Part A what is the measure of the missing angle in the triangle?

​

Answer:

Slope Calculator

Step-by-step explanation:

Search up slope calculator and put in those expressions

Answer:

1/3

Step-by-step explanation:

is the answer because is a decimal

Given:

The center of the circle is the origin and the radius is 5.

Required:

Find the equation of the circle.

Explanation:

The equation of the circle when the center is (a,b) and the radius is r is given as:

The center (a,b) = (0,0)

radius r = 5

So the equation of the circle is:

Final Answer:

Option C is the correct answer.

Answer:

12   50/50 chance

Step-by-step explanation:

The method of periodization that an athlete performs is  traditional periodization method.

Given,

An athlete perform five sets of five repetitions at 90% of 1rm on the first day of the week, five sets of fourteen repetitions at 85% of 1rm on the next training day, and five sets of two repetitions at 62.5%of 1rm on the last training day of the week;

Here,

The example above, where the percentage of one-repetition maximum (1RM) decreases as the training day progresses, is essentially a traditional periodization method.

As a result, during the course of the training cycle, the athletes' completed work gradually grows. As a result, as the load increases over time, there is a corresponding decrease in volume.

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Answer: 10 inches

Step-by-step explanation:

I looked up the question and saw another person answered it with 10 so I trust them.

Answer:

-32x-60y+1122=0

-(32x+60y-1122)=0

32x+60y-1122=0

by factorize

Answer:

24,30

Step-by-step explanation:

The correct answer is (a) X/(X+Y) and X+Y are independent random variables.(b) X/(X+Y) follows a beta distribution with parameters r and s.

(a) To show that X/(X+Y) and X+Y are independent, we need to demonstrate that their joint distribution is the product of their marginal distributions.

Let's start by finding the joint probability density function (pdf) of X/(X+Y) and X+Y. Since X and Y are independent, their joint pdf is the product of their individual pdfs.

Let fX(x) and fY(y) be the pdfs of X and Y, respectively. The joint pdf of X and Y is given by fXY(x, y) = fX(x) * fY(y).

Now, let's transform the variables to U = X/(X+Y) and V = X+Y. We want to find the joint pdf of U and V.

Using the transformation method, we can write X = UV and Y = V - UV.

Taking the absolute value of the Jacobian determinant, we have |J| = |∂(X,Y)/∂(U,V)| = |V|.

Now, we can express the joint pdf of U and V as:

fUV(u, v) = fXY(uv, v - uv) * |J|

Substituting fXY(x, y) = fX(x) * fY(y) and |J| = |V|, we get:

fUV(u, v) = fX(uv) * fY(v - uv) * |V|

Since the joint pdf factorizes into a product of the marginal pdfs, we can conclude that X/(X+Y) and X+Y are independent.

(b) To show that X/(X+Y) ∈ β(r, s), we need to demonstrate that its pdf can be expressed in terms of the beta distribution.

Let U = X/(X+Y). We know that U = X/(X+Y) = X/V, where V = X+Y.

Substituting U and V into the relation X = UV, we have X = UV.

Since X follows a gamma distribution with parameters r and 1, we can write its pdf as:

fX(x) = (1/Γ(r)) * x^(r-1) * exp(-x)

Substituting X = UV, we get:

fX(uv) = (1/Γ(r)) * (uv)^(r-1) * exp(-uv)

The pdf of V is given by the gamma distribution with parameters r+s and 1:

fV(v) = (1/Γ(r+s)) * v^(r+s-1) * exp(-v)

Now, we can express the pdf of U = X/V as:

fU(u) = ∫[0,∞] (1/v) * fX(uv) * fV(v) dv

Evaluating the integral, we obtain:

fU(u) = (1/Γ(r)Γ(r+s)) * u^(r-1) * (1-u)^(s-1)

The obtained pdf is the probability density function of the beta distribution with parameters r and s.

Therefore, we have shown that X/(X+Y) follows a beta distribution with parameters r and s.

(c) Using the result from part (a) that X/(X+Y) and X+Y are independent, and the relation X = (X+Y) * (X/(X+Y)), we can compute the mean and variance of the beta distribution.

The mean of the beta distribution with parameters r and s is given by:

μ = r / (r + s)

The variance of the beta distribution with parameters r and s is given by:

σ^2 = (r * s) / ((r + s)^2 * (r + s + 1))

Therefore, using the values of r and s, we can substitute them into the formulas to compute the mean and variance of the beta distribution.

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The value of C, which represents the upper control limit (UCL) for the X-bar chart in the process of filling baby formula into bottles, is approximately 3.40552. This means that any average amount of baby formula above this limit may indicate a process out of control and require investigation.

To determine the value of C in this scenario, we need to use the formula for the control chart limits for an X-bar chart. The control limits for an X-bar chart with sample size n can be calculated using the following formula:

Upper Control Limit (UCL) = mean + A2 * R

Lower Control Limit (LCL) = mean - A2 * R

In this case:

The target value for the baby formula is 3 ounces.

The average amount of baby formula placed in the bottles is 2.941 ounces (mean).

The sample size is 200 bottles.

The standard deviation of the amounts is 0.1 ounce.

To calculate the value of C, we need to determine the value of A2, which depends on the sample size. The value of A2 can be found in statistical tables or calculated using statistical software. For a sample size of 200, A2 is typically 2.574.

Using the formula for the control limits, we can calculate the upper and lower control limits:

UCL = mean + A2 * R

= 2.941 + 2.574 * 0.18

= 2.941 + 0.46452

= 3.40552

LCL = mean - A2 * R

= 2.941 - 2.574 * 0.18

= 2.941 - 0.46452

= 2.47648

The value of C is the value of the upper control limit (UCL) in this case, which is approximately 3.40552.

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Answer: To find the rotation in revolutions per minute (RPM) given the angular speed and the radius, we can use the formula:

RPM = (Angular Speed (rad/s)) / (2 * pi)

To find the RPM, we first need to convert the linear speed to angular speed. We can do this by using the formula:

Angular Speed (rad/s) = Linear Speed (m/s) / Radius (m)

Angular Speed = 82.3 m/s / 0.131 m = 630 rad/s

RPM = (630 rad/s) / (2 * pi) = 131 rev/min

To find the RPM, we first need to convert the linear speed to angular speed. We can do this by using the formula:

Angular Speed (rad/s) = Linear Speed (ft/min) / (Radius (ft) * 12)

Angular Speed = 144.2 ft/min / (10.9 ft * 12) = 10.9 rad/s

RPM = (10.9 rad/s) / (2 * pi) = 10.9 rev/min

To find the RPM, we first need to convert the linear speed to angular speed. We can do this by using the formula:

Angular Speed (rad/s) = Linear Speed (in/h) / (Radius (in) * 3600)

Angular Speed = 553 in/h / (553 in * 3600) = 0.09 rad/s

RPM = (0.09 rad/s) / (2 * pi) = 0.09 rev/min

Step-by-step explanation:

The values of the given trig functions in terms of sinθ and/or cosθ are:

sinθ = tanθ.cosθ

cosθ = sinθ/tanθ

secθ = 1/cosθ

cscθ = 1/sinθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

From the question, we are to determine the values of the given trig functions in terms of sinθ and/or cosθ

NOTE: tanθ = sinθ / cosθ

∴ sinθ = tanθ.cosθ

From above, we can write that

cosθ = sinθ/tanθ

Secant is the inverse of cosine

∴ secθ = 1/cosθ

Cosecant is the inverse of sine

∴ cscθ = 1/sinθ

tanθ = sinθ/cosθ

Cotangent is the inverse of tangent
∴ cotθ = 1/tanθ

But, tanθ = sinθ/cosθ

∴ cotθ = cosθ/sinθ

Hence, the values of the given trig functions in terms of sinθ and/or cosθ are:

sinθ = tanθ.cosθ

cosθ = sinθ/tanθ

secθ = 1/cosθ

cscθ = 1/sinθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

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No Solution.

Since, the x-axis (equation y=0) does not intersect y=-7 at any point. The given pair of equations has no solution

Consider the pair of linear equations in two variables x and y.

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

Here a1, b1, c1, a2, b2, c2 are all real numbers.

Note that, a12 + b12 ≠ 0, a22 + b22 ≠ 0

1. If (a1/a2) ≠ (b1/b2), then there will be a unique solution. If we plot the graph, the lines will intersect. This type of equation is called a consistent pair of linear equations.

2. If (a1/a2) = (b1/b2) = (c1/c2), then there will be infinitely many solutions. The lines will coincide. This type of equation is called a dependent pair of linear equations in two variables

3. If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. If we plot the graph, the lines will be parallel. This type of equation is called an inconsistent pair of linear equations.

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Answer:

Step-by-step explanation:

\( \frac{ log_{a}(x) }{ log_{a}(b) } = log_{b}(x) \)

\( log_{x}( {x}^{b} ) = b\)

\(step - 1 : define\)

\( \frac{ log_{5}(8) }{ log_{5}( \sqrt{8} ) } \)

\(step - 2 : simplify\)

\( log_{ \sqrt{8} }(8) \)

\( log_{ \sqrt{8} }(( \sqrt{8}) ^{2} ) \)

\( \huge \therefore \: 2\)

The product of the rational expressions shown is  x² / x² + 5x + 6.

The product of the rational expressions given is calculated by performing multiplication operation as show below.

The given rational expressions;

(x / x + 3)*(x / x + 2)

The product of the numerator = x²

The product of the denominator = (x + 3)(x + 2)

(x + 3)(x + 2) = x² + 2x + 3x + 6

(x + 3)(x + 2) = x² + 5x + 6

final expression of the products = numerator / denominator

                                                     = x² / x² + 5x + 6

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The total duration of the roller coaster ride is 16 seconds.

To answer the questions based on the given piecewise function and graph for the roller coaster project, we need to analyze the different parts of the function:

- For 0 < x < 4 seconds, the roller coaster starts at ground level and goes up to a maximum height of 10 feet before returning to ground level at 4 seconds. This is represented by the equation f(x) = 5(2).
- For 4 seconds ≤ x ≤ 5.5 seconds, the roller coaster drops down rapidly from the peak height to a depth of -5 feet (below ground level) at 5.5 seconds. This is represented by the equation f(x) = -5x2 + 40x.
- For 5.5 seconds < x < 12 seconds, the roller coaster rises gradually to a height of 35 feet at 12 seconds. This is represented by the equation f(x) = 35.
- For x ≥ 12 seconds, the roller coaster drops down from 35 feet to a depth of -5 feet (below ground level) at 14 seconds before rising back up to a peak height of 80 feet at 16 seconds. This is represented by the equation f(x) = -5(x - 12)2 + 80.

Now, let's answer some questions based on this information:

1. What is the maximum height of the roller coaster and when does it occur?
The maximum height of the roller coaster is 35 feet and it occurs at 12 seconds.

2. At what time does the roller coaster reach its lowest point?
The roller coaster reaches its lowest point at 5.5 seconds.

3. What is the peak height of the roller coaster and when does it occur?
The peak height of the roller coaster is 80 feet and it occurs at 16 seconds.

4. What is the total duration of the roller coaster ride?
The total duration of the roller coaster ride is 16 seconds.

By understanding the piecewise function and analyzing the graph, we can answer questions and make calculations related to the roller coaster project. Good luck with your dream job at Six Flags!

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Answer:

10.58 feet

Step-by-step explanation:

Use the Pythagorean theorem where 11 is the hypotenuse and 3 is a leg

a^2+b^2=c^2

3^2+b^2=11^2

9+b^2=121

b^2=112

b=10.58 feet

The trick is to recognize a few things.

1. These are similar triangles, so the ratio of BU to BC is the same as BT to BA and UT to CA.

    \(\dfrac{BU}{BC}=\dfrac{BT}{BA}=\dfrac{UT}{CA}\)

2. BC = 2 BUs and BA = 2 BTs

This means the sides of the short triangle are half the length of the sides of the big triangle.

Put in other words, CA = 2 UT

Put into an equation x+29 = 2(x+19).

   x + 29 = 2x + 38

        –9  = x

So that means UT = 10 and CA = 20

Answer:

Step-by-step explanation:

in the form y = mx + b m is the slope and y is the y intercept. Rewrite each problem to solve.

11) y = 7x - 5

-5 is the y intercept

12) y = -x + 9

9 is the y intercept

13) 4y - 8 = 2x

4y = 2x + 8

y = (2x + 8)/4

y = 1/2x + 2

2 is the y intercept

14) 11x - 8y = - 48

-8y = -11x - 48

y = (-11x - 48)/-8

y = 11/8x + 6

6 is the y intercept

15) x - 3y = 8

-3y = 8 - x

y = (8 - x)/-3

y = -3/8 + 1/3x

y = 1/3x - 3/8

-3/8 is the y intercept

Answer:

-2y-4y=-15+9-1

-6y=-7

Step-by-step explanation:

you can go ahead and move the -6 over to make it

y=-7/6

y=-1.17

Answer:

it is C

Step-by-step explanation:

Its c because i had the exact same problem

Answer:

A

Step-by-step explanation:

Remember that tangent is the ratio of sine over cosine.

\(\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}\)

In the unit circle:

Our x-coordinate is -√2/2 and our y-coordinate is √2/2.

So, substitute -√2/2 for cosine and √2/2 for sine. This yields:

\(\tan(\theta)=\frac{\sqrt2/2}{-\sqrt2/2}\)

Since the numerator and the denominator are the same save for a negative, we can cancel them:

\(\tan(\theta)=-1\)

So, our answer is A.

Answer:

your correct answer cuz is

A

Step-by-step explanation:

15 books to 21 books

21 is greater then 15 : 15 < 21

So, 15 books to 21 books is increasing

Answer : Increase

Answer:

The answer is 0.02

Given:

The figure of a triangular prism.

To find:

The surface area of the triangular prism.

Solution:

We know that, a triangular prism contains 2 congruent triangular surface and 3 rectangular surface.

Triangles have base 3 ft and height 2 ft.

Area of a triangle is

\(Area=\dfrac{1}{2}\times base\times height\)

\(A_1=\dfrac{1}{2}\times (3)\times (2)\)

\(A_1=3\)

Area of congruent triangles are congruent. So,

\(A_1=A_2=3\text{ sq. units}\)

Now the three rectangular surface have dimensions 10 by 3, 10 by 3 and 10 by 3 because the triangles are equilateral and the length of the prism is 10 ft.

Area of a rectangle is

\(Area=Length\times width\)

\(A_3=10\times 3\)

\(A_3=30\)

Dimensions of all three rectangles are same, therefore there areas are equal.

\(A_3=A_4=A_5=30\)

Now, the total surface area of the prism is

\(A=A_1+A_2+A_3+A_4+A_5\)

\(A=3+3+30+30+30\)

\(A=96\)

Therefore, the total surface area of the prism is 96 sq. ft.

Answer:

a. 7/50 or .14 feet or 1.68 inches

b. 0.1 feet or 1.2 inches

Step-by-step explanation:

Basically, just divide the lengths by 50 since the ratio is 50:1.

Based on the absolute deviations and the predicted values, the sum of absolute deviations will be 4.8.

This can be found as:

= ∑ (Observed value - Predicted value)

The observed values are given in the table and the predicted values will be calculated using y = 3.6x - 0.4.

Solving gives:

=  [3 - (3.6 x 1 - 0.4)] + [7 - (3.6 x 2 - 0.4)] + [ 9 - (3.6 x 3 - 0.4)] + [14 - (3.6 x 4 - 0.4)] + [15 - (3.6 x 5 - 0.4)] + [21 - (3.6 x 6 - 0.4)] + [25 - (3.6 x 7 - 0.4)]

= 0.2 + 0.2 + 1.4 + 0 + 2.6 + 0.2 + 0.2

= 4.8

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Answer:

x= 80

Step-by-step explanation:

70 +30=180

sum of angles is triangle is 180 degree

sp 180-100= 80

Answer:

80 degrees

Step-by-step explanation:

Triangle= 180 degrees

70+30=100

180-100=80

Answer:

$1200

Step-by-step explanation:

20 hours makes $400

so when you add 20 hours to 40 hours its basically adding $400 to $800

The probability P(X < 30) is 0.5000 or 50%.

To find the probability P(X < 30) for a normally distributed variable X with a mean of 30 and a standard deviation of 4, we can utilize the properties of the standard normal distribution and z-scores.

First, let's calculate the z-score for the value 30 using the formula:

z = (X - μ) / σ

where X is the value (30), μ is the mean (30), and σ is the standard deviation (4).

Plugging in the values, we have:

z = (30 - 30) / 4 = 0

The resulting z-score is 0.

Next, we can use a standard normal distribution table or a calculator to find the cumulative probability up to the z-score of 0. The cumulative probability represents the area under the curve to the left of the given z-score.

Looking up the z-score of 0 in the standard normal distribution table or using a calculator, we find that the cumulative probability is 0.5000.

Therefore, the probability P(X < 30) is 0.5000 or 50%.

This means that there is a 50% chance that a randomly selected value from the normally distributed variable X will be less than 30.

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