Jason and his sister are planning an anniversary party for their parents. They make inquiries at two different party venues. One charges a base fee of $800 and $18.50 per guest. The other venue charges a base fee of $750 and $21 per guest. For how many guests is the total cost of the party the same at the two venues?


Hint: Write your two linear equations using the start value (y intercept) plus the slope. Graph the equations in DESMOS to see where they intersect. Remember - x represents the amount of guests, and y represents the total cost of the party.\


1. 30

2. 20

3. They cancel the party because they can't decide on a good place to have it.

4. 25

The solution of the given initial value problem y'' + y = f(t), y(0) = 7, y'(0) = 4 where f(t) = \(\left\{\begin{matrix}1, & 0\leq t\leq \frac{\pi}{2}\\ 0, & \frac{\pi}{2}\leq t < \infty\end{matrix}\right.\) is 1 + 6cost + 4sint + u(t - π/2)(cos(t - π/2) - 1).

The initial value problem y'' + y = f(t), y(0) = 7, y'(0) = 6 where

f(t) = \(\left\{\begin{matrix}1, & 0\leq t\leq \frac{\pi}{2}\\ 0, & \frac{\pi}{2}\leq t < \infty\end{matrix}\right.\)

Now f(t) = 1[u(t-0) - u(t-π/2)]

f(t) = u(t) - u(t-π/2)

Laplace transformation of f(t) is

L{f(t)} = L{u(t)} - L{u(t-π/2)}

L{f(t)} = 1/S - \(e^{\pi S/2}\)/S

Now taking the Laplace transformation on both side to the equation y'' + y = f(t).

L{y''} + L{y} = L{f(t)}

S^2Y(S) - SY(0) - Y'(0) + Y(S) = 1/S - \(e^{\pi S/2}\)/S

S^2Y(S) - 7S - 4 +Y(S) = 1/S - \(e^{\pi S/2}\)/S

(S^2 + 1)Y(S) - 7S - 4 = 1/S - \(e^{\pi S/2}\)/S

(S^2 + 1)Y(S) = 1/S - \(e^{\pi S/2}\)/S + 7S + 4

Divide by (S^2 + 1) on both side, we get

\(Y(S) = \frac{1}{S(S^2 + 1)} -\frac{e^{\pi S/2}}{S(S^2 + 1)} + \frac{7S}{(S^2 + 1)}+\frac{4}{S^2 + 1}\)

Simplify

\(Y(S) = \frac{1}{S}-\frac{S}{S^2 + 1} -\left[\frac{1}{S}-\frac{S}{S^2 + 1}\right]e^{\pi S/2} + \frac{7S}{(S^2 + 1)}+\frac{4}{S^2 + 1}\)

Now Y(t) = \(L^{-1}(Y(S))\)

Y(t) = \(L^{-1}\left[\frac{1}{S}\right]-L^{-1}\left[\frac{S}{S^2 + 1}\right] -L^{-1}\left[\frac{e^{\pi S/2}}{S}\right]-L^{-1}\left[\frac{Se^{\pi S/2}}{S^2 + 1}\right] + L^{-1}\left[\frac{7S}{(S^2 + 1)}\right]+L^{-1}\left[\frac{4}{S^2 + 1}\right]\)

Y(t) = 1 - cost - u(t - π/2) + cos(t - π/2) u(t - π/2) + 7cost + 4sint

Y(t) = 1 + 6cost + 4sint + u(t - π/2)(cos(t - π/2) - 1)

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The complete question is:

Find the solution of the given initial value problem y'' + y = f(t), y(0) = 7, y'(0) = 4 where f(t) = \(\left\{\begin{matrix}1, & 0\leq t\leq \frac{\pi}{2}\\ 0, & \frac{\pi}{2}\leq t < \infty\end{matrix}\right.\)

Answer: binary searches, finding the smallest or largest value in a binary search tree, and certain divide and conquer algorithms.

Step-by-step explanation: O(log N) is a common runtime complexity. Examples include binary searches, finding the smallest or largest value in a binary search tree, and certain divide-and-conquer algorithms. If an algorithm is dividing the elements being considered by 2 in each iteration, then it likely has a runtime complexity of O(log N).

The equation of the curve that passes through the point (4,9) and has a slope of 6√x at each point is y = 4x × (3/2) - 23.

To find the curve in the xy-plane that passes through the point (4,9) and has a slope of 6√x at each point, we can use calculus to integrate the slope function to find the corresponding equation of the curve.

Let's denote the equation of the curve as y = f(x), where f(x) is the function we want to find.

Given that the slope at each point is 6√x, we can express this as:

dy/dx = 6√x

To find the function f(x), we integrate both sides of the equation with respect to x:

∫ dy/dx dx = ∫ 6√x dx

Integrating both sides:

∫ dy = ∫ 6√x dx

y = 6 ∫ √x dx

Using the power rule of integration:

y = 6 × (2/3) × x × (3/2) + C

where C is the constant of integration.

Now, we can substitute the given point (4,9) to find the specific value of the constant C:

9 = 6 × (2/3) × 4 × (3/2) + C

Simplifying the equation:

9 = 6 ×(2/3) × 8 + C

9 = 4 * 8 + C

9 = 32 + C

C = 9 - 32

C = -23

Substituting the value of C back into the equation:

y = 6 × (2/3) × x × (3/2) - 23

Simplifying further:

y = 4x × (3/2) - 23

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The interval that contains the median temperature is 70-79 in the frequency table showing the observed high temperatures in Buffalo.

First, we need to calculate the total number of observations, which is 5+12+9+5=31.

The median is the middle value of the data set when arranged in ascending or descending order. Since there are 31 observations, the median will be the 16th value.

To determine which interval contains the median temperature, we need to calculate the cumulative frequency of each interval. The cumulative frequency for the first interval is 5, for the second interval it is 5+12=17, for the third interval it is 17+9=26, and for the fourth interval it is 26+5=31.

Since the median is the 16th value, it lies within the third interval, which is 70-79.

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The question is -

The following frequency table shows the observed high temperatures in Buffalo, New York, in May 2007. Which interval contains the median temperature?

temperature                     frequency

50-59                                 5

60-69                                 12

70-79                                  9

80-89                                 5

Answer:

25/8 in decimal form is 3.125.

Step-by-step explanation:

I hope this helps! :)

The length of one edge of the tabletop is 4.89 feet.

We know that square is a shape that has all the side equal. Based on this using the formula to find the length of edge of the tabletop.

The area of square table is given by the formula -

Area of square table = side²

We will keep the value of area of square table to find the value of side which will be length of edge

24 = side²

Side = ✓24

Taking square root for the value on right side of the equation

Side = 4.89

Hence, the length of one edge of the tabletop is 4.89 feet.

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Answer:

False

Rise is the vertical change not the horizontal

Step-by-step explanation:

The value of θ for which the inverse cosine of (startfraction startroot 2 endroot over 2 endfraction) is equal to θ is option b. startfraction pi over 4 endfraction.

We know that the cosine of pi/4 is startfraction startroot 2 endroot over 2 endfraction, so cos(startfraction pi over 4 endfraction) = startfraction startroot 2 endroot over 2 endfraction.

Since the question asks for the inverse cosine of startfraction startroot 2 endroot over 2 endfraction, we need to find the angle whose cosine is startfraction startroot 2 endroot over 2 endfraction. This angle is pi/4, so the answer is b. startfraction pi over 4 endfraction.

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Answer:

9.36 x 10^(-10)

Step-by-step explanation:

The probability of picking a chocolate-covered cherry is 0.

The probability that an a fell on the floor is 0.08

The probability that an a or a o would be picked is 0.36

The probability a girl would be picked is 1.

Probability is used to calculate the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability of picking a chocolate-covered cherry is zero because there is no chocolate-covered cherry in the bag.  

The probability that an a fell on the floor = number of a in the letter / total number of letters

= 1/13 = 0.08

The probability that an s or a o would be picked is = (number of s in the letter / total number of letters) +  (number of 0 in the letter / total number of letters)

= 4/11 + 0 = 4/11 = 0.36

The probability a girl would be picked is one since its an all-girls school.

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Answer:

ORANGE: 160

APPLE: 108°

GRAPE: 60

OTHER: 32

Step-by-step explanation:

THE SUM OF 40, 27, 15 AND 8 IS 90

90 GOES INTO 360 (THE ANGLES OF A CIRCLE) EXACTLY FOUR TIMES

TO GET EACH ANGLE OF THE PIE CHART YOU SIMPLY NEED TO TIMES EACH NUMBER BY FOUR!

Answer:

\(49xy + 56x = 7x(7y + 8)\)

Answer:

4t-s

Step-by-step explanation:

Answer:

if it's easy why dont you do it,that picture dont even take good

Find the price of 1 wing:

9.50 / 5 = 1.90 per wing

Divide total spent by price per wing:

26.60 / 1.90 = 14

Answer: 14

Answer:

14

Step-by-step explanation:

$9.50 / 5 = $1.90

$26.60 / $1.90 = 14

The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

a) Here the area of the parallelogram determined by d and e is given as 10. The area of the parallelogram is given as `|d×e|`.

We have,

d=(2,4)

and e=(4k,3k)

Then,

d×e= (2 * 3k) - (4 * 4k) = -10k

Area of parallelogram = |d×e|

= |-10k|

= 10

As we know, area of parallelogram can also be given as,

|d×e| = |d||e| sin θ

where, θ is the angle between the two vectors.

Then,10 = √(2^2 + 4^2) * √((4k)^2 + (3k)^2) sin θ

⇒ 10 = √20 √25k^2 sin θ

⇒ 10 = 10k sin θ

∴ k sin θ = 1

Therefore, sin θ = 1/k

Hence, the value of k is 1.

Part(b) The volume of the parallelepiped determined by vectors a, b and c is given as,

| a . (b × c)|

Here, a=(1,1,2),

b=(5,3,λ), and

c=(4,4,0)

Therefore,

b × c = [(3 × 0) - (λ × 4)]i + [(λ × 4) - (5 × 0)]j + [(5 × 4) - (3 × 4)]k

= -4i + 4λj + 8k

Now,| a . (b × c)|=| (1,1,2) .

(-4,4λ,8) |=| (-4 + 4λ + 16) |

=| 12 + 4λ |

Therefore, the volume of the parallelepiped is 12 + 4λ.

Part(c) The vector component of a + c orthogonal to c is given by [(a+c) - projc(a+c)].

Here, a=(1,1,2) and

c=(4,4,0).

Then, a + c = (1+4, 1+4, 2+0)

= (5, 5, 2)

Now, projecting (a+c) onto c, we get,

projc(a+c) = [(a+c).c / |c|^2] c

= [(5×4 + 5×4) / (4^2 + 4^2)] (4,4,0)

= (4,4,0.5)

Therefore, [(a+c) - projc(a+c)] = (5,5,2) - (4,4,0.5)

= (1,1,1.5)

Therefore, the vector component of a + c orthogonal to c is (1,1,1.5).

Conclusion: The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

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Answer:

\(\frac{1}{2}\) is a rational number

Step-by-step explanation:

Given

\(Real\ Number = \frac{1}{5}\)

Required

Determine which set of numbers it belongs to

Analyzing the options one after the other;

1. Whole numbers: 0, 1, 2, 3....

2. Natural numbers: 1, 2, 3, 4... 3.

3. Irrational numbers are numbers that can't be expressed as fractions

The option that answers this question is rational numbers because \(\frac{1}{2}\) can be expressed as decimal and fraction interchangeable.

Hence;

\(\frac{1}{2}\) is a rational number

The difference quotient of the function f(x) = x² - 8x + 5 is given by (f(x + h) - f(x)) / h, and we need to simplify it.

To find f(x + h), we substitute x + h for x in the expression for f(x):

f(x + h) = (x + h)² - 8(x + h) + 5

= x² + 2hx + h² - 8x - 8h + 5

Subtracting f(x) = x² - 8x + 5 from f(x + h), we get:

f(x + h) - f(x) = (x² + 2hx + h² - 8x - 8h + 5) - (x² - 8x + 5)

= 2hx + h² - 8h

Dividing this expression by h, we obtain the difference quotient:

(f(x + h) - f(x)) / h = (2hx + h² - 8h) / h

= 2x + h - 8

Therefore, the difference quotient of the function f(x) = x² - 8x + 5 is 2x + h - 8. This expression represents the average rate of change of the function over the interval [x, x + h]. As h approaches zero, the difference quotient approaches the instantaneous rate of change of the function at x, which is the derivative of the function at x. The difference quotient is a fundamental concept in calculus and is used to define the derivative of a function.

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Answer:

I think its 53

Step-by-step explanation:

It's a right angle

so its equal to 90 degrees

90-27-11= 53 aka x

1/3 glass of water in one hour.

Using simple unitary method

What is unitary method?

 This method allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

What do you mean by fractions?

The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. It displays the total number of identical objects in a collection or the total number of equal sections the whole is divided into.

Solution are given below:

4/5 of 10-ounce glass is 8 ounce of water.

=2 2/5

=12/5

=2.4

8 ounce of water in 2.4 hours.

8/2.4 ounce of water in 1 hour.

3.33 ounce of water in an hour.

1 glass consist of 10 ounce of water.

1/10 glass consist of 1 ounce of water.

3.33/10 glass consist of 3.33 ounce of water.

1/3 glass of water in one hour.

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The Perimeter of wall in inches is 4.724412 inches.

We have the Perimeter = 120 m

We know 1 m = 39.3701 inch

Then, the perimeter inches

= 39.3701 x 120

= 472.4412 inches  

and, 1 cm= 0.393701 inch

Then, perimeter

= 12 x 0.393701

= 4.724412 inches

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If p is a prime number and a is a positive integer, then pa has (a+1) distinct positive divisors.

A prime number is a positive integer greater than 1, which is divisible only by 1 and itself. Divisors are the numbers that evenly divide a given number.

For a prime number p raised to the power of a (p^a), the number of distinct positive divisors can be found using the following formula:

Number of divisors = (a + 1)

This is because each power of p from 0 to a can divide p^a without any remainder, giving us a total of a + 1 distinct divisors. These divisors are:

1, p, p^2, p^3, ..., p^(a-1), p^a

For example, if p = 2 (a prime number) and a = 3 (a positive integer), then the number of distinct positive divisors for 2^3 (which is 8) would be:

Number of divisors = (3 + 1) = 4

The divisors for 2^3 (8) are 1, 2, 4, and 8.

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Answer:

55.1

Step-by-step explanation:

solo se multiplica

1.90*29 =55.1

The number of Dimes are 28 and there is one nickel.

Two or more expressions with an Equal sign is called as Equation.

$1.90 in dimes and nickels.

Total of 29 dimes and nickels

We form equations by given data

0.1D+0.05N=1.9...(1)

D+N=29..(2)

D=29-N

Substitute value of D in equation 1.

0.1(29-N)+0.05N=1.9

2.9-0.1N=1.9

2.8N=1.9

Divide both sides by 2.8

N=0.678

Now substitute N value in 2.

D+0.678=29

substitute 0.678 from both sides

D=29-0.678

D=28.322=28

Hence, the number of Dimes are 28 and there is one nickel.

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Answer:

38

Step-by-step explanation:

2(\(a^{2}\)+ab) + 3 - ab

= \(2a^{2}\) + 2ab + 3 - ab

= \(2a^{2}\) + ab + 3

= 2x\(5^{2}\) + 5x(-3) + 3

= 50 - 15 + 3

= 38

Answer:

zero

Step-by-step explanation:

The product of any number and zero is always zero.

Answer:

496

Step-by-step explanation:

992/2 =496

It takes 5.9 minutes for the Ferris wheel to complete one revolution. It takes 5.9 minutes for the Ferris wheel to complete one revolution. “A Ferris wheel has a radius of 34 feet and completes two revolutions every 11.8 minutes.

How long does it take for the Ferris wheel to complete one revolution?”, we need to use the concept of time and angle taken by the Ferris wheel to complete one revolution.The Ferris wheel’s radius is 34 feet.

Thus, the diameter of the Ferris wheel is 2 × radius = 2 × 34 = 68 feet.Circumference of the Ferris wheel = 2 × π × r = 2 × π × 34 = 68π feetNow, we need to find out how much time it takes for the Ferris wheel to complete one revolution.

Time taken for two revolutions = 11.8 minutesThus, time taken for one revolution = (11.8/2) minutes = 5.9 minutes

So, it takes 5.9 minutes for the Ferris wheel to complete one revolution. It takes 5.9 minutes for the Ferris wheel to complete one revolution.

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The strawberries that are way more than 2 ounces will be 24 strawberries.

It should be noted that the information stated that 30 of the 54 strawberries she picked the way less than 2 ounces.

Therefore, the strawberries that are way more than 2 ounces will be the difference between the total number picked and 30.

This will be:

= 54 - 30

= 24

Therefore, the strawberries that are way more than 2 ounces will be 24 strawberries.

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Answer:

90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you.

Step-by-step explanation:

Answer: no, because it’s he total distance of 32 miles is repeated in the table

Step-by-step explanation:

I passed the test