QUESTION 8
Solve the problem that involves probabilities with events that are not mutually exclusive.
Consider a political discussion group consisting of 8 Democrats, 3 Republicans, and 7 Independents. Suppose that two
group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting
an Independent and then a Democrat.
14/81, 25/153, 7/306/ or 4/153?

The maximum height reached by the ball is 908.5 feet.

Using the given values, we can substitute v0 = 152 and h0 = 6 into the equation:

\(h(t) = -16t^2 + 152t + 6\)

This quadratic function models the height of the ball at any time t after it is thrown.

To find the maximum height of the ball, we need to find the vertex of the parabolic curve described by the quadratic function. The vertex can be found using the formula:

t = -b / 2a

where a = -16 and b = 152 are the coefficients of the quadratic function.

t = -152 / 2(-16) = 4.75

So the maximum height is reached after 4.75 seconds. To find the maximum height, we can substitute this value back into the equation:

\(h(4.75) = -16(4.75)^2 + 152(4.75) + 6 = 908.5\)feet

Therefore, the maximum height reached by the ball is 908.5 feet.

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Question

A ball is thrown vertically upward from a height of 6 feet with an initial velocity of 152 feet per second. Write a quadratic function to model the vertical motion of the ball, given that the height of the ball at time t is given by: h(t) = -16t^2 + v0t + h0

Answer:

Step-by-step explanation:

This is a central angel so the degree of the angle is equal to the degree of the arc which is 111.

X+114=111

add negative -114 to each side to get X alone.

-114+X+114= 111+-114

X=-3 .   Answer negative 3

There are 29% of the Planes are Green.

The percentage is defined as a ratio expressed as a fraction of 100.

Total number of green planes = 250

The total number of green vehicles = 870

The percent of green planes = (number of green planes/number of total green vehicles) x 100

The percent of green planes = (250/870) x 100

The percent of green planes = 0.2873 x 100

The percent of green planes = 28.73

Round to the nearest percent, and we get

The percent of green planes = 29%

Thus, 29% of Planes are Green.

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The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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Answer:

x=73

Step-by-step explanation:

The two angles are equivalent, therefore x=73

Answer:1.325

Step-by-step explanation:

Answer:

9e+97

Step-by-step explanation:

Answer:

knjiqjwefiro fejweiejf

Step-by-step explanation:

The confidence interval for the population proportion, p is (0.766, 0.833)

The formula for calculating the confidence interval for proportion is expressed as:

CI = p±√pq/n

Given the following

p = 112/140 = 0.8

q = 1-p = 0.2

Substitute

CI = 0.8±√(0.8)(0.2)/140

CI = 0.8±0.0338

CI = (0.766, 0.833)

Hence the confidence interval for the population proportion, p is (0.766, 0.833)

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Answer:

68cm2

Step-by-step explanation:

area of a triangle= \(\frac{1}{2}\)*8*2

                            = 8 cm2

area of big squre=10*10

                           = 100cm2

area of shaded one= 100- (8*4)

                                =100-32

                                = 68 cm2

above is the solution to the question

The correct statement for the given diagram are-

Two angles are said to be supplementary if their sums total 180 degrees.

case A: m∠5+m∠3=m∠4  ...eq A

From the definition of supplementary angles

m∠3+m∠4=180°

m∠4=180°-m∠3   ....eq B

Put eq B in eq A

m∠5+m∠3=180°-m∠3

m∠5+m∠3+m∠3=180°

The result is true for m∠2=m∠3

Thus,

The case is not always true.

case B: m∠3+m∠4+m∠5=180°  ...eq A

From the definition of supplementary angles

m∠3+m∠4=180°

m∠4=180°-m∠3    ....eq B

Put eq B in eq A

m∠3+(180°-m∠3)+m∠5=180°

m∠5=0°

The case is not  true.

case C: m∠5+m∠6=180°

From the definition of supplementary angles

m∠5 and +m∠6 = 180

The case is always true.

case D: m∠2+m∠3=m∠6  ...eq A

From the definition of supplementary angles

m∠5+m∠6 = 180°

m∠6=180°-m∠5    ....eq B

Put eq B in eq A

m∠2+m∠3=180°-m∠5

m∠2+m∠3+m∠5=180°

Sum of interior angles of triangle equals 180 degrees

Thus,

This option will always be true.

case E:

m∠2+m∠3+m∠5=180°

Sum of interior angles of triangle equals 180 degrees

Thus,

This option will always be true.

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The correct question is attached.

Answer:

We use the rule,

\((a^b)^c = a^{bc}\)

a. (10^7)²

\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)

10^14

b. (10^9)³

\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)

10^27

c. (10^6)³

\(10^{(6)(3)}= 10^{18}\)

10^18

d. (10^2)³

\(10^{(2)(3)} = 10^{6}\)

10^6

e. (10³)²

\(10^{(3)(2)}=10^{6}\)

10^6

f. (10^5)^7

\(10^{(5)(7)} = 10^{35}\)

10^35

Step-by-step explanation:

Number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7. This can be obtained by assuming the value of number of seats in each row, forming quadratic equation and using quadratic formula to find root.

Here in the question it is given that,

We have to find the number of seats in each row.

Let us assume that the number of seats in each row be x.

From the given statement, number of seats in each row exceeds the number of rows by 7, we can write that,

Number of seats in one row = Number of rows + 7

x = Number of rows + 7

⇒ Number of rows = x - 7

Total number of seats in the auditorium can be written as,

⇒ (Number of seats in one row)(Number of rows) = Total number of seats

(x)(x - 7) = 2244

x² - 7x = 2244

⇒ x² - 7x - 2244 = 0

By using quadratic formula we can find the root,

x = (-b ± √b² - 4ac)/2a

here in the question, a = 1, b = -7, c = -2244

√b² - 4ac = √(-7)² - 4(1)(-2244)

√b² - 4ac = √49 + 8976

√b² - 4ac = √9025

√b² - 4ac = 95

x = (-b ± √b² - 4ac)/2a

x = (7 ± 95)/2

x = 102/2 or x = -88/2

⇒ x  = 51 or x = -44

Hence number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7.

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The equation that represent the situation of the quadrilateral is 40 = 3q + 7

A quadrilateral is a polygon with 4 sides.

Three sides of a quadrilateral are the same length, q.

The length of the fourth side is 7 inches.

The perimeter of the quadrilateral is 40 inches.

The equation to represent the situation is as follows:

perimeter of a figure is the sum of the whole sides.

Hence,

perimeter of the quadrilateral = q + q + q + 7

perimeter of the quadrilateral = 3q + 7

Therefore,

40 = 3q + 7

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Answer:

3q + 7 = 40

Step-by-step explanation:

I got this lesson

Answer:

\(6x^4y^8\sqrt{5x}\)

Step-by-step explanation:

\(\textsf{When $x > 0$ and $y > 0$, we want to find the expression that is equivalent to}\) \(\sqrt{180x^9y^{16}}.\)

\(\textsf{First, apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{180}\sqrt{x^9}\sqrt{y^{16}}\)

\(\textsf{Rewrite $x^9$ as $x^{8+1}$:}\)

\(\sqrt{180}\sqrt{x^{(8+1)}}\sqrt{y^{16}}\)

\(\textsf{Apply the exponent rule:} \quad a^{b+c}=a^b \cdot a^c\)

\(\sqrt{180}\sqrt{x^{8}\cdot x^1}\sqrt{y^{16}}\)

\(\sqrt{180}\sqrt{x^{8}}\sqrt{x}\sqrt{y^{16}}\)

\(\textsf{Apply\:the\:radical\:rule:\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad a\geq 0\)

\(\sqrt{180}\;x^{\frac{8}{2}}\sqrt{x}\;y^{\frac{16}{2}}\)

\(\sqrt{180}\;x^4\sqrt{x}\;y^8\)

\(\sqrt{180}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Rewrite $180$ as $(6^2 \cdot 5)$:}\)

\(\sqrt{6^2 \cdot 5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{6^2} \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0\)

\(6 \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}\)

\(6 \sqrt{5x}\;x^4\;y^8\)

\(\textsf{Rearrange:}\)

\(6x^4y^8\sqrt{5x}\)

\(\textsf{Therefore, when $x > 0$ and $y > 0$, the expression that is equivalent to}\)

\(\sqrt{180x^9y^{16}}\;\textsf{is}\;\;\boxed{6x^4y^8\sqrt{5x}}\:.\)

Answer:  15 + |−6| = 21 steps

Its stated that Joy walked 15 steps forward, meaning it would be a positive value. Shaunte walking backwards would give a negative value.

Answer:2,440,000,000

Step-by-step explanation:

Answer:

3.45445554 is irrational.

Hope this helps!

Please can you mark as Brainliest!

Step-by-step explanation:

Answer:

\(3.45445554\)

Rational number ✔️

rational number is the number that can form a fraction

Answer:

This should be a permutation

Step-by-step explanation:

P (n, r) = n!/(n-r)!

P (12,5) = 12!/(12-5)!

P (12,5) = 12!/7!

P(12,5) = 95040

Answer:

A translation, yes.....ok! the answer is below! ;)

In my explanation:

A translation is a type of transformation, it is when there is a plane and an object slides from one place to another without changing it's size, shape, or rotation.

Web explanation:

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system.

Look at the image below, there is a figure, called the pre-image, and then when it slides the new image is called the image.

Hope this helps!

Have a nice day!

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Answer: For instance, if we cut the pie into 6 equal slices, then 1 slice represents 1/6 of the whole pie. In the same way, if we break 1 into 6 equal parts, 1 part represents 1/6 of 1. Unit fractions are 1 part of the number 1. Notice that the more pieces you slice the pie into, the smaller the pieces of pie become.

Step-by-step explanation:

The total number of workers that were studied can be found to be 139,340,000.

The percent of workers unemployed would be 5. 4 %.

Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.

Number of employed workers :

= 74,624,000 + 64, 716, 000

= 139,340,000

Percentage unemployed :

= ( 4, 209,000 + 3,314,000 ) / 139,340,000

= 5. 4 %

Percentage of unemployed men :

= 4,209,000 / 74,624,000

= 5.6 %

Percentage of unemployed women:

= 3,314,000 / 64, 716, 000

= 5. 1 %

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The full question is:

a. How many workers were studied?

b. What percent of the workers were unemployed?

c. Compare the percent unemployed for the men and the women.

The probability of rolling a 3 on a fair 6-sided die that P(3) is 0.17.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Since each side of the die is equally likely to land face up,

So the number of favorable outcomes n(E) = 1

And the total number of outcomes n(S) = 6

Thus, P(3) is the probability of rolling a 3 on a fair 6-sided die :

P(3) = n(E)/n(S)

P(3) = 1/6

P(3) = 0.17

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There are 152 red pens and 190 blue pens in Max's drawer, given that there are a total of 342 pens altogether.

Let's solve the problem step by step:

Identify the given information:

The ratio of red pens to blue pens is 4 to 5.

There are a total of 342 pens in the drawer.

Set up the ratio equation:

Let's assume the number of red pens is 4x, and the number of blue pens is 5x.

Here, 'x' is a scaling factor that allows us to find the actual number of pens.

We can write the equation as: 4x + 5x = 342.

Simplify and solve the equation:

Combining like terms, we have 9x = 342.

Divide both sides of the equation by 9 to solve for 'x':

x = 342 / 9 = 38.

Calculate the number of red pens and blue pens:

Now that we have the value of 'x', we can find the number of red and blue pens:

Number of red pens: 4x = 4 × 38 = 152.

Number of blue pens: 5x = 5 × 38 = 190.

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:  Choice C

This is because the input n = 2 leads to the output n-2 = 2-2 = 0

As another example: the input n = 4 leads to the output n-2 = 4-2 = 2

Whatever the input is, subtract 2 from it to get the output.

This means, it's the graph of:

Answer is option 2.

The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

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Answer:

X=14 , 5 , 2.5 , 9 , 5 , 15 , -2 ,-2 ,-10 , 13 ,- 3 , -11 , 0 , 0.5833..., -1.666....