A bike path is 3 mi long they are distant markers every 1/4 mi to the end of the path which number line is correctly models this solution and the total number of the distant markers?

Let's first write the vector equation of the two lines r1​ and r2​. r1​(t)=⟨3t+5,−3t−5,2t−2⟩r2​(t)=⟨11−6t,6t−11,2−4t⟩

​The direction vector for r1​ will be (3,-3,2) and the direction vector for r2​ will be (-6,6,-4).If the dot product of two direction vectors is zero, then the lines are orthogonal or perpendicular. But here, the dot product of the direction vectors is -18 which is not equal to 0.

Therefore, the lines are not perpendicular or orthogonal. If the lines are not perpendicular, then we can tell if the lines are distinct parallel lines or skew lines by comparing their direction vectors. Here, we see that the direction vectors are not multiples of each other.So, the lines are skew lines. Choice: The lines are skew.

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Answer:

$1281.39

Step-by-step explanation:

use formula given

Answer:

I’m good at math but not that good

Step-by-step explanation:

If a red ball is drawn from two urns containing colored balls , then the probability that it came from the first urn is  0.625 or 62.5%   .

Let A = the event that the first urn is chosen, and

B is = the event that a red ball is drawn.

We have to find P(A|B), which means , the probability that the first urn was chosen given that a red ball was drawn.

So , By Bayes' theorem:

we have , P(A|B) = P(B|A) × P(A) / P(B)  ;

Since each urn has an equal probability of being chosen, we have P(A) = P(B) = 1/2 ; and

the probability of drawing a red ball is the same regardless of which urn was chosen.

We need to find P(B|A), the probability of drawing a red ball from the first urn is 50/100 = 0.5   ;

To find P(B), the overall probability of drawing a red ball, we can use the law of total probability:

that is ; P(B) = P(B|A) × P(A) + P(B|A') × P(A')  ;

where A' = event that the second urn was chosen.

Now , we find P(B|A'), which is the probability of drawing a red ball from the second urn is = 30/100 = 0.3    ;

We know that P(A') = 1/2 = 0.5 , because there are only 2 urns.

So , we have : P(A|B) = P(B|A)×P(A) / P(B)  ;

= (0.5×0.5) / (0.5×0.5 + 0.3×0.5)

= 5/8

= 0.625

Therefore, the probability that the red ball came from the first urn is 0.625 or 62.5%   .

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p-value < 0.0001, reject null hypothesis. Proportion of supporters for issue 1 is significantly different from the majority.

To find the p-an incentive for this present circumstance, we really want to direct a speculation test. We should expect the invalid speculation is that the extent of allies for issue 1 is equivalent to the larger part, and the elective theory is that the extent of allies is not the same as the larger part.

Utilizing a two-followed z-test with an importance level of 0.05, we can work out the z-measurement as:

z = (210/400 - 0.5)/sqrt(0.5 * 0.5/400) = 4.14

The p-an incentive for this test is the likelihood of getting a z-score more noteworthy than 4.14 or not exactly - 4.14, which is tiny (under 0.0001). In this way, we can dismiss the invalid speculation and presume that there is sufficient proof to propose that the extent of allies for issue 1 is altogether not quite the same as the larger part.

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So on solving the provided question, we can say that by unitary method task done of 15 days done = 7/5 X 15hours = 21 hours

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

task done of 5 days done = 7 hours.

task done of 1 days done = 7/5 hours.

task done of 15 days done = 7/5 X 15hours = 21 hours

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Answer:

a) 70 m

b) 35 m

c) 57 m

d) 500 m

e) 7.5 m

f) 57 m

Step-by-step explanation:

10 dm = 100 cm = 1 m.

1 dam = 10 m

1 km = 1000 m

100 cm = m

Correct ☑ ✔ Question :-

Transform in metre

a) 7 dam

b) 350 dm

c) 57000 mm

d) 0.5 km

e) 750 cm

f) 5.7 dam

a) 7 dam

1 dam = 10 m

so, 7 dam = 7 × 10 m = 70 m

b) 350 dm

10 dm = 1 m

so, 350 dm = 350/10 = 35 m

c) 57000 mm

1000 mm = 1 m

so, 57000mm = 57000/1000 = 57 m

d) 0.5 km

1 km = 1000 m

0.5 km = 1000 × 0.5 = 500 m

e) 750 cm

100 cm = 1 m

750 cm = 750/ 100 = 7.5 m

f) 5.7 dam

1 dam = 10 .

5.7 dam = 5.7 × 10 = 57 m

Answer:

34.5 i thiNK

Step-by-step explanation:

PEMDAS

2 times 34 is 68 plus 1 is 69

Therefore for it to be equal f would have to be half of 69 which is 34.5

Answer:

706.5 ft^2

Step-by-step explanation:

area = radius^2 (Pi)

15^2(3.14) = 706.5

Answer:

706.95ft^2

Step-by-step explanation:

Find area of a circle

A=πr^2

A=22/7*15ft^2

A=706.95ft^2

Answer:

Caroline's age is 21 years which is an odd integer.

Integers are a subset of real numbers.

Integers are rational numbers except decimals and fractions.

There are 3 types of integers positive , negative and Zero.

Positive integers are 3, 6, 789 ...

Negative integers are -87, -345, -234 ...

Zero integers is 0

It is given that Caroline is the youngest of 4 siblings and all of their ages are odd consecutive integers.

Let us consider the age of Caroline's age to be x years(x is an odd integer).

She is the youngest so the sibling's age who is just older than Caroline is given by x+2 which is also another odd integer.

Ages of the other two siblings will be x + 4 , x + 6 .

Now sum of their ages is 96.

Therefore: x + (x+2) + (x+4) + (x+6) =96

or, 4x + 12 = 96

or, 4x = 84

or, x = 21 (odd integer)

Carline's age is 21 years

Step-by-step explanation:

Answer:

First we distribute the -5:

-5(7+x) = -5(7) - 5(x) = -35 - 5x

Then we combine like terms:

-35 - 5x + 2 5/6x = -35 + 2/6x - 5x = -35 + 1/3x - 5x

So:

-5(7+x)+2 5/6x = -35 + 1/3x - 5x

The approximate area of the window that is not cleaned by the wiper is:

240 - 100.5 ≈ 139.5 square inches. Answer: \boxed{139.5}.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center.

To solve this problem, we need to find the area of the trapezoid and subtract the area of the semicircle.

The area of a trapezoid is given by the formula:

A = (a + b)h/2

where a and b are the lengths of the parallel sides, and h is the height (the perpendicular distance between the parallel sides).

In this case, we have:

a = 24 inches (the top parallel side)

b = 16 inches (the bottom parallel side)

h = 12 inches (the height)

Using the formula, we get:

A = (24 + 16) x 12/2

A = 240 square inches

The area of a semicircle is given by the formula:

A = πr²/2

where r is the radius of the circle.

In this case, the radius is half of the length of the wiper, so we have:

r = 16/2 = 8 inches

Using the formula, we get:

A = π(8²)/2

A ≈ 100.5 square inches

Therefore, the approximate area of the window that is not cleaned by the wiper is:

240 - 100.5 ≈ 139.5 square inches. Answer: \boxed{139.5}.

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1   Y is distributed as N(aμ + b, a^2σ^2), as desired.

2  We have shown that under these conditions, E[XY] = E[X]E[Y].

To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.

First, let's find the mean of Y:

E(Y) = E(aX + b) = aE(X) + b = aμ + b

Next, let's find the variance of Y:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2

Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.

We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:

E[XY] = ∫∫ xy f(x,y) dxdy

where f(x,y) is the joint probability density function of X and Y.

Then, we can use the fact that X and Y are independent to simplify the expression:

E[XY] = ∫∫ xy f(x) f(y) dxdy

= ∫ x f(x) dx ∫ y f(y) dy

= E[X]E[Y]

where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.

Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].

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Answer:

They will provide a warranty that guarantees a replacement if the calculator stopsworking within the specified time frame, and are trying to ...

Step-by-step explanation:

make me as brain liest

Answer:

The formula for average total cost (ATC) is:

ATC = TC/Q

where TC is the total cost of production, and Q is the quantity of output produced.

Total cost (TC) is the sum of all the costs of production, including fixed costs (FC) and variable costs (VC). Fixed costs are costs that do not vary with the level of production, such as rent or salaries, while variable costs are costs that vary with the level of production, such as raw materials or labor.

Therefore, the formula for total cost (TC) is:

TC = FC + VC

Substituting this formula for TC into the formula for ATC, we get:

ATC = (FC + VC)/Q

This formula shows that average total cost is the sum of the average fixed cost (AFC) and the average variable cost (AVC), which are calculated as follows:

AFC = FC/Q

AVC = VC/Q

Therefore, the formula for ATC can also be written as:

ATC = AFC + AVC

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

75 / 5 = 15

5 + 5 = 10

so 5 does both

Answer:

Step-by-step explanation:

p = k / sqrt(q)

The first job is to find k.

p = 12

q = 36

Solution for k

12 = k / sqrt(36)

sqrt(36) = +/- 6

Multiply both sides by +/-6

12 * +/- 6 = k

k = +/- 72

Solution for q = 16

p = +/-72/ sqrt(16)

p  = +/- 72 / sqrt(16)

p = +/- 72 / +/-4

p = 18

Answer:4.5ft

Step-by-step explanation:

To find the inverse function of F(x) = 2x - 3, we replace F(x) with y, swap the positions of x and y, and solve for y. The inverse function is f⁻¹(x) = (x+3)/2.

To find the inverse function of F(x) = 2x - 3, follow these steps

Replace F(x) with y. The equation now becomes y = 2x - 3.

Switch the positions of x and y, so the equation becomes x = 2y - 3.

Solve for y in terms of x. Add 3 to both sides: x + 3 = 2y.

Divide both sides by 2 (x + 3)/2 = y.

Replace y with the notation for the inverse function, f⁻¹(x): f⁻¹(x) = (x + 3)/2.

So, the inverse function of F(x) = 2x - 3 is f⁻¹(x) = (x + 3)/2.

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--The given question is incomplete, the complete question is given

" How do I find the inverse function of F(x) = 2x - 3"--

The solution to the initial value problem can be written in the form:

y(x) = (1/K)∫|sin(5x)|⁵ (3x³ - csc(5x)) dx

where K is a constant determined by the initial condition.

To solve the initial value problem and find the solution y(x), we can use the method of integrating factors.

Given: dy/dx + 5cot(5x)y = 3x³ - csc(5x), y = 0

Step 1: Recognize the linear first-order differential equation form

The given equation is in the form dy/dx + P(x)y = Q(x), where P(x) = 5cot(5x) and Q(x) = 3x³ - csc(5x).

Step 2: Determine the integrating factor

To find the integrating factor, we multiply the entire equation by the integrating factor, which is the exponential of the integral of P(x):

Integrating factor (IF) = e^{(∫ P(x) dx)}

In this case, P(x) = 5cot(5x), so we have:

IF = e^{(∫ 5cot(5x) dx)}

Step 3: Evaluate the integral in the integrating factor

∫ 5cot(5x) dx = 5∫cot(5x) dx = 5ln|sin(5x)| + C

Therefore, the integrating factor becomes:

IF = \(e^{(5ln|sin(5x)| + C)}\)

= \(e^C * e^{(5ln|sin(5x)|)}\)

= K|sin(5x)|⁵

where K =\(e^C\) is a constant.

Step 4: Multiply the original equation by the integrating factor

Multiplying the original equation by the integrating factor (K|sin(5x)|⁵), we have:

K|sin(5x)|⁵(dy/dx) + 5K|sin(5x)|⁵cot(5x)y = K|sin(5x)|⁵(3x³ - csc(5x))

Step 5: Simplify and integrate both sides

Using the product rule, the left side simplifies to:

(d/dx)(K|sin(5x)|⁵y) = K|sin(5x)|⁵(3x³ - csc(5x))

Integrating both sides with respect to x, we get:

∫(d/dx)(K|sin(5x)|⁵y) dx = ∫K|sin(5x)|⁵(3x³ - csc(5x)) dx

Integrating the left side:

K|sin(5x)|⁵y = ∫K|sin(5x)|⁵(3x³ - csc(5x)) dx

y = (1/K)∫|sin(5x)|⁵(3x³ - csc(5x)) dx

Step 6: Evaluate the integral

Evaluating the integral on the right side is a challenging task as it involves the integration of absolute values. The result will involve piecewise functions depending on the range of x. It is not possible to provide a simple explicit formula for y(x) in this case.

Therefore, the solution to the initial value problem can be written in the form: y(x) = (1/K)∫|sin(5x)|⁵(3x³ - csc(5x)) dx

where K is a constant determined by the initial condition.

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Considering that each input is related to only one output, the correct option regarding whether the relation is a function is:

A. yes.

A relation represents a function when each value of the input is mapped to only one value of the output.

For this problem, we have that:

There are no repeated inputs, hence the relation is a function and option A is correct.

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Answer:

\(\huge\boxed{y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{2}{3}x+\dfrac{4\sqrt{13}}{3}}\)

Step-by-step explanation:

The equation of a line:

\(y=mx+b\)

We have

\(m=\dfrac{2}{3}\)

substitute:

\(y=\dfrac{2}{3}x+b\)

The formula of a distance between a point and a line:

General form of a line:

\(Ax+By+C=0\)

Point:

\((x_0,\ y_0)\)

Distance:

\(d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+b^2}}\)

Convert the equation:

\(y=\dfrac{2}{3}x+b\)     |subtract \(y\) from both sides

\(\dfrac{2}{3}x-y+b=0\)    |multiply both sides by 3

\(2x-3y+3b=0\to A=2,\ B=-3,\ C=3b\)

Coordinates of the point:

\((0,\ 0)\to x_0=0,\ y_0=0\)

substitute:

\(d=4\)

\(4=\dfrac{|2\cdot0+(-3)\cdot0+3b|}{\sqrt{2^2+(-3)^2}}\\\\4=\dfrac{|3b|}{\sqrt{4+9}}\)

\(4=\dfrac{|3b|}{\sqrt{13}}\qquad|\)    |multiply both sides by \(\sqrt{13}\)

\(4\sqrt{13}=|3b|\iff3b=-4\sqrt{13}\ \vee\ 3b=4\sqrt{13}\)   |divide both  sides by 3

\(b=-\dfrac{4\sqrt{13}}{3}\ \vee\ b=\dfrac{4\sqrt{13}}{3}\)

Finally:

\(y=\dfrac{2}{3}x-\dfrac{4\sqrt{13}}{3}\ \vee\ y=\dfrac{4\sqrt{13}}{3}\)

Answer:

D 17.43

Step-by-step explanation:

3.5 times 3.63 equals 12.67 and 2 1/3 times 2.04 equals 4.76.  When you add them together you get 17.43.

The exact change Rodney needs to take with him to the produce stand is 17.42 dollars.

A unitary method is a mathematical technique for obtaining the value of a single unit and then deriving the required units by multiplying it with the single unit.

The exact change Rodney needs to take with him to the produce stand is the price of 3.5 pounds of cherries which is (3.5×3.62) dollars = 12.67 dollars added to the price of 2.33 pounds of peaches which is (2.33×2.04) dollars = 4.75 dollars.

∴ The total amount is (12.67 + 4.75) dollars.

= 17.42 dollars.

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Answer:

-5x-4y

Step-by-step explanation:

Combine like terms:

-4x-x+5y-9y rearrange

-5x-4y.

Hope this helps :D

Answer:

I think it'd be 19

Step-by-step explanation:

well 3 ( +4 ) 7 ( +4) 11 ( +4 ) 15 ( +4) 19

The standard error of the random variable is 6 .

Given,

Mean = $450

Standard deviation = $48

Samples = 64

Now,

According to the formula of standard error,

Standard error (SE) = σ / √(n)

σ = 48

n = 64

SE = 48 / sqrt(64)

SE = 6

Thus

standard error of the sampling distribution of the mean samples are 6.

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Answer:

5 ( or ) - 5

Step-by-step explanation:

12/3 = 4

240/4 = 60

m² + 35 = 60

m² = 60 - 35

m² = 25

m = - 5 ( or ) 5

Because,

( - 5 )² = - 5 * - 5 = 25

5² = 5 * 5 = 25