14. Jill tossed a coin three times. Draw a tree diagram to represent the sample space.

Answer:

  (a)  7(x +3.5x) = 56

Step-by-step explanation:

You want an equation to solve for x, the length of a morning run, if the evening run is 3.5 times as long, and these runs total 56 miles when done every day of the week.

The morning run is given as x.

The evening run is 3.5 times as long, so is 3.5x

The total mileage each day is (x +3.5x).

In 7 days, the mileage will be 7 times the daily mileage. That total is given as 56 miles:

  7(x +3.5x) = 56

The scale factor for this right triangles is equal to 5/4.

In Mathematics, the scale factor of any geometric figure can be determined by dividing the dimension or side length of the new figure (image) by the dimension or side length of the original figure (pre-image):

Scale factor = Dimension of new figure (image)/Dimension of original figure (pre-image)

By substituting the given dimensions into the formula for scale factor, we have;

Scale factor = image dimension/pre-image dimension

Scale factor = 15/12 = (25/4)/5

Scale factor = 5/4.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The triangle has one solution. The remaining side c ≈ 4 and remaining angles B = 30°; C = 31°.

Option D is correct.

if angle A is obtuse and if a > b then the triangle has one solution

We are given ∠ = 119° which is obtuse and side a= 7 and side b - 4 i.e 7>4 so, the triangle has one solution.

Finding remaining sides c and ∠B and ∠C

Using the Law of sines to find ∠B

a/sin A = b/sin B

7/sin 119° = 4/sin B

7 * sin B = 4 * sin 119

7*sin B = 4(0.874)

sin B = 3.496/7

B = sin^-1(0.4994)

B = 29.96 = 30°

We know that sum of angles of triangle = 180°

So, 180° = 119° + 30° +∠C

180° = 149° + ∠C

=> ∠C = 180° - 149°

∠C = 31°

Now finding c

b/sin B = c /sin C

4/Sin 30 = c/sin 31

4* sin 31 = c*sin 30

4*0.515 = c* 0.5

=> c =  4*0.515/0.5

c = 4.12 ≈ 4

So, Option D one solution; c ≈ 4; B = 30°; C = 31° is correct.

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Determine whether the given triangle has no solution, one solution or two solutions. Then solve the triangle. Round measures of sides to the nearest tenth and measures of angles to the nearest degree

A = 119°, a=7, b=4

Question 7 options:

one solution; c ≈ 7; B = 30°; C = 119°

no solution

one solution; c ≈ 4; B = 31°; C = 30°

one solution; c ≈ 4; B = 30°; C = 31°

Answer:

2600This is a probability conversion problem.

Answer: To calculate the mean weekly earnings for each occupation in 2010, we need to add up the weekly earnings for each occupation and divide by the number of occupations.

For Forestry, logging and support:

Mean weekly earnings = (971) / (1) = $971

For Manufacturing:

Mean weekly earnings = (977) / (1) = $977

For Transportation and warehousing:

Mean weekly earnings = (900) / (1) = $900

For Construction:

Mean weekly earnings = (1071) / (1) = $1071

For Retail trade:

Mean weekly earnings = (501) / (1) = $501

Therefore, the mean weekly earnings for workers in the listed occupations in 2010 are:

Forestry, logging and support: $971

Manufacturing: $977

Transportation and warehousing: $900

Construction: $1071

Retail trade: $501

Step-by-step explanation:

The initial temperature of the soda is 18 degrees Celsius.

Its temperature after 20 minutes is 2.73 degrees Celsius.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = a(b)^x

Where:

When time, t = 0, the initial value can be calculated as follows;

[tex]C(t)=18(0.91)^{t}\\\\C(0)=18(0.91)^{0}[/tex]

C(0) = 18(1)

C(0) = 18 degrees Celsius.

When time, t = 0 = 20, the temperature can be calculated as follows;

[tex]C(t)=18(0.91)^{t}\\\\C(20)=18(0.91)^{20}[/tex]

C(20) = 2.73 degrees Celsius.

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Complete Question:

A can of soda is placed inside a cooler. As the soda cools its temperature C (t) in degrees Celsius after t minutes is given by the following exponential function.

[tex]C(t)=18(0.91)^{t}[/tex]

Find the initial temperature of the soda and its temperature after 20 minutes?

The transformation in the function y = -1/3f(x + 4) - 5 is described below

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

y = f(x)

The transformed function g(x) is given as

y = -1/3f(x + 4) - 5

The sequence of transformation on the transformed function is as follows

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The mean number of processes to be performed before a commercially successful one is 8.

The probability of success in each attempt is 0.125, so the parameter of the geometric distribution is p=0.125.

The mean of a geometric distribution with parameter p is equal to 1/p, so:

Mean = 1/p = 1/0.125 = 8

Therefore, the mean number of processes to be performed before a commercially successful one is 8.

In probability and statistics, the mean (or average) is a measure of the central tendency of a set of numbers. It is calculated by adding up all the numbers in a set and then dividing the sum by the total number of values in the set. The mean is a commonly used measure of the central tendency because it takes into account all the values in the set and provides a single value that represents the "typical" value.

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Answer: 6

Step-by-step explanation:

Therefore, area of the base 'B' of given rectangular prism is equal to 6 in².

Answer:

Step-by-step explanation:

B= area of the triangle 1+area of triangle 2

(1/2*3*1)+(1/2*2*1)

=1.5+1

=2.5

Answer:

247

Step-by-step explanation:

The volume of the prism is V = 4000 cm³

Given data ,

Let the volume of the prism be represented as V

Now , the value of V is

Let the height of the prism be h = 10 cm

Let the width of the prism be w = 20 cm

Let the length of the prism be l = 20 cm

So , the base area of prism = l x w

Base area = 400 cm²

Now , the volume of the prism is V = 400 x 10

V = 4000 cm³

Hence , the volume of prism is V = 4000 cm³

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The measure of ∠ADC is equal to 180 degrees.

The measure of ∠ABC is equal to 90 degrees.

In Mathematics and Geometry, a circle simply refers to a closed, two-dimensional (2D) curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the measure of angle ADC (∠ADC) is equal to 180 degrees.

In conclusion, the angle subtended by chord AB at point B has a measure of 90 degrees.

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The correct angle of elevation for the lighthouse's top is roughly 1.91°.

Consider the diagram drawn below, P is the position of the person in the lift-raft, B is the base of the lighthouse and the T is top of the lighthouse.

The diagram shows that the angle produced between the person in the life raft's line of sight to the top of the lighthouse and the horizontal is equal to the angle formed by the top of the lighthouse's height. Call this angle "[tex]\alpha[/tex]".

a) The distance "d" between the life raft and the lighthouse can be calculated using trigonometry.

[tex]tan\alpha = \frac{opposite}{adjacent} \\tan\alpha = \frac{20}{d}[/tex]

putting the value of [tex]\alpha[/tex] = 3 degrees put into the above equation.

[tex]tan3 = \frac{20}{d}[/tex]

[tex]d = \frac{20}{tan3}[/tex]

d = 354.14 (rounded to 2 decimal points

The life raft is therefore roughly 354.14 meters away from the lighthouse.

b)

Let's now calculate the proper angle of elevation for the situation when the life raft is 600 meters from the lighthouse.

[tex]tan\alpha = \frac{opposite}{adjacent}\\ tan\alpha = \frac{20}{600}[/tex]

solving for [tex]\alpha[/tex] we get,

[tex]\alpha = tan^{-1} (\frac{20}{100})\\\alpha = 1.91 degree\\[/tex]

Since the life raft is 600 meters from the lighthouse, the correct angle of elevation for the lighthouse's top is roughly 1.91°.

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The complete question in the form of the image below:

Anna has $165 left in the jar. The solution has been obtained by using the arithmetic operations.

All real numbers are supposed to be explained by the four fundamental operations, often known as "arithmetic operations." In mathematics, operations like quotient, product, sum, and difference occur after operations like division, multiplication, addition, and subtraction.

We are given that Anna saved $20 in a jar each month for 2 complete years and for 9 months of next year.

So, total months = 9 + 12 + 12 = 33

Now, using the multiplication operation, we get

⇒ Total money saved = 33 * 20

⇒ Total money saved = $660

It is given that she spent 75% of her savings on computer.

So, using the subtraction operation, we get

⇒ Amount left = 660 - 75%

⇒ Amount left = $165

Hence, Anna has $165 left in the jar.

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The distance from which the sprinkler can spread water is  4.37 feet

To determine the value, we need to know the area of the circle.

The formula for the area of a circle is expressed as;

A = πr²

Given that the parameters are;

Substitute the values, we have;

15 = 3.14r²

Divide both sides by the coefficient, we get;

r² = 4. 77

find the square root of both sides, we get;

r = 2. 19 feet

But note that the formula for diameter is given as;

Diameter = 2radius

Diameter = 2(2.19)

multiply the values

Diameter = 4.37 feet

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The probability that Mrs. Burke selects a non-Mathematical major, given that she chooses randomly from only Sophomores is 51.5%.

Probability refers to the chance or likelihood of an event occurring given many possible events that could have occurred.

Probability is expressed as a quotient of the expected event or success and the total possible events, outcomes, or successes.

The number of Sophomores in Mathematics Majors = 16

The number of Sophomores in Non-Mathematics Majors = 17

The total number of Sophomores in Mrs. Burke's Mathematics Class = 33

The probability of selecting a non-Mathematical major, given that Mrs. Burke chooses randomly from only Sophomores = 51.5% (17 ÷ 33 x 100)

Mrs. Burke's Mathematics Class

Academic Year   Mathematics Majors   Non-Mathematics Majors  Total

Freshmen                          19                             18                                 37

Sophomores                     16                             17                                 33

Juniors                               11                             15                                 26

Seniors                              12                             13                                25

Total                                 58                            63                                121

Thus, the likelihood of choosing a non-Mathematical major from the Sophomores is 51.5%.

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Mrs. Burke's Mathematics Class

Academic Year   Mathematics Majors   Non-Mathematics Majors

Freshmen                          19                             18

Sophomores                     16                             17

Juniors                               11                             15

Seniors                              12                             13

p = 3, q = 41, and r = 2, and we can write:

[tex]Sn = 3(gt^2 - t) + 41(gt - t).[/tex]

According to the given information we are given that the first term of an arithmetic series is (21 + 1), which simplifies to 22. We are also given that the common difference of the series is 3. Therefore, the second term of the series is 22 + 3 = 25, the third term is 22 + 2(3) = 28, and so on.

To find the nth term of this arithmetic series, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the number of terms, and d is a common difference. We are given that the nth term is (141-5), so we can set up an equation and solve for n:

(141-5) = 22 + (n - 1)3

136 = 22 + 3n - 3

117 = 3n

n = 39

Therefore, there are 39 terms in the arithmetic series.

To find the sum of the first n terms of an arithmetic series, we can use the formula:

Sn = n/2(a1 + an)

where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term. We know that a1 = 22, an = (141-5), and n = 39, so we can substitute these values into the formula:

S39 = 39/2(22 + (141-5))

S39 = 19(136)

S39 = 2584

Therefore, the sum of the first 39 terms of the series is 2584.

Now, we need to write the sum of the first n terms of the series as p(gt - 1), where p, q, and r are integers.

We know that the common difference is 3, so we can write the nth term as:

an = a1 + (n - 1)d

an = 22 + (n - 1)3

an = 3n + 19

Substituting this into the formula for the sum of the first n terms, we get:

Sn = n/2(a1 + an)

Sn = n/2(22 + 3n + 19)

Sn = n/2(3n + 41)

[tex]Sn = 3/2 n^2 + 41/2 n[/tex]

Therefore, p = 3, q = 41, and r = 2, and we can write:

[tex]Sn = 3(gt^2 - t) + 41(gt - t).[/tex]

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Answer:

20 : 4 : 15

Step-by-step explanation:

1 : 0.2 : 0.75

1 : 2/10 : 75/100

1 : 20/100 : 75/100

(×100)

100 : 20 : 75

(÷5)

20 : 4 : 15

The calculated area of the triangle B is 1.8 square units

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

Triangle A and B

Where

Area of A = 1/2 base * height

Sp, we have

Area of A = 1/2 * 2 * 5

Next, we have

Area of B = Area of A * Scale factor^2

Using the above as a guide, we have the following:

Area of B = 1/2 * 2 * 5 * (3/5)^2

Evaluate

Area of B = 1.8

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a) The volume of the box can be expressed as V = x(20-2x)(6-2x) cm³.

b) The domain of V is [0, 3) in interval notation.

c) The dimensions of the box that maximize the volume are L = 40/3 cm, W = 2/3 cm, and H = 10/3 cm.

d) The maximum volume is 160/27 cm³.

(a) To form the box, squares of side x are cut out of each corner. So, the length of the box will be (20-2x) cm and the width of the box will be (6-2x) cm.

Since the height of the box is x cm, the volume of the box can be expressed as

V = x(20-2x)(6-2x) cm³.

(b) The domain of V is the set of all possible values of x for which the length, width, and height of the box are positive. This is equivalent to the condition that 0<x<3. So, the domain of V is [0, 3) in interval notation.

(c) To maximize the volume, we need to find the critical points of V. Differentiating V with respect to x, we get

dV/dx = 4x³ - 52x² + 120x.

Setting dV/dx = 0, we get

x = 0 or x = 3 or x = 10/3.

Since the domain of V is [0, 3), we need to check the values of V at x = 0 and x = 3.

We also need to check the value of V at the critical point x = 10/3. Evaluating V at these values, we get

V(0) = V(3) = 0

and

V(10/3) = 160/27.

(d) To find the dimensions of the box that maximize the volume, we substitute the value of x = 10/3 into the expressions for the length, width, and height of the box.

So, the length of the box is

20-2(10/3)

= 40/3 cm,

the width of the box is

6-2(10/3)

= 2/3 cm, and

the height of the box is 10/3 cm.

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Answer:

47 months

Step-by-step explanation:

find 6.1% of 15k then divide that by 300

6.1% = 915

15,000 - 915 = 14085

14085 divided by 300 is 46.95 then rounded is 47

the probability of selecting a number less than 6 both times is 1/19 or approximately 0.0526.

a) The events are dependent because the selection of the first number affects the probability of selecting a number less than 6 on the second draw.

b) To calculate the probability of selecting a number less than 6 both times, we need to first find the probability of selecting a number less than 6 on the first draw and then the probability of selecting a number less than 6 on the second draw given that a number less than 6 was selected on the first draw.

The probability of selecting a number less than 6 on the first draw is 5/20, or 1/4, since there are 5 numbers less than 6 (1, 2, 3, 4, and 5) out of 20 total numbers.

Given that a number less than 6 was selected on the first draw, there are only 4 numbers less than 6 left in the box out of a total of 19 remaining numbers. So, the probability of selecting a number less than 6 on the second draw is 4/19.

To find the probability of both events occurring, we multiply the probabilities:

P(selecting a number less than 6 both times) = P(selecting a number less than 6 on the first draw) × P(selecting a number less than 6 on the second draw given that a number less than 6 was selected on the first draw)

P(selecting a number less than 6 both times) = (1/4) × (4/19) = 1/19

Therefore, the probability of selecting a number less than 6 both times is 1/19 or approximately 0.0526.

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Answer:

P=4/15

Step-by-step explanation:

P(dancer first) = 8/30=4/15

Answer:

Step-by-step explanation:

decimal: 0.44444444444

fraction: 4/9

Answer:

15, 18, 21, 24, 27, 30 ( +3)

7, 14, 28, 56, 112, 224, 448 ( x 2)

77, 70, 63, 56, 49, 42, 35 ( - 7)

20, 31, 42, 53, 64, 75, 86, 97 (+11)

22, 35, 48, 61, 74, 87 (+13)

The graph of the function g(x) has an equation of g(x) = 6√(x - 3)

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

f(x) = 3√x

The transformed function g(x) is given as

g(x) = 2f (x − 3)

In f(x) = 3√x , we have

f(x - 3) = 3√(x - 3)

Multiply both sides by 2

So, we have

2f(x - 3) = 2 * 3√(x - 3)

Evaluate the products

2f(x - 3) = 6√(x - 3)

Recall that

g(x) = 2f (x − 3)

So, we have

g(x) = 6√(x - 3)

This means that the graph of the function g(x) has an equation of g(x) = 6√(x - 3)

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Answer:

The equation x² - 1 = x can be rewritten as x² - x - 1 = 0. We can use the quadratic formula to find the solutions:

x = (-b ± sqrt(b² - 4ac)) / 2a

In this case, a = 1, b = -1, and c = -1. So:

x = (1 ± sqrt(1 - 4(1)(-1))) / 2(1)

x = (1 ± sqrt(5)) / 2

Therefore, the equation has two real solutions, and the discriminant is positive. The answer is 2. Its discriminant is 5, so it has two real solutions.