the Angle opposite The OPP is​

Good luckvsvsvsbsbsjsjhsbsbsbsb

The equation is: G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph, we see that:

y-intercept = 15 gallons

Now, the slope is gotten from the formula:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (10 - 5)/(4 - 8)

Slope = -⁵/₄

Thus, equation is:

G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

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The parametric equations for the motion of the particle are:

x(t) = 10 cos(2πt/9)

y(t) = 10 sin(2πt/9)

Here, t represents time in seconds, and 2π/9 represents the angular speed of the particle, since it completes one revolution every 9 seconds. The radius of the circle is 10, which is used in the equations for the x and y coordinates of the particle's position at any given time t.

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7n² + 48n + 42

Combine like terms, -8n x -6n= 48n

                                  -6 x -7= 42

Answer:

-49n^3 -n²+92n+42

Step-by-step explanation:

(7n²-8n-6)(-6n-7)

-42n^3-49n²+48n²+56n+36n+42

-49n^3 -n²+92n+42

Answer:

x=-27/11

Step-by-step explanation:

This answer is x=-27/11

Answer:

O

Step-by-step explanation:

Answer:

.0024

Step-by-step explanation:

3 = 225 x 5k

3/255 = 5k

5k = 0.117

k=0.0024

x=2/3

6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10

Answer:

2x-1=y,2y+3=x

Step-by-step explanation:

no explanation

A minimum sample size of 121 individuals needs to be surveyed, ensuring a rounded-up value to estimate the proportion of non-graduates within the 25 to 30 age group with a 10% margin of error and 90% confidence.

To determine the sample size required to estimate the proportion of non-graduates within the 25 to 30 age group with a certain level of confidence and margin of error, we can use the formula:

n = (Z^2 * p * (1 - p)) / E^2

Where:

n is the required sample size

Z is the Z-score corresponding to the desired confidence level (90% confidence corresponds to a Z-score of approximately 1.645)

p is the estimated proportion of non-graduates (0.21 based on the information provided)

E is the desired margin of error (10% or 0.10)

Substituting the values into the formula:

n = (1.645^2 * 0.21 * (1 - 0.21)) / 0.10^2

n ≈ 120.41

Rounding up to the nearest integer, the required sample size is 121.

Therefore, you would need to survey at least 121 individuals in the 25 to 30 age group to estimate the proportion of non-graduates within 10% margin of error with 90% confidence.

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Answer:

A. y = -4x + 3

Step-by-step explanation:

Parallel lines have the same slope, but will have a different y-intercept.

In the equation y = -4x + 5, -4 is the slope.

This means a line that is parallel to this one will also have a slope of -4.

So, this means that A is the correct answer, because it has a slope of -4.

y = -4x + 3 denotes a line that is parallel to y = - 4x +5. Parallel lines are two lines in the same plane that are equal in length and never intersect.

Therefore,

Points of axis interception y = -4x + 5

-4x + 5 :  m = -4

Same as,

y = -4x + 3

Simplifying the above equation, then we get

-4x + 3 :  m = -4

Hence, y = -4x + 3 denotes a line that is parallel to y = - 4x +5.

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Answer: 7

Step-by-step explanation:

First order the numbers by least to greatest

2, 3, 5, 9, 12, 21

Then find the number inbetween

In this case it's a tie between 5 and 9.

Find the average of those two numbers

The average is 5+9/2 = 7

Median is 7

Answer: 6 3/7

Step-by-step explanation:

9/1 x 5/7

If we multiply the numerators and denominators, we get 45/7 or 6 3/7 as a mixed number.

Answer:

\(\frac{45}{7}\) or 6.4285

Step-by-step explanation:

First, multiply 9 and 5, which gives you 45.

9(5)=45

Then, divide 45 by 7.

45/7=6.4285

That gives  you  \(\frac{45}{7}\) or 6.4285

Hope this helps!

90 + x + 3x = 180

4x = 90

x = 22.5

Your answer: 22.5

Answer:

\( \frac{88}{7} units\)

Step-by-step explanation:

Circumference of semi-circle=

\(\pi \: r\)

\( \frac{22}{7} \times 4 \\ \frac{88}{7} \)

Step-by-step explanation:

-7 and -4? I guess here u go

Answer:

9

Step-by-step explanation:

 There is a simple formula that can be applied here, appropriately termed the distance formula. It is d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 ), where (x1,y1) and (x2,y2) are the two given points. It doesn't matter which point is which, it ends up being the same since both binomials are being squared. The formula is simply an application of the Pythagorean theorem. In coordinate space, you're constructing a right triangle using the line connecting the two points as the hypotenuse, with horizontal and vertical lines as the legs. Then it's simply c^2 = a^2 + b^2, and you can get the distance formula by square rooting both sides.

To find the surface area of a pyramid using nets with base side length of 5 units and height of 5 units, calculate the area of the base and the area of the triangular faces, then sum them up. Therefore, the surface area of the pyramid, using the given net, is approximately 68.32 square units.

To determine the surface area of a pyramid, we can use the concept of nets. A net is a two-dimensional representation of a three-dimensional shape that can be unfolded to reveal its faces. In the case of a pyramid, the net consists of a base shape and triangular faces that connect to the apex.

Given that the base side length is 5 units and the height is also 5 units, we first calculate the area of the base. Since the base is a square, the area is given by multiplying the length of one side by itself: 5 * 5 = 25 square units.

Next, we calculate the area of each triangular face. The formula for the area of a triangle is 1/2 * base * height. The base of each triangular face is the side length of the base, which is 5 units. The height can be found using the Pythagorean theorem, where one leg is half the base length and the other leg is the height of the pyramid. So the height is √(5^2 - \((5/2)^2) = √(25 - 6.25) = √18.75\) ≈ 4.33 units. Thus, the area of each triangular face is 1/2 * 5 * 4.33 = 10.83 square units.

Finally, we sum up the area of the base and the area of the triangular faces: 25 + (4 * 10.83) = 68.32 square units. Therefore, the surface area of the pyramid, using the given net, is approximately 68.32 square units.

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To find the surface area of a pyramid using nets with base side length of 5 units and height of 5 units, you can calculate the area of the base and the area of the triangular faces. Then, sum up these areas to determine the total surface area of the pyramid.

so hmmm tripling $380 we end up with $1140, now, since 7/8 is 0.875, that means that Layla's rate is 5.875, whilst Brandon's is 6.125.

\(~~~~~~ \stackrel{ \textit{\LARGE Layla}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1140\\ P=\textit{original amount deposited}\dotfill &\$380\\ r=rate\to 5.875\%\to \frac{5.875}{100}\dotfill &0.05875\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases}\)

\(1140 = 380\left(1+\frac{0.05875}{4}\right)^{4\cdot t} \implies \cfrac{1140}{380}=1.0146875^{4t} \\\\\\ 3=1.0146875^{4t}\implies \log(3)=\log(1.0146875^{4t}) \\\\\\ \log(3)=t\log(1.0146875^{4})\implies \cfrac{\log(3)}{\log(1.0146875^{4})}=t\implies \boxed{18.84\approx t} \\\\[-0.35em] ~\dotfill\)

\(~~~~~~ \stackrel{ \textit{\LARGE Brandon}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1140\\ P=\textit{original amount deposited}\dotfill &\$380\\ r=rate\to 6.125\%\to \frac{6.125}{100}\dotfill &0.06125\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years \end{cases}\)

\(1140 = 380\left(1+\frac{0.06125}{12}\right)^{12\cdot t} \implies \cfrac{1140}{380}=\left( \cfrac{9649}{9600} \right)^{12t}\implies 3=\left( \cfrac{9649}{9600} \right)^{12t} \\\\\\ \log(3)=\log\left[ \left( \cfrac{9649}{9600} \right)^{12t} \right]\implies \log(3)=t\log\left[ \left( \cfrac{9649}{9600} \right)^{12} \right]\)

\(\cfrac{\log(3)}{ ~~ \log\left[ \left( \frac{9649}{9600} \right)^{12} \right] ~~ }=t\implies \boxed{17.98\approx t} \\\\[-0.35em] ~\dotfill\\\\ 18.84~~ - ~~17.98 ~~ \approx ~~ \text{\LARGE 0.86}\)

Answer:

184.26

Step-by-step explanation:

28.275 + 60 + 96 = 184.26

Answer:

10 Km/h

Step-by-step explanation:

Let the speed of the container ship be y

The speed of the aircraft = y + 5

Next, we shall determine the time taken by the aircraft to travel 450 Km. This can be obtained as follow:

Speed of aircraft (Sₐ) = y + 5

Distance travelled (dₐ) = 450 Km

Time for aircraft (tₐ) =?

Speed = distance / time

Sₐ = dₐ / tₐ

y + 5 = 450 / tₐ

Cross multiply

(y + 5) × tₐ = 450

Divide both side by (y + 5)

tₐ = 450 / (y + 5)

Finally, we shall determine the speed of the carrier. This can be obtained as follow:

Speed of container ship (S꜀) = y

Distance travelled (d꜀) = 300 Km

Time for container ship (t꜀) = Time for aircraft (tₐ)

Time for aircraft (tₐ) = 450 / (y + 5)

t꜀ = tₐ

t꜀ = 450 / (y + 5)

Speed = distance / time

S꜀ = d꜀ / t꜀

y = 300 ÷ 450 / (y + 5)

y = 300 × (y + 5) / 450

y = (300y + 1500) / 450

Cross multiply

450y = 300y + 1500

Collect like terms

450y – 300y = 1500

150y = 1500

Divide both side by 150

y = 1500 / 150

y = 10 Km/h

Thus, the speed of the container ship is 10 Km/h.

a) The probability that the bank is empty is approximately 0.0026.

b) the average time the customer spends waiting to be called is approximately -0.25 c) hours the average number of customers in the bank is -1.5 d) the average number of customers waiting to be served is approximately 9.

To answer these questions, we can use the M/M/4 queuing model, where the arrival rate follows a Poisson distribution and the service time follows an exponential distribution. In this case, we have four bank tellers, so the system is an M/M/4 queuing model.

Given information:

Arrival rate (λ) = 12 customers per hour

Service rate (μ) = 1 customer every 15 minutes (or 4 customers per hour)

(a) To calculate the probability that the bank is empty, we need to find the probability of having zero customers in the system. In an M/M/4 queuing model, the probability of having zero customers is given by:

P = (1 - ρ) / (1 + 4ρ + 10ρ² + 20ρ³)

where ρ is the traffic intensity, calculated as ρ = λ / (4 * μ).

ρ = (12 customers/hour) / (4 customers/hour/teller) = 3

Substituting ρ = 3 into the formula, we have:

P = (1 - 3) / (1 + 4 * 3 + 10 * 3² + 20 * 3³) ≈ 0.0026

Therefore, the probability that the bank is empty is approximately 0.0026.

(b) The average time the customer spends waiting to be called is given by Little's Law, which states that the average number of customers in the system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In this case, we want to find W.

L = λ * W

W = L / λ

Since the average number of customers in the system (L) is given by L = ρ / (1 - ρ), we can substitute this into the equation to find W:

W = L / λ = (ρ / (1 - ρ)) / λ

W = (3 / (1 - 3)) / 12 ≈ -0.25

Therefore, the average time the customer spends waiting to be called is approximately -0.25 hours, which is not a meaningful result. It seems there might be an error in the given data.

(c) The average number of customers in the bank (L) can be calculated as:

L = ρ / (1 - ρ) = 3 / (1 - 3) = -1.5

Therefore, the average number of customers in the bank is -1.5, which is not a meaningful result. It further suggests an error in the given data.

(d) The average number of customers waiting to be served can be calculated as:

\(L_q\) = (ρ² / (1 - ρ)) * (4 - ρ)

Substituting ρ = 3, we have:

\(L_q\\\) = (3² / (1 - 3)) * (4 - 3) ≈ 9

Therefore, the average number of customers waiting to be served is approximately 9.

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Answer:

5

Step-by-step explanation:

Given:

77 + 20 = 97

450 + 20 = 470

Keep multiplying 97 with random numbers until it passes 470.

97 × 4 = 388

97 × 5 = 485

So, the skier will have to pay daily passes 5 times to be more expensive than the season pass.

Hope this helped.

Answer: 0.6 espero haberte ayuado

Step-by-step explanation:

Answer:

-4+12

12-4

Step-by-step explanation:

Expression 1:

-4 - (-12)=

-4+12=

8

Expression 2:

12-4=

8

Answer:

12-(-4)

Step-by-step explanation:

1. T(n) = Θ(n)

2. T(n) = Θ(n)

3. T(n) = Θ(n²)

4. T(n) = Θ(1)

The master theorem is an algorithmic approach for solving recurrence relations (both divide and conquer and recursive equations). Let us use the master theorem to read off the Θ order of the following recurrences:

(a) T(n) = 2T(n/2) + n²:

Using the Master theorem: a = 2, b = 2 and f(n) = n² so

logba = log2/ log2 = 1 = c(n²) = Θ(nlogba) = Θ(n)

Therefore T(n) = Θ(nlogba) = Θ(nlog₂2) = Θ(n)

(b) T(n) = 2T(n/2) + n:

Using the Master theorem: a = 2, b = 2 and f(n) = n so

logba = log2/ log2 = 1 = c(n) = Θ(nlogba) = Θ(n)

Therefore T(n) = Θ(nlogba) = Θ(nlog₂2) = Θ(n)

(c) T(n) = 4T(n/2) + n:

Using the Master theorem: a = 4, b = 2 and f(n) = n so

logba = log4/ log2 = 2 = c(n²) = Θ(n²)

Therefore T(n) = Θ(nclogba) = Θ(n²log₂4) = Θ(n²)

(d) T(n) = T(n/4) + 1:

Using the Master theorem: a = 1, b = 4 and f(n) = 1 so logba = log4/ log1 = undefined

Therefore T(n) = Θ(nclogba) = Θ(n⁰) = Θ(1)

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Answer:

Yes

Step-by-step explanation:

I'm guessing so tell me if I'm wrong :(

Answer:

X=2

Step-by-step explanation:

5x+15+6x+8+4x+7=60

combine like term

5x+6x+4x=15x

15+8+7=30

subtract 30 from both sides

15x+30=60

-30. -30

15x=30

divide 15 from 30

X=2

We have defined the criteria for SAS congruency of triangles.

What is SAS?

The SAS theorem states that "Triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle."

According to the SAS criteria for triangle similarity, two sides of one triangle are similar to two sides of another triangle if their included angles are congruent.

Hence, we have defined the criteria for SAS congruency of triangles.

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