Gabriella ran several laps around a 1/4-mile track. Then she ran 2 1/2 miles on a trail. In all, she ran 4 miles. Write and solve an equation to find l, the number of laps Gabriella ran.

Answer:

4370*10^2

437*10^3

43.7*10^4

The average is calculated by adding up all the data sets, then dividing that total by the total number of data points. She used 6 gallons of gas on her trip.

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

The two unit rates of (30 miles per gallon) and can be used to convert three hours to gallons of gas (60 miles per hour).

30 miles = 1 gallon of gas used

For (30 × 2) 60 miles = 2 gallons of gas used

2 gallons of gas she used per hour.

Susan goes 180 miles in 3 hours (60 miles per hour).

Therefore,

For 3 hrs = 3 × 2 = 6 gallons of gas used.

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Answer:

10.9899097

Step-by-step explanation:

Trigonometry.

Tan = opposite/adjacent

Adjacent = Opposite / Tan(20)

Answer:

Z_1 = 3
Z_2 = 2.5
Z_3 = 2.25

Step-by-step explanation:

To find the next three terms in the sequence defined by Z_0 = 4 and Z_n = (1/2) Z_(n-1) + 1, we can use the recursive formula to calculate each term.

First, we can calculate Z_1 by substituting n = 1 into the recursive formula:

Z_1 = (1/2) Z_0 + 1 = (1/2) (4) + 1 = 3

This means that the second term in the sequence is 3.

Next, we can calculate Z_2 by substituting n = 2 into the recursive formula:

Z_2 = (1/2) Z_1 + 1 = (1/2) (3) + 1 = 1.5 + 1 = 2.5

This means that the third term in the sequence is 2.5.

Finally, we can calculate Z_3 by substituting n = 3 into the recursive formula:

Z_3 = (1/2) Z_2 + 1 = (1/2) (2.5) + 1 = 1.25 + 1 = 2.25

This means that the fourth term in the sequence is 2.25.

Therefore, the next three terms in the sequence are 3, 2.5, and 2.25.

Each term in the sequence is calculated by taking half of the previous term and adding 1. The sequence starts at 4, so the second term is calculated by taking half of 4, which is 2, and adding 1, which gives 3. The third term is calculated by taking half of 3, which is 1.5, and adding 1, which gives 2.5. The fourth term is calculated by taking half of 2.5, which is 1.25, and adding 1, which gives 2.25. This pattern continues for each subsequent term in the sequence.

Answer:

Fair well i hope you lived a good life

Step-by-step explanation:

Answer:

2.2

Step-by-step explanation:

11*.20 = 2.2

So that is 20% on 11.

Hope this helps!

Therefore, the probability that the toll collector will have to wait longer than 26.30 minutes before collecting the eighth toll is approximately 0.038.

Since the arrival of cars at a tollbooth follows a Poisson process with a rate of 5 cars every 10 minutes, the time between arrivals of cars follows an exponential distribution with a mean of 2 minutes (10 minutes / 5 cars). Let X be the time between arrivals of cars. Then, X ~ Exp(1/2) since the mean of an exponential distribution is equal to the reciprocal of the rate.

To find the probability that the toll collector will have to wait longer than 26.30 minutes before collecting the eighth toll, we need to find the probability that the sum of the waiting times for the first seven cars is less than 26.30 minutes and the waiting time for the eighth car is greater than the remaining time.

Let Y be the waiting time for the eighth car. Then, Y ~ Exp(1/2) since the waiting time for each car is independent and identically distributed. Therefore, the probability that the toll collector will have to wait longer than 26.30 minutes before collecting the eighth toll can be calculated as follows:

P(Y > 26.30 - T), where T is the sum of waiting times for the first seven cars.

Since the waiting times for each car are independent, the sum of the waiting times for the first seven cars follows a gamma distribution with parameters k = 7 and θ = 1/2. Therefore, we have:

T ~ Gamma(7, 1/2)

Now, we can calculate the desired probability as follows:

\(P(Y > 26.30 - T) = ∫∫\int\limits^a_b { (e^(-t/2) * (1/2)^{7})/6! } \, dx\)

= 0.038

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The closing cost for Barry and Ella Ellerbee's mortgage agreement with Kenmore Savings and Loan Association is $2,811.25.

The closing cost, which is a fee for closing an estate agreement, can be computed as the product of the closing cost rate and the mortgage loan.

The mortgage loan is the difference between the cost of the house and the down payment.

Down payment represents an advance deposit to assure the lender of the borrower's willingness and capacity to enter into a mortgage agreement.

The cost of the house = $96,500

Lending rate = 12.25%

Mortgage period = 25 ears

Down payment = $10,000

Closing cost = 3.25%

Mortgage loan = $86,500 - ($96,500 - $10,000)

Closing cost = $2,811.25 ($86,500 x 3.25%)

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Answer:

a = 9 , b = 5 , c = 25

Step-by-step explanation:

using the Cosine rule in the triangle

a² = b² + c² - 2bc cosA

where a is the side opposite ∠ A and b, c the sides adjacent to ∠ A

here

a = y , b = x + 5 , c = 3x and A = Θ , then

y² = (x + 5)² + (3x)² - [ 2(x + 5) × 3x × cosΘ ]

y² = x² + 10x + 25 + 9x² - [ 6x(x + 5) × \(\frac{1}{6}\) ]

y² = 10x² + 10x + 25 - x(x + 5)

y² = 10x² + 10x + 25 - x² - 5x

y² = 9x² + 5x + 25 ← in the form y² = ax² + bx + c

with a = 9 , b = 5 , c = 25

Question 1The input-output equation for the output y = x2 can be determined by taking Laplace Transform of the given differential equations: mx₁ + ₁x₁ + (K₁ + K₂)X₁ - K₂X₂ = fa(t)                            

(1) b₂x₂ + (K₂ + K3)x₂ - K₂X1 = 0                                                      

.(2) Taking Laplace Transform on both sides, we have;LHS of (1)

=> [mx₁ + ₁x₁ + (K₁ + K₂)X₁ - K₂X₂]

⇔ mX₁p + X₁

⇔ [m + p]X₁and RHS of (1)

=> [fa(t)]

⇔ F(p)Similarly,LHS of (2)

=> [b₂x₂ + (K₂ + K3)x₂ - K₂X1]

⇔ b₂X₂p + X₂

⇔ [b₂p + K₂]X₂RHS of (2)

=> [0] ⇔ 0

Hence, we have;[m + p]X₁ + (K₁ + K₂)X₁ - K₂X₂

= F(p)    

(3)[b₂p + K₂]X₂ = [m + p]X₁      

(4)Now, Solving (4) for X₂, we have;

X₂ = [m + p]X₁/[b₂p + K₂]     .(

5)Multiplying (5) by p gives;

pX₂ = [m + p]pX₁/[b₂p + K₂]    

(6)Substituting (6) into (3), we have;

[m + p]X₁ + (K₁ + K₂)X₁ - [m + p]pX₁/[b₂p + K₂] =

F(p)Now, Solving for X₁, we have; X₁

= F(p)[b₂p + K₂]/[D], where D

= m + p + K₁[b₂p + K₂] - (m + p)²

Hence, the Input-output equation for the output y

=x2 is given by;Y(p) = X₂(p) = [m + p]X₁(p)/[b₂p + K₂]    

(7)Substituting X₁(p), we have;Y(p)

= [F(p)[m + p][b₂p + K₂]]/[D],

where D

= m + p + K₁[b₂p + K₂] - (m + p)²

The block diagram for the dynamic system described by the above equations can be constructed using the equations as follows;\( \begin{cases} mx_{1} + \dot{x}_{1} + (K_{1}+K_{2})x_{1} - K_{2}x_{2}

= f_{a}(t) \\  b_{2}x_{2} + (K_{2}+K_{3})x_{2} - K_{2}x_{1}

= 0 \end{cases}\)

Taking Laplace Transform of both equations gives:

\( \begin{cases} (ms + s^{2} + K_{1}+K_{2})X_{1} - K_{2}X_{2}

= F_{a}(s) \\  b_{2}X_{2} + (K_{2}+K_{3})X_{2} - K_{2}X_{1}

= 0 \end{cases}\)

Rearranging and Solving (2) for X2, we have;X2(s)

= [ms + s² + K1 + K2]/[K2 + b2s + K3] X1(s)        ..............

(8)Substituting (8) into (1), we have;X1(s)

= [1/(ms + s² + K1 + K2)] F(p)[b2s + K2]/[K2 + b2s + K3].

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Answer:

5+6=11+1=12

Step-by-step explanation:

what is 12 halves? 6

Answer: AAS

Step-by-step explanation:

Lets call the intersection point between AC and DE F.

I think he meant the two triangles AFE and DFC.

We know angle A is congruent to angle D.

We also know AE is congruent to DC.

There is also a hidden piece of evidence which is AFE is congruent to DFC due to vertical angles.

We know two angles and 1 side, so we can use AAS to figure out that the two smaller triangles are congruent.

Answer:

31 and 37

Step-by-step explanation:

Those are the only two numbers

Answer:

The two numbers between 30 and 40 which have only 2 factors are -

31 and 37

Hope it helps you.

Answer:

12

Step-by-step explanation:

(5+d)-(d-7)

5--7 = 5+7 = 12

To prove this:

d = 10

e = 5+10 =15

f = 10-7 = 3

15 - 3 =12

Answer:

\(.12 \times 360 \: degrees = 43.2 \: degrees\)

Answer:

Orange juice that is 3 dollars per 1 jug

Step-by-step explanation:

A unit rate is per 1 of an item

The only 1 that is per 1 of an item is

Orange juice that is 3 dollars per 1 jug

Answer:

❍ The cost of orange juice is $ 3 per 1 jug.

Step-by-step explanation:

So, The cost of orange juice is $ 3 per 1 jug is represent the unit rate.

Answer: 68

Step-by-step explanation:

Answer:

14  + 9 +10

Step-by-step explanation:

The y-intercept of the straight line crosses the x-axis at (3,0) and the y-axis at (0,2) is 2.

The point of the line is the x-axis at (3,0) and the y-axis at (0,2)

Using two-point line equation

\((y_{2} - y) = m(x_{2} - x)\)

m = slope = change in y / change in x

m = 2-0/0-3

m = -2/3

(2 - y) = -2/3 (0-x)

3(2-y) = -2(-x)

6 - 3y = 2x

-3y = 2x - 6

y = -2/3 x + 2

On comparing equation with y = mx + c

c in y intercept we get c = 2

Hence y - intercept = 2

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Answer:

-18

Step-by-step explanation:

9/4 x -8/1

-72/4

-18

Answer:

k = -7

Step-by-step explanation:

Find the difference of the y-values of both vertexes:

f(x): y = 1

g(x): y = -6

g(x) - f(x)

-6 - 1 = -7

Answer:

your answer would be 339

Step-by-step explanation:

i used a circle calculator

you would multiply 2.25 and 24

which gives you 54

and you wanna find the circumference i dont knowhow to do that but it would be 339

The value of x in the given quadratic equation is determined as -7 ± 8i.

The solutiion to the linear equation is determined as follows;

x² + 14x + 17 = -96

x² + 14x + 17 + 96 = 0

x² + 14x + 113 = 0

solve the equation using formula method;

a = 1, b = 14, c = 113

\(x = \frac{-b \ \ \pm\sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{- 14\ \ \pm\sqrt{(14)^2 - 4(1\times 113)} }{2(1)} \\\\x = \frac{- 14\ \ \pm\sqrt{-256} }{2}\\\\x = \frac{- 14\ \ \pm\sqrt{256} \times \sqrt{-1} }{2}\\\\x = \frac{-14 \ \ \pm 16 \times i}{2} \\\\x = -7 \pm 8i\)

Thus, the value of x in the given quadratic equation is determined as -7 ± 8i.

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Answer:

-7 ± 8i.

Step-by-step explanation:

I took the test

The yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons, if the =bond is currently trading for a price of $884, is 6.23%. Thus, option a and option b is correct

Yield to maturity (YTM) is the anticipated overall return on a bond if it is held until maturity, considering all interest payments. To calculate YTM, you need to know the bond's price, coupon rate, face value, and the number of years until maturity.

The formula for calculating YTM is as follows:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

Where:

C = Interest payment

F = Face value

P = Market price

n = Number of coupon payments

Given that the bond has a coupon rate of 5.2%, a face value of $1000, a maturity of ten years, semi-annual coupon payments, and is currently trading at a price of $884, we can calculate the yield to maturity.

First, let's calculate the semi-annual coupon payment:

Semi-annual coupon rate = 5.2% / 2 = 2.6%

Face value = $1000

Market price = $884

Number of years remaining until maturity = 10 years

Number of semi-annual coupon payments = 2 x 10 = 20

Semi-annual coupon payment = Semi-annual coupon rate x Face value

Semi-annual coupon payment = 2.6% x $1000 = $26

Now, we can calculate the yield to maturity using the formula:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

YTM = (2 x $26 + ($1000-$884)/20) / (($1000+$884)/2) x 100

YTM = 6.23%

Therefore, If a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons is now selling at $884, the yield to maturity is 6.23%.

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Rounding this to the nearest hundredth, the area of the sector is approximately 28.88 f\(t^2\).

To find the area of a sector, we can use the formula:

Area = (θ/360) × π × \(r^2\)

where θ is the central angle in degrees, π is approximately 3.14, and r is the radius.

Given a central angle of 131° and a radius of 7.2 ft, we can plug in these values into the formula to find the area:

Area = (131/360) × 3.14 × (7.2\()^2\)

Calculating this expression:

Area = (0.3639) × 3.14 × (7.2\()^2\)

Area ≈ 28.879 f\(t^2\)

Rounding this to the nearest hundredth, the area of the sector is approximately 28.88 f\(t^2\).

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Answer:

B

Step-by-step explanation:

The process of planning and controlling how much time to spend on specific activities.

Time management is the process of planning and controlling how much time to spend on specific activities in order to use your time productively and efficiently.

It involves setting goals, prioritizing tasks, creating schedules and to-do lists, and monitoring progress to ensure that time is used effectively.

Effective time management can help individuals to complete tasks and achieve their goals in a timely manner, reduce stress, and increase productivity.

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Answer:

$5,671.84

Step-by-step explanation:

To find the third side, we can use the law of cosines:

c^2 = a^2 + b^2 - 2ab*cos(theta)

c^2 = 157^2 + 157^2 - 2*157*157*cos(65)

c^2 = 28463.7649

c = 168.71 feet

The perimeter of the playground is:

P = 157 + 157 + 168.71 = 482.71 feet

If each foot costs $11.75, the final cost is:

Cost = 482.71 * 11.75 = $5,671.84

Answer:

Step-by-step explanation:

The standard form of this exponential function is

\(y=a(b)^x\) where a is the initial value and b is the growth rate. Our initial value is 490 and our growth rate is .2 so the equation is

\(y=490(.2)^x\)