The height of the roof is 30ft and the radius of the base is 15tf. what is the area of the roof? what is the lateral surface area of the roof

Answer:

m<A = 36 degrees

Step-by-step explanation:

we know that the top angle is 90 degrees and so (x+46) + (x + 66) = 90

simplify and we get 2x + 110 = 90

x = -10

substitute -10 for x

m<A = (-10) + 46

m<A = 36

Answer:

Exponential growth, as the sign of the basis (the number 1.15) is positive.

Step-by-step explanation:

The equation Y = 250,000(1.15)ˣ represents exponential growth.

In this equation, the base of the exponential term is 1.15, which is greater than 1. When the exponent x increases, the value of the term (1.15)ˣ also increases, leading to exponential growth.

Exponential growth occurs when a quantity increases at an accelerating rate over time. In this case, as x increases, the value of Y grows exponentially, indicating growth rather than decay.

Therefore, the equation Y = 250,000(1.15)ˣ represents exponential growth.

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For a system of linear equations, the number of solutions depends on the coefficient matrix and the augmented matrix. To determine the number of solutions, we need to look at the row echelon form or reduced row echelon form of the augmented matrix.

1. If the row echelon form has a row of zeros with a non-zero entry in the augmented column, the system will have no solution.
2. If there are no rows of zeros and the number of pivot columns is equal to the number of variables, the system will have a unique solution.
3. If there are no rows of zeros and the number of pivot columns is less than the number of variables, the system will have infinitely many solutions.

To find the values of k for each case, we need to set up the augmented matrix and row reduce it. Since you didn't provide the system of equations, I'm unable to provide the specific values of k. However, you can follow the steps above to determine the number of solutions for any given system of equations.

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The possible outcomes for each trial are two (having type O+ blood or not having type O+ blood), and the probability of having type O+ blood is 33%.

(a) A fair die is rolled 40 times, x = number of times a 2 is rolled.

n = 40 (number of trials)

p = 1/6 (probability of rolling a 2)

There are 6 possible outcomes for each trial (the numbers 1, 2, 3, 4, 5, and 6), and only one of those outcomes is considered a success (rolling a 2).

So, the probability of success is 1/6, and the probability of failure is 5/6.

(b) A cereal company puts a game card in each box of cereal and 50% of them are winners. You buy 10 boxes of cereal, and x = number of times you win.

n = 10 (number of trials)

p = 1/2 (probability of winning)

There are only two possible outcomes for each trial (winning or not winning), and the probability of winning is 1/2.

(c) The percentage of people in a particular country with type O+ blood is 33%. x = number of blood donors in a sample of 55 unrelated blood donors who have type O+ blood.

n = 55 (number of trials)

p = 33/100 = 11/33 (probability of having type O+ blood)

There are two possible outcomes for each trial (having type O+ blood or not having type O+ blood), and the probability of having type O+ blood is 33%.

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Answer:

49 square feet

Step-by-step explanation:

Area of square

\( = {7}^{2} \\ \\ = 49 \: {ft}^{2} \\ \)

When the parameter a has a value of 2, the given lines 2x – 3y +1 = 0, x+ay-8=0 will form an angle of size φ = arctg(-3/2).

To find the parameter a for which the given lines 2x - 3y + 1 = 0 and x + ay - 8 = 0 form an angle of size φ = arctg(-3/2), we first need to find the slopes of these lines.

For the first line, 2x - 3y + 1 = 0, we can rewrite it in the slope-intercept form (y = mx + b) to find the slope:
-3y = -2x - 1
y = (2/3)x + 1/3
The slope of the first line, m1, is 2/3.
For the second line, x + ay - 8 = 0, we can rewrite it in the slope-intercept form as well:
ay = -x + 8
y = (-1/a)x + 8/a
The slope of the second line, m2, is -1/a.
Now, we can use the formula for the tangent of the angle between two lines:
tan(φ) = (m1 - m2) / (1 + m1 * m2)
Given φ = arctg(-3/2), we know that:
tan(φ) = -3/2
Now, we can plug in the slopes of the lines and solve for a:
(-3/2) = (2/3 - (-1/a)) / (1 + (2/3) * (-1/a))
Solving this equation for a, we get:

a = 2

Thus, the given lines form an angle of size φ = arctg(-3/2)  when the parameter a has a value of 2,

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a) The MLE for p is p = n / (x1+x2+...+xn).

b) The Cramer-Rao lower bound applies.

c) The estimator in part (a) is unbiased.

(a) The probability mass function of the geometric distribution is given by:

P(X=k) = (1-p)^(k-1) * p

The likelihood function for a random sample of size n from the geometric distribution is given by:

L(p) = P(X=x1) * P(X=x2) * ... * P(X=xn)

= (1-p)^(x1-1) * p * (1-p)^(x2-1) * p * ... * (1-p)^(xn-1) * p

= (1-p)^(x1+x2+...+xn-n) * p^n

Taking the natural logarithm of the likelihood function, we get:

ln(L(p)) = (x1+x2+...+xn-n) * ln(1-p) + n * ln(p)

Differentiating with respect to p and setting the derivative equal to zero to find the maximum, we get:

d/dp ln(L(p)) = - (x1+x2+...+xn-n)/(1-p) + n/p = 0

Solving for p, we get:

p = n / (x1+x2+...+xn)

Therefore, the MLE for p is p = n / (x1+x2+...+xn).

(b) The regularity conditions necessary for the Cramer-Rao lower bound to apply are:

The random variable X is independent and identically distributed (i.i.d.).

The probability density function or probability mass function of X depends on a parameter θ that is to be estimated.

The function g(θ) = d/dθ ln(f(X;θ)) is continuous and has finite variance for all θ in an open interval containing θ0.

The integral of |g(θ)|^2f(X;θ) dx over the range of X and the open interval containing θ0 is finite.

For the geometric distribution, these conditions are satisfied:

The random variable X is i.i.d. because each trial is independent and has the same probability of success.

The probability mass function of X depends on the parameter p, which is to be estimated.

g(p) = d/dp ln(f(X;p)) = (1-p)/(p ln(1-p)) is continuous and has finite variance for all p in (0,1).

The integral of |g(p)|^2 f(X;p) dx over the range of X and the interval (0,1) is finite.

Therefore, the Cramer-Rao lower bound applies.

(c) To determine if the estimator in part (a) is asymptotically normal and/or consistent, we need to use the properties of MLEs:

MLEs are asymptotically unbiased, meaning that as the sample size n approaches infinity, the expected value of the estimator approaches the true value of the parameter being estimated.

MLEs are asymptotically efficient, meaning that as the sample size n approaches infinity, the variance of the estimator approaches the Cramer-Rao lower bound.

For the geometric distribution, the expected value of the estimator is:

E(p) = E(n/(x1+x2+...+xn))

= n / E(x1+x2+...+xn)

= n / (n/p)

= p

Therefore, the estimator in part (a) is unbiased.

The variance of the estimator is:

Var(p) = Var(n/(x1+x2+...+xn))

= n^2 Var(1/(x1+x2+...+xn))

= n^2 Var(1/X)

where X = x1

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Question 1: The item not included in the cost of merchandise inventory is "Purchase discounts."

2: The total cost of the merchandise is $3,332.00.

5: The company's gross margin and operating expenses, are $211,000 and $191,720.

Merchandise inventory expenses normally consist of the price paid for the inventory, deductions from the purchase price resulting from purchase returns and allowances, and freight expenses paid by the purchaser.

Although purchase discounts reduce the cost of merchandise inventory, they are not considered part of it. Instead, they are treated as a distinct discount in the accounting records.

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Answer:

it equals =204 y=12

Mathematical approaches to aggregate planning involve using quantitative methods to determine the optimal production and resource allocation strategies over a specified planning horizon. These approaches utilize mathematical models to optimize various factors such as production costs, inventory levels, and customer demand.

One mathematical approach to aggregate planning is linear programming, which formulates the planning problem as a linear optimization model. Linear programming considers constraints such as capacity limits, labor availability, and demand variability to find the best allocation of resources and production levels. The objective is to minimize costs or maximize profit while meeting demand requirements.

Another approach is the use of mathematical forecasting techniques to predict future demand. Time series analysis, regression analysis, and other statistical methods can be employed to forecast demand patterns. These forecasts serve as inputs to mathematical models, such as inventory control models or production planning models, which determine the optimal production levels and inventory policies based on the anticipated demand.

Simulation modeling is another mathematical approach where computer-based simulations are used to evaluate different scenarios and make decisions about production levels, inventory levels, and workforce scheduling. These models consider various factors like demand variability, production capacity, and resource availability to simulate the system's behavior and analyze the impact of different planning strategies.

Overall, mathematical approaches to aggregate planning provide a systematic and quantitative way to optimize production and resource allocation decisions, considering factors such as demand, capacity, costs, and constraints. These approaches help organizations make informed decisions to meet customer demand efficiently while minimizing costs and maximizing operational performance.

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The width of the original piece of sheet metal is (w^2 - l^2)/(3w + 3l), and the length is (l^2 - w^2)/(3w + 3l).

To solve this problem, we can use the formula for the volume of a rectangular box, which is V = lwh, where l is the length, w is the width, and h is the height.

First, let's find the height of the box. Since we cut squares from each corner, the height of the box is the length of the square that was cut out. Let's call this length x.

The width of the box is the original width minus the lengths of the two squares that were cut out, which is w - 2x.

Similarly, the length of the box is the original length minus the lengths of the two squares that were cut out, which is l - 2x.

Now we can write the volume of the box in terms of x, w, and l:

V = (w - 2x)(l - 2x)(x)

Expanding this expression, we get:

V = x(4wl - 4wx - 4lx + 8x^2)

Simplifying further:

V = 4x^3 - 4wx^2 - 4lx^2 + 4wlx

To find the dimensions of the original piece of sheet metal, we need to maximize this volume. We can do this by taking the derivative of the volume with respect to x and setting it equal to zero:

dV/dx = 12x^2 - 8wx - 8lx + 4wl = 0

Solving for x, we get:

x = (2wl)/(3w + 3l)

Now we can use this value of x to find the width and length of the original piece of sheet metal:

w - 2x = w - 2(2wl)/(3w + 3l) = (w^2 - l^2)/(3w + 3l)

l - 2x = l - 2(2wl)/(3w + 3l) = (l^2 - w^2)/(3w + 3l)

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Answer:

they are correct

Step-by-step explanation:

Answer:

317m

Step-by-step explanation:

I am not sure its the perimeter (p) you need because thats what i understood.

p=2(109.7)+2(48.8)=317m

Answer:

The answer is 0.18 cubic meters

Answer:

.21 cubic meters

Step-by-step explanation:

L x W x H

It is true that 400 elephants are blue in color. This happens because number of elephants remaining is twice 400.

Given that,

Total number of elephant = 1200

Strips colors available are: Pure Pink

                                             Pure blue

                                             Pink and Green

Pure Pink = 1/3 of 1200

                = 1/3 × 1200

                = 400

Rest elephant who are definitely blue:

Remaining elephant = Total number of elephant - Pure Pink

                                  = 1200 - 400

                                  = 800

∴ It is true that 400 elephants are blue because the  number of elephants remaining twice 400.

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volume of sphere is increasing at a rate of  62,832 mm3/s.

 The volume of a three-dimensional space can be determined. It is frequently numerically expressed in terms of several imperial units or SI-derived units. Volume and length are dependent on one another.

Step 1: Define an equation that relates the volume of a sphere to its radius.

V = 4/3*π*r3

Step 2: Take the derivative of each side with respect to time (we will define time as "t").

(d/dt)V = (d/dt)(4/3*π*r3)

dV/dt = 4πr2*dr/dt

Step 3: We are told in the problem statement that diameter is 100m, so therefore r = 50mm. We are also told the radius of the sphere is increasing at a rate of 2mm/s, so therefore dr/dt = 2mm/s. We are looking for how fast the volume of the sphere is increasing, or dV/dt.

dV/dt = 4π(50mm)2*(2mm/s)

dV/dt = 62,832 mm3/s

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Answer:

Step-by-step explanation:

(5x )4 +(5x )3 = (10x)12

Answer:

$18 less than the cost of 5 hot dog combos

Step-by-step explanation:

First, we see from the minus sign that this will be subtraction.  PEMDAS (order of operations) says we do the multiplication first, then the subtraction.

Answer:

Step-by-step explanation:

Photo Proof

The missing value should be in the table is 750 and 1250.

1                     250

2                    500

3                     750

4                    1000

5                    1250

Since we can see that there is the gap of 250 in each words

like

= 250 + 250

= 500

So

= 500 + 250

= 750

And, so on

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Step-by-step explanation:

When we have a function in formula form, it is usually a simple matter to evaluate the function. For example, the function \displaystyle f\left(x\right)=5 - 3{x}^{2}f(x)=5−3x

2

can be evaluated by squaring the input value, multiplying by 3, and then subtracting the product from 5.

Answer: omm

but I need this so

Step-by-step explanation:

Explanation:

90° is 90/360 = 1/4 of a full 360° rotation. Meaning that if the central angle of the pizza slice is 90°, then we have four equal slices.

One slice is 7 square inches, so all four slices combine to 7*4 = 28 square inches

Answer:

above is the solution to the question

Answer:

Step-by-step explanation:

Ans:-

m∠x = 28°

m∠y = 52°

m∠z = 80°

~

5x-17=3x+7

5x-3x=7+17

2x=24

2x/2=24/2

x=12

Answer:

If a heavy object were to be hung on a spring then released, the weight would movedownward. The two variables would be the weight and the force. The force enacted by the weight stretching the spring and the force returning the spring to its original shape is determined by its height the “h” variable.

The two forces repel each other over “t” /time.

Answer:

The force enacted by the weight stretching the spring and the force returning the spring to its original shape is determined by its height the “h” variable.

The two forces repel each other over “t” /time.

Step-by-step explanation: hope his helps ;)

Answer:

Yes

Step-by-step explanation:

But not all rational numbers are natural numbers, so be careful of that.

= (6x² + 7x + 2)- (-9x² -10)

= 6x² + 7x + 2 + 9x² +10

= 9x² + 6x² + 7x +10 + 2

= 15x² + 7x +12

Answer:

15x^2+7x+12

Step-by-step explanation:

Distribute the Negative Sign:

=6x2+7x+2+−1(−9x2−10)

=6x2+7x+2+−1(−9x^2)+(−1)(−10)

=6x2+7x+2+9x^2+10

Combine the terms:

6x2+7x+2+9x2+10

=(6x2+9x2)+(7x)+(2+10)

=15x2+7x+12

(All the 2's with the 9 that aren't added(so for example 9x2. That means 9x to the power of 2) are the exponents. I do not know how u write them up on the thing but here u go.)

Answer: y=-4x+9

Step-by-step explanation:

m= -4

b=9

Answer:

the slope is 4

y-intercept is -2

and the equation is

y=4x -2

Answer:

so I'm guessing you're solving for x

because angle 2 is the vertical angle to angle 3 so this means that they are congruent

4x-26=3x+4

4x-3x=4+26

x=30