What happens to the mean of the data set {10, 2, 8, 9, 5, 2, 6} if the number 9 is removed from the data set?

a) i.  the probability of two rainy days is 0.2 * 0.85 = 0.17.

   ii. The total probability of having exactly one rainy day is the sum of    these two probabilities is  0.18.

   iii. probability of having At least one dry day is 0.83.

b)i. The probability of having Three rainy days is 0.1447.

ii. The probability of having Exactly one dry day is 0.1881

iii. The probability of having At most two rainy days is 0.35

a) On two consecutive days, the probability of having:

i. Two rainy days: The probability of two rainy days can be found by multiplying the probabilities of rain on each day, given that the previous day was rainy. In this case, the probability of two rainy days is 0.2 * 0.85 = 0.17.

ii. Exactly one rainy day: There are two ways to have exactly one rainy day in two consecutive days: either the first day is rainy and the second day is dry, or the first day is dry and the second day is rainy. The total probability of having exactly one rainy day is the sum of these two probabilities, which can be calculated as:

P(rainy day first) * P(dry day second) + P(dry day first) * P(rainy day second) = 0.2 * 0.9 + 0.8 * 0.1 = 0.18

iii. At least one dry day: To find the probability of at least one dry day, we can subtract the probability of two rainy days from 1, since the only possibility in which there is no dry day is if both days are rainy:

1 - P(two rainy days) = 1 - 0.17 = 0.83

b) On three consecutive days, the probability of having:

i. Three rainy days: The probability of three rainy days can be found by multiplying the probabilities of rain on each day, given that the previous day was rainy. In this case, the probability of three rainy days is 0.2 * 0.85 * 0.85 = 0.1447.

ii. Exactly one dry day: To have exactly one dry day in three consecutive days, we need two rainy days followed by a dry day, or a rainy day followed by two dry days, or two dry days followed by a rainy day. The total probability of having exactly one dry day can be calculated as:

P(rainy day first, rainy day second, dry day third) + P(rainy day first, dry day second, dry day third) + P(dry day first, rainy day second, rainy day third)

= 0.2 * 0.85 * 0.9 + 0.2 * 0.9 * 0.9 + 0.8 * 0.1 * 0.1 = 0.1881

iii. At most two rainy days: To find the probability of at most two rainy days, we need to add up the probabilities of two rainy days and one rainy day.

P(at most two rainy days) = P(two rainy days) + P(one rainy day) = 0.17 + 0.18 = 0.35

So, the probability of having at most two rainy days in three consecutive days is 0.35.

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Answer:

x > 2

Step-by-step explanation:

To solve the inequality 56x - 13 > 113, you can start by isolating the variable on one side of the inequality. Subtract 113 from both sides:

56x - 113 > 0

Next, add 113 to both sides:

56x > 113

Finally, divide both sides by 56:

x > 2

So the solution is x > 2, meaning that x can be any value greater than 2.

Answer:

[tex]x > \dfrac{9}{4} \\\\[/tex]

or

x > 2.25

This does not fit any of the provided answer choices. Either the inequality is copied wrong or the answer choices are copied wrong

Step-by-step explanation:

The inequality is 56x - 13 > 113

Add 13 to both sides:
56x - 13 + 13 = 113 + 13

56x > 126

Divide by 56 both sides
[tex]\dfrac{56x}{56} > \dfrac{126}{56}[/tex]

Reducing the above fraction to lowest by dividing numerator and denominator by 14 to get:
[tex]x > \dfrac{126 \div 14}{56\div 14}\\\\x > \dfrac{9}{4}[/tex]

None of your answer choices fit. So not sure whether the inequality given is incorrectly copied/pasted or the answer choices are.

The closest this comes to is x > 2 but the inequality will not be satisfied for any value of x between 2(excluded) and 2.25(included)

The answer is 38 degrees because the angle of HZJ is 38, its a reflection

Answer:

m<FZG= 38

Step-by-step explanation:

<JZG is a straight line equivalent to 180 degrees. Because m<HZJ is 38 degrees, m<HZG is 142 degrees because 180-38=142. Looking now at line HF, equivalent to 180 degrees, we know that m<HZG is 142 degrees. To solve for m<FZG, we use the equation 142+x=180. 180-142=x; x=38. You can also use the vertical angle theorem to solve for m<FZG.

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Using the double angle property of the trigonometric functions the value of tan 2θ = 4/3.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

Given that the value of cos θ = 2√5 / 5.

The cosine is given as:

Cos θ = adjacent side / Hypotenuse

So, the value of adjacent side = 2√5 and the value of hypotenuse = 5.

To find the value of opposite side we use the Pythagorean theorem:

a² + b² = c²

a² + (2√5)² = (5)²

a² + 4(5) = 25

a² = 25 - 20

a = √5

Now, the value of tan θ = opposite side / adjacent side so,

tan θ = √5 / 2√5 = 1/2

The tan 2θ is given as:

tan 2θ = 2(tan θ) / 1 - tan² θ

Substituting the value of tan θ:

tan 2θ = 2(1/2) ÷ (1 - (1/2)²)

tan 2θ = 1 ÷ (3/4)

tan 2θ = 4/3

Hence, using the double angle property of the trigonometric functions the value of tan 2θ = 4/3.

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Una tabla estadística para resumir los resultados de la encuesta podría ser la siguiente:

Emoción/Sentimiento Porcentaje de Encuestados

Impaciente 43%

Preocupado por salud 34%

Solo 15%

Enojado 12%

Preocupado por vulnerables 55%

Feliz de pasar tiempo con familia 31%

Inspirado por adaptación 22%

Esta tabla muestra los diferentes sentimientos y emociones que los encuestados experimentaron durante la encuesta realizada por Global Advisor.

The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.

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The three consecutive integers are 52, 53, 54, if the sum of the first two is 51 more than the third integer.

Consecutive Integer:

An integer is the number zero (0), a positive natural number (1, 2, 3, etc.), or a negative integer with a minus sign (−1, −2, −3, etc.). A negative number is the additive reciprocal of the corresponding positive number. In math language, the set of integers is often written as bold Z.

Consecutive integers are integers that follow each other in a regular counting pattern. When listing consecutive integers in a sequence, the difference between them is always fixed because there are no skipped digits between them. Consecutive integers are integers that follow each other in ascending order. The Sequential Integer Formula helps to find these integers for a given number or to determine whether a series of integers are consecutive.

According to the Question:

Let the three consecutive integers are

x , x+1, x+2

Since we have given that:

The sum of the first two is 51 more than the third,

Now,

   (x + x + 1) - (x+2) = 51

⇒ 2x +1 -x - 2 = 51

⇒ x - 1 = 51

⇒ x = 52

So, the three consecutive integers are

52, 52+1, 52+2

Therefore,

52,53,54.

Hence, the integers are 52,53,54.

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The equation of the line parallel to the given line is 3x - 2y + 5 = 0.

What is the equation of a line?

The set of points that make up a line in a coordinate system is represented algebraically by a line's equation.

A straight line's equation is y=mx+c, where m denotes the gradient and c, commonly known as the y-intercept, is the height at which the line crosses the y-axis.

The given line is -3x+2y = 4

Then,  [tex]y = \frac{3}{2}x + 2[/tex]

Slope [tex](m_1) = \frac{3}{2}[/tex] and [tex]c_1[/tex] = 2

Now, the slope of the parallel line [tex]m_2[/tex] = [tex]m_1[/tex] = 3/2

and passes through a point (-1,1)

Then,

the equation of the parallel line is

[tex]or, y-y_1=m(x-x_1) \\\\or, y-1=\frac{3}{2}(x+1) \\\\ or, 2y-2=3x+3\\\\or, 3x-2y+5=0[/tex]

Hence, the required equation of the line is 3x - 2y + 5 = 0.

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There are 720 possible pins, as no digit can be repeated. This is calculated by taking 3! (3 factorial) which is 3x2x1, which equals 6, and then multiplying it by 10, as there are 10 digits, 0-9.

A pin can contain 3 numerical digit and no digit can be repeated. To calculate the amount of pins possible, we use 3! (3 factorial), which is 3x2x1, equaling 6. Then, we multiply this by 10, as there are 10 digits, 0-9. Therefore, 6x10 = 720. In order to calculate 3! (3 factorial) we start by multiplying 3x2x1. This is because each digit has to be multiplied by the number of digits before it, as no digit can be repeated. The first digit has no digits before it, so it stays as 3. The second digit has one digit before it, so it is multiplied by 2. The third digit has two digits before it, so it is multiplied by 1. Therefore, 3x2x1 = 6. Then, we multiply 6 by 10, as there are 10 digits, 0-9. 6x10 = 720, which means there are 720 possible pins with no digit being repeated.

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a) The experimental probability that the pointer lands in section 5 is 7.5%

b) The theoretical probability that the pointer lands in section 5 is 10%.

c)  The actual number of times is lower than the expected number, so we can say that the spinner landed in section 5 less often than expected.

a. Experimental probability:

The experimental probability is found by dividing the number of times the spinner lands in section 5 by the total number of spins.

In this case, the spinner landed in section 5 3 times in 40 spins, so the experimental probability is:

Experimental probability = 3/40 = 0.075 or 7.5%

b. Theoretical probability:

The theoretical probability is the expected probability based on the assumption that the spinner is fair and each section has an equal chance of being selected.

With 10 equal sections, the theoretical probability that the spinner lands in section 5 is:

Theoretical probability = 1/10 = 0.1 or 10%

c. Comparison between actual and expected:

The actual number of times the spinner landed in section 5, 3, is compared to the expected number of times, 4 (based on the theoretical probability of 10% and 40 spins).

The actual number of times is lower than the expected number, so we can say that the spinner landed in section 5 less often than expected.

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Based on the provided information, the graph of y = v(3x) - 4 must contain the point (-4, -8) and (b) the graph of y = 1/4 v(x) + 9 must contain the point (-12, 6).

As the graph of y = v(x) contains the point (−12, −7), point that must be on the graph of each of the functions below are:

(a) y = v(3x) - 4

3x = -12

x = (-12)/3= -4

y = -4 – 4 = -8

The graph of y = v(3x) - 4 must contain the point (-4, -8).

(b) y = 1/4 v(x) + 9

x = -12

y = 1/4 (-12) + 9 = 6

The graph of y = 1/4 v(x) + 9 must contain the point (-12, 6).

Note: The question is incomplete. The complete question probably is:  The graph of y=v(x) contains the point (−12,−7). What point must be on the graph of each of the functions below? Enter points as (a,b) including the parentheses. (a) The graph of y = v(3x) - 4 must contain the point _ (b) The graph of y = 1/4 v(x) + 9 must contain the point _ .

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The perimeter of the triangles will be 24 inches.

With two triangles she forms a rectangle of 6in by 8 in.

Then the triangles will have legs with these dimensions, and the last side (the hypotenuse) has a length equal to the diagonal of the rectangle:

diagonal = √( (6in)² + (8in)²) = 10in

Then the perimeter of te triangle is:

P = 10in + 8in + 6in = 24in

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Answer:

Step-by-step explanation: is half cut up so therefore the shape thats cut is a trapeziod

Answer:

16π

Step-by-step explanation:

π is the ratio between the circumference and the diameter. 2x8xπ = 16π

Answer: 16π, or 50.2655

Step-by-step explanation:

Circumference is calculated using πd, where d is the diameter. Since d = 2r, where r is the radius, this can be rewritten as circumference = π2r. Plugging our radius, 8, into the equation gives us π(2)(8), which simplifies to 16π, or 50.2655.

Candidate A may not be giving an honest reading of the poll results.

When interpreting poll results, it is important to consider the margin of error, which indicates the level of precision of the results. In this case, the margin of error is plus or minus 5%. This means that the true support for each candidate could be as much as 5% higher or lower than the reported numbers.

Based on this information, it is possible that candidate A's lead is not as large as he claims, or that his opponent is actually leading by a narrow margin. Furthermore, it is important to note that the results of a single poll should not be taken as the definitive outcome of an election. Instead, multiple polls should be considered and the results should be viewed in the context of other factors such as the demographic makeup of the polling sample and the timing of the poll.

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The height of the prism with base area of 40 square meters and volume of 320 cubic meters is 8 meters

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The volume of the prism is the amount of space that the solid figure occupies.

The volume of prism = area of base * height

The area of the base of the nonagonal prism below is 40 square meters. Its volume is 320 cubic meters. Hence:

The volume of prism = area of base * height

Substituting:

320 m³ = 40 m² * height

height = 8 m

The height of the prism is 8 meters

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The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 26 over 60.

The ratio between the number of favorable events and the total number of conceivable outcomes is known as the theoretical probability.

The experimental probability can be calculated mathematically using the following formula: Probability of an Event P(E) = Number of Times an Event Occurs / Total Number of Trials.

The experimental probability will be:

= Frequency for swimming / Total frequency

= 26 / 60

Therefore, it should be noted the correct option is D.

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Answer:

44h

Step-by-step explanation:

money earned per extra hour worked=100+25/100×10.80=13.50

amount earned if working for 38 hours=10.80×38=410.40

remaining money=491.40-410.40=81

number of extra hours worked=81÷13.50=6

total hours worked=38+6=44h

Step-by-step explanation:

I guess for #9

An exponent to an exponent is multiplication

[tex] {x {}^{ \\ y} }^{z} = {x}^{y \times z} [/tex]

So that first part...

[tex] {2}^{5 {}^{2} } = {2}^{5 \times 2} = {2}^{10} [/tex]

Doing the same for the other parts, you'll get a final of

273 246

[tex] \frac{ {2}^{10 } \times {2}^{21} }{ {2}^{24} } [/tex]

Now solving those

[tex] \frac{1024 \times2097152 }{16777216} = 128[/tex]

For a right triangle TMR the equation that is true is -

Option 3: sin T = cos R

What is a right-angled triangle?

Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.

In a right triangle, the sine of an acute angle is defined as the length of the opposite side divided by the length of the hypotenuse, and the cosine of an acute angle is defined as the length of the adjacent side divided by the length of the hypotenuse.

In triangle TMR, the right angle is at M, which means that T and R are acute angles.

Using the definitions of sine and cosine, determine which equation is true -

1. sin M = cos T

The angle M is the right angle, which means that its sine is 1 and its cosine is 0.

Therefore, this equation is false.

sin R = cos R

2. The sine and cosine of the same angle cannot be equal, except in the case of a 45° angle where both sine and cosine are equal to 1/√2.

Therefore, this equation is false.

3. sin T = cos R

The angle T is the acute angle opposite the side TR, and the angle R is the acute angle adjacent to the side TR.

Therefore, this equation is true.

4. sin T = cos M

The angle M is the right angle, which means that its cosine is 0.

Therefore, this equation is false.

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(a) To find the product of -2x^3+x and x^3-3x-4, we can use the distributive property of multiplication:

(-2x^3 + x)(x^3 - 3x - 4)

= -2x^3(x^3) - 2x^3(-3x) - 2x^3(4) + x(x^3) - x(-3x) - x(4)

= -2x^6 + 6x^4 - x

= -2x^6 + 6x^4 - x

Therefore, the product of -2x^3+x and x^3-3x-4 is -2x^6 + 6x^4 - x.

(b) No, the product of 2x^3+x-5 and x^3-3x-4 is not equal to the product of x^3-3x-4 and -2x^3+x-5. This is because the order of the factors in a multiplication expression affects the outcome. When we expand both products using the distributive property, we get different expressions:

(2x^3 + x - 5)(x^3 - 3x - 4) = 2x^6 - 5x^3 - 3x^2 - 17x + 20

(x^3 - 3x - 4)(-2x^3 + x - 5) = -2x^6 + 11x^4 + 13x^3 - 3x^2 - x + 20

So the expanded expressions are not equal. Therefore, the two products are not equal.

If researchers use statistical tests and determine that there is a low probability that their experimental results occurred purely by chance, then their results are considered statistically significant.

Statistically significant results suggest that the observed effects in the experimental group are unlikely to have happened by chance and are likely to reflect a real effect of the treatment or intervention being tested.

However, it's important to note that statistical significance does not necessarily mean practical significance or real-world importance. For example, a small effect may be statistically significant but still not large enough to have practical implications.

Additionally, it's important to be aware of potential sources of error and bias in the experimental design and data analysis, and to consider the results in the context of other relevant evidence. Statistical significance should not be used as the sole criterion for accepting or rejecting research results, and should always be accompanied by a thorough evaluation of the quality of the evidence and the implications of the results.

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The annual net income and annual yield are $3400 and 2.335 respectively

a) To find the annual net income, we need to subtract the annual expenses from the annual rental income. The annual rental income can be calculated as follows:

$3,875 * 6 months = $23,250

The annual net income would be:

$23,250 - $19,850 = $3,400

b) The annual yield can be calculated as the annual net income divided by the total cost of the property, including the down payment:

$3,400 / ($185,900 - $40,000) = 0.023 or 2.33%

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The number of residents that support more are 350

Sets are a collection of well-defined objects or elements. A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}.

The number of residents that support more will be number of residents that support Moore only plus the number of residents that support both Moore and Allen

therefore ;

the number of residents that support Moore =

250+100 = 350 residents

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(a) perimeter:54cm, area:108 cm 2 (squared)

The perimeter of a rectangle with length 15 cm and width 12 cm is 54 cm (2 * (15 + 12) cm).

The area of the rectangle is 180 square cm (15 * 12 cm^2).

Measure the length (l) and the width (w) of the rectangle. In this case, the length is 15 cm and the width is 12 cm.

To find the perimeter, calculate the sum of twice the length and twice the width. This is done by multiplying each measurement by 2 and then adding them together: 2 * l + 2 * w. In this case, the calculation is 2 * 15 + 2 * 12 = 30 + 24 = 54 cm.

To find the area, multiply the length and the width: l * w. In this case, the calculation is 15 * 12 = 180 cm^2.

The perimeter of the rectangle is the sum calculated in step 2. In this case, the perimeter is 54 cm.

The area of the rectangle is the product calculated in step 3. In this case, the area is 180 cm^2.

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The area of the region inside the rectangle that surrounds the square is 147 square in.

The side of square is 10 in

Area of square is = side x side

A = 10 x 10

A = 100 square in.

Therefore, Area of square  is 100

The length of rectangle is 19 in and width of rectangle is 13in

area of rectangle  = l x w

A = 19 x 13

A = 247 square in.

Area of rectangle is 247 square in.

To calculate area of the region inside the rectangle that surrounds the square,

= A[rectangle] - A[square]

= 247 - 100

= 147 square in.

Therefore, The area of the region inside the rectangle that surrounds the square is 147 square in.

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In circle Y, the measure of m∠SZT is equal to: B. 94°.

In Mathematics, a chord of circle can be defined as a line segment that typically join any two (2) points of a circle.

Generally speaking, the inscribed angle of a circle is equal to half of the central angle of a circle. Mathematically, this is given by this mathematical expression:

m∠STR = 1/2(SYR)

m∠STR = 1/2(50)

m∠STR = 50°.

m∠TSU = 1/2(TYU)

m∠TSU = 1/2(72)

m∠TSU = 36°.

For m∠SZT, we have the following:

m∠SZT = 180° - (m∠STR + m∠TSU)

m∠SZT = 180° - (50 + 36)

m∠SZT = 180° - 84°

m∠SZT = 94°

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The x-intercept and the y-intercept of each line include the following ordered pairs:

x-intercept = (2, 0).

y-intercept = (0, -10).

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In Mathematics, the y-intercept is sometimes referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this exercise, we would use an online graphing calculator to plot the linear function in order to determine the x-intercepts and y-intercepts as shown in the image attached below.

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The approximate value of π for 15.42 is 3.855.

What is the Pi?

π (Pi) is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is an irrational number, which means that its decimal representation never terminates or repeats.

In a study of Mathematics, the number π read as pi is used.

The value of π is 3.1415926535 is the approximate value of 22/7

For this, in consideration of calculation, we take π as 22/7

The approximate value of π (pi) for 15.42 can be calculated as:

15.42 / 4 = 3.855

Hence, the approximate value of π for 15.42 is 3.855.

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The inequality that represents the situation when the number of lessons would mean that it is cheaper for Satvik to pay $60 for the month is x ≥ 15.

Inequality is a mathematical statement that two mathematical expressions are unequal.

Inequality is represented as either:

Payment Plans:

Plan A = $18 + $3 per lesson

Plan B = $60

Let each lesson = x

18 + 3x = 60

3x = 42

x = 14

x ≥ 15

Thus, if the number of lessons is greater than or equal to 15, it is cheaper for Satvik to pay under Payment Option B.

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