Cassie rolls a fair number cube with 6 faces labeled 1 through 6. She rolls the number cube 300 times. Which result is most likely?

Let's call the time it takes to install all the chairs from start to finish "t". The workers install 840 chairs per day, so in "t" days they will have installed 840 * t chairs.

At the end of 5 days, they still have 240 chairs to install, so they have installed 840 * 5 chairs so far. We can use this information to write an equation:

840 * t - 840 * 5 = 240

Expanding and simplifying the equation gives us:

840t - 4200 = 240

Adding 4200 to both sides gives us:

840t = 4440

Finally, dividing both sides by 840 gives us:

t = 5.2857142857...

So it takes approximately 5.29 days to install all the chairs from start to finish.

Answer:

1

Step-by-step explanation:

6 is tenths and after is 1 which is hundredths

The explicit formula for the geometric series is [tex]a_n = 3(5)^{n-1}[/tex].

A geometric series is one in which there is a constant separating the two succeeding numbers. In other words, to create a geometric progression, each succeeding term is multiplied by the constant term.

Given that the geometric sequence is,

3, 15, 75......

The common ratio of the series is calculated as the ratio of the second term to the first term,

r = 15 / 3

r = 5

The explicit formula can be written as:-

[tex]a_n = a_1(r)^{n-1}[/tex]

[tex]a_n = 3(5)^{n-1}[/tex]

Therefore, the formula is [tex]a_n = 3(5)^{n-1}[/tex].

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Answer:

Second string, first fret.

Step-by-step explanation:

Sample variance and standard deviation are considered biased estimates of population variance and standard deviation because they tend to underestimate the true population variance and standard deviation.

The reason for this is that the sample variance and standard deviation are based on a sample of the population, not the entire population. The sample may not accurately represent the entire population, and thus the sample variance and standard deviation may not accurately reflect the true population variance and standard deviation. To correct for this bias, a correction factor is usually added to the sample variance calculation. For example, when estimating the population variance from a sample of size n, the sample variance is divided by (n-1) instead of n. This correction factor helps to provide a more accurate estimate of the population variance. Similarly, the sample standard deviation is calculated as the square root of the sample variance, and the correction factor is also applied to the sample standard deviation calculation. This corrected sample standard deviation is known as the unbiased sample standard deviation.

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Complete Question

sample variance and standard deviation are considered biased estimates of population variance and standard deviation because they tend to: What?

The solutions to the system of linear equation (x, y) are 1 and 4/3 respectively

A system of linear equations is a collection of two or more linear equations with the same variables. The goal of solving a system of linear equations is to find the values of the variables that simultaneously satisfy all the equations in the system.

From the question given;

-x + 6y = 7 ...eq(i)

6x - 30y = -34 ...eq(ii)

From eq (i)

x = 6y - 7 ..eq (iii)

Put eq (iii) into eq (ii)

6(6y - 7) - 30y = -34

36y - 42 - 30y = -34

6y - 42 = -34

6y = -34 + 42

6y = 8

y = 4/3

Put y = 4/3 into eq (i)

-x + 6(4/3) = 7

-x + 24 / 3 = 7

x = 24/3 - 7

x = 1

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Answer: 41 degrees

Step-by-step explanation:

121-39=82

82/2=41

Answer:

240/2, 360/3

Step-by-step explanation:

240/2 and 360/3 both involve division and both of their answers are equal to 120, assuming these count as number sentences.

The formula used to calculate the surface area of a square pyramid is A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]

The square pyramid is the geometric shape that has a square base and 4 lateral face. The total number of faces will be five. The base shape is square and the side shape will be triangle. Number of edges in the square pyramid is eight

The surface area is the amount space covered by the surface of the object

Here the surface area of the square pyramid is

A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]

Where A is the surface area of the square pyramid

a is the base edge

h is the height of the square pyramid

Therefore, the surface area is A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]

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To find the balance of the account at the end of the week, we need to calculate all the transactions:

Initial balance: $150

Shoes: -$180

Cash advance: +$300

Repaid debt: -$250

Bank fee: +$110

Cash deposit: -$150

So the final balance would be $150 - $180 + $300 - $250 + $110 - $150 = $-70.

This means the balance of the account at the end of the week would be -$70.

Answer:

2 × 3 × 3 × 5 = 2 × 3 × 3 × 5

Step-by-step explanation:

The prime factorization of 90 is 2 × 3 × 3 × 5, so the prime factors are 2, 3, 3, and 5. Ordering the factors from least to greatest, we have:

2 × 3 × 3 × 5 = 2 × 3 × 3 × 5.

112.8 is the the total sound power, when three drill presses are operating

A relation is a function if it has only One y-value for each x-value.

Given that a function P(n) = 108 + 10 log(n) gives the total sound power in decibels when n drill presses are operating in a factory.

We need to find the total sound power, to the nearest decibel, when three drill presses are operating

We have to consider n as 3

P(3) = 108 + 10 log(3)

=108+10×0.477

=108+4.77

=112.77

Hence, 112.8 is the the total sound power when three drill presses are operating

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The most accurate estimated sum of 181 and 204 is 380

The given numbers are 181 and 204

The compatible numbers are defined as the numbers that are easy to do the arithmetic operations. The arithmetic operations are addition, subtraction, division and multiplication etc.

To find the sum of the compatible numbers first we have to round the given numbers to the nearest tens or hundreds and do the the arithmetic operation

Round 181 to the nearest tens = 180

Round 204 to the nearest tens = 200

Then the sum of compatible numbers will be

180 + 200 = 380

Therefore, the most accurate estimation is 380

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The length of the third side of a triangle with perimeter 9x + 6 and measures of other two sides of the triangle is equal to option a. x + 13.

Perimeter of the triangle is equal to

= 9x + 6

First side of the triangle = 5x

Second side of the triangle = 3x - 7

Let 'n' be the third side of the triangle

perimeter of the triangle = 9x + 6

⇒ 5x + 3x - 7 + n = 9x + 6

⇒ n + 8x - 7 = 9x + 6

⇒ n = 9x -8x + 6 + 7

⇒ n = x + 13

Therefore, the third side of the triangle with given perimeter of the triangle is equal to option a. x + 13.

The above question is incomplete , the complete question is :

A triangle has a perimeter of 9x + 6. the first side of the triangle has a length of 5x, and the second side has a length of 3x − 7. what is the length of the third side of the triangle?

a. x + 13       b. x − 1            c. 8x − 7         d. 17x − 1

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The number of possible requests for free samples is 5^1 = 5. This means that the customer has 5 different requests that they can make for free samples.

The number of possible requests for free samples can be calculated using the combination formula. The combination formula is used to calculate the number of combinations with repetitions of size “n” taken from a set of “r” elements . The formula is: [tex]C(n,r) = n^r[/tex] In this case, n = number of requests (1 request) and r = number of free samples offered (let’s say, 5). Therefore, the number of possible requests for free samples is[tex]5^1 = 5.[/tex]This means that the customer has 5 different requests that they can make for free samples.

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Answer:

To solve the problem, Sarah used the equation:

Left-handed people = (11/100) * Total people

Step 1: Plug in the total number of people (30) into the equation.

Left-handed people = (11/100) * 30

Step 2: Simplify the right side of the equation.

Left-handed people = (11/100) * 30

Left-handed people = 3.3

Step 3: Round the answer to the nearest whole number.

Left-handed people = 3

So, Sarah expects 3 people in a class of 30 to be left-handed. Each step of Sarah's work is justified because she used the percentage formula to find the number of left-handed people in a class and rounded the answer to the nearest whole number.

In a magnetometry experiment, It will take 1 more minute for data be collected in order to reduce error the statistical noise by a factor of 10.

To reduce the random error by a factor of 10, we need to reduce the statistical noise to 1/10 picotesla. Since the statistical noise was initially 1 picotesla, this means we need to reduce it by a factor of 10.

We can use the following formula to calculate the time needed to reduce the statistical noise by a certain factor:

t = (log (final noise / initial noise)) / (log (reduction factor))

Here, the final noise is 1/10 picotesla, the initial noise is 1 picotesla, and the reduction factor is 10.

Plugging in these values, we get:

t = (log (1/10 / 1)) / (log (10))

t = (log (1/10)) / (log (10))

t = -1 / 1

t = -1

The negative value of t doesn't make sense in this context, so we need to take the absolute value:

t = |-1|

t = 1

Therefore, it will take 1 more minute to reduce the statistical noise by a factor of 10.

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____The given question is incomplete, the complete question is given below:

Reduction of the standard error

In a magnetometry experiment, after a minute of collecting

data the statistical noise was reduced to 1 picotesla.

For how much longer should data be collected in order

to reduce the random error by a factor of 10?

Answer:

(assuming the 2 was an exponent, if I am wrong don't use this answer) 6a^2 + 12b

Step-by-step explanation:

Add like terms

6a^2 + 12b

Answer:

Gordon will have $106892.8 in three years

Step-by-step explanation:

92338 (0.05 + 1)³=

92338(1.05)³=

92338 x 1.16 =

106892.8

According to the above, we can infer that the value of FE is: 10 cm

To find the value of FE we must analyze the image of this triangle. Additionally, we must take into account the information we know, that is, the length of two sides (5 cm) and the height (4 cm), the area (20cm²).

So we must use the formula for the area of a triangle and isolate the values that we do know to find the value of the base.

According to the above, the value of segment FE is 10 cm.

Note: This question is incomplete. Here is the complete information:

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Answer:

Diatance biked = rate • time

The number is 2. To find the unknown number that satisfies the equation "4x = 8x - 8," we can simplify and solve for x, which gives us the answer x = 2.

Let's call the unknown number "x".
According to the problem statement, "A certain number is multiplied by 4 and the result equals 8 less than 8 times of the number" can be translated into the following equation:
4x = 8x - 8
Simplifying this equation, we can move 4x to the right side of the equation:
4x - 8x = -8
Simplifying further, we get:
-4x = -8
Dividing both sides by -4, we find:
x = 2
Therefore, the number is 2.

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Amount of square feet of outdoor carpet needed for the hole is 6 feet².

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Given is a triangular region with a hole in the shape of a rectangle.

We need to find the area of the hole in order to find the amount of square feet of outdoor carpet needed for the hole.

Area of a rectangle = Length × Width

From the figure,

Length = 3 feet and Width = 2 feet

Area = 3 × 2 = 6 feet²

Hence 6 feet² of outdoor carpet is needed for the hole.

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The side lengths on the similar polygons are given as follows:

Similar polygons are polygons that share these two features presented as follows:

Considering the equivalent side lengths, the proportional relationship for the side lengths in this problem is given as follows:

18/16 = 18/EI = ST/24.

Hence the length of EI is given as follows:

EI = 16.

The length of ST is obtained as follows:

18/16 = ST/24

16ST = 18 x 24

ST = 18 x 24/16

ST = 27.

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The minimum number of tables the store must sell is 5.

Two or more expressions with an Equal sign is called as Equation.

Using t and c as variables, we get

100c + 400t ≥ 3000

c+t≤16

The online furniture store must sell at least $3000 worth of chairs and tables each day, and can ship at most 16 pieces of furniture.

If the store sells 9 chairs for a total of $900, it needs to sell at least 5 tables to reach a total revenue of $3000.

Since the total number of pieces of furniture sold is 14 (9 chairs + 5 tables), which is less than the maximum of 16, the store meets the daily shipping requirement.

Therefore, the minimum number of tables the store must sell is 5.

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The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in

(4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in

(6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

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Keenan has placed his solar panel at an optimal angle.

The cosine law is a mathematical relationship between the sides and angles of a triangle. The cosine law states that:

cos(C) = (a² + b² - c²) / 2ab

where a, b, and c are the lengths of the sides of the triangle and C is the measure of one of the angles. This law can be used to find unknown side lengths or angle measures in a triangle when given the other values.

Check the attached image for labelling.

The angle we are trying to calculate is labelled C.

cos (C) = (20² + 18² - 19²) / (2*20*18)

cos (C) = 363/720

C = cos⁻¹(363/720)

C = 59.72°

Since the angle obtained is between 58° and 60°. Thus, Keenan has placed his solar panel at an optimal angle.

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Complete Question

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