It measure the degree of accuracy of the sample mean as an estimate of the population mean​

The probability of drawing a diamond, then a black card, and then a face card from a standard deck of 52 cards with replacement is 3/104 or 0.028846 .

The probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card is given by the expression, `(13/52) × (26/52) × (12/52)`.

In a standard deck of 52 cards, there are 13 diamonds, 26 black cards (13 clubs and 13 spades), and 12 face cards (4 Jacks, 4 Queens, and 4 Kings).

To calculate the probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card, we use the formula of probability:

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

where, P(E) = Probability of an event

n(E) = Number of favorable outcomes

n(S) = Total number of outcomes

Total number of outcomes = 52

First card will be a diamond

Number of diamonds in a deck of 52 cards = 13

Total number of outcomes after drawing the first card = 52

Probability of drawing a diamond in the first attempt = P(diamond)`= 13/52

Probability of drawing a black card in the second attempt, given that the first card is a diamond= `P(black/diamond)`= (26/52) = `(1/2)`

Probability of drawing a face card in the third attempt, given that the first card is a diamond and second card is a black card= `P(face/diamond and black)`= `(12/52)` = `(3/13)`

Therefore, probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card`= P(diamond) × P(black/diamond) × P(face/diamond and black) = (13/52) × (1/2) × (3/13)= 3/104`

Therefore, the required probability is 3/104 or 0.028846 rounded to the nearest millionth.

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Answer:

[tex]x = 4\sqrt{3}[/tex]

Step-by-step explanation:

The triangle is right-angled

In a right-angled triangle, the following equality holds

[tex]\tan x = \dfrac{\text{Side Opposite x}}{\text{Side adjacent to x}}\\\\\tan 30 = \dfrac{4}{x}\\\\[/tex]

[tex]\tan 30 = \dfrac{1}{\sqrt{3}}\\\\\dfrac{1}{\sqrt{3}} = \dfrac{4}{x}\\\\[/tex]

Cross multiply:
[tex]1 \times x = 4 \times \sqrt{3}\\\\x = 4\sqrt{3}[/tex]

There are 169 outcomes in the complement of the given event.

To find the number of outcomes in the complement of the given event, which is that out of 344 high school students in their senior year, 175 are left-handed, you need to follow a few steps. So, let's get started. To find the number of outcomes in the complement of the given event, you will first find the total number of students that are right-handed, which can be found by subtracting the number of left-handed students from the total number of students:344 - 175 = 169Therefore, there are 169 right-handed students.

Next, to find the number of outcomes in the complement of the given event, you will need to subtract the number of outcomes in the given event from the total number of possible outcomes. Since the number of possible outcomes is equal to the total number of students, the number of outcomes in the complement of the given event can be found by subtracting the number of left-handed students from the total number of students:344 - 175 = 169 Therefore, there are 169 outcomes in the complement of the given event.

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Jen has 54 pages left to read to meet her assignment requirement.

The inequality that represents this situation is p ≥ 85 - 31

To find how many pages Jen has left to read, we can subtract the number of pages she has already read from the minimum number of pages she needs to read.

The minimum number of pages Jen needs to read is 85, and she has already read 31 pages. So, the number of pages she has left to read, p, can be found by:

p = 85 - 31

p = 54

Therefore, Jen has 54 pages left to read.

To represent this situation with an inequality, we can use:

p ≥ 85 - 31

This inequality states that the number of pages Jen still needs to read, p, must be greater than or equal to the difference between the minimum number of pages she needs to read (85) and the number of pages she has already read (31).

Solving for p:

p ≥ 85 - 31

p ≥ 54

This means that Jen must read at least 54 more pages to meet her assignment requirement.

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Answer:

Step-by-step explanation:

150

Using the property of a kite: the angles formed by two unequal sides of a kite are equal. The value of ∠BCD∠BCD is

∠BCD = ∠BAD ⇒ ∠BCD = 106°  

Answer:

Step-by-step explanation:

Angle L can be calculated as follows:

angle L = angle - 180 LMO stands for angle. MNO \sangle L = 180 - 150 - 30 degree angle L = 0

As a result, angle L is 0 degrees.

1. We know that sides AB and CD of trapezoid ABCD are parallel. We can use the tangent function to find the length of side AD because angle B is a right angle and angle ABD is 45 degrees:

AD/AB = tan(45)

AD=AB * tan(45) AD=AB

As a result, AD = 10.

2. We know that the sides PQ and RS of the trapezoid PQRS are parallel. We can use the sine function to find the length of side PS because angle Q is a right angle and angle PSQ is 60 degrees:

PS/QS sin(60) =

PS = sin * QS (60)

5 * sqrt = PS (3)

As a result, PS = 5*sqrt (3).

3. We know that the sides UV and WX of a trapezoid UVWX are parallel. We can use the cosine function to find the length of side WU because angle V is a right angle and angle WVU is 30 degrees:

WU/UV cos(30) =

UV * cos WU (30)

5 * sqrt(3) / 2 = WU

As a result, WU = (5/2)*sqrt (3).

4. We know that the sides LM and NO of the trapezoid LMNO are parallel. We can use the sine function to find the length of side MO because angle L is a right angle and angle MNO is 30 degrees:

MO/NO sin(30) =

MO = 4 / 2 MO = NO * sin(30)

As a result, MO = 2.

Because angles MNO and LMO add up to 180 degrees, we can calculate angle LMO as follows:

LMO angle = 180 - angle LMO MNO angle = 150 degrees

Finally, because angle N is a right angle, we can calculate angle L as follows:

angle L = angle - 180 LMO stands for angle. MNO\sangle L = 180 - 150 - 30 degree angle L = 0

As a result, angle L is 0 degrees.

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The equation that correctly represents this situation is c(t) = 45 + 45(t-2). This equation states that the total number of credits the student will have after t semesters is equal to 45 (the number of credits they had before beginning college) plus 45 times the number of semesters after two (t-2).

To explain this equation in more detail, we need to break it down. First, the student had some credits earned while in high school, so the equation starts off with c(t) = 45, which is the number of credits the student had before beginning college.

Next, 45(t-2) represents the number of credits earned in the additional semesters since college began. The t-2 part of the equation means that the total number of credits earned in the additional semesters starts at zero for t = 2. Then, for each additional semester, 45 credits are added. So, for example, when t = 5, 45 credits are added to the initial 45 credits the student had before beginning college, resulting in 90 credits.Therefore, the equation  c(t) = 45 + 45(t-2)  correctly represents this situation.

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The position of C on the number line is 1/8th position.

A number line is a visual representation of the real numbers as points or marks on a straight line. The number line is usually represented horizontally, with zero in the middle and positive numbers to the right of zero and negative numbers to the left of zero.

From the given number line, there are total 8 points between 0 to 1

That means, it's fractions of 8.

Location of point C is on the 1st point,

So, position of C on this number line = (1/8) ÷ (1-0) = 1/8

Therefore, In the number line, C is located in the 1/8th place.

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The  value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.

(a) To verify that C(3) < C(6), we have to find the values of C(3) and C(6).The given function is C(x) = s(x x+3)The order size is measured in hundreds. So, when x = 3, the order size is 300 and when x = 6, the order size is 600.Therefore, C(3) = s(3 x 3+3) = s(18) and C(6) = s(6 x 6+3) = s(39)Now, as s(x) > 0, we can see that C(6) > C(3). Hence, C(3) < C(6).(b) According to Rolle's Theorem, the rate of change of the cost must be 0 for some order size in the interval (3 < x < 6).We know that the function is continuous and differentiable in the interval (3 < x < 6). Now, the rate of change of the cost is given by the derivative of the function C(x) with respect to x.C(x) = s(x x+3)C'(x) = s[1 + (x + 3) . 1] = s(1 + x + 3) = s(x + 4)As per Rolle's Theorem, there must exist a value of x in the interval (3 < x < 6) such that C'(x) = 0.So, s(x + 4) = 0x + 4 = 0x = -4Thus, the order size is -4 x 100 = -400. However, this is an absurd answer as the order size cannot be negative. Therefore, there is no value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.

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The given conditional statements are false, true, false, True.

They are determined by following:

(a) False - The statement "If 10<7,10<7, then 3=43=4" is false, since 10 is not less than 7.
(b) True - The statement "If 7<10,7<10, then 3=43=4" is true, since 7 is less than 10.
(c) False - The statement "If 10<7,10<7, then 3+5=83+5=8" is false, since 10 is not less than 7.
(d) True - The statement "If 7<10,7<10, then 3+5=83+5=8" is true, since 7 is less than 10.

Conditional statements are used in mathematics and logic to express relationships between events and conditions. These statements consist of an "if-then" structure, where the "if" clause is the antecedent or condition, and the "then" clause is the consequent or outcome.

The truth value of the conditional statement depends on whether the condition is true or false. If the condition is true, then the outcome is also true, and the statement is considered true.

If the condition is false, then the outcome may be true or false, and the statement is considered false. Conditional statements are widely used in mathematical proofs, programming, and reasoning to establish logical connections between different events and conditions.

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(a) Symbol used for sample standard deviation is “s” or “σˆ” (s-hat). The unit for the sample standard deviation is grams, as it is calculated from a sample.

(b) Symbol used for population standard deviation is “σ” (sigma).The unit for the population standard deviation is also grams, as it is calculated for the entire population.

The population standard deviation is a parameter, which is a fixed value calculated from every individual in the population.

A sample standard deviation is a statistic. This means that it is calculated from only some of the individuals in a population. Since the sample standard deviation depends upon the sample, it has greater variability.

(c) Symbol used for sample variance is “s²” or “σ²ˆ” (sigma-hat squared). The unit for the sample variance is grams², as it is calculated from a sample.

(d) Symbol used for population variance is “σ²” (sigma squared). The unit for the population variance is also grams², as it is calculated for the entire population.

Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data.

Due to this value of denominator in the formula for variance in case of sample data is ‘n-1’, and it is ‘n’ for population data. As a result both variance and standard deviation derived from sample data are more than those found out from population data.

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Answer: 31.8 years

Step-by-step explanation:

The formula to calculate the simple interest is:

I = Prt

where:

I = Interest

P = Principal amount

r = Rate of interest

t = Time (in years)

We want to know how long it will take for the investment to double in value. That means the interest earned should be equal to the principal amount. So, we can write:

2P = P + I

Simplifying:

P = I

Now, we can substitute the values given in the problem:

1400 = 14000.044t

Simplifying:

t = 1400/(1400*0.044) = 31.82 years

Therefore, it will take approximately 31.8 years for the investment to double in value.

Answer:

10 sides

Step-by-step explanation:

We can use the formula for the sum of the interior angles of a polygon to solve this problem. The formula for the sum of the interior angles of a polygon with n sides, where S is the sum of the interior angles, and n is the number of sides of the polygon is:

S = (n - 2) x 180 degrees

If the sum of the interior angles is 1440 degrees, we can set this equal to the formula and solve for n:

1440 = (n - 2) x 180

Dividing both sides by 180, we get:

8 = n - 2

Adding 2 to both sides, we get:

n = 10

Therefore, a polygon with a sum of interior angles of 1440 degrees has 10 sides.

Answer: profit

Step-by-step explanation:

3.95 (price of one share) multiplied by 40 (the amount of shares bought) would have cost $158. so selling all for $200 would be a $42 profit

The cost of sales for liquor, expressed as a percentage is 19.39%.

To compute for the cost of sales for liquor, expressed as a percentage given that you have spent $2,500 on liquor for your bar and your bar sales have been $12,890, you can use the formula:

Cost of sales = (Cost of Goods Sold / Total Sales) × 100

where, Cost of Goods Sold (COGS) = Beginning Inventory + Purchases - Ending Inventory (or the total cost of goods sold during the period)

Total Sales = Gross sales - Sales discounts - Sales returns and allowances

Let's compute for the COGS first:

COGS = Beginning Inventory + Purchases - Ending Inventory

= $0 + $2,500 - $0

= $2,500

Total Sales = Gross sales - Sales discounts - Sales returns and allowances

= $12,890 - $0 - $0

= $12,890

Cost of sales is obtained as follows:

Cost of sales = (Cost of Goods Sold / Total Sales) × 100

= ($2,500 / $12,890) × 100

= 19.39%.

Therefore, the cost of sales for liquor, expressed as a percentage is 19.39%.

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The survey ratings provide valuable feedback for drivers who are looking for quality tires for their vehicles. These ratings can give insight on steering responsiveness, how quickly a tire wears, and overall customer satisfaction. Drivers can also see how their tire of choice stacks up against other tires, making it easier to make an informed decision when shopping for tires.

The Tire Rack is America’s leading online distributor of tires and wheels. They conduct extensive testing to ensure that customers are provided with the most suitable tires for their vehicles, driving styles, and driving conditions. They also use an independent consumer survey to help drivers gain insight on long-term tire experiences.

The following data show survey ratings on a 1-10 scale, with 10 being the highest rating, of 18 maximum performance summer tires, as of February 3, 2009 (Tire Rack website). The variables are Steering (steering responsiveness), Tread Wear (quickness of wear), and Buy Again (overall tire satisfaction and desire to purchase the same tire again). The Yokohama Aegis LS4 has a Steering rating of 7.9, Tread Wear rating of 7, and Buy Again rating of 7.1. The Dunlop SP20 FE has a Steering rating of 5.7, Tread Wear rating of 5, and Buy Again rating of 3.3.

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a) To write the ratio of the number of machines to the number of crates packed per day in the form 1: n, we need to find the number of crates packed per day per machine. We can do this by dividing the total number of crates packed per day by the number of machines:

Number of crates packed per day per machine = 150 crates/day ÷ 60 machines = 2.5 crates/machine/day

Therefore, the ratio of the number of machines to the number of crates packed per day in the form 1: n is 1:2.5 or 2:5.

b) To find out how many crates of limes 70 of these machines would pack per day, we can use the ratio from part (a) to set up a proportion:

1 machine : 2.5 crates/day = 70 machines : x crates/day

Solving for x, we get:

x = (70 machines × 2.5 crates/day) / 1 machine = 175 crates/day

Therefore, 70 of these machines would pack 175 crates of limes per day.

Step-by-step explanation:

a) The ratio of the number of machines to the number of crates packed per day can be written as:

60 : 150

To simplify this ratio, we can divide both sides by 10:

6 : 15

Finally, we can divide both sides by 3 to get the ratio in the form 1 : n:

1 : 2.5

Therefore, the ratio of the number of machines to the number of crates packed per day is 1 : 2.5.

b) If 60 machines can pack 150 crates per day, then one machine can pack:

150/60 = 2.5 crates per day

So, 70 machines can pack:

70 × 2.5 = 175 crates per day

Therefore, 70 machines can pack 175 crates of limes per day.

Answer:

x = 45.

Step-by-step explanation:

Given a straight line with the equation.

First collect like terms:

2x + x = 180 - 45

Then calculate:

3x = 135

Finally after dividing both sides by 3:

x = 45

Answer: The answer for the first question goes as follows: Which one(s) have both pairs of opposite sides that are parallel? Rectangle, Rhombus, and square. Which one(s) have both pairs of opposite sides that are congruent? Rectangle, square, and rhombus. Which one(s) have all four sides congruent? Square and rhombus.

The answers to the second question are:

Step-by-step explanation:

Essentially, all of these parallelograms have different properties and properties that they share. For example, a property they share by the definition of a parallelogram is that all of them have two pairs of opposing sides that are parallel. Another property they share from the definition of a parallelogram is that opposite sides are congruent.

As such, rectangles, squares, and rhombuses have the properties that all parallelograms have because they are all parallelograms. However, they also have their own properties.

Second Question Explanation:

1. The question is describing a theater that has a circular base. Therefore, you can use the formula for the circumference of a circle, pi * diameter, to find the circumference (or distance around) the theater. The diameter is given to you: 100 ft. So just multiply that by pi.

2. The question is asking for the area of the theater. This means that you can use the formula for the area of a circle, A = pi * r^2. Note that it is asking you for the area, not the volume, so you would find the area of the circle, not the volume of the hemisphere. r represents the radius of the circle/theater. The diameter is given as 100 ft, and the radius is half of the diameter, so it is 50 ft. Now just plug the radius into the equation and you get the answer I showed.

Answer: 54 square in

Step-by-step explanation:

I don't know if this is the same person but I answered this same question just now please check my profile or comment if you want the explanation

a) Biker A follows the hypotenuse of the triangle on a straight path.

It is probable that the bikers will meet at the vertex located at the base of the triangle.

The bikers have created a triangle with sides measuring 12, 21, and 24 miles and angles measuring 61, 89, and 30 degrees, respectively.

a) Biker A follows the hypotenuse of the triangle on a straight path.

It is probable that the bikers will meet at the vertex located at the base of the triangle.

They cover almost equal distances from their starting points:

24 miles ≈ √12²+21² miles

b) They encounter each other.

c) The angle at one vertex measures 30 degrees.

d) e) As shown in the attached picture, it is an almost right triangle.

f) Together, they cover a total distance of 57 miles (12+21+24).

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Answer:

5 less than or equal to x

Step-by-step explanation:

make x subject

Answer:

It has no solution within Real numbers. Its solutions are Complex/imaginary, since its discriminant is negative (-64).

Step-by-step explanation:

The normalized form of the equation

(x+2)^2= - 16

x^2 + 4x + 4 = - 16

x^2 + 4x + 20 = 0

We have in the form ax^2 + abx + c = 0

a = 1

b = 4

c = 20

Discriminant is b^2 - 4ac = 4^2 - 4*1*20 = 16 - 80 = - 64

Discriminant is negative, therefore, no Real solutions.

Step-by-step explanation:volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length

The distance from points A(-2, 2) to B (4, -2)​ is equal to √52 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical expression:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given points into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(4 - (-2))² + (-2 - 2)²]

Distance = √[(6)² + (-4)²]

Distance = √(36 + 16)

Distance = √52 units.

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Answer:

Step-by-step explanation:

2(2x-5) = 18 (FOIL)

4x-10=18

4x = 28

x= 7

Answer:

x = -2

Step-by-step explanation:

2(2x - 5) = -18

Divide both sides by 2.

2x - 5 = -9

Add 5 to both sides.

2x = -4

Divide both sides by 2.

x = -2

Answer:

Step-by-step explanation:

120