probability is 0.5987 when we look up the z-value of 0.25.

Calculating the area -

Area = First cumulative probability - Second cumulative probability

= 0.5987 - 0.5000

= 0.0987

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Answer:

5

Step-by-step explanation:

3x -12 = -36

-36 ÷ -3 = 12

-7 + 12 = 5

Answer:

The value of -7 + 3(-12) ÷ (-3) is 5

Step-by-step explanation:

First: -7 + -36 ÷ (-3)

Second: -7 + 12

Third: = 5

Therefore your value of this equation is 5.

your welcome.

The population of interest in this case is (d) All of the answer options are correct. It includes all veterinarians, all veterinarians treating large animals, and all veterinarians in the United States treating large animals, including horses.

The population of interest in this study is defined as all veterinarians in the United States who treat large animals, including horses. This population includes all individuals who fit this criteria, regardless of their location or any other specific characteristics.

The researchers wanted to gather information about the prevalence of using nonsteroidal anti-inflammatory drugs (NSAIDs) for treating lameness in horses among veterinarians in the United States. To do this, they obtained a list of all veterinarians who treat large animals, including horses, and sent questionnaires to each of them.

The response rate refers to the percentage of veterinarians who completed and returned the questionnaires out of the total number of questionnaires sent. In this case, the response rate was 40%, meaning that 40% of the veterinarians who received the questionnaires responded to them.

By surveying a representative sample of veterinarians, the researchers can gather information and make inferences about the larger population of veterinarians in the United States who treat large animals, including horses. The data collected from the survey can provide insights into the widespread use of NSAIDs for treating lameness in horses and contribute to the overall understanding of veterinary practices in this context.

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Answer:

72

Step-by-step explanation:

32pi×360/2pi(8)=72

central angle= arc length 360/2pi×r

The measure of the arc is 72 degree

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

The measure of the arc, we use the formula:

⇒ Arc length = (angle measure / 360°) x 2πr

where r is the radius of the circle.

Now, We know that;

The radius is 8 inches, and that the arc length is 3.2π inches.

So, we can plug in those values and solve for the angle measure:

3.2π = (angle measure / 360°) x 2π(8)

3.2π = (angle measure / 360°) x 16π

Divide both sides by 16π:

0.2 = angle measure / 360°

Multiply both sides by 360°:

Angle measure = 72°

Thus, The measure of the arc is 72 degree

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Answer:

E Z

10

Step-by-step explanation:

15 = 1.5t

so t = 15/1.5

      = 10

Answer: t = 10

1. Switch sides

- 1.5t = 15

2. Multiply both sides by 10

- 15t = 150

3. Divide both sides by 15

4. Simplify

t = 10

Answer:

Step-by-step explanation:

range = [-4,6,26]

Step-by-step explanation:

y = 5x - 9.....domain = [1,3,7]....the domain is ur x values, and I am assuming ur looking for the y values that go with the x ones

y = 5x - 9.....when ur domain (ur x) = 1

y = 5(1) - 9

y = 5 - 9

y = -4

y = 5x - 9...when ur domain (x) = 3

y = 5(3) - 9

y = 15 - 9

y = 6

y = 5x - 9...when ur domain(x) is 7

y = 5(7) - 9

y = 35 - 9

y = 26

so ur range (ur y valus) = [-4,6,26]

To find out on which interval are both functions f(x) = x^2 + 2x and g(x) = log (2x + 1) negative, we need to analyze the intervals of negative values of both functions.

We can plot their graphs to have a better understanding:

Graphs of f(x) = x² + 2x and g(x) = log(2x + 1)

Now, we need to observe the intervals where both functions lie below the x-axis: The function f(x) = x^2 + 2x is below the x-axis on the interval (-∞, -2).

The function g(x) = log(2x + 1) is below the x-axis on the interval (-1/2, 0).

Therefore, the interval on which both functions are negative is (-2, 0).Thus, the correct option is (–2, 0).

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Answer:

$130.06

Step-by-step explanation:

Interest is calculated as shown;

I = A - P

A is the amount

P is the principal

Given

Principal = $316

Rate R = 9% = 0.09

Time t = 4yrs

Substiutte and get Amount A

A  =P(1+r)^n

A = 316 (1+0.09)^4

A = 316(1.09)^4

A = 316(1.4116)

A = 446.06

Interest = 446.06 - 316

Interest = 130.06

Hence the interest is $130.06

The exponential distribution is a continuous probability distribution that is widely used in probability theory and statistics. In probability theory, an exponential random variable is a continuous random variable that represents the waiting time between events in a Poisson process.

Suppose X is an exponential random variable. We have to show that E(X²) = 2/λ². We can show this by using the definition of expectation that is, E(X) = ∫[0,∞] xf(x) dx

where f(x) is the probability density function of X.

Similarly, E(X²) = ∫[0,∞] x²f(x) dx

We know that the probability density function of an exponential distribution with parameter λ is given by f(x) = λe^(-λx)So, E(X²) = ∫[0,∞] x²λe^(-λx) dx

Using integration by parts, we have ∫[0,∞] x²λe^(-λx) dx= [-x²e^(-λx)/λ] + [2xe^(-λx)/λ²] + [(-2/λ³)e^(-λx)]∞ 0= (2/λ²)

E(X²) = 2/λ².

The exponential distribution is a continuous probability distribution that is widely used in probability theory and statistics. In probability theory, an exponential random variable is a continuous random variable that represents the waiting time between events in a Poisson process.

Suppose X is an exponential random variable. We have to show that E(X²) = 2/λ². We can show this by using the definition of expectation that is, E(X) = ∫[0,∞] xf(x) dx

where f(x) is the probability density function of X.

Similarly, E(X²) = ∫[0,∞] x²f(x) dx

We know that the probability density function of an exponential distribution with parameter λ is given by f(x) = λe^(-λx)So, E(X²) = ∫[0,∞] x²λe^(-λx) dx

Using integration by parts, we have ∫[0,∞] x²λe^(-λx) dx= [-x²e^(-λx)/λ] + [2xe^(-λx)/λ²] + [(-2/λ³)e^(-λx)]∞ 0= (2/λ²)Therefore, the main answer to this question is E(X²) = 2/λ².

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Answer:

i believe your answer is.

4,789,658,950

Step-by-step explanation:

Answer:

To figure out your average, you add them together then divide by2

Step-by-step explanation:

A quadratic function with leading coefficient 1 and roots of p can be expressed as f(x) = (x - p)(x - p), which simplifies to f(x) = x^2 - 2px + p^2.

To construct a quadratic function with leading coefficient 1 and roots of p, we utilize the relationship between the roots and the factors of a quadratic equation. Since p is a root, the factors of the quadratic function would be (x - p) and (x - p). By multiplying these factors together, we obtain the quadratic function f(x) = (x - p)(x - p). Simplifying further, we can expand the expression:

f(x) = (x - p)(x - p) = x^2 - px - px + p^2 = x^2 - 2px + p^2

Hence, the quadratic function with leading coefficient 1 and roots of p is given by f(x) = x^2 - 2px + p^2. This form allows for easy identification of the coefficients and reveals that the constant term of the quadratic is p^2.

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Answer: 3,347 pounds

Step-by-step explanation:

Curb weight is simply the weight of a car with no passengers, cargo, or anyting other than the standard base model options.

Basically it's the weight of a base model car sitting on the dealership lot.  Curb weight would be different if ANYTHING is added to the base model car such as a passenger, any cargo, or any upgrades aftermarket or otherwise.

Answer:

Not sure if this the correct type of way your looking but its between 1 and 2 tons which is 1000

Step-by-step explanation:

I think...

Answer:

f = 6

Step-by-step explanation:

Plug in what you know then solve:

f = d + 1

f = 5 + 1

f = 6

Answer:

1/5x12 and 12/5

Step-by-step explanation:

both are dividing by five or equal to 2.4 which is the same as 1/5 of 12

Answer Of means to multiply so two correct answer would be B,D  

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

Confidence interval are 5.9 < μ < 8.5 for the population mean.

Given:

Let x = 6,9,3,9, 6, 6, 8, 8, 7, 10,5,9

N = 12, ∑x = 86 x = 86/12 = 7.16

[tex]s=\sqrt{\frac{(x-\bar x)^2}{N-1} } = \sqrt{\frac{(6-7.16)^2+.....+(9-7.16)}{12-1} }[/tex]

[tex]\sqrt{\frac{45.66}{11} } =2.03[/tex]

At 98% confidence interval.

[tex]z=1-\frac{95}{100} =0.05\\[/tex]

[tex]t=2.201[/tex]

Confidence interval.

[tex]\bar x \pm t\frac{s}{\sqrt{n} } = 7.16\pm 2.201(\frac{2.03}{\sqrt{12} } )[/tex]

[tex]5.9 < \mu < 8.5[/tex]

Therefore, 95% confidence interval are 5.9 < μ < 8.5

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The variable that could theoretically be measured on a continuous scale is task completion time.

Task completion time is the duration between the initiation and completion of a specific task. It is continuous as it can take a large range of values on a continuous scale without any gap. It is frequently calculated in various businesses and researches to determine the efficiency and productivity of a particular task or process.

The other variables, such as method of contraception used, length of time of residence in a state, intelligence, authoritarianism, alienation, and county of residence, are all discrete variables. These variables take non-numerical values and are separate from each other by a gap.

These variables can be classified and counted into different categories, such as the number of individuals using a particular method of contraception, number of years of residence in a particular state, number of individuals belonging to a particular county, or number of individuals showing authoritarianism.

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Answer:

A. Reduction

B. 2

Step-by-step explanation:

A: A reduction is when the image is getting smaller. The apostrophes show the new, or second, image. It is called "prime." Because the prime is smaller than the original, it is a reduction.

B: Scale factor is when you divide, which number changes it. In other words, the image moved from 4 to 2, from 2 to 1, etc, which means we are DIVIDING by 2.

Answer:

Joe's been riding 4 hours because if you divide 48 by 12 it gives you 4 and it's by hours so it would be 4 hours. point blank period.

Step-by-step explanation:

Answer:

they are subtracting 6 from each number

Answer:

try your best

Step-by-step explanation: