If cot x° = three fourths, what is the value of b? Triangle LMN in which angle M measures 90 degrees, angle L measures x degrees, LM measures 10.5 units, and NM measures 2b units b = 4 b = 5 b = 6 b = 7

The Riemann sum Le for f(T) = 3 – 2-4 on the interval (-1,2] can be found by dividing the interval into six subintervals of equal width.

(a) Plotting y = f(2) shows that the function takes the value 1 at the left endpoint and -5 at the right endpoint. Drawing the six rectangles whose areas are the terms of Le shows that each rectangle has width 1/3 and heights 1, 1, -5, -5, 1, and 1. (b) Calculating L6 gives L6 = (1/3)[1 + 1 - 5 - 5 + 1 + 1] = -2. Approximating this to one decimal place gives L6 ≈ -2.0. (c) Based on the plot, Lo appears to be an underestimate for the area.
For the function f(T) = 3 - 2T - 4 on the interval (-1, 2], let's use the Riemann sum L6 with 6 subintervals. (a) To plot y = f(2), substitute T=2 and obtain y = -5. The subintervals endpoints are -1, -0.5, 0, 0.5, 1, 1.5, and 2. Draw 6 rectangles using the left endpoint height.
(b) L6 = ΔT[f(-1) + f(-0.5) + f(0) + f(0.5) + f(1) + f(1.5)] = 0.5[1 - 0.5 - 2 - 3.5 - 5 - 6.5] = -9. Exact answer is -9 and approximated is -9.0.
(c) Based on the plot, L6 appears to be an underestimate for the area since the rectangles lie below the curve.

To know more about function visit:

https://brainly.com/question/30721594

#SPJ11

Answer:

119 inches

Step-by-step explanation:

cos 42° = \(\frac{b}{160}\)

b = 160 × cos 42° ≈ 119 in.

To find a differentiable function y(x) that satisfies the initial value problem (IVP) y' = |x| and y(-1) = 2, we can integrate the given differential equation and then apply the initial condition.

Integrating both sides of the differential equation y' = |x| with respect to x, we get:

∫ y' dx = ∫ |x| dx

Integrating ∫ y' dx gives us y(x) + C₁, where C₁ is an arbitrary constant of integration.

Integrating ∫ |x| dx involves considering the different cases for x. Since x > 0 (as given in the problem), we have:

∫ |x| dx = ∫ x dx (for x > 0)

= (x^2)/2 + C₂, where C₂ is another arbitrary constant of integration.

Now, we have:

y(x) + C₁ = (x^2)/2 + C₂

To determine the values of C₁ and C₂, we can use the initial condition y(-1) = 2:

y(-1) + C₁ = ((-1)^2)/2 + C₂

2 + C₁ = 1/2 + C₂

Simplifying further:

C₁ = 1/2 - 2 + C₂

C₁ = C₂ - 3/2

We can rewrite the equation for y(x) by substituting C₁ with C₂ - 3/2:

y(x) = (x^2)/2 + (C₂ - 3/2)

Therefore, a differentiable function that satisfies the given IVP y' = |x| and y(-1) = 2 is:

y(x) = (x^2)/2 + (C₂ - 3/2), where C₂ is an arbitrary constant.

Learn more about differentiable function here:

https://brainly.com/question/18962394

#SPJ11

We are given the following statement:Wilfredo, who is currently 42 years old, is 8 years older than twice Alejandro's age. We have to determine Alejandro's age.Let's suppose the age of Alejandro to be A.So, according to the given statement, the age of Wilfredo can be calculated by the following equation:Wilfredo's age = 8 + 2ANow, we have been given that Wilfredo's age is 42 years. Therefore:42 = 8 + 2A⇒ 2A = 42 - 8 = 34⇒ A = 17Therefore, Alejandro's age is 17 years old.

Alejandro's age is given as follows:

17 years old.

Alejandro's age is obtained solving a system of equations, considering it's age as x.

Double his age is given as follows:

2x.

Eight more than double is given as follows:

2x + 8.

Wilfredo's age is of 42, hence the value of x is given as follows:

2x + 8 = 42

2x = 34

x = 17.

More can be learned about a system of equations at https://brainly.com/question/13729904

#SPJ1

Answer:

a to x is 20 hope i helped if not correct me please

We have the function:

We must identify the function that:

0. reflects the function across the y-axis,

1. shift it 6 units up.

1) To reflect the function across the y-axis we replace x by -x:

2) To shift the result 6 units up, we sum +6 on the right side:

Plotting both functions, we get:

Answer

Second option

Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

Learn more on monthly payment here;

https://brainly.com/question/25599836

#SPJ1

Answer: 2 Kilometers(km) a minute(min).

Step-by-step explanation:

If we look at the graph, the 1km and 2min meet.

Answer:

24 km/h

Step-by-step explanation:

The graphic shows 4 km in ten minutes

\(s=\frac{4 km}{10 min} (\frac{60 min}{1 hour}) =\frac{(4)(60)}{10} =24km/hr\)

I hope this help you

The answer choice which represents the solution to the inequality as given in the task content is; x>-2 or x≤ 1.

On this note, it follows that the inequalities can be solved individually as follows;

-4 < 3x +2

-6 < 3x

x > -2

Also, 3x +2 ≤ 5

3x ≤ 3

x ≤ 1.

Ultimately, the correct answer choice is; Choice C; x>-2 or x≤ 1.

Read more on complex inequality;

https://brainly.com/question/24761100

#SPJ1

Leave a tip of $3.00 on a $20.00 bill is an appropriate gesture for a 15% tip based on appropriate percentage.

Leaving a tip for good service at a restaurant is a common practice, and it shows appreciation and respect for the hard work of the staff. Mary and John's bill at a restaurant is $20.00, and they plan to leave a 15% tip for the server based on percentage.

To calculate the tip amount, we need to convert the percentage into a decimal form by dividing it by 100. Therefore, 15% becomes 0.15 in decimal form. Multiplying this decimal value by the total bill amount of $20.00 gives us the tip amount, which is $3.00.

It is important to note that while tipping is a customary practice, it is not mandatory. The amount of the tip is also subjective and may depend on various factors such as the quality of service, the atmosphere of the restaurant, and the level of satisfaction of the customer. However, a general rule of thumb for good service is to leave a tip of 15% to 20% of the total bill amount.

In conclusion, a $3 tip on a $20 note is a suitable gesture for a 15% tip. It is a modest gesture to thank the server for their hard work and recognize their efforts in making the dining experience enjoyable.

Learn more about percentage here:

https://brainly.com/question/26352729

#SPJ1

Complete Question: Mrs. Johnson wishes to leave a 15% tip on a $100 bill at the restaurant. How much money should she leave behind, roughly?

About $5.00 Brought to you by A

B. roughly $15.00 C. roughly $20.00

Answer:

X = 17

Step-by-step explanation:

If you created equivalent expressions with equal bases that should be the answer.

Answer:

10 feet is the width. (5on each side)

Step-by-step explanation:

If you multiply 5.25x2=10.5 then you subtract the perimeter 20.5-10.5= 10ft

Hope this helped! ;-)

Perimeter is the sum of the length of the sides used to make the given figure. The width of their sandbox is 5 feet.

Perimeter is the sum of the length of the sides used to make the given figure. The perimeter of the rectangle is two times the sum of the length and the width of the rectangle.

Therefore, the perimeter of the rectangle is written as,

The perimeter of the rectangle = 2 × (Length + Width)

Given that the length of a sandbox is 5.25 feet. Also, the perimeter of the sandbox is 20.5 feet. Therefore, the perimeter of the sandbox can be written as,

Perimeter of the sandbox = 2 × (Length + Width)

20.5 feet = 2 × (5.25 feet + Width)

20.5 feet/ 2 = (5.25 feet + Width)

10.25 feet = (5.25 feet + Width)

10.25 feet - 5.25 feet = Width

Width = 5 feet

Hence, the width of their sandbox is 5 feet.

Learn more about Perimeter here:

https://brainly.com/question/10466285

#SPJ2

Answer:

The percent of the bill he paid as the tip is 20% (explanation below)

Step-by-step explanation:

7.15/35.75 x 100% = 20%

he theater sold 356 adult tickets and 144 child tickets for a certain showtime to make a total of $3157 in ticket sales.

We have,

Let's assume that the number of adult tickets sold is x, and the number of child tickets sold is y.

We know that the total number of tickets sold cannot exceed the maximum capacity of the theater, so we have the inequality:

x + y ≤ 500

We also know that the total revenue from ticket sales is $3157, so we can write another equation based on the ticket prices:

7.25x + 4y = 3157

We have two equations with two variables, so we can solve for x and y using any method of our choice.

Here, we will use substitution.

We can write,

y ≤ 500 - x.

We can substitute this into the second equation.

7.25x + 4(500 - x) = 3157

Simplifying and solving for x.

7.25x + 2000 - 4x = 3157

3.25x = 1157

x = 355.69

We can't sell a fractional number of tickets, so we must round x to the nearest whole number.

Let's assume that x = 356.

Then, from the first inequality.

356 + y ≤ 500

y ≤ 144

Therefore, we can sell at most 144 child tickets.

To check if this solution satisfies the equation 7.25x + 4y = 3157, we substitute x = 356 and y = 144 into the equation:

7.25(356) + 4(144) = 3157

This is true, so our solution is valid.

Therefore,

The theater sold 356 adult tickets and 144 child tickets for a certain showtime to make a total of $3157 in ticket sales.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

The system of equations is consistent and has a unique solution at (-4, 1).

To solve the system of equations by graphing, we can plot the lines represented by each equation on a coordinate plane and find their point of intersection.

The given system of equations is:

1) 3x + y = -3

2) 6x - 6y = -30

Let's graph these equations:

For equation 1, 3x + y = -3, we can rewrite it as y = -3x - 3.

For equation 2, 6x - 6y = -30, we can simplify it to x - y = -5, and then y = x + 5.

Now, let's plot these lines on a graph:

The line for equation 1, y = -3x - 3, has a slope of -3 and y-intercept of -3. It will have a negative slope, and we can plot two points on the line: (0, -3) and (-1, 0).

The line for equation 2, y = x + 5, has a slope of 1 and y-intercept of 5. We can plot two points on this line as well: (0, 5) and (-5, 0).

Plotting these lines on a graph, we can see that they intersect at the point (-4, 1).

Now, let's analyze the system:

Since the lines intersect at a single point, the system is consistent. The solution to the system is the coordinates of the point of intersection, which is (-4, 1).

In summary, the system of equations is consistent and has a unique solution of x = -4 and y = 1.

To know more about system of equations, refer here:

https://brainly.com/question/21620502

#SPJ4

y = -3/2x - 20.5 is the line crossing through (-7,10) perpendicular to 2x - 3y= -3

In an equation, parallel lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.

Here given that  2x - 3y= -3

can also be written as

y = 2/3x + 1

Here 2/3 is the slope and 1 is the y-intercept

To find a parallel line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.

y - y₁ = m(x - x₁)

We have, m = -3/2,  x₁ = -7 and y₁ = 10

y - 10 = -3/2(x - (-7))

y - 10 = -3/2(x + 7)

y - 10 = -3/2x - 21/2

y = -3/2x - 21/2 + 10

y = -3/2x - 20.5

Learn more about point-slope formula

https://brainly.com/question/24907633

#SPJ9

Answer:

H₀: μ = 4 vs. H ₐ: μ > 4

Step-by-step explanation:

A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.  

It is a hypothesis of no difference.

It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.

Whereas, the alternate hypothesis is the contradicting statement to the null hypothesis.

The alternate hypothesis describes direction of the hypothesis test, i.e. if the test is left tailed, right tailed or two tailed.

It is also known as the research hypothesis and is denoted by H ₐ.

In this case we need to test whether the amount is paid after the grace period, on average, more than 4 times in 2018.

The hypothesis can be defined as follows:

H₀: μ = 4 vs. H ₐ: μ > 4

The completed statements with regards to the compound interest of the amount in the account are;

If the account has a 5% interest rate and is compounded monthly, you have $101.655 million money after 2 years

If the account has a 5% interest rate compounded continuously, you would have $106.096 million money after 2 years

Compound interest is the interest calculated based on the initial amount and the accumulated interests accrued from the periods before the present.

The compound interest formula indicates that we get;

\(A = P\cdot (1 + \frac{r}{n}) ^{n\cdot t}\)

Where;

P = The principal amount invested = $92 million

r = The interest rate = 5% monthly

n = The number of times the interest is compounded per annum = 12

t = The number of years = 2 years

Therefore; \(A = 92\cdot (1 + \frac{0.05}{12}) ^{12\times 2}\approx 101.655\)

The amount in the account after 2 years is therefore about $101.655 million

The formula for the amount in the account if the principal is compounded continuously, we get;

A = \(P\cdot e^{(r\cdot t)}\)

Therefore, we get;

\(A = 96 \times e^{0.05 \times 2} \approx 106.096\)

The amount in the account after 2 years, compounded continuously therefore, is about $106.096 million

Learn more on compound interest here: https://brainly.com/question/21487182

#SPJ1

How old am I now?: You are  65 years old now

Let y represent father's age now

Let x represent daughter age now

First step

y=13x

y+1=11×(x+1)

Second step

y+1=11x+11

y-11x=d

Third step

Substitute

13x-11x=10

2x=10

x=10/2

x=5

Last step

y=13x

y=13×5

y=65

Inconclusion How old am I now?: You are  65 years old now

Learn more here:

https://brainly.com/question/7203160

The correct option is; 4: this contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) (7 − 1) , but f is not continuous at x = 3.

The function being used is;

f(x) = (x - 3)⁻²

If we separate this function according to x, we obtain;

f'(x) = -2/(x - 3)³

Finding all c values f(7) − f(1) = f '(c)(7 − 1).is our goal.

This suggests that;

0.06 - 0.25 = -2/(c - 3)³ x 6

-0.19 =  -12/(c - 3)³

(c - 3)³ = 63.157

c = 6.98

If the Mean Value Theorem holds for this function, then f must be continuous on [1,7] and differentiable on (1,7).

But when x = 3, f is not continuous, hence the Mean Value Theorem's prediction is false.

To know more about the Mean Value Theorem, here

https://brainly.com/question/19052862

#SPJ4

The complete question is-

Let f(x) = (x − 3)−2. Find all values of c in (1, 7) such that f(7) − f(1) = f '(c)(7 − 1). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) c = Based off of this information, what conclusions can be made about the Mean Value Theorem?

it depends on a variety of factors such as the size of the new flock, the availability of resources, and the adaptability of both the existing and new bird populations.

If the new flock is relatively small and the existing population is well-established, the impact may be minimal. However, if the new flock is large and competes for resources such as food, nesting sites, and mates, it could lead to a decrease in the size of the existing population.

Additionally, if the new birds bring new diseases or predators to the area, this could also impact the population size of both groups. On the other hand, if the new birds are able to integrate well and find their own niche within the ecosystem, the population size could potentially increase.

the impact of a new flock of birds on the existing population size can vary depending on a range of factors. It is difficult to predict the exact outcome, but it is important to consider the potential impacts on both the new and existing populations.

To know more about factors visit:

https://brainly.com/question/14209188

#SPJ11

The alternate hypothesis for the directional z-test is:

Local resident's average > National average

A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge.

One of the ideas put out in the hypothesis test is the alternate hypothesis.

A researcher wants to know if people in his neighborhood have a better well-being than people nationwide.

The appropriate hypothesis for a one-tailed or directional z test for the test will be that the average local residents are higher than the national average.

Learn more about hypothesis here:

brainly.com/question/606806

#SPJ4

Answer:

No solution

Step-by-step explanation:

On the left side we have one half x plus one half x  which equals x.  On the right side we have x + 1.  So the equation becomes x = x + 1.  Subtracting x from both sides we get 0 = 1, which is false.  Therefore there is no solution to this problem.  

Answer:

x=40

y=− 17 /6

Step-by-step explanation:

Answer:

Use Symbolab i think thats how you spell it

Step-by-step explanation:

Answer:

0.125

Step-by-step explanation:

The correct answer to the given question is 0.125.

Explanation is provided below:

First we convert the fractions into decimals

3 / 10 = 0.30

5 / 12 = 0.4167

and now we will calculate the missing part asked in the question

= 0.4167 of 0.30

= 0.4167 * 0.30

= 0.125

5/12 of 3/10 is 0.125

The answer to the given question is 0.125