what is the area of the parallelogram in square centimeters? show your work

The angle of elevation of the worker is 48.6°

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

In this scenario, the ladder and the building will at an angle (phi).

The height of the building is the opposite to the angle and the slant height of the ladder is the hypotenuse.

Therefore:

Sin(phi) = opposite/hypotenuse

sin(phi) = 30/40

phi = sin^-1(0.75)

phi = 48.6°

Therefore for the ladder to reach the top of the building l, the angle of elevation must be 48.6°

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Answer:

31/3

Step-by-step explanation:

The 10 1/3  written as the improper fraction 31/3.

To convert the mixed number 10 1/3 into an improper fraction, follow these steps:

Multiply the whole number (10) by the denominator of the fraction (3):

10 × 3 = 30

Add the result from step 1 to the numerator of the fraction (1):

30 + 1 = 31

Place the result from step 2 over the original denominator (3) to form the improper fraction:

10 1/3 = 31/3

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The length of the rivet should be 3/8 inch to pass through the two sheets of metal.

We must take into account the shank length as well as the thickness of the two metal sheets.

Assumed:

The thickness of the two metal sheets and the shank length must be added to determine the overall length of the rivet:

Total length = 2 * (Thickness of sheet metal) + Shank length

Substituting the values:

Total length = 2 * (1/16 inch) + 1/4 inch

Calculating the values:

Total length = 1/8 inch + 1/4 inch

Total length = 1/8 inch + 2/8 inch

Total length = 3/8 inch

So, the length of the rivet should be 3/8 inch to pass through the two sheets of metal.

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Answer:

A. x-y=192 and 9/64x+3/32y=42

Step-by-step explanation:

i got it right dw

Answer:

Step-by-step explanation:

Let x be the amount at 5%

Then 2200 - x is the amount at 3%

The total interest is:

Find the amount at 3%:

The optimal values of x and y that minimize the objective-function x + y, subject to the given constraints, are x = 4 and y = 0.

We can find the corner points of the feasible region and evaluate the objective function at those points to determine the optimal solution.

Graph the constraints:

Start by graphing the inequalities:

x + y ≥ 7

5x + 2y ≥ 20

x ≥ 0

y ≥ 0

Plot the lines x + y = 7 and 5x + 2y = 20. To graph x + y = 7, plot two points that satisfy the equation, such as (0, 7) and (7, 0), and draw a line through them. To graph 5x + 2y = 20, plot two points such as (0, 10) and (4, 0), and draw a line through them.

Shade the region that satisfies the inequalities x ≥ 0 and y ≥ 0.

The feasible region will be the shaded region.

Identify the feasible region:

The feasible region is the shaded region where all the constraints are satisfied. In this case, the feasible region will be a polygon bounded by the lines x + y = 7, 5x + 2y = 20, x = 0, and y = 0.

Find the corner points:

Locate the intersection points of the lines and the axes within the feasible region. These are the corner points. In this case, we have the following corner points:

Intersection of x + y = 7 and x = 0: (0, 7)

Intersection of x + y = 7 and y = 0: (7, 0)

Intersection of 5x + 2y = 20 and x = 0: (0, 10)

Intersection of 5x + 2y = 20 and y = 0: (4, 0)

Evaluate the objective function:

Evaluate the objective function, which is x + y, at each corner point:

(0, 7): x + y = 0 + 7 = 7

(7, 0): x + y = 7 + 0 = 7

(0, 10): x + y = 0 + 10 = 10

(4, 0): x + y = 4 + 0 = 4

Determine the optimal solution:

The optimal solution is the corner point that minimizes the objective function (x + y). In this case, the optimal solution is (4, 0) because it has the smallest objective function value of 4.

Therefore, the optimal values of x and y that minimize the objective function x + y, subject to the given constraints, are x = 4 and y = 0.

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Answer:

The beginning temperature at 5:00 a.M was 27°F

The answer they both arrived at was 27°F

Step-by-step explanation:

From the question,

The temperature dropped by 8°F each hour from 5:00 a.M. To 9:00 a.M.

From 5:00 a.M to 9:00 a.M, there are 4 hours.

Hence, the temperature dropped by 8°F each hour for 4 hours.

Also, from the question

The temperature at 9:00 a.M. was -5°F,

To determine the beginning temperature at 5:00 a.M,

Let the beginning temperature be x

For Dan's method, his method involved multiplication, He could have done it this way:

Since the temperature dropped by 8°F each hour for 4 hours,

This means the temperature would have reduced by 4 × 8°F  = 32°F

Now, we can write that

x - 32°F = -5°F

Then, x = -5°F + 32°F

x = 27°F  

For Claire's method, she did not use multiplication, she could have done it step-wisely, reducing the temperature by 8°F every hour.

Since the temperature dropped by 8°F each hour from 5:00 a.M. To 9:00 a.M,

Let the beginning temperature be x

After 1 hour, that is at 6:00 a.M, the temperature will be x - 8°F

After 2 hours, that is at 7:00 a.M, the temperature will be x - 8°F - 8°F = x -16°F

After 3 hours, that is at 8:00 a.M, the temperature will be x -16°F - 8°F = x -24°F

After 4 hours, that is at 9:00 a.M, the temperature will be x -24°F - 8°F = x -32°F

From the question, the temperature at 9:00 a.M. was -5°F

Hence,

x -32°F = -5°F

Then,

x = -5°F + 32°F

x = 27°F

Hence, the answer they both arrived at was 27°F.

Answer:

1st time: 50% chance or 8/16 chance

2nd time: 46% chance or 7/15

I can try again if its wrong

Answer:

7/30

Step-by-step explanation:

8/16 that she picks a red cube.

7/15 that she picks another red cube after keeping the first red cube.

multiply 8/16 (1/2) times 7/15 to get 7/30 as your final answer

Answer:

Convergent

Step-by-step explanation:

One method to determine if  \(\displaystyle \sum^\infty_{k=1}ke^{-k^2}\)is convergent or divergent is the Integral Test.

Suppose that the function we use is \(f(x)=xe^{-x^2}\). Over the interval \([1,\infty)\), the function is always positive and continuous, but we also need to make sure it is decreasing before we can proceed with the Integral Test.

The derivative of this function is \(f'(x) = e^{-x^2}(1-2x^2)\), so our critical points will be \(\displaystyle x=\pm\frac{1}{\sqrt{2}}\), but we can drop the negative critical point as we are starting at \(k=1\). Using some test points, we can see that the function increases on the interval \(\bigr[0,\frac{1}{\sqrt{2}}\bigr]\) and decreases on the interval \(\bigr[\frac{1}{\sqrt{2}},\infty\bigr)\). Since the function will eventually decrease, we can go ahead with the Integral Test:

\(\displaystyle \int_{{\,1}}^{{\,\infty }}{{x{{{e}}^{ - {x^2}}}\,dx}} & = \mathop {\lim }\limits_{t \to \infty } \int_{{\,1}}^{{\,t}}{{x{{{e}}^{ - {x^2}}}\,dx}}\hspace{0.5in}u = - {x^2}\\ & = \mathop {\lim }\limits_{t \to \infty } \left. {\left( { - \frac{1}{2}{{{e}}^{ - {x^2}}}} \right)} \right|_1^t\\ & = \mathop {\lim }\limits_{t \to \infty } \left( {-\frac{1}{2}{{e}}^{ - {t^2}}-\biggr(-\frac{1}{2e}\biggr)}} \right) = \frac{1}{2e}\)

Therefore, since the integral is convergent, the series must also be convergent by the Integral Test.

Answer:

y = 5x

Step-by-step explanation:

Answer:

B, y= 5x

Step-by-step explanation:

If you look closely to the graph on the "bake sale items" side, when they sold 1 item they earned 5$. And when they sold 5 items they earned 25$. Which would mean every item they sold they get 5$ back which would make it B

The graph of the player two's function g(t)=16(t-5)²+290 is given in the attachment. The baseball's maximum height is 290 ft. At 5 seconds the baseball was at its maximum height. After 9.25 second the baseball hit the ground.

A function is a mathematical device that converts one value to another in a predictable manner. We can think of it as a machine. You give the machine an input, it performs some calculations on it, and then returns another value - the result of the calculations.

The function's name is f. We can call it anything we want, but single letters are common. The input* value is referred to as x. Again, we could use anything, but x is common. What the function does with the input is shown to the right of the equals sign.

In this case, the function takes the input x, multiplies it by three, and returns the result.

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Answer:

1.  Y = -1/4x + 1

3. Y = 2/5x + 1

5. Y = 4/5x + 5

7. Y = -x + 5

9. Y = -5/2x - 16

Step-by-step explanation:

Find the slope using the formula

Use the slope and one of the points to find the y-intercept

Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.

Value of X6 = N6 - N5. From the given realization of the Bernoulli counting process, N5 = 3 and N6 - N5 = X6. Hence, X6 = N6 - N5 = 5 - 3 = 2. The value of S is the largest value of n for which Nn = 3. From the given realization of the Bernoulli counting process, N3 = 1, N4 = 2, N5 = 3, and N6 = 5. Hence, the value of S is 5.

The value of T2 is the time at which the second success occurs. From the given realization of the Bernoulli counting process, N2 = 1. Hence, the time at which the second success occurs is T2 = 2.d) P{N2=1, Ns=3, N7-4} = P{N2=1} × P{Ns-N2=2} × P{N7-Ns=1} × P{No=4}.Using the Bernoulli counting process, the probability of a success is p = 0.2 and the probability of a failure is q = 1 - p = 0.8. Therefore, P{N2=1} = pq, P{Ns-N2=2} = p²q, P{N7-Ns=1} = pq², and P{No=4} = p³.Thus, P{N2=1, Ns=3, N7-4} = (0.2)(0.8)(0.2²)(0.8)(0.2)(0.8²)(0.2³) = 0.0016384. A Bernoulli counting process is a stochastic process that consists of a sequence of independent and identically distributed random variables, where each random variable takes the value 1 or 0 with probability p and q = 1 - p, respectively. The Bernoulli counting process is often used to model the arrival times of events that occur randomly over time. The Bernoulli counting process has many applications in areas such as reliability theory, queueing theory, and inventory management.In this question, we are given the realization of a Bernoulli counting process, and we are asked to find various quantities associated with this process. We are first asked to find the value of X6, which is the number of successes that occur between times 5 and 6. We are then asked to find the value of S, which is the largest time at which three successes have occurred. We are also asked to find the value of T2, which is the time at which the second success occurs. Finally, we are asked to find the probability of a specific sequence of events occurring, given that the success probability is p = 0.2.To find the value of X6, we simply subtract the value of N5 from the value of N6. Similarly, to find the value of S, we look for the largest time at which Nn = 3. To find the value of T2, we look for the time at which N2 = 1. Finally, to find the probability of a specific sequence of events occurring, we use the probabilities of success and failure to calculate the probability of each event occurring, and then multiply these probabilities together. Thus, we have found the value of X6, the value of S, the value of T2, and the probability of a specific sequence of events occurring.

In conclusion, the Bernoulli counting process is a powerful tool for modeling the arrival times of events that occur randomly over time. By using the probabilities of success and failure, we can calculate various quantities associated with this process, such as the value of X6, the value of S, the value of T2, and the probability of a specific sequence of events occurring. The Bernoulli counting process has many applications in areas such as reliability theory, queueing theory, and inventory management.

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The set builder form of the set b = {1/10, 1/00, 1/1000} is b = {x | x = 1/10ⁿ, where n is a positive integer}

In mathematics, set builder notation is a concise way of describing a set using a rule or a formula.

Let's explore how we can use set builder notation to write the set b={1/10, 1/100, 1/1000}.

To begin, we need to identify the common property that these elements share. In this case, we can observe that each element is a rational number with a power of ten as the denominator. So, we can write the set b as follows:

b = {x | x = 1/10ⁿ, where n is a positive integer}

In this notation, the vertical bar represents "such that" and separates the description of the element from the rule that defines the set. The letter x is a variable that represents any element that satisfies the rule. We use the power of ten as a common property to describe the set b.

In this set builder form, we can see that b is a set of elements that can be expressed as 1/10 to the power of a positive integer. We can also use set builder notation to define other sets with different properties, such as sets of even numbers or sets of prime numbers.

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Answer:

C 28.7

Step-by-step explanation:

Remember this formula if you want to find the Area of rectangle = A = L X W

Answer:

use a calculator to find 3x3x7 for step one and for step 2 times 3x3 in a calculator

Step-by-step explanation:

Answer: this is the answer

Step-by-step explanation:

Answer:

231.77

we have length as9.8cm

breadth as 5.5cm

height as 4.3cm

solution

we know that

volume =l*b*h

=9.8*5.5*4.3

=231.77

Answer:

Step-by-step explanation:

6\(\sqrt{5\\\)

\(\sqrt{5*36}\)

\(\sqrt{180}\)

If you think about it logically, how can you take 6 out? So there was a number 36 under the root, and because of that there is a possibility to take it out, because 6 squared is 36

Answer:

1) The monthly payment is approximately $292.96

2) The total interest is approximately $2,061.84

Step-by-step explanation:

1) The financing method Nathan Reynolds applied to buy the car is given as follows;

The purchase price of the car = $15,000

The down payment made for the car = $3,000

The

The interest on the loan he took for the balance of the purchase price, R = 8%

The number of years for which he took the loan, n = 4 years = 48 months

We have;

The balance of the purchase price = (The purchase price of the car) - (The down payment made for the car)

∴ The balance of the purchase price = $15,000 - $3,000 = $12,000

The balance of the purchase price = $12,000 = The loan Nathan secured

The monthly payment on a loan is given by the following formula

\(A = P \times \dfrac{r \cdot (1 + r)^n}{(1 + r)^n - 1}\)

Where;

A = The payment amount made  monthly

P = The principal or loan amount = $12,000

r = The interest rate divided by 12 = R/12 = 8/12 = 2/3

n = The number of months the monthly payment will be made = 48 months

By plugging in the variable values, we get;

\(A = 12,000 \times \dfrac{\dfrac{2}{300} \times \left (1 + \dfrac{2}{300} \right ) ^{48}}{ \left (1 + \dfrac{2}{300} \right )^{48} - 1} = 292.955068099 \approx 292.96\)

Therefore, the payment amount made  monthly, A ≈ $292.96

2) The total payment made in the 48 months = A × 48 = 292.955068099 × 48 ≈ 14,061.84

The total payment made in the 48 months ≈ $14,061.84

The total interest = (The total payment made in the 48 months) - (The loan amount)

∴ The total interest = $14,061.84 - $12,000 ≈ $2,061.84

Answer:

Piecewise

Step-by-step explanation:

For a piecewise function, the domain is broken into pieces, with a different rule defining the function for each piece.

Piecewise functions are usually a function that equals two or more equations depending on the x or the domain.

Google piecewise functions to see examples.

I hope this helps!

Answer: Piecewise

Step-by-step explanation:

There will be breaks and jumps in the curve, particularly when a value would undefined. So the solution curve looks like disconnected pieces.

Answer:

x = 8

Step-by-step explanation:

-4x + 10 = -2x - 6

-4x + 2x = -6 - 10 (Calculate)

-2x = -16 (Divide both sides by -2)

x = 8

Have a nice day! :D

Answer:

x=8

Step-by-step explanation:

-4x+10=-2x-6   original equation

-4x+16=-2x      add 6 both sides

16=2x              add 4 both sides

x=8                 divide 2 both sides

As per given by the question,

There are given that four point.

The point is,

Now,

From given point,

Then, the factor is,

Now, solve the above equation,

The factorial formd will be,

Now, find the value of "a" with the help of given point (0, -8).

So,

Puth the value of x =0, and y=-8 in above equation,

Then,

Then, a=2.

Now,

The value of a is 2.

And,

The polynomial in the factored form is,

Hence, the value of a is 2 and the polynomial in the factored form is,

Answer:

12.50k

Step-by-step explanation:

I came to this answer as k is the number of hours, and 12.50 is how much per hour.

Answer:

We know that 6² = 36 , which is very close to 37 . Thus square root of 37 will be very close to 6

To find first-order linear differential equations solution, we have to derive the general form or representation of the solution.

With the help of the steps shown below, we can learn how to solve the first-order differential equation.

1. Reorder the terms in the given equation so that they have the form \($\frac{dy}{dx}+Py=Q\) where P and Q are constants or functions of the independent variable x only.

2. Integrate P (obtained in step 1) with respect to x and then put this integral as a power of e to determine the integrating factor.

\($e^{\int P d x}\) = IF

3. The linear first-order differential equation's two sides should be multiplied by the IF.

4. The L.H.S of the equation is always a derivative of \($y \times M(x)$\) i.e. L.H.S \($= \frac{d(y \times I . F)}{dx}\)

\($d(y \times I . F) d x=Q \times I . F$\)

5. In order to arrive at the solution, we simply integrate both sides with respect to x in the last step.

Therefore \(y \times I . F=\int Q \times I . F d x+C$,\)

where C is some arbitrary constant

Similarly, we can also solve the other form of linear first-order differential equation \($\frac{dy}{dx}+Py=Q\) using the same steps.

P and Q are y's functions in this manner. We determine the solution, which will be, by using the integrating factor (I.F), which is

\($(x) \times(I . F)=\int Q \times I . F d y+c$\)

Now, to get a better insight into the linear differential equation, let us try solving some questions. where C is some arbitrary constant.

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Answer:

m = − 2

Step-by-step explanation:

Answer:

0 Is the answer 0 - 1 / 0 - 3 = 0

The expressions when simplified are

(a) 3x² - 7x - 48

(b) 2x² - 10x + 12

(c) 2x² + 7x + 12

From the question, we have the following parameters that can be used in our computation:

The expressions

To simplify the expressions, we collect the like terms and evaluate them

Using the above as a guide, we have the following equations

2x² −2x −24 + x² −5x −24​ = 3x² - 7x - 48

x² − 10x + 16 + x² − 4​ = 2x² - 10x + 12

2x² − 5x − 12 + 12x + 24​ = 2x² + 7x + 12

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Question

Simplify

2x² −2x −24 + x² −5x −24​

x² − 10x + 16 + x² − 4​

2x² − 5x − 12 + 12x + 24​

Step-by-step explanation:

D = b² - 4ac

D = 10² - 4 · 3 · 2

D = 100 - 24

D = 76

D = (-5)² - 4 · 1 · (-4)

D = 25 - (-16)

D = 26 + 16

D = 42

D = 7² - 4 · 1 · (-8)

D = 49 - (-32)

D = 49 + 32

D = 81

D = 0² - 4 · 1 · (-9)

D = 0 - (-36)

D = 36

D = (-6)² - 4 · 5 · 10

D = 36 - 200

D = - 164