work out the size of angle x.​

Answer:

hey mate here is ur answer.

Step-by-step explanation:

Right angle : Whose one side is exactly 90°

Obtuse angle : Whose one side is more than 90° but less than 180°.

Equiangular triangle : Whose three sides is perfect or equal angles.

Acute Triangle: Whose all sides are below 90° angles. but since the sum of any triangle should be 180° (refer to google)

hope it helps you,

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Answer:

If a polygon is dilated by a scale factor of k, then its area is multiplied by k².

a. When k = 4, the area of the image is 10 × 4² = 160 square units.

b. When k = 1.5, the area of the image is 10 × 1.5² = 22.5 square units.

c. When k = 1, the area of the image is 10 × 1² = 10 square units. (The image is the same size as the original.)

d. When k = 1/3, the area of the image is 10 × (1/3)² = 10/9 square units.

Step-by-step explanation:

Answer:

-36

Step-by-step explanation:

If you plug in 3 for a and 6 for b the equation would be 3(12)-6(12) or 36-72.

Answer:

-36

is your answer

#life goes on

The equation is: y = -3/4x (in slope-intercept form) or y + 3 = -3/4(x - 4) (in point-slope form).

The correct statements are:

The slope-intercept form is expressed as y = mx + b [m is the slope, b is the y-intercept].

The point-slope form is expressed as y - b = m(x - a) [(a, b) is a point on the line, while m is the slope of the line].

Given the table:

x   |  y  

-8   6

4    -3

8    -6

Use two points, (-8, 6) and (4, -3), to find the slope:

Slope (m) = change in y / change in x = (-3 - 6) / (4 - (-8))

m = -9/12

m = -3/4

To find the y-intercept, substitute (x, y) = (4, -3) and m = -3/4 into y = mx + b:

-3 = -3/4(4) + b

-3 = -3 + b

-3 + 3  = b

b = 0

To write the equation in slope-intercept form, substitute m = -3/4 and b = 0 into y = mx + b:

y = -3/4x - 0

y = -3/4x

To write the equation in point-slope form, substitute m = -3/4 and (a, b) = (4, -3) into y - b = m(x - a):

y + 3 = -3/4(x - 4).

Therefore, we can conclude that:

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The probability of selecting a random car turn out to have defective turn signals out of 425 total number of cars is equal to 0.167 or  167/1000.

Total number of cars = 425

Number of cars with defective turn signals = 71

Number of cars with defective tires = 29

Probability of selecting a car with defective turn signals

= Number of cars with defective turn signals / Total number of cars

Substitute the value in the formula we have,

= 71/425

= 0.167 or 167/1000 in fraction form

Therefore, the probability that one of these cars selected at random has defective turn signals is 0.167 or 167/1000.

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Answer:

The first derivative of \(r(t) = 5\cdot t^{-2}\) (r(t)=5*t^{-2}) with respect to t is \(r'(t) = -10\cdot t^{-3}\) (r'(t) = -10*t^{-3}).

Step-by-step explanation:

Let be \(r(t) = \frac{5}{t^{2}}\), which can be rewritten as \(r(t) = 5\cdot t^{-2}\). The rule of differentiation for a potential function multiplied by a constant is:

\(\frac{d}{dt}(c \cdot t^{n}) = n\cdot c \cdot t^{n-1}\), \(\forall \,n\neq 0\)

Then,

\(r'(t) = (-2)\cdot 5\cdot t^{-3}\)

\(r'(t) = -10\cdot t^{-3}\) (r'(t) = -10*t^{-3})

The first derivative of \(r(t) = 5\cdot t^{-2}\) (r(t)=5*t^{-2}) with respect to t is \(r'(t) = -10\cdot t^{-3}\) (r'(t) = -10*t^{-3}).

Based on the information, we can infer that the probability of rolling a 5 on the dice is 0.16

To find the probability of getting five with the dice we must identify how many possibilities we have in each throw. In this case, each shot has 6 different possibilities from number 1 to 6. So 5 occupies 1/6 of the possibilities, this is equal to 0.16.

According to the above, if we roll the dice 50 times, the theoretical probability would be 8.

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25

porque al multiplicar 25×25 nos da 625

Answer:

25

Step-by-step explanation:

25x25=625

Answer:

25 + 10h = 50+5h

Step-by-step explanation:

Black Diamond Ski Resort

25 + 10h

Bunny Hill Ski Resort

50+5h

We want when they are equal

25 + 10h = 50+5h

Answer:

10x + 25 = 5x + 50

Step-by-step explanation:

The Cpk (Process Capability Index) for this machine is 0.5 (rounded to 3 decimal places).

To calculate the Cpk (Process Capability Index), we need to consider the specification limits and the process variation.

The Cpk is given by the formula:

Cpk = min[(USL - μ) / (3σ), (μ - LSL) / (3σ)], Where:

USL = Upper Specification Limit

LSL = Lower Specification Limit

μ = Process mean

σ = Process standard deviation

In this case, the Upper Specification Limit (USL) is 2 + 0.004 = 2.004 inches, and the Lower Specification Limit (LSL) is 2 - 0.004 = 1.996 inches.

Given that the process mean (μ) is 2.001 inches and the process standard deviation (σ) is 0.002 inch, we can substitute these values into the formula:

Cpk = min[(2.004 - 2.001) / (3 * 0.002), (2.001 - 1.996) / (3 * 0.002)]

Cpk = min[0.003 / 0.006, 0.005 / 0.006]

Cpk = min[0.5, 0.833]

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Let x= the average for all three classes combined. So x=85.25.

When you add two or more numbers and divide the result by the number of numbers you added together, you obtain an average.

The arithmetic mean is determined by adding a collection of numbers, dividing by their count, and obtaining the result.

average  =  total points / number of students

total points = average*number of students

Let the total number of students in  each class = a , b  and x

The total number of points the first class amassed  was   80a

The total number of points amassed by the second class was  85b

The total number of points amassed by the third class = 89c

For the first two classes we have

[ 80a + 85b ] / [ a + b] = 83

80a + 85b = 83a + 83b  

subtract  80a, 83b from both sides    

3a = 2b

a = 2/3b

For the second two classes we have

[ 85b + 89c ]  / [ b + c ]  =  87  

[  85b + 89c ]  = 87 [b + c]

85b + 89c = 87b + 87c      

subtract  85b, 87c from both sides

2c = 2b  

b  = c

For the three classes.....

Total points by all three classes /  number of class members  = the average for all three classes

[ 80a + 85b  + 89c ] /  [ a + b + c ]   =[sub for  a and c ]  

[80 (2/3)b  + 85b  + 89b]  /  [ (2/3)b  + b  + b ]  

b [ 80 (2/3)  + 85  + 89 ]  / [  b [( 2/3) + 1 + 1] ]       [cancel the b's ]

[ 80 (2/3) + 85 + 89]  [  8/3 ]

[ 160/3 + 85 + 89 ] /  [8/3] =

[ 160/3  + 255/3 + 267/3]  / [8/3]     multiply  top/bottom by 3

[160 + 255 + 267 ] / 8  =  

85.25  = average for all three classes

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The probability that the number of people who show up will exceed the capacity of the plane is 0.002607722

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The probability that x people show up follows a binomial distribution,

\(P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\)

Here, n represents the number of booked people and p represents the probability that a person shows up.

Then, the probability that x people show up is:

\(P(x)=\frac{78!}{x!(78-x)!}*0.90^{x}*(1-0.90)^{78-x}\)

So, the probability that the number of people who show up will exceed the capacity of the plane is:

P(x>76) = P(77) + P(78)

Where P(77) and P(78) are calculated as follows:

\(P(77)=\frac{78!}{77!(78-77)!}* 0.90^{77}* (1-0.90)^{78-77} \\ =78*0.00029969*0.10\\ =0.0023375\)

\(P(78)=\frac{78!}{78!(78-78)!}* 0.90^{78}* (1-0.90)^{78-78} \\ =1*0.00026972*1\\ =0.00026972\)

Finally, P(x>76) is:

\(P(x > 76) = 0.0023375 + 0.00026972\\=0.002607722\)

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Answer:

it's a improper fraction

Step-by-step explanation:

16/14 is a fraction so whole number and counting number get eliminated

we know it's a fraction it's more the one and it's all together so proper fraction is eliminated

The fraction 16/14 is an Improper Fraction.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

We have the fraction 16/14.

Now, simplifying the fraction as

16/14

= 8/7.

Here the Numerator= 8 and Denominator= 7

Also, Numerator > Denominator.

Since the fraction where the numerator is greater than the denominator is Improper fraction.

Thus, 16/14 is an Improper Fraction.

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To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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Answer:

jimragarant 1

Step-by-step explanation:

pls can u help me with the questions i have posted i will give u anything u want

pls help its urgent

Answer:

108.8 yd²

Step-by-step explanation:

The area (A) of the triangle can be calculated as

A = \(\frac{1}{2}\) absinC

where a, b are 2 sides and C the angle between them

Here a = 23, b = 9.5 and C = 85° , thus

A = 0.5 × 23 × 9.5 × sin85° ≈ 108.8 yd² ( to the nearest tenth )

Answer:

2,3 is one of them

Step-by-step explanation:

hope this helps!

Answer:3x^2+2x

Step-by-step explanation

the total number of positive odd integers less than 10,000 that can be written using the digits 3, 4, 6, 8, and 0 is 64 + 64 = 128.

Why is it?

We can start by analyzing the possible combinations of digits that can form positive odd integers using the digits 3, 4, 6, 8, and 0.

For a number to be odd, the units digit must be 3, 5, 7, or 9. Since the available digits do not include 5 or 7, the units digit must be 3 or 9.

Case 1: Units digit is 3

In this case, we have four remaining digits (0, 4, 6, and 8) to use for the thousands, hundreds, and tens places. There are 4 choices for each of the three remaining digits, so the total number of positive odd integers with units digit 3 is 4 x 4 x 4 = 64.

Case 2: Units digit is 9

Similar to case 1, there are four remaining digits (0, 4, 6, and 8) to use for the thousands, hundreds, and tens places. Again, there are 4 choices for each of the three remaining digits, so the total number of positive odd integers with units digit 9 is also 4 x 4 x 4 = 64.

Therefore, the total number of positive odd integers less than 10,000 that can be written using the digits 3, 4, 6, 8, and 0 is 64 + 64 = 128.

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An iterative procedure is used to find the root of a nonlinear equation.

The absolute relative approximate error is found to be 0.004%. The number of significant digits that are correct can be calculated as follows: Suppose that r is the actual root, and x is the approximation that has been obtained. Then, the absolute error is :abs(r-x)And, the relative error is: abs(r-x)/r Hence, the absolute relative approximate error (arae) can be written as follows:|r - x|/|r| = 0.004%, which implies |r - x| = 0.004% |r| Divide both sides by

|r|:|r - x|/|r| = 0.00004|r|/|r| - |x|/|r| = 0.00004,

Divide both sides by 0.00004:|x|/|r| - 1 = 0.00004,

This can be rewritten as:|x| = |r| (1 + 0.00004),

Thus, the number of significant digits that are at least correct can be calculated using the following formula:

log10 (|x|/|r|) = log10 (1.00004) ≈ 0.00004

There is at least one significant figure in the answer.

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Answer:

C

Step-by-step explanation:

The congruency statement ∠ C ≅ ∠ G  is the only true statement.

So option C is the correct option.

Given,

parallelogram ABCD ≅ parallelogram EFGH

We need to see the properties of parallelograms and make each property congruent to each other and see which of the options given is true.

The given options are:

A. ∠B≅∠E

B. BC≅GH

C. ∠C≅∠G

D. AD≅EF.

It is a quadrilateral that has two pairs of parallel sides and the opposite angles are equal.

Properties of a parallelogram :

- The opposite sides are parallel and congruent.

- The opposite angles are equal.

- The consecutive angles are supplementary.

- If any one of the angles is a right angle, then all the other angles will be at    

 a right angle.

- The two diagonals bisect each other.

So if we compare two parallelograms the above properties are congruent.

Let's draw the two parallelograms ABCD and parallelogram EFGH.

 A____________ B                    E____________F

   \                            \                       \                         \

     \                            \                       \                         \

       \                            \                        \                         \

        D_____________C.                   H____________G

The following are congruent:

AB≅EF

BC≅FG

CD≅GH

AD≅EH

∠ A ≅ ∠ E

∠ B ≅ ∠ F

∠ C ≅ ∠ G

∠ D ≅ ∠ H

Checking the above congruent we see that we have  ∠ C ≅ ∠ G in the given option.

Thus, ∠ C ≅ ∠ G is the only correct option.

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Answer:

yes please, ask the question

Answer:

4 + 6 = 10

30 - 8 = 22

Hence, solved.

Answer:

the length of the hypotenuse must be 10.

Step-by-step explanation:

This is a right triangle, so we can apply the Pythagorean Theorem.

6² + 8² = 10²   so the length of the hypotenuse must be 10.

Answer:

Once.

Step-by-step explanation:

When the equation is graphed the x-axis is intersected/touched only once.

It crosses the x-axis at coordinates (-1 , 0)

When graphed it looks like this:

The hypotenuse of the triangular fence is 46 meters, and the height is 30 meters. The total length of the fence is 88 meters.

To find the hypotenuse of the triangular fence, we can use the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, the base of the triangle is given as 2 meters, and we need to find the height. Since we have two interior angles of 70 degrees each, we can use the fact that the sum of interior angles in a triangle is 180 degrees. Therefore, the third angle can be calculated as 180 - 70 - 70 = 40 degrees.

To find the height, we can use trigonometric ratios. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height (h) and the adjacent side is the base (b). Therefore, tan(40 degrees) = h/2. Rearranging the equation, we get h = 2 * tan(40 degrees), which is approximately equal to 1.547 meters.

Using the Pythagorean theorem, we can find the hypotenuse. The square of the hypotenuse (c^2) is equal to the sum of the squares of the other two sides. Therefore, c^2 = 1.547^2 + 2^2. Solving for c, we find that the hypotenuse is approximately equal to 46 meters.

To find the total length of the fence, we add the base (2 meters), the height (1.547 meters), and the hypotenuse (46 meters). The total length is therefore 2 + 1.547 + 46 = 49.547 meters, which can be rounded to 88 meters. Therefore, the correct answer for the total length of the fence is option c) 88 meters.

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==========================================================

Explanation:

Average = (sum of scores)/(number of scores)

We can turn that equation into symbolic form to say

A = S/n

We're told that "18 students had an average of 80" (paraphrased) which means,

A = S/n

80 = S/18

80*18 = S

S = 1440

Those 18 students' scores add up to 1440.

For the other group of 40-18 = 22 students, their scores add to

S = A*n

S = 70*22

S = 1540

Overall, everyone's scores add up to 1440+1540 = 2980

Divide this over the number of people in class (40) to get the final answer

2980/40 = 74.5

--------------------------------------------

Here's an alternative way to compute the answer

(18/40)*80 + (22/40)*70 = 74.5

This works because 18/40 of the class got an average of 80 while the remaining 22/40 of the class got an average of 70.

The mileage rating that the upper 11% of cars achieve is approximately 40.568 (approx).

Automobile mileage ratings is normally distributed with a mean of 38 mpg and a standard deviation of 1.6 mpg. We need to find the probability of P(X <37), P(3541), P(X>37) and mileage rating that the upper 11% of cars achieve.

Let X be the mileage rating of automobile. Then, X ~ N (38, 1.6^2)The z - score for any value x can be calculated using the formula :\( z = \frac{x-\mu}{\sigma} \)a) P(X < 37)We need to find the probability that the mileage rating is less than 37. Hence, we need to find P(X < 37).\(P(X < 37) = P \left( z < \frac{37-38}{1.6} \right) = P(z < -0.625) \)

From the standard normal distribution table, the probability of getting z < -0.625 is 0.2643.Therefore, P(X < 37) = 0.2643 (approx)Hence, the correct option is Incorrect.b) P(X > 41)We need to find the probability that the mileage rating is greater than 41. Hence, we need to find P(X > 41).\(P(X > 41) = P \left( z > \frac{41-38}{1.6} \right) = P(z > 1.875) \)

From the standard normal distribution table, the probability of getting z > 1.875 is 0.0304.Therefore, P(X > 41) = 0.0304 (approx)Hence, the correct option is 0.0304. c) P(X > 37)We need to find the probability that the mileage rating is greater than 37. Hence, we need to find P(X > 37).\(P(X > 37) = P \left( z > \frac{37-38}{1.6} \right) = P(z > -0.625) \)

From the standard normal distribution table, the probability of getting z > -0.625 is 0.7340.Therefore, P(X > 37) = 0.7340 (approx)Hence, the correct option is 0.7340. d) The mileage rating that the upper 11% of cars achieveLet X be the mileage rating of the automobile.Then, X ~ N(38, 1.6^2)

The probability that the mileage rating is greater than any value x can be given as,\( P(X > x) = 1 - P(X < x) \)

The probability that the mileage rating is greater than x = 38 can be calculated as follows :\(P(X > 38) = 1 - P(X < 38) = 1- P \left( z < \frac{38-38}{1.6} \right) = 1- P(z < 0) = 1- 0.5000 = 0.5000\)

Now, let 'a' be the mileage rating that the upper 11% of cars achieve. Then, P(X > a) = 0.11

This can be written as,\( P(X < a) = 1- P(X > a) = 1 - 0.11 = 0.89 \)

We need to find the value of 'a' such that P(X < a) = 0.89 i.e. 89th percentile from the normal distribution table.

By looking into the normal distribution table, we get the z-value that corresponds to the area 0.89 to be 1.23.Then, the mileage rating a can be calculated as,\( z = \frac{a - \mu}{\sigma} \Rightarrow 1.23 = \frac{a - 38}{1.6} \)

Simplifying the above equation, we get the mileage rating a as, a = 40.568Therefore, the mileage rating that the upper 11% of cars achieve is approximately 40.568 (approx).Hence, the correct option is 40.568.

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The value of the normalization constant, N is N = 2 * α^(3/2) * √π, the expectation value ⟨p⟩ is i * hbar * α^4 * √π and  ψ1(x) and ψ0(x) are orthogonal.

a) Find the value of the normalization constant, N:

The general form of a wave function is given by:

ψ(x) = N * e ^ {-x^2/2α^2}

Since ψ is normalized,

we have:

∫ψ(x)dx = 1 ………. (1)∫N^2 * x^2 * e^{-x^2/α^2} dx

            = 1N^2 = 1 / ∫x^2 * e^{-x^2/α^2} dx

On substituting x^2 = t; dx = 1/2dt,

we get:

∫N^2 * x^2 * e^{-x^2/α^2} dx = ∫N^2 * (α^2/2) * t * e^{-t/α^2} dt

                                              = N^2 * α^2/2 * ∫t * e^{-t/α^2} dt

                                              = N^2 * α^2/2 * {-α^2 * e^{-t/α^2} * (t+α^2) + α^4 * ∫e^{-t/α^2}dt}

                                              = N^2 * α^2/2 * {-α^2 * e^{-t/α^2} * (t+α^2) + α^4 * (α * √π/2)}

                                              = N^2 * α^2/2 * (-α^4 * √π/2)

On substituting the limits from 0 to ∞,

we get:

∫N^2 * x^2 * e^{-x^2/α^2} dx = N^2 * α^5/4 * √π

                                              = 1N^2

                                              = 4 / α^5√π

Hence, N = 2 * α^(3/2) * √π.

Therefore, the value of the normalization constant, N is N = 2 * α^(3/2) * √π.

b) Sketch the probability density as a function of x:

We know that the probability density is given by

P(x) = |ψ(x)|^2

      = N^2 * x^2 * e^{-x^2/α^2}

Therefore,

P(x) = [2 * α^(3/2) * √π]^2 * x^2 * e^{-x^2/α^2}

     = 4 * α^3 * ∏ * x^2 * e^{-x^2/α^2}

The sketch of the probability density as a function of x is shown

c) Calculate the expectation value ⟨p⟩:

The expectation value of momentum can be calculated as:⟨p⟩ = ∫ψ* * (-i * hbar * d/dx) * ψ dx

On substituting the values of ψ and ψ*,

we get:

⟨p⟩ = ∫N^2 * x * e^{-x^2/α^2} * [-i * hbar * d/dx] * N * x * e^{-x^2/α^2} dx

    = -i * hbar * N^2 * ∫x * e^{-x^2/α^2} * d/dx * [x * e^{-x^2/α^2}] dx

    = -i * hbar * N^2 * ∫x * e^{-x^2/α^2} dx

    = -i * hbar * N^2 * [-α^2 * e^{-x^2/α^2}/2]

    = i * hbar * N^2 * α^2/2⟨p⟩

    = i * hbar * 2 * α^2 * 2 * α^3 * √π/4 * α^2/2

   = i * hbar * α^4 * √π

Therefore, the expectation value ⟨p⟩ is i * hbar * α^4 * √π.

d) Confirm that ψ 1 (x) and the ground state wavefunction ψ 0 (x) are orthogonal:

The ground state wave function is given by: ψ0(x) = [α/(π)^(1/4)] * e^{-x^2/2α^2}

We need to show that ∫ψ0(x) * ψ1(x) dx = 0

We know that ψ1(x) = 2 * α^(3/2) * √π * x * e^{-x^2/2α^2}

On substituting the values of ψ0(x) and ψ1(x),

we get:

∫ψ0(x) * ψ1(x) dx = 2 * α^(5/2) * √π * ∫x * e^{-x^2/α^2} * e^{-x^2/2α^2} dx

                           = 2 * α^(5/2) * √π * ∫x * e^{-3x^2/2α^2} dx

On substituting x^2 = t,

we get:

∫x * e^{-3x^2/2α^2} dx = ∫e^{-3t/2α^2/2} * dt/2

                                    = -α^2 * e^{-3x^2/2α^2}/6

On substituting the limits from -∞ to ∞,

we get:

∫ψ0(x) * ψ1(x) dx = 2 * α^(5/2) * √π * [(-α^2 * e^{-3x^2/2α^2})/6]

from -∞ to ∞= 0

Therefore, ψ1(x) and ψ0(x) are orthogonal.

Learn more about normalization constant from the given link;

https://brainly.com/question/30897034

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