Person 1 and Person 2 visited Washington D.C. for the weekend. Person 1 rode the metro train one stop, 5 times at the peak fare price and 3 times at the off peak fare price for a total cost of $21.00. Person 2 rode with Person 1, 4 times at the peak fare price and 2 times at the off peak fair price for a total cost of $16.00. How much was the peak fare price

Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

Answer:

The right answer is 16m

Step-by-step explanation:

4*4=16

Answer:

16 m

Step-by-step explanation:

→ Remember how sides a square has

4

→ Multiply that by the side length of 4

4 × 4 = 16

Answer:

10-23= -13 is the answer

Answer:

think -13 is the answer

Answer:

It is a cord

Step-by-step explanation:

i just took the quiz and got it right :)

Answer:

D. arc

Step-by-step explanation:

everyone keeps saying its "chord" but I tried that and I got it wrong...

By shifting the appropriate numbers to the appropriate locations, the equations become true with \(f(-6) = 5, f(x) = 3\) , and  \(x = -5,\) and  \(f(7) = 8\) .

An equation is a claim that two expressions are equivalent in mathematics. Usually, it has one or more factors, which stand in for the unknowable elements we're trying to figure out how to calculate.

Equations can be used to depict actual-world circumstances or to explain relationships between various mathematical things.

For instance, the equation  \("x + 3 = 7"\) indicates that the total of the constant "3" and the variable "x" equals 7. By taking 3 out of both parts of the equation, we can find "x" and get \("x = 4"\) as a result.

Given

To make the equations true, move the right values to the right places in the table below:

\(f(-6) = 5\)

\(f(x) = 3; x = -5\)

\(f(7) = 8\)

By shifting the appropriate numbers to the appropriate locations, the equations become true with  \(f(-6) = 5, f(x) = 3,\) and \(x = -5\) , and \(f(7) = 8\) .

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The complete question is :- Use the table below to drag the correct numbers to their appropriate spots to make the equations true:

(Fill in the blank)

X                                      f(x)

-6                                     8

7                                        3

4                                      -5

3                                      -2

-5                                     12

Answer:

Yes, AA

Step-by-step explanation:

These triangles are similar because 2 angles in each triangle are congruent.

The line's slope is \(\frac{1}{2}\) and the distance increases by 1 mile every 2 hours.

What is a good example of a line's slope?

The proportion of the increase in the y-value to the increase in the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) & Q = (4,1) on the line.

A. Since the line's slope is 2, it follows that the y-variable, which is most likely distance, grows by 2 units for every increment in the x-variable, which is most likely time. The accurate statement is thus: speed is increased by Two miles per hour.

B. Since the line's slope is 2, it follows that the y-variable will drop by 2 units for every unit rise in the x-variable, which is most likely time. The accurate description is thus: speed drops by Two miles per hour.

C. If the line's slope is 1/2, the y-variable will rise by 1/2 unit for every increment in the x-variable, which is probably time. The precise description is that the distance grows by a mile every two hours.

D. If indeed the line's slope is 1/2, the y-variable will drop by 1/2 unit for every unit rise in the x-variable, which is probably time. The precise description is: distance shrinks by a mile every two hours.

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Step-by-step explanation:

8. 120° - Obtuse angle

9. 40° - Acute angle

10. 180° - Straight angle

11. 90° - Right angle

Answer:

15) K'(t) = 5[5^(t)•In 5] - 2[3^(t)•In 3]

19) P'(w) = 2e^(w) - (1/5)[2^(w)•In 2]

20) Q'(w) = -6w^(-3) - (2/5)w^(-7/5) - ¼w^(-¾)

Step-by-step explanation:

We are to find the derivative of the questions pointed out.

15) K(t) = 5(5^(t)) - 2(3^(t))

Using implicit differentiation, we have;

K'(t) = 5[5^(t)•In 5] - 2[3^(t)•In 3]

19) P(w) = 2e^(w) - (2^(w))/5

P'(w) = 2e^(w) - (1/5)[2^(w)•In 2]

20) Q(W) = 3w^(-2) + w^(-2/5) - w^(¼)

Q'(w) = -6w^(-2 - 1) + (-2/5)w^(-2/5 - 1) - ¼w^(¼ - 1)

Q'(w) = -6w^(-3) - (2/5)w^(-7/5) - ¼w^(-¾)

Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;

f(x) = 2x + 2         ⇒   (0, 2).

f(x) = 2x² - 2        ⇒   (-1, 0).

\(f(x) = 2\sqrt{x+1}\)   ⇒   (0, 2).

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;

For the ordered pair (0, 2), we have:

f(x) = 2x + 2

2 = 2(0) + 2

2 = 2 (True).

For the ordered pair (-1, 0), we have:

f(x) = 2x² - 2

0 = 2(-1)² - 2

0 = 2 - 2

0 = 0 (True).

For the ordered pair (0, 2), we have:

\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)

2 = 2 (True).

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Answer:

Area= 70x^3y^2

Perimeter = 20x^2 + 14 xy^2

Step-by-step explanation:

Area is just multiplying the length and width, I multiplied the constants first which gets us 70 then multiplied the variables, they combine however only the x's can be multiplied to each other which results in 70x^3y^2 .  The perimeter you just multiply the length by two and the width by two, they are separate because the variables when added to each other do not combine.  

The parametric equations for the tangent line to the curve at the given point are x = 1 - 7e−7cos(6)t + 6e−7sin(6)t, y = -7e−7sin(6)t - 6e−7cos(6)t, and z = 1 - 7e−7t.

The given parametric equations are x = e−7t cos(6t), y = e−7t sin(6t), z = e−7t, and the point is (1, 0, 1).

We can find the tangent line in two steps. First, we'll find the slope at the given point (1, 0, 1). Second, we'll use the point-slope form of a line equation to find the equation of the tangent line.

At the given location, determine the slope.

We can find the slope by taking the partial derivative of each coordinate with respect to t.

∂x/∂t = -7e−7tcos(6t) + 6e−7tsin(6t)

∂y/∂t = -7e−7tsin(6t) - 6e−7tcos(6t)

∂z/∂t = -7e−7t

Evaluating these derivatives at t = 1, we find:

∂x/∂t = -7e−7cos(6) + 6e−7sin(6)

∂y/∂t = -7e−7sin(6) - 6e−7cos(6)

∂z/∂t = -7e−7

At the given point, x = 1, y = 0, and z = 1.

Thus, the slope of the tangent line is:

m = (∂x/∂t, ∂y/∂t, ∂z/∂t) = (-7e−7cos(6) + 6e−7sin(6), -7e−7sin(6) - 6e−7cos(6), -7e−7)

Use the point-slope form of a line equation to find the equation of the tangent line.

The point-slope form of a line equation is:

r(t) = r₀ + m*t

Where r₀ is the point and m is the slope.

Thus, the equation of the tangent line is:

r(t) = (1, 0, 1) + (-7e−7cos(6) + 6e−7sin(6), -7e−7sin(6) - 6e−7cos(6), -7e−7)*t

Simplifying, we find:

x = 1 - 7e−7cos(6)t + 6e−7sin(6)t

y = -7e−7sin(6)t - 6e−7cos(6)t

z = 1 - 7e−7t

Therefore, the parametric equations for the tangent line to the curve at the given point are x = 1 - 7e−7cos(6)t + 6e−7sin(6)t, y = -7e−7sin(6)t - 6e−7cos(6)t, and z = 1 - 7e−7t.

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The parametric equations for the tangent line to the curve with the given parametric equations at the point (1,0,1) are:

x = 1 + e^-7t * (-7cos(6t) + 6sin(6t))

y = e^-7t * (-7sin(6t) - 6cos(6t))

z = e^-7t

The tangent line at a given point on a curve is a line that is locally closest to the curve at that point. To find the tangent line, we need to first find the derivative of the curve at the given point and then use it to find the slope of the tangent line. In this case, the given curve is a parametric equation and we can find the partial derivatives with respect to the parameter t.

Next, we use the partial derivatives to calculate the slope of the tangent line at the given point. Finally, we use the slope and the given point to write the parametric equations of the tangent line.

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The mean of 10 randomly selected students is definitely more likely to be closer to 75. 10 randomly selected students to include information and are more like to reflect the class’s scores. Consider an extreme example. Seventy-five students in a class of 100 earned perfect scores. The other 25 earned zeros. The average score of the class would be 75. A sample of 10 random students would almost certainly include more 100s then 0s, but both would be included in the sample. The mean of this samples score is closer to 75 than any individuals.

The mean of this sample score is closer to 75 than any individuals.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

The mean of 10 randomly selected students is definitely more likely to be closer to 75. 10 randomly selected students to include information and are more like to reflect the class’s scores. Consider an extreme example. Seventy-five students in a class of 100 earned perfect scores.

The other 25 earned zeros. The average score of the class would be 75. A sample of 10 random students would almost certainly include more 100s than 0s, but both would be included in the sample. The mean of this sample score is closer to 75 than any individuals.

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Answer: the answer is e

Step-by-step explanation:

If ax + b = 0, is x > 0

(1) a + b > 0

(2) a - b > 0

Answer:

c. Not significant at .055

Step-by-step explanation:

When a pair of dice is rolled, we have 6²=36 possible outcomes. Only 2 of these outcomes have a total score of 11:

Then, we can calculate the probability of getting 11 as the quotient between the successs outcomes and the total outcomes.

Then, the probability of getting 11 is:

\(P=\dfrac{X}{N}=\dfrac{2}{36}=0.055\)

This probability is not equal or less than 0.05, so it is not significant at 0.055.

The area of ΔQRS is 26.10 square units.

What is triangle?

A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles.

To find the area of \($\triangle QRS$\), we can use the formula:

\($Area = \frac{1}{2} \times base \times height$\)

where the base and height are the length of two sides of the triangle that are perpendicular to each other. We can find these sides using trigonometry.

First, we need to find the length of side \($QR$\). We can use the Law of Cosines:

\($QR^2 = QS^2 + RS^2 - 2(QS)(RS)\cos(R)$\)

where \($R$\) is the angle at vertex \($R$\). Substituting the given values, we get:

\($QR^2 = 9^2 + 5^2 - 2(9)(5)\cos(57^\circ)$\)

\($QR \approx 8.02$\)

Next, we need to find the height of the triangle, which is the perpendicular distance from vertex \($R$\) to side \($QS$\). We can use the sine function:

\($\sin(R) = \frac{opposite}{hypotenuse}$\)

\($\sin(57^\circ) = \frac{height}{8.02}$\)

\($height \approx 6.51$\)

Now we can find the area of the triangle:

\($Area = \frac{1}{2} \times QR \times height$\)

\($Area = \frac{1}{2} \times 8.02 \times 6.51$\)

\($Area \approx 26.10$\) square units

Therefore, the area of \($\triangle QRS$\) is approximately \($26.10$\) square units.

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The total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

Given:

Court lines are 50 mm wide.

Court paint covers 7 m² per litre of paint.

The centre circle is a complete circle, so the circumference is given by the formula: Circumference = 2πr

Radius of the entire circle = 9 m / 2 = 4.5 m

Radius of the centre circle = 4.5 m - 0.05 m (converted 50 mm to meters) = 4.45 m

Circumference of the centre circle = 2π(4.45 m) = 27.94 m

Next, let's calculate the circumference of the semicircles:

The semicircles are half circles, so the circumference is given by the formula: Circumference = πr

The radius (r) of the semicircles is the same as the radius of the entire circle, which is 4.5 m.

Circumference of a semicircle = π(4.5 m) = 14.14 m

Total length = Circumference of the centre circle + 2 x Circumference of a semicircle

Total length = 27.94 m + 2(14.14 m)

Total length = 56.22 m

Therefore, the total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

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The 5th term of the arithmetic series is  1179/ 19.

The 10th term of the arithmetic series , S is 66.

Using arithmetic formula,

aₙ = a + (n - 1)d

where

Therefore,

66 = a + 9d

The sum of the first 20 terms of S is 1290.

Therefore,

Sₙ = n / 2 (2a + (n - 1)d)

1290 = 10(2a + 19d)

1290 = 20a + 190d

combine the equation

66 = a + 9d

1290 = 20a + 190d

Hence,

a = 66 - 9d

1290 = 20(66 - 9d) + 190d

1290 = 1320 - 180 + 190d

1290 - 1320 + 180 = 190d

190d = 150

d = 150 / 190

d = 15 / 19

Hence,

a = 66 - 9(15  /19)

a = 66 - 135 / 19

a = 1254 - 135/ 19

a = 1119 / 19

Hence, let's find the fifth term.

a₅ = a + 4d

a₅ = 1119 / 19 + 4(15 / 19)

a₅ = 1119 / 19 + 60 / 19

Therefore,

a₅ =  1179/ 19

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Answer:

No, Tina is not correct since 3.4 × 105 = 357 and 8.25 × 104 = 858

Answer:

y = 3.2

Step-by-step explanation:

Simplifying

5y + -6 = 10

Reorder the terms:

-6 + 5y = 10

Solving

-6 + 5y = 10

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '6' to each side of the equation.

-6 + 6 + 5y = 10 + 6

Combine like terms: -6 + 6 = 0

0 + 5y = 10 + 6

5y = 10 + 6

Combine like terms: 10 + 6 = 16

5y = 16

Divide each side by '5'.

y = 3.2

Simplifying

y = 3.2

Answer:

18 in

Step-by-step explanation:

Because thats what it says

Answer:

d = 2.75 or 11/4

Step-by-step explanation:

15 = 5 + 4(2d - 3)

15 = 5 + 8d - 12

15 = 8d - 7

+7        + 7

22 = 8d

22/8 = d

2.75 = d

Check:

15 = 5 + 4(2(2.75) - 3)

Answer: \(\dfrac15\)

Step-by-step explanation:

Given : A cloth bag contains 6 cards numbered 1 through 6. Two cards are drawn without replacement.

Favorable outcome: sum of the numbers on the two drawn cards is 7

Since 1+6 = 7 , 2+5=7, 4+3 = 7

So, sum of 7 can be obtained as (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1)

Probability of getting (first 1, second 6) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 2, second 5) = (\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 3, second 4) =\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 4, second 3) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 5, second 2) = \(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Probability of getting (first 6, second 1) =\(\dfrac16\times\dfrac15=\dfrac{1}{30}\)

Required probability =\(6\times\dfrac{1}{30}=\dfrac15\)

Hence, the required probability = \(\dfrac15\)

Answer: 1134.11

A=3.14*r^2

Step-by-step explanation:

Answer:

a ≈ 1134.11 cm2

Step-by-step explanation:

The formula:

\(a=\pi r^{2}\)

\(a=\pi (19)^{2} =361\pi\)

\(a=1134.11cm^{2}\)

Hope this helps

Answer:

\(Probability = 0.56\)

Step-by-step explanation:

Represent the probability that Alice does well with P(A), the probability that Bob does well with P(B).

So, we have:

\(P(A) = 0.8\)

\(P(B) = 0.4\)

Required

Determine the probability that only one of them do well

This event is represented as: (A and B') or (B and A')

Where B' means Bob does not perform well and A' means Alice does not perform well.

And:

\(P(B') = 1 - P(B)\)

\(P(A') = 1 - P(A)\)

So, the probability becomes:

\(Probability = P(A\ and\ B')\ or\ P(B\ and\ A')\)

\(Probability = P(A) * P(B')\ +\ P(B)*P(A')\)

\(Probability = P(A) * (1-P(B)) +\ P(B)*(1-P(A))\)

\(Probability = 0.8 * (1-0.4) +\ 0.4*(1-0.8)\)

\(Probability = 0.8 * 0.6 +\ 0.4*0.2\)

\(Probability = 0.48 + 0.08\)

\(Probability = 0.56\)

Hence, the required probability is 0.56

Answer:

because the density or mass of the object doesn't change