There is a 7% chance that a band's lead singer's voice isn't working due to illness on any given Saturday. This band has played 19 Saturday gigs so far this year, and at each of these the lead singer's voice has been fine. What is the probability that the lead singer's voice will be fine at the band's next Saturday gig, which is 2 weeks from now? Assume she never is sick for more than 6 consecutive days, and the interval between bouts of illness is inherently unpredictable.

Answer:

Step-by-step explanation:

In the given figure, the triangle ABC is a right triangle with a right angle at C. We need to find the length of the side AB.

Using the Pythagorean theorem, we know that in a right triangle with sides of length a, b, and c (where c is the hypotenuse), we have c^2 = a^2 + b^2.

In this case, we have AC = 4 and BC = 3. So, applying the Pythagorean theorem, we get:

AB^2 = AC^2 + BC^2

AB^2 = 4^2 + 3^2

AB^2 = 16 + 9

AB^2 = 25

Therefore, AB = 5.

Answer:

Part A: ∠A ≈ 27.7 °

Part B: c ≈ 8.75

Step-by-step explanation:

Part A:

Use the Law of Cosines.

Cosθ =

[ a² + b² - c² ] / [ 2ab ]

Sub in all the information where θ is A.

A = cos⁻¹ { [10² + 7² - 5²] / [2×10×7]

A ≈ 27.7 ° (1 decimal place)

Part B:

Use the Law of Cosines, but instead the unknown is the side c.

Rearrange to isolate c:

c² = a² + b² - 2ab×cosθ

c = √(5² + 6² - 2×5×6×cos(105°))

c ≈ 8.75 (2 decimal places)

Answer:

Step-by-step explanation:

Let's use variables to represent the amount of money each person had at first.

Let x be the amount of money that Theriault Luigi had.

Then, according to the problem, Faber Kozlowski had 6 times as much money as Theriault Luigi, which means Faber Kozlowski had 6x dollars.

After Faber Kozlowski spent 1/3 of his money, he had 2/3 of his money left, which is (2/3)(6x) = 4x dollars.

After Theriault Luigi spent 4/5 of his money, he had 1/5 of his money left, which is (1/5)x dollars.

Together, they had a total of $1155 left, which means:

4x + (1/5)x = 1155

Multiplying both sides by 5 to eliminate the fraction gives:

20x + x = 5775

Combining like terms gives:

21x = 5775

Dividing both sides by 21 gives:

x = 275

Therefore, Theriault Luigi had $275 at first, and Faber Kozlowski had 6 times as much, which is $1650 at first.

So, the answer to (a) is $275 + $1650 = $1925.

For (b), Theriault Luigi spent 3/4 of his remaining money on a hoodie, which means he spent (3/4)(1/5)x = 3/20 of his original amount of money on the hoodie.

Therefore, Theriault Luigi spent 3/20 of his original amount of money on the hoodie.

Answer:

(a) $1925

(b) 15%

Step-by-step explanation:

(a)

Let f = original amount of money Faber had.

Let t = original amount of money Theriault had.

"Faber Kozlowski had 6 times as much money as Theriault Luigi. "

f = 6t

"After Faber Kozlowski spent 1/3 of his money"

He has now: 2/3 f

"and Theriault Luigi spent 4/5 of his money"

He has now: 1/5 t

"they had a total of $1155 left"

2/3 f + 1/5 t = 1155

f = 6t

2/3 f + 1/5 t = 1155

2/3 (6t) + 1/5 t = 1155

4.2t = 115

t = 1155/4.2

t = 275

f = 6t = 6(275) = 1650

f + t = 275 + 1650 = 1925

Part (a) answer: $1925

(b)

Original amount: t = 275

He first spent 4/5 of the original amount, so he had 1/5 left.

275/5 = 55

He spent 3/4 of $55 on the hoodie.

3/4 × $55 = $41.25

$41.25/$275 × 100% = 15%

Part (b) answer: 15%

The answer is , (a) Empirical probability of sunfish rental = 0.5417 or 54.17% , (b) Empirical probability of kayak rental = 0.125 or 12.5% , (c) Empirical probability of rowboat rental = 0.3333 or 33.33% .

Empirical probability is an estimate of the probability of an event based on the frequency of its occurrence in a sample of data. It is calculated by dividing the number of times the event occurred by the total number of observations in the sample. Empirical probability is often used when there is no theoretical probability available, or when the theoretical probability is difficult to calculate or unknown. It is a useful tool in fields such as statistics, finance, and machine learning.

a) The empirical probability that the next boat rental is a sunfish is the number of sunfish rentals divided by the total number of rentals:

Empirical probability of sunfish rental = number of sunfish rentals / total number of rentals

Empirical probability of sunfish rental = 26 / 48

Empirical probability of sunfish rental = 0.5417 or 54.17%

b) The empirical probability that the next boat rental is a kayak is the number of kayak rentals divided by the total number of rentals:

Empirical probability of kayak rental = number of kayak rentals / total number of rentals

Empirical probability of kayak rental = 6 / 48

Empirical probability of kayak rental = 0.125 or 12.5%

c) The empirical probability that the next boat rental is a rowboat is the number of rowboat rentals divided by the total number of rentals:

Empirical probability of rowboat rental = number of rowboat rentals / total number of rentals

Empirical probability of rowboat rental = 16 / 48

Empirical probability of rowboat rental = 0.3333 or 33.33%

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The equation sin(4x) = 1/2 has two solutions on the interval (0, 2π]: x = π/24 and x = 5π/24.

The equation sin(4x) = 1/2 has two solutions on the interval (0, 2π].

The first solution occurs when 4x = π/6, or x = π/24. This corresponds to an angle of π/24 radians, or 7.5°.

The second solution occurs when 4x = 5π/6, or x = 5π/24. This corresponds to an angle of 5π/24 radians, or 112.5°.

Therefore, the equation sin(4x) = 1/2 has two solutions on the interval (0, 2π]: x = π/24 and x = 5π/24.

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The standard form equation of the ellipse as described in the task content is;

It follows from the task content that the standard form equation of the ellipse is to be determined.

Recall, the equation of an ellipse takes the form;

(x - h)²/a² + (y - k)²/b² = 1

where (h, k) is the center and a represents the distance of the center to each vertex on the major axis and b represents the distance from the center to each vertex on the minor axis.

Therefore, for the given scenario where center is at the origin; the equation of the ellipse is;

x²/4² + y²/(5/2)² = 1

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Answer:

[tex]\boxed{17}[/tex]

Step-by-step explanation:

Pythagorean theorem:

[tex]c^2=a^2+b^2[/tex]

where:

[tex]c=[/tex] hypothenuse

[tex]a=[/tex] the small size of the triangle

[tex]b=[/tex] the large size of the triangle

In this problem, we have the values of a and b, so:

[tex]c^2=(8)^2+(15)^2\\c^2=64+225\\c^2=289\\\sqrt{c^2}=\sqrt{289}\\ c=17[/tex]

Therefore the value of the unknown side of the triangle is 17.

Hope it helps.

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

That's correct. An observation is considered an outlier if it is more than 1.5 times the interquartile range (IQR) above the third quartile (Q3) or below the first quartile (Q1).

The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

In this case, the first quartile Q1 is 5 and the third quartile Q3 is 16. So the IQR is:

IQR = Q3 - Q1 = 16 - 5 = 11

An observation is considered an outlier if it is more than 1.5 times the IQR above Q3 or below Q1.

To find the upper outlier bound, we add 1.5 times the IQR to Q3:

Upper outlier bound = Q3 + 1.5(IQR) = 16 + 1.5(11) = 32.5

So any observation above 32.5 is considered an outlier.

To find the lower outlier bound, we subtract 1.5 times the IQR from Q1:

Lower outlier bound = Q1 - 1.5(IQR) = 5 - 1.5(11) = -11.5

So any observation below -11.5 is considered an outlier.

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Answer:

V = 16155.3 cubic feet

Step-by-step explanation:

The formula for volume (V) of a cone is

[tex]V=1/3\pi r^2h[/tex], where r is the radius and h in the height.

In the diagram, we're shown that the radius is 21 feet and the height is 35 feet.  Thus, we can plug everything into the formula including 3.14 instead of the entire pi number:

[tex]V=1/3(3.14)(21)^2(35)\\V=16155.3[/tex]

The expressions B and C are equivalent to the given expression:

A logarithmic function is the inverse of an exponential function. In other words, if we have an exponential function that takes a base, b, and raises it to a power, x, to get a result, y, then the logarithmic function is the inverse of that process.

Simplify the expression using logarithmic property,

log m + log n = log (m.n)

Expression can be written as,

log₂(2) + log₂(8) = log₂(2x8)

                         = log₂ 16

simplify further,

log₂16 = log₂(2)⁴

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The measurement of angle Y which is a twin angle will be equal to 116 degrees which is option A.

What is an Isosceles Triangle?

The triangle which has any two sides equal in length is called as Isosceles Triangles. Also the two angles which is opposite to the equal sides are equal and third angle is unequal. The unequal side which is present is called the base of the triangle. Measurement of the altitude can be done from base to the vertex (which is topmost) of the triangle.

Here, the value of angle X is given 32 degree.

Therefore the value of angle Z will also be 32 degree (due to the property of isosceles triangle)

By angle sum property:

X+Y+Z=180

32+Y+32=180

Therefore, Y = 116 degree

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The probability that a designer does not prefer red is 0.77. The Option 2 is correct.

Probability is a measure of how likely an event is to happen. Probability is represented as a fraction and always lies between 0 and 1.

The total number of opinions is:

= 92 + 86 + 46 + 91 + 37 + 46 + 2

= 400

The number of designers who do not prefer red is the sum of the opinions for all colors except red:

= 86 + 46 + 91 + 37 + 46 + 2

= 308

Therefore, the probability that a designer does not prefer red is:

= 308/400

= 0.77.

Full question "A study of interior designers' opinions with respect to the most desirable primary color for executive offices showed that:

Primary Color Number of Opinions

Red 92

Orange 86

Yellow 46

Green 91

Blue 37

Indigo  46

Violet 2

What is the probability that a designer does not prefer red? 1.00 0.77 0.73 0.23".

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Answer:b

Step-by-step explanation:

The solution of the graph is approximately

The solution of a graph depends on the type of graph and the problem being represented. In general, a solution of a graph refers to a point or set of points that satisfy the conditions or constraints of the problem.

For the problem, the solution of the graph is the point where the two graphs intersects.

Deducing from the graph this is at point x approximately 4.455 the closest value to this point in the option is x = 71/16

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Answer:

r/p = 2

Step-by-step explanation:

The proportional relationship between the amount of raisins and the amount of peanuts can be expressed as:

r/p = k

where k is the constant of proportionality.

To find an equation with a constant of proportionality greater than 1, we simply need to choose a value of k that is greater than 1. For example, if we choose k = 2, the equation becomes:

r/p = 2

To check that this equation is correct, we can use the original ratio of 4 cups of raisins for every 6 cups of peanuts:

4/6 = 2/3

This confirms that the constant of proportionality is indeed 2, and that the equation for the relationship with a constant of proportionality greater than 1 is:

r/p = 2

Answer:

i'm pretty sure its c, but if not then sorry

Step-by-step explanation:

Answer:

The equation of the line in the point-slope form is y+3=2/3(x−5)

Step-by-step explanation:

B

Start by putting the possible integers your friend can select

[tex]\text{S}=\{1,2,3,4,5,6,7,8,9,10\}[/tex]

Then, call the 2 possible events as A and B, and what are the possible integers in each event:

A = Be more than 6

B = The number is odd

 [tex]\text{A}=\{7,8,9,10\}[/tex]

 [tex]\text{B}=\{1,3,5,7,9\}[/tex]

The probability of the union of two events can be calculated as:

[tex]\text{P}(\text{A}\cup\text{B})=\text{P(A)}+\text{P(B)}-P(\text{A}\cap\text{B})[/tex]

Then,

         [tex]\text{P(A)}=\dfrac{\text{number of elements in A}}{\text{number of elements in S}}[/tex]

                             [tex]\text{P(A)}=\dfrac{4}{10}[/tex]

         [tex]\text{P(B)}=\dfrac{\text{number of elements in B}}{\text{number of elements in S}}[/tex]

                              [tex]\text{P(B)}=\dfrac{5}{10}[/tex]

[tex]\text{P(A}\cap\text{B})=\dfrac{\text{number of elements in A and B}}{\text{number of elements in S}}[/tex]

                        [tex]\text{P(A}\cap\text{B})=\dfrac{2}{10}[/tex]

Finally,

[tex]\text{P(A}\cup\text{B})=\dfrac{4}{10}+\dfrac{5}{10}- \dfrac{2}{10}[/tex]

          [tex]\text{P(A}\cup\text{B})= \dfrac{7}{10}[/tex]

Answer:

the probability that the number will be more than 6 or odd is: 7/10

Start by putting the possible integers your friend can select

[tex]\text{S}=\{1,2,3,4,5,6,7,8,9,10\}[/tex]

Then, call the 2 possible events as A and B, and what are the possible integers in each event:

A = Be more than 6

B = The number is odd

 [tex]\text{A}=\{7,8,9,10\}[/tex]

 [tex]\text{B}=\{1,3,5,7,9\}[/tex]

The probability of the union of two events can be calculated as:

[tex]\text{P}(\text{A}\cup\text{B})=\text{P(A)}+\text{P(B)}-P(\text{A}\cap\text{B})[/tex]

Then,

         [tex]\text{P(A)}=\dfrac{\text{number of elements in A}}{\text{number of elements in S}}[/tex]

                             [tex]\text{P(A)}=\dfrac{4}{10}[/tex]

         [tex]\text{P(B)}=\dfrac{\text{number of elements in B}}{\text{number of elements in S}}[/tex]

                              [tex]\text{P(B)}=\dfrac{5}{10}[/tex]

[tex]\text{P(A}\cap\text{B})=\dfrac{\text{number of elements in A and B}}{\text{number of elements in S}}[/tex]

                        [tex]\text{P(A}\cap\text{B})=\dfrac{2}{10}[/tex]

Finally,

[tex]\text{P(A}\cup\text{B})=\dfrac{4}{10}+\dfrac{5}{10}- \dfrac{2}{10}[/tex]

          [tex]\text{P(A}\cup\text{B})= \dfrac{7}{10}[/tex]

Answer:

the probability that the number will be more than 6 or odd is: 7/10

The area of the rhombus by decomposition is

The rhombus is decomposed into simpler elements which are

Area of 2 triangles

= 2 * 1/2 * base * height

= 2 * 1/2 * x * h

= 2 * 1/2 * 3 * 4

= 12 square units

Area of a parallelogram

= base x height

= y * h

= 5 * 4

= 20 square units

Area of the rhombus

= 20 square units + 12 square units

= 32 square units

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Part A: The Table for the data set above and it's title are attached accordingly.

Part B:

1) The shortest marker in the data set is Marker 1, which has a length of 4.00 inches.

2) The longest marker in the data set is Marker 14, which has a length of 6.75 inches.

3) The range of the data set is 2.75 inches, calculated by subtracting the shortest marker (4.00 inches) from the longest marker (6.75 inches).

4) To find the median, we need to arrange the data set in order from smallest to largest:

4.00, 4.25, 4.75, 5.00, 5.00, 5.25, 5.50, 5.50, 5.625, 6.00, 6.25, 6.25, 6.25, 6.50, 6.75

The median is the middle value, which is 5.50 inches.

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Answer:

D. The data has an outlier, therefore the range will be much greater than it would be without the outlier.

Step-by-step explanation:

The given data consists of six values, ranging from 187 to 1984. The numbers are not listed in order. There is an obvious outlier value, 1984, which is potentially impacting the spread and central tendencies of the data. However, without calculating the range or interquartile range, it is difficult to determine the extent of its impact.

Answer:

d got it right in edge.

Answer:

[tex] a_{old} = \frac{1}{2} (x)(4x) = 2 {x}^{2} [/tex]

[tex] a_{new} = \frac{1}{2} (x + 9)(4x + 2)[/tex]

[tex] = (x + 9)(2x + 1)[/tex]

[tex] = 2 {x}^{2} + 19x + 9[/tex]

Answer:

Since the given quadratic function has zeros of -8 and 4, we know that the factors of the quadratic equation are (x + 8) and (x - 4).

The maximum of the function occurs at the midpoint between the zeros, which is (-8 + 4)/2 = -2. So, the x-coordinate of the vertex is -2.

We also know that the y-coordinate of the vertex is 18. So, the vertex of the quadratic function is (-2, 18).

Using the vertex form of the quadratic function, we can write:

F(x) = a(x + 2)^2 + 18

Since the function has zeros of -8 and 4, we can write:

F(x) = a(x + 8)(x - 4)

a(x + 2)^2 + 18 = a(x + 8)(x - 4)

ax^2 + 6ax - 128a - 576 = ax^2 + 16ax - 32a

10ax - 96a - 576 = 0

10a(x - 6) = 0

a = 0 or x = 6.

Since the vertex is a maximum and the coefficient of the x^2 term is positive, we know that a > 0. Therefore, we can conclude that x = 6 and a = 3.

Hence, the value of "a" in the function equation is 3.

The length of the shorter leg is 6 centimeters, and the length of the longer leg is x + 14 = 20 centimeters.

Explanation:

Let x be the length of the shorter leg of the right triangle.

According to the problem, the longer leg is 14 centimeters longer than the shorter leg, so its length is x + 14.

We also know that the length of the hypotenuse of the right triangle is 26 centimeters.By the Pythagorean theorem, we have:

x^2 + (x + 14)^2 = 26^2

Simplifying the left side:

x^2 + x^2 + 28x + 196 = 676

Combining like terms:

2x^2 + 28x - 480 = 0

Dividing by 2:

x^2 + 14x - 240 = 0

Factoring:

(x + 20)(x - 6) = 0

Therefore, x = -20 or x = 6.

Since the length of a side cannot be negative, we reject x = -20 and conclude that x = 6.

So the length of the shorter leg is 6 centimeters, and the length of the longer leg is x + 14 = 20 centimeters.

Answer:

Step-by-step explanation:arcsin(1) = pi/2

Sample Response: I subtracted the highest and lowest numbers. The range for new cars was 31. The range for old cars was 75. The range for used cars was much bigger.

Answer:

Without access to specific data on monthly car sales, it is impossible to determine which type of car had the largest range in monthly sales. However, one possible method for finding this information would be to gather sales data for various car models across multiple months and compare the ranges of their sales figures. Alternatively, one could use industry reports or market analysis to determine which car types tend to have the largest fluctuations in sales from month to month.

Step-by-step explanation:

Without access to specific data on monthly car sales, it is impossible to determine which type of car had the largest range in monthly sales. However, one possible method for finding this information would be to gather sales data for various car models across multiple months and compare the ranges of their sales figures. Alternatively, one could use industry reports or market analysis to determine which car types tend to have the largest fluctuations in sales from month to month.

A) The speed of the object is 6.71 units per second.

B) , the equation of the line is y = -3x + 9

C) The magnitude of the resultant force is 4.36N

a) The position of the  object at time t is given by:

(x, y) = (4, -3) + t  (-3 , 6)

v = (dx/ dt, dy/dt) = (-3, 6)

So the velocity vector is ( -3, 6).

For speed of the object, we need to find the magnitude of the velocity vector....

|v| = √((-3)^2 + 6^2)

= √(45)

= 3 √(5)

= 6.71 units

B

The equation given  as (x, y) = (4, -3) + t (-3, 6)

Written in form of y=mx + b we have:
y = -3 t + 9
Thus,

EQuation is y = -3x + 9

C)

The angle between the two forces can be calculated as 90 ° - 30° = 60°.
To find the magnitude of the resultant force using the law of cosines, we can use the formula.....

c ² = a ² + b ² - 2ab cos(C)
In this case, we have...

a = 3N

b = 5N

C = 60 degrees

c ² = 3 ² + 5 ² - 2(3)(5) cos(60)

c ² = 9 + 25 - 30(0.5)

c ² = 19

c = √(19)

c = 4.35889894354
c ≈ 4.36

So it is right to state that  the magnitude of the resultant force is 4.36N

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