Vicky jogged 2 3/4 in 1/2 hour. What was her average rate of speed in miles per hour

Answer:

Sin theta = 12/13

Step-by-step explanation:

From the question;

Cot theta = 5/12

Kindly recall;

Cot theta = 1/ tan theta

Hence, tan theta = 12/5

Mathematically

tan theta= opposite/adjacent

to get hypotenuse, we will use Pythagoras’ theorem which states that the square of the hypotenuse equals sum of the squares of the two other sides

let hypotenuse be h

h^2 = 12^2 + 5^2

h^2 = 144 + 25

h^2 = 169

h = √169

h = 13

But sine theta = opposite/ hypotenuse = 12/13

Answer:

not 12/13

Step-by-step explanation:

got wrong

The selling price of the TV is 300 euro (250 euro original price + 20% VAT).

What is VAT(Value Added Tax) ?

VAT stands for Value Added Tax, it is a consumption tax that is added to the price of goods and services. VAT is imposed on most goods and services in many countries around the world, and it is usually a percentage of the sale price. The percentage can vary depending on the country and the type of goods or services being sold.

To calculate the VAT, we can use the formula:

VAT = (original price x VAT percentage) / 100

So, in this case:

VAT = (250 x 20) / 100 = 50

Now we add the VAT to the original price to find the selling price:

selling price = original price + VAT

250 + 50 = 300 euro.

Therefore , The selling price of the TV is 300 euro (250 euro original price + 20% VAT).

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VAT = (original price x VAT percentage) / 100

So, in this case:

VAT = (250 x 20) / 100 = 50

Now we add the VAT to the original price to find the selling price:

selling price = original price + VAT

250 + 50 = 300 euro.

Therefore , The selling price of the TV is 300 euro (250 euro original price + 20% VAT).

Answer:

(a)59

(b)\(d=\dfrac{1}{2}\)

Step-by-step explanation:

Part A

The nth term of an arithmetic sequence, \(T_n=a+(n-1)d\)

Let the first angle of the triangle =a

Let the common difference = d.

Since the measures of the angles are in an arithmetic progression

We have:

a + (a + d) + (a + 2d) = 180

3a+3d=180

a+d=60

Since a or d cannot be equal to zero, the minimum possible values of a and d is 1 and the maximum possible values of a and d is 59.

Therefore, there are 59 non-similar triangles.

Part B

In an arithmetic sequence

\(a_7 -2a_4 = 1, a_3 = 0.\)

\(2a_4=a_7-1\\a_4=\dfrac{a_7-1}{2}\)

Common difference,

\(d=a_4-a_3\\=\dfrac{a_7-1}{2}-0\\d=\dfrac{a_7-1}{2}\)

\(a_7=a_4+3d\\=\dfrac{a_7-1}{2}+3(\dfrac{a_7-1}{2})\\=\dfrac{a_7-1}{2}+\dfrac{3a_7-3}{2}\\=\dfrac{a_7-1+3a_7-3}{2}\\a_7=\dfrac{4a_7-4}{2}\\$Cross multiply\\2a_7=4a_7-4\\2a_7-4a_7=-4\\-2a_7=-4\\a_7=2\)

Therefore:

\(d=\dfrac{2-1}{2}\\d=\dfrac{1}{2}\)

Answer:

Mean

Step-by-step explanation:

Answer: answer is b

Step-by-step explanation: I know it’s b

Tri-County will have to charge approximately $83.1 per MWh to break even.

To calculate the break-even price that Tri-County will have to charge to cover its costs, we need to consider both the fixed costs and the variable costs. The fixed costs are given as $80.1 million per year.

The variable costs are calculated by multiplying the quantity of electrical power sold (150,000 MWh per year to Boulder) by the variable cost per MWh ($20). Therefore, the variable costs amount to 150,000 MWh/year * $20/MWh = $3 million per year.

To cover both fixed and variable costs, Tri-County needs to charge a total amount that equals the sum of these costs. The total cost is $80.1 million + $3 million = $83.1 million per year.

Now, let's calculate the break-even price per MWh. Since Tri-County has a demand of 1,000,000 MWh from its customers (other than Boulder), we can divide the total cost by this quantity to find the break-even price.

Break-even price = Total cost / Quantity of electrical power demanded
Break-even price = $83.1 million / 1,000,000 MWh = $83.1/MWh

Therefore, Tri-County will have to charge approximately $83.1 per MWh to break even.

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The pick-up rate in this scenario would be 80%. This is calculated by dividing the number of rooms occupied (160) by the number of rooms reserved (200), and then multiplying by 100 to get a percentage. So, (160/200) x 100 = 80%. This means that 80% of the reserved rooms were ultimately occupied.

It's important to note that a pick-up rate of 80% is generally considered to be a good result in the hospitality industry. It indicates that the hotel was able to accurately predict the number of rooms that would be needed by the groups, and that the groups themselves followed through on their reservations. A lower pick-up rate could suggest that the hotel overestimated demand, or that some of the groups cancelled their bookings at the last minute. On the other hand, a higher pick-up rate could indicate that the hotel was too conservative in its initial estimates, or that some of the groups requested additional rooms after the initial reservation was made. Ultimately, the pick-up rate is a useful metric for assessing the accuracy of a hotel's forecasting and planning processes.

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Answer:

20 and 19

Step-by-step explanation:

The answer is above in the picture....

Hope it helps you

Answer:

(t x 7) 5 - 2

Step-by-step explanation:

I think that is how it would look, I hope it helps!

By convention, we often reject the null hypothesis if the probability of our result, given that the null hypothesis were true, is less than .05

By convention, we often reject the null hypothesis if the probability of our result, given that the null hypothesis were true, is considered statistically significant, which is typically set at a level of alpha = .05.

This means that if there's less than a 5% chance of obtaining our result when the null hypothesis is true, we consider the result statistically significant and reject the null hypothesis in favor of the alternative hypothesis.

Therefore, option B is the correct answer.

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The sin function from the graph is y 4 sin x.

We have,

The general form of a sine function is:

y = A sin (Bx - C) + D

Where,

A is the amplitude.

B = 2π / T represents the frequency or number of cycles in a given interval.

C is the phase shift.

D is the vertical shift.

From the graph,

A = 4

T = 2π

B = 1

C = 0

D = 0

Substituting,

y = A sin (Bx - C) + D

y = 4 sin x

Thus,

The sin function from the graph is y 4 sin x.

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Answer:

To get to system B the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 4. The solution to system B is the same as the solution to system A.

Step-by-step explanation:

A system of equations and it’s solution are given below.

System A.

x-y=3

-2x+4y=-2

Solution: (5,2)

Complete the sentences to explain what steps were followed to option the system of equations below.

System B

x-y=3

2x=10

To get to system B the (first/second) equation in system A was replaced by the sum of that equation and the (first/second) equation multiplied by (4....2.....-3) . The solution to system B (is/ is not) the same as the solution to system A.

Solution:

To get system B:

First write the first equation in system A. x - y = 3

Multiply the second equation in system A by 4 and add to the first equation in system A to get:

2x = 10

x = 10/2 = 5

Put x = 5 in x - y = 3

5 - y = 3

y = 5 - 3 =2

The solution to system B is the sam as that of system A

To get to system B the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 4. The solution to system B is the same as the solution to system A.

This question makes exactly no sense.

However, if yall want the answer to

Question:
System A
x-y= 7       -3x+9y = -39   Solutions (4,-3)

Complete the sentences to explain what steps were followed to obtain the system of equations below

x-y= 7    6y= -18

Solution:

To get system B, the second equation in system A was replaced by the sum of that equation and 3 times the first equation. The solution to system B is the same as the solution to system A.

Check the picture below.

well, ∡CED is the same as ∡CEA and those are right-angles so those are pretty much given, now

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{29}\\ a=\stackrel{adjacent}{20}\\ o=\stackrel{opposite}{CE} \end{cases} \\\\\\ CE=\sqrt{ 29^2 - 20^2}\implies CE=\sqrt{ 841 - 400 } \implies CE=\sqrt{ 441 }\implies \boxed{CE=21} \\\\\\ \stackrel{\textit{since we know the radius CB=29}}{CB-CE = EB\implies }\boxed{EB=8}\)

Answer:

angle CED 90°. CE = 21. EB = 8.

Step-by-step explanation:

angle CED = 90° (right angle).

the radius (centre to edge) is the same right around the circle.

so that means that distance CD = 29.

draw a line from C to D. notice how that has just become an hypotenuse?

we know that DE = 20.

we have a right-angled triangle.

CE² = hypot² - DE²

       = 29² - 20²

       = 841 - 400

       = 441

CE = √441 = 21.

EB must be radius subtract CE. that is, 29 - 21 = 8.

Answer:

Negative associaction

Answer:

( 2, - 1 )

Step-by-step explanation:

( x - h )² + ( y - k )² = r²

( h, k ) are coordinates of the center of a circle with radius r

~~~~~~~~~

x² + y² - 4x + 2y - 11 = 0

( x² - 4x + 4 ) - 4 + ( y² + 2y  + 1 ) - 1 - 11 = 0

( x - 2 )² + ( y + 1 )² = 4²

Coordinates of the center of a circle are ( 2, - 1 )

Step-by-step explanation:

y = 4x - 7

Comparing the given equation with y = mx + c Then

slope (m) = 4

y -intercept (c) = - 7

Hope it will help :)

Answer: the slope is negative 4

Step-by-step explanation:

because its ez

Yes, the least squares solution is unique in fitting a straight line y = x0 + x1t to the three data points (ti, yi) = (0,0), (1,0), (1,1).

To find the least squares solution, we want to minimize the sum of the squared differences between the predicted values and the actual data points. In this case, the equation for the straight line is y = x0 + x1t.

By substituting the values of the data points into the equation, we get the following system of equations:

\(For (0,0): 0 = x0 + x1(0) --- > 0 = x0\\For (1,0): 0 = x0 + x1(1) --- > 0 = x0 + x1\\For (1,1): 1 = x0 + x1(1) --- > 1 = x0 + x1\)

Simplifying these equations, we find that x0 = 0 and x1 = 1. Therefore, the least squares solution is unique, with x0 = 0 and x1 = 1.

This means that the straight line y = x0 + x1  

It is the best fit for the given data points, minimizing the sum of the squared differences between the predicted values and the actual data points.

\(For (0,0): 0 = x0 + x1(0) --- > 0 = x0\\For (1,0): 0 = x0 + x1(1) --- > 0 = x0 + x1\\For (1,1): 1 = x0 + x1(1) --- > 1 = x0 + x1\)

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Answer:

$7.5 = 3 pounds

Step-by-step explanation:

1. If $5 is equal to 2 pounds of cherries, you want to find what 1 pound of cherries cost. You should divided 5 by 2 and 2 by 2 to find what 1 pound of cherries cot.

2. That means that 1 pound of cherries cost $2.5.

3. Now we want to find how much money 3 pounds cost, so you should multiply the 2.5 and the 1 by 3.

4. Now that gets you to $7.5 for 3 pounds of cherries.s

When we divide 3 by 2.5, we get a quotient of 1.2. This means that 2.5 goes into 3 one and two-fifths times. The division expression for this is 3 ÷ 2.5 = 1.2. However, we can also express this as a fraction, which is 6/5.

To find the division expression that this model represents, we need to divide 3 by 2.5. So the division expression would be:
3 ÷ 2.5
This expression can also be written as a fraction, which is:
3/2.5
To simplify this fraction, we can multiply both the numerator and denominator by 2, which gives us:
6/5
So the division expression that this model represents is:
3 ÷ 2.5 = 6/5
In division, we have a dividend, divisor, and quotient. The dividend is the number being divided, the divisor is the number we are dividing by, and the quotient is the result of the division. In this case, the dividend is 3, and the divisor is 2.5. We need to find out how many times 2.5 goes into 3. To do this, we can use long division or simply divide 3 by 2.5 using a calculator.
In summary, the division expression that the model represents is 3 ÷ 2.5, which simplifies to 6/5. This means that 2.5 goes into 3 one and two-fifths times. Understanding division is an important skill in mathematics as it helps us to solve problems and make calculations more efficiently.

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Answer:

x = -3/2y + 3

Step-by-step explanation:

2x + 3y = 6

2x = -3y + 6

x = -3/2y + 3

The slope of the secant line between x=-2 and x=4 for the function f(x)=-x2-2/x-2 can be calculated using the following equation:
Slope = (f(x2) - f(x1)) / (x2 - x1)

In this equation, x1 is the starting point (-2) and x2 is the endpoint (4). Plugging in the values into the equation, we get:
Slope = [(−(−2)2−2 / (−2)−2] - [(−(4)2−2 / (4)−2)] / (4 − (−2))
Simplifying the equation, we get:
Slope = (-6 - 2) / 6 = -4/3
Therefore, the slope of the secant line between x=-2 and x=4 for the function f(x)=-x2-2/x-2 is -4/3 in exact notation. Alternatively, the slope of the secant line can be rounded to four decimal places and expressed as -1.3333.
To find the equation of the secant line between x=-2 and x=4, use the point-slope form of the equation, which is given by:
Equation of the line = y - y1 = m(x - x1)
In this equation, (x1, y1) is a point on the line, and m is the slope. Since the point (-2, -6) lies on the line and the slope is -4/3, the equation of the secant line is:
Equation of the line = y + 6 = -4/3 (x + 2)
Therefore, the equation of the secant line between x=-2 and x=4 for the function f(x)=-x2-2/x-2 is y + 6 = -4/3 (x + 2).

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About Nevada state, it is true that "The rural air pollution level for this state is much higher or much lower than the rest of the states in the data set."

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Answer:

His answer was correct:

(200*0.09)=18

18*16=288

200+288=488

Since the y-intercept of the polynomial must be 3600, then:

Since the only zeroes of the polynomial must be x=5, -4, -6 and 1, then the factors of the polynomial, are:

Let the multiplicity of the factor (x-1) be equal to 3 and let the multiplicity of the rest of the factors to be equal to 1. Then:

Where a is a constant. Notice that the degree of that polynomial is 6. Evaluate it at x=0 to find the value of a that makes the y-intercept to be equal to 3600:

Since p(0)=3600, then:

Therefore, the following polynomial is a 6th degree polynomial with zeroes at the values of 5, -4, -6 and -1 with a y-intercept equal to 3600:

Answer:

Step-by-step explanation:

The truck is 315 inches long

Using a linear function, the total charge from parking in the lot for 72 hours is of:

b. $146.

A linear function is modeled by:

y = mx + b

In which:

Both the basic fee, which is the y-intercept, and the hourly fee, which is the slope, are of $2, hence the cost of parking x hours is given by:

C(x) = 2x + 2

Hence the cost for parking 72 hours is:

C(72) = 2 x 72 + 2 = 2 x 73 = $146.

Which means that option b is correct.

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The growth of the lily pad is in geometric progression, and it covers half the pond in 29 days.

In the question, we are given that the size of the lily pad doubles itself every day.

If we assume the size of the lily pad on the first day as a, then on the second day its size will be 2a, on the third day it will be 2(2a) = 4a, and on the fourth day, it will be 2(4a) = 8a, and so on.

This makes a geometric progression, with the first term as a, and the constant ratio as 2.

We are given that on the 30th day, the size of the lily pad, covers the entire pond.

The size on the 30th day can be shown as the 30th term of this geometric progression

Therefore, size of the  pond = a(2)³⁰⁻¹ = a.2²⁹. {Using the formula, aₙ = arⁿ⁻¹, where aₙ is the n-th term, a is the first term, and r is the constant ratio}.

We are asked the day on which the pond is half covered.

The size of the pond in this case = (a.2²⁹)/2 = a.2²⁸.

The day can be calculated as follows:

a.2ⁿ⁻¹ = a.2²⁸,

or, 2ⁿ/2 = 2²⁸,

or, 2ⁿ = 2²⁹,

or, n = 29.

Thus, the lily pad covers half the pond on the 29th day.

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The simple interest rate that is equivalent to the discount rate can be determined by multiplying the discount rate by (Time / 365).

i) To determine the maker of the note, we need to identify who issued the promissory note. Unfortunately, the information provided does not specify the name of the maker or issuer of the note. Without additional information, it is not possible to determine the maker of the note. ii) To calculate the face value of the note, we can use the formula for the maturity value of a promissory note: Maturity Value = Face Value + (Face Value * Interest Rate * Time). Given that the maturity value is RM7,266 and the note matured on 11 June 2022 (assuming a 365-day year), and Zafran held the note for 52 days, we can calculate the face value: 7,266 = Face Value + (Face Value * 0.09 * (52/365)). Solving this equation will give us the face value of the note.

iii) The discount date is the date on which the note was discounted at the bank. From the information provided, we know that Zafran discounted the note after holding it for 52 days. Therefore, the discount date would be 52 days after 10 January 2022. iv) The discount rate can be calculated using the formula: Discount Rate = (Maturity Value - Discounted Value) / Maturity Value * (365 / Time). Given that the discounted value is RM7,130.77 and the maturity value is RM7,266, and assuming a 365-day year, we can calculate the discount rate. v) The simple interest rate that is equivalent to the discount rate can be determined by multiplying the discount rate by (Time / 365). This will give us the annualized interest rate that is equivalent to the discount rate.

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