Irving lives in Appletown, and plans to drive along Highway 42, a straight highway that leads to Bananatown, located 143 miles east and 45 miles north. Carol lives in Coconutville, located 98 miles east and 32 miles south of Appletown. Highway 86 runs directly north from Coconutville, and junctions with Highway 42 before heading further north to Durianville. Carol and Irving are planning to meet up at park-and-ride at the junction of the highways and carpool to Bananatown. Irving leaves Appletown at 8am, driving his usual 45 miles per hour. If Carol leaves Coconutville at 9am, how fast will she need to drive to arrive at the park-and-ride the same time as Irving?

Answer: B. 1 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Percentages are a powerful way to compare samples with different numbers of observations. By standardising measures using a scale of 0 to 100, samples can be compared quickly and easily. Any graph of the data, however, must include the full range of 0 to 100 to ensure that false impressions are not created.

A function representing the line that includes the points (3,3) and (-6,15) is 3y=-4x+21.

The given coordinate points are (3,3) and (-6,15).

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Now, slope=(y2-y1)/(x2-x1)

= (15-3)/(-6-3)

= 12/(-9)

= -4/3

Substitute m=-4/3 and (x, y)=(3, 3) in y=mx+c, we get

3=-4/3 (3) +c

c=7

Put, m=-4/3 and c=7 in y=mx+c, we get

y=-4/3 x+7

3y=-4x+21

Therefore, a function representing the line that includes the points (3,3) and (-6,15) is 3y=-4x+21.

To learn more about the slope intercept form visit:

brainly.com/question/9682526.

#SPJ5

P(8, 3 < X < 9) = 0.5. So, option (D) is correct.

A uniformly distributed continuous random variable is defined by the density function f(x) = 0 on the interval [8, 10]. So, we have to find P(8, 3 < X < 9).

We know that a uniformly distributed continuous random variable is defined as

f(x) = 1 / (b - a) for a ≤ x ≤ b

Where,b - a is the interval on which the distribution is defined.

P(a ≤ X ≤ b) = ∫f(x) dx over a to b

Now, as given, f(x) = 0 on [8,10].

Therefore, we can say, P(8 ≤ X ≤ 10) = ∫ f(x) dx over 8 to 10= ∫0 dx over 8 to 10= 0

Thus, P(8, 3 < X < 9) = P(X ≤ 9) - P(X ≤ 3)P(3 < X < 9) = 0 - 0 = 0

Hence, the correct answer is 0.5. Thus, we have P(8, 3 < X < 9) = 0.5. So, option (D) is correct.

Know more about random variable here,

https://brainly.com/question/30789758

#SPJ11

Answer: 2

Step-by-step explanation:

Domain of the function is \(0\leq b\leq 10\) and range of the function is \(0\leq W\leq 120\).

The range of values that we are permitted to enter into our function is known as the domain of a function.

A function's range is the collection of values it can take as input.

Each birdhouse uses 12 square feet of wood. Owen has enough to build 10 birdhouses, so he has 120 square feet of wood.

The function has an input of the number of birdhouses, b, and W as an output of the amount of wood needed. b is domain, and W is the range. The domain is 0 to 10 and range is 0 to 120.

Therefore, the domain of the function is  \(0\leq b\leq 10\) and the range of the function is \(0\leq W\leq 120\).

To learn more about domain and range of a function from the below link

https://brainly.com/question/1942755

#SPJ4

Answer:

Step-by-step explanation:

1593/13

122.538

answer: 122.5

The IRA (individual retirement account) of a 22-year-old college student, who deposits $55 into the account each month, will have a total balance at retirement. To calculate this, we need to consider the time period, the monthly deposit, and the annual percentage rate (APR).

The student plans on retiring at age 65, which means the IRA will have 65 - 22 = 43 years to grow. Since the student deposits $55 each month, we can calculate the total number of deposits over the 43-year period: 43 years * 12 months/year = 516 deposits.

To calculate the total balance at retirement, we need to consider the growth of the account due to the APR. The annual growth rate is 6%, which can be expressed as 0.06 in decimal form. To calculate the monthly growth rate, we divide the annual growth rate by 12: 0.06/12 = 0.005.

Using the formula for the future value of an ordinary annuity, we can calculate the total balance at retirement:
FV = PMT * [(1 + r)^n - 1] / r

Where:
FV = future value (total balance at retirement)
PMT = monthly deposit ($55)
r = monthly interest rate (0.005)
n = number of deposits (516)

Plugging in these values into the formula:
FV = 55 * [(1 + 0.005)^516 - 1] / 0.005

Calculating this equation, the IRA will contain $287,740.73 at retirement.

To know more about percentage , visit ;

https://brainly.in/question/10002322

#SPJ11

Answer:

x = 13.08 or 0.917

Step-by-step explanation:

\(x^{2} -5x=9x-12\)

First, subtract 9x by both sides.

\(x^{2} -5x-9x=-12\\x^{2} -14x=-12\)

And now we can use completing square method to solve for x.

\(x^{2} -14x=-12\)

Add (14/2)² to both sides of the equation.

\(x^{2} -14x+(14/2)^{2} =-12+(14/2)^{2} \\\\x^{2} -14x+49=-12+49\\\\x^{2} -14x+49=37\)

Factor the left side of the equation into a perfect square.

\((x-7)^{2} =37\)

Square root both sides of the equation and solve for x.

\(x-7=\±\sqrt{37}\)

Add 7 to both sides.

\(x = \±\sqrt{37} +7\)

Therefore,

x = √37 + 7

x = 13.08

or

x = -√37 + 7

x = 0.917

The perimeter and area of the original are 20 ft and 23.5 square ft and the enlarged figure are50 ft and 146.875 square ft.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The figure is the combination of a triangle and a square.

The area of the original (A₀) figure will be

\(\rm A_o = \dfrac{1}{2} \times 3 \times 5 + 4 \times 4\\\\A_o = 23.5 \ ft^2\)

The perimeter of the original figure (P₀) will be

\(\rm P_o = 3 + 5 + 4 + 4 + 4\\\\P_o = 20 \ ft\)

The scale factor is 2.5.

Then the dimension of the triangle will be

h = 2.5 × 3 = 7.5 ft

b = 2.5 × 5 = 12.5 ft

Then the dimension of the square will be

a = 2.5 × 4

a = 10 ft

The area of the new figure will be

\(\rm A = \dfrac{1}{2} \times 7.5\times 12.5 + 10*10\\\\ A = 146.875 \ ft^2\)

The perimeter of the new figure will be

\(\rm P= 7.5 + 12.5 + 10+ 10+ 10\\\\P = 50 \ ft\)

More about the geometry link is given below.

https://brainly.com/question/7558603

#SPJ1

Answer:

To find the perimeter of an enlarged figure, you can multiply the original figure’s perimeter by the scale factor. You could also multiply each dimension of the original figure by the scale factor to find the dimensions of the enlarged figure, and then add to find the perimeter.

Answer:

C - 1 / sin^2x

Step-by-step explanation:

as csc x = 1 / sin x

so, csc^2 x = 1 / sin^ 2x

Let the given sides be,

x=7

y=11

z=6

To find:

Using the formula,

On substitution we get,

Hence, the ange of X is,

Next, we need to find the angle of y:

Using the formula,

On substitution we get,

Hence, the ange of Y is,

Next, we need to find the angle of Z:

Using the formula,

On substitution we get,

Hence, the ange of Z is,

Answer:

the answer is c you welcome

Solving a system of equations, we can see that the rational number is 7/15.

Let's define the variables:

x = numerator.

y = denominator.

First, we know that the denominator is greater than the numerator by 8, so:

y = x+ 8.

Then we also can write:

(x + 17)/(y + 1) = 3/2

So we have a system of equations, we can rewrite the second equation to get:

(x + 17) = (3/2)*(y + 1)

x + 17 = (3/2)*y + 3/2

Now we can replace the first equation here, we will get:

x + 17 = (3/2)*(x + 8) + 3/2

x + 17 = (3/2)*x + 12 + 3/2

17 - 12 - 3/2 = (3/2)*x - x

5 - 3/2 = (1/2)*x

2*(5 - 3/2) = x

10 - 3 = x

7 = x

then the denominator is:

y = x + 8 = 7 + 8 = 15

The rational number is 7/15.

Learn more about systems of equations at:

https://brainly.com/question/13729904

#SPJ1

The formula would you use to calculate the floor space of Firm 3's structure is πr²h.

It should be noted that the formula that can be used on this scenario will be:

= πr²h

where,

h = 60

r = 70/2 = 35

The volume will be:

= πr²h

= 3.14 × 35² × 60

= 230790 feet ³

Learn more about volume on:

brainly.com/question/1972490

#SPJ1

There are two local minima which are: x = sqrt(12/5), x = -sqrt(12/5)

To find the x-coordinates of all local minima using the second derivative test;

1. Find the first derivative of f(x): f'(x)
2. Set f'(x) to 0 and solve for x to find critical points
3. Find the second derivative of f(x): f''(x)
4. Evaluate f''(x) at the critical points
5. If f''(x) > 0 at a critical point, it is a local minimum

Find the first derivative of f(x) = x^5 - 4x³ + 10:
f'(x) = 5x^4 - 12x²

Set f'(x) to 0 and solve for x:
0 = 5x^4 - 12x²
x² (5x² - 12) = 0

Solutions: x = 0, x = sqrt(12/5), x = -sqrt(12/5)

Find the second derivative of f(x):
f''(x) = 20x³ - 24x

Evaluate f''(x) at the critical points:
f''(0) = 0
f''(sqrt(12/5)) = 20(sqrt(12/5))³ - 24(sqrt(12/5))
f''(-sqrt(12/5)) = -20(sqrt(12/5))³ - 24(-sqrt(12/5))

Determine if the critical points are local minima:
f''(0) = 0, inconclusive
f''(sqrt(12/5)) > 0, local minimum
f''(-sqrt(12/5)) > 0, local minimum

So, there are two local minima: x = sqrt(12/5), x = -sqrt(12/5)

More on local minima: https://brainly.com/question/29428785

#SPJ11

A small change in x can change the conclusion of our test.

Given :

how would your conclusion change if your sample mean had been 1.355 mg/l.

t - test :

A t-test is a statistical test that compares the means of two samples. It is used in hypothesis testing, with a null hypothesis that the difference in group means is zero and an alternate hypothesis that the difference in group means is different from zero.

if x = 1.355

t = 1.355 - 1.3 / 0.18 / \(\sqrt{30}\)

= 0.055 / 0.18 / \(\sqrt{30}\)

= 0.055 * \(\sqrt{30}\) / 0.18

= 1.67

df = n - 1

= 30 - 1

= 29

P - value from t table :

p = 0.525

fail to reject \(H_0\)

Learn more about the sample mean here:

https://brainly.com/question/14127076

#SPJ4

Full question :

The Environmental Protection Agency has determined that safe drinking water should contain no more than 1.3 mg/liter of copper. You are testing water from a new source, and take 30 water samples. The mean copper content in your samples is 1.36 mg/l and the standard deviation is 0.18 mg/l. There do not appear to be any outliers in your data .

how would your conclusion change if your sample mean had been 1.355 mg/l? what point does this make about statistical significance?

Answer:

D

Step-by-step explanation:

In picture

Brainliest please ~

Answer:

The answer is most likely the last option.

Step-by-step explanation:

While the 2 triangles have different orientations, the two triangles are similar to one another. From my perspective, the scale would most likely be:

\( \frac{ab}{de} = \frac{bc}{ef} = \frac{ca}{fd} \)

Note that the fractions can be flipped the other way around too.

\( \frac{de}{ab} = \frac{ef}{bc} = \frac{fd}{ca} \)

Now, I can add in the values into the equation

This will give the answer

\( \frac{15}{22.5} = \frac{18.75}{bc} = \frac{fd}{ca} \)

We are only looking at the first 2 fractions which were given, and the final option is the answer.

Answer:

B - yes

Step-by-step explanation:

If (n - 9) is a factor then when evaluated at n = 9, if the result is zero then it is a factor of the polynomial, that is

9³ + 9² - 84(9) - 54

= 729 + 81 - 756 - 54

= 0

Since the result is zero then (n - 9) is a factor of the polynomial

Answer:

61.92°

Step-by-step explanation:

Sine Inverse of (75/85)

=61.92°

equation A

we have that

Its a vertical line

x=-4

equation B

Its a vertical line

x=4

equation C

Its a horizontal line

y=4

equation D

Its a horizontal line

y=-2

equation E

we need tow points to calculate the slope

we have the points (-4,4) and (4,-2)

the slope is equal to

m=(-2-4)/(4+4)

m=-6/8

m=-3/4

Find the equation of the line in slope intercept form

y=mx+b

we have

m=-3/4

point (4,-2)

substitute

-2=(-3/4)*(4)+b

solve for b

-2=-3+b

b=1

the equation is

y=(-3/4)x+1

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Given, Height of the cliff = 20 m Distance of the car from the foot of the cliff = 10 m.

The time taken by the car to fall from the cliff can be found using the formula:

\(`h = (1/2) g t^2`\)

Where h is the height of the cliff, g is the acceleration due to gravity and t is the time taken by the car to fall from the cliff.

Substituting the given values,`20 = (1/2) × 9.8 × t^2`

Solving for t, `t = sqrt(20/4.9)` = 2.02 s

Let the initial velocity of the car be V0 and the time taken for the car to come to rest after applying brakes be t1.

Distance covered by the car before coming to rest can be found using the formula: `\(s = V0t1 + (1/2) (-5) t1^2\)`

Where s is the distance covered by the car before coming to rest.

Simplifying the above equation,\(`2.5 = V0 t1 - (5/2) t1^2`\)

Substituting the given values,`5 = V0 - 5 t1`

Solving the above two equations,\(`V0 = 32.5/2 t1`\)

Simplifying the above equation,`V0 = 16.25 t1`

Substituting the value o\(f t1,`V0 = 16.25 × 2` = 32.5 m/s\)

Therefore, the speed of the car before the start of braking is 32.5 m/s.

To know more about  Height  visit :

https://brainly.com/question/29131380

#SPJ11

The goals does the team score in total in the first 9 matches of the competition is 36 and  their mean number of goals after 10 matches is 3.9.  

Given that the mean number of goals a netball team scores per match in the first 9 matches of a competition is 4.

Thus the average of the goals in 9 matches is 4.

Total number of goals is = 9*4 = 36 goals .

Given that the team scores 3 goals in their next match .

Thus the total number of goals scored in 10 matches is 36 + 3 = 39 goals,

Required mean = Total goals / 10 matches .

∴ Required mean = 39/10 = 3.9 .

Therefore, the goals does the team score in total in the first 9 matches of the competition is 36 and  their mean number of goals after 10 matches is 3.9.  

To learn more about mean, refer -

https://brainly.com/question/1635504

#SPJ9

Answer:

8. slope: = 1/2

9. equation: y=1/2x

Answer:

angle CDE is 10 degree

Step-by-step explanation:

As angle C is 90

Angle E is equal to angle B which is 80 (180-100)

so 90+80+X=180

X=180-170

X=10

The bilateral and unilateral Laplace transforms for the signal x(t) = e^(-t)δ(t)e^(-2tu(t)) are as follows:

Bilateral Laplace Transform: X(s) = 1/(s + 1)(s + 2)

Unilateral Laplace Transform: X(s) = 1/(s + 1), Re(s) > -1

To find the bilateral and unilateral Laplace transforms of the given signal, we apply the definitions and properties of Laplace transforms.

The bilateral Laplace transform is used when the signal x(t) is defined for both positive and negative values of t. For the given signal, x(t) = e^(-t)δ(t)e^(-2tu(t)), where e^(-t) represents the decay factor, δ(t) is the Dirac delta function, and e^(-2tu(t)) represents the unit step function.

Using the properties of Laplace transforms, we can separate the terms and find the individual transforms. The Laplace transform of e^(-t)δ(t) is 1/(s + 1), and the Laplace transform of e^(-2tu(t)) is 1/(s + 2).

Thus, the bilateral Laplace transform of x(t) is given by:

X(s) = 1/(s + 1)(s + 2)

On the other hand, the unilateral Laplace transform is used when the signal x(t) is defined only for t ≥ 0. In this case, we consider the Laplace transform of e^(-t)δ(t)e^(-2tu(t)) with the restriction Re(s) > -1.

Therefore, the unilateral Laplace transform of x(t) is:

X(s) = 1/(s + 1), Re(s) > -1

The bilateral Laplace transform of x(t) = e^(-t)δ(t)e^(-2tu(t)) is X(s)

= 1/(s + 1)(s + 2), while the unilateral Laplace transform is X(s) = 1/(s + 1), Re(s) > -1. These transforms allow us to represent the signal x(t) in the frequency domain and facilitate analysis and calculations involving the signal in the Laplace domain.

To know more about Laplace ,visit:

https://brainly.com/question/29583725

#SPJ11

The sum of forecast errors is also known as total forecast error. Therefore, the correct answer is option A, which is "2."

The absolute error of the given data is calculated by subtracting the actual value from the forecasted value, followed by the absolute value.

The errors are then summed up to get the mean absolute deviation. The value used for ||18−20|| in the calculation of MAD and summing up the forecast errors is 2.

Therefore, the correct answer is option A, which is "2."Formula for calculating MAD:MAD = Σ ( | A_i - F_i | ) / n

Where: MAD is the mean absolute deviation|A_i - F_i| represents the absolute error between the actual value (A) and the forecasted value (F)n is the total number of observations, Sum of forecast errors:Σ ( A_i - F_i )Where: A_i is the actual valueF_i is the forecasted value

The sum of forecast errors is also known as total forecast error.

Learn more about absolute deviation here:

https://brainly.com/question/32547820

#SPJ11