A factory is making screws. The weight of the crews is normally distributed, and the variance is 0.64g^2.
In a sample the mean of the screws was 44g. Calculate a two sided(symmetrical) confidence interval with confidence level 95% for the expected value of the weight, if the sample size was
a)13
b)1300

Answer:

Step-by-step explanation: 17/5

The sequence represented by means of the equation a n =4(3)^ n-1 is an exponential sequence with a commonplace ratio of 3 and an preliminary term of 4.

To see this, we can plug within the values of n and study the pattern:

Whilst n = 1:

a 1 = 4(3)^0 = 4(1) = 4

Whilst n = 2:

a 2 = 4(3)^1 = 4(3) = 12

Whilst n = 3:

a three = 4(3)^2 = 4(9) = 36

While n = 4:

a 4 = 4(3)^3 = 4(27) = 108

And so on.

We can see that every time period in the sequence is received by way of multiplying the previous term by using 3, and that the first term is 4.

Thus, the sequence is an exponential sequence with a commonplace ratio of 3 and an preliminary term of 4.

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Therefore, the value of x that satisfies the equation √x = 14i√3 is -588. The answer is (a). The only value of x that satisfies this equation is option (b): which is -2i.

We can start by squaring both sides of the equation to eliminate the square root:

We have to apply the knowledge of multiplying or squaring a complex number will give us a negative value.

(√x)^2 = (14i√3)^2

x = (14i)^2 x (√3)^2

We have to take the square of the complex number and the square root of 3.

x = -196 x 3

Multiply the value

x = -588

The value of x in the equation is -588.

2. We can factor out x from the expression as follows:

x(x^4 + 6x^2 + 8)

Now, we need to find the value(s) of x that make the expression equal to 0.

We can see that one solution is x = 0, since anything multiplied by 0 is 0.

To find the other solution(s), we can solve the quadratic equation inside the parentheses:

x^4 + 6x^2 + 8 = 0

Substitute y = x^2:

y^2 + 6y + 8 = 0

Factor the quadratic equation:

(y + 4)(y + 2) = 0

Therefore, the possible values of y are -4 and -2. Substituting back y = x^2, we get:

x^2 = -4 or x^2 = -2

Since x^2 cannot be negative for real numbers, there are no real solutions to this equation. However, if we allow complex numbers, we can find the solutions by taking the square roots of -4 and -2:

x = ±2i or x = ±sqrt(2)i

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Answer:

549

Step-by-step explanation:

The order of operations is a sequence in which operations should be performed to evaluate a mathematical expression correctly. A common way to remember is PEMDAS:

To simplify the expression 19×33−2(16+23) using the order of operations, first solve the operations inside the parentheses:

Now we multiply:

The expression now looks like this:

Perform the multiplication before the subtraction:

Now that we have done the multiplication, we can subtract:

Therefore, the expression simplified is 549.

Answer:

b

Step-by-step explanation:

Answer: -22

Step-by-step explanation:

replace the variables with their given values and calculate

-3(2) + 4(-4)

Mathematically, this can be expressed as follows: Percentage Increase = (15 - 10) / 10 x 100= 5 / 10 x 100= 50%.

The percentage increase can be calculated by taking the difference between the two weights and dividing it by the original weight. In this case, the percentage increase is 25%. Mathematically, this can be expressed as follows: Percentage Increase = (5 kg - 4 kg) / 4 kg x 100= 1 kg / 4 kg x 100= 25%In a broader sense, the formula for calculating the percentage increase of any quantity is given by: Percentage Increase = (Final Value - Initial Value) / Initial Value x 100This formula can be used to determine the percentage increase of any quantity, not just weight. For example, if the price of a product increases from $10 to $15, then the percentage increase in the price can be calculated using the same formula. In this case, the percentage increase would be 50%. Mathematically, this can be expressed as follows: Percentage Increase = (15 - 10) / 10 x 100= 5 / 10 x 100= 50%.

Step 1: Calculate the difference between the two weights:

5 kg - 4 kg = 1 kg

Step 2: Calculate the percentage increase:

(1 kg / 4 kg) x 100 = 25%

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The addition of the two numbers in scientific notation is given as follows:

[tex](3.5 \times 10^7) + (7.1 \times 10^9) = 7.135 x 10^9[/tex]

A number in scientific notation is given by the notation presented as follows:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.

The addition operation for this problem is given as follows:

[tex](3.5 \times 10^7) + (7.1 \times 10^9)[/tex]

To add two terms, they must have the same exponent, hence I am going to convert 3.5 x 10^7 to exponent 9, as follows:

[tex]3.5 \times 10^7 = 0.35 \times 10^8 = 0.035 \times 10^9[/tex]

Two add two terms, we add the bases and keep the exponents, hence:

[tex](0.035 \times 10^9) + (7.1 \times 10^9) = 7.135 \times 10^9[/tex]

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The division of labor, or specialization of tasks, has boosted efficiency and productivity in the United States, thereby stimulating economic growth. It also facilitates the growth of factories and mass production, which further contributes to the overall economic growth of the country.

Division of labor:

Division of labor is the process of dividing the work of producing goods and services into separate tasks performed by different people or groups of people. Division of labor is an economic concept that states that dividing a production process into stages allows workers to focus on specific tasks. If workers can concentrate on a small aspect of production, as long as sufficient quantities and quantities are produced, overall efficiency will increase.

This division is generally based on the skills, expertise and resources of the worker, as well as the wants and needs of the market.

The purpose of division of labor is to increase efficiency and productivity by allowing workers to specialize in specific tasks and develop expertise in those tasks. This can lead to better quality products and services and lower costs. The division of labor is a key concept in economics and an important factor in the development and growth of societies.

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Answer:

boron

particle 1

Step-by-step explanation:

boron is number 5 on the periodic table of elements.

mass - protons= neutrons

11(rounded up) - 5 = 6 neutrons

ions are when an atom is positively or negatively charged. for example electrons are higher than protons or vice versa.

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{y varies inversely with x}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=8\\ y=6 \end{cases} \\\\\\ 6=\cfrac{k}{8}\implies 48=k\hspace{10em}\boxed{y=\cfrac{48}{x}}[/tex]

The width of the rectangular cornfield is 400 meters.

The circumference of a two-dimensional shape's perimeter is its entire length. In geometry, perimeter is used to calculate the length of a polygon's perimeter, such as a circle, square, triangle, or rectangle. By adding up the lengths of each side, one may determine a polygon's perimeter. For instance, the formula P = 2L + 2W may be used to determine the perimeter of a rectangle, where P stands for the perimeter, L for the length, and W for the width. The idea of perimeter is crucial to understanding geometry because it allows us to estimate how much material is required to enclose a form, such as fencing for a rectangular area or carpeting for a room.

Let us suppose the width of the field = w.

The perimeter of the rectangle is given as:

P = 2(l + w)

Substituting the given values, we get:

1,800 = 2(500) + 2w

1,800 = 1,000 + 2w

800 = 2w

w = 400

Therefore, the width of the rectangular cornfield is 400 meters.

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Answer: the speed of the train that started from point M is 92.5 mph, and the speed of the train that started from point N is 97.5 mph (92.5 + 5).

Step-by-step explanation:

Let's use the following variables:

x = speed of the train that started from point M

x + 5 = speed of the train that started from point N

We know that:

The total distance between the trains is 380 miles.

In 2 hours, the distance between the trains decreased by 30 miles.

Using the formula: distance = rate x time, we can write two equations:

Equation 1: 2x + 2(x + 5) = 380 (the sum of the distances traveled by the two trains equals the total distance between them)

Equation 2: 2x - 2(x + 5 - 30/2) = 30 (the difference in distances traveled by the two trains in 2 hours equals the decrease in distance between them)

Simplifying Equation 1:

4x + 10 = 380

4x = 370

x = 92.5

Therefore, the speed of the train that started from point M is 92.5 mph, and the speed of the train that started from point N is 97.5 mph (92.5 + 5).

To check, let's substitute these values into Equation 2:

2(92.5) - 2(97.5 - 30/2) = 30

185 - 155 = 30

30 = 30

This confirms that our solution is correct.

Answer:

Step-by-step explanation:

Knowing that we have a Right triangle find the third angle first, 53 + 90 =180 which the answer will be 37 degrees then add that answer to 41 to get you the second degree of your whole triangle, which will be 78 degrees. Then you can find the last angle by adding 78 + 53 = 180, the answer is 49 degrees. Now you have enough information to find the second triangles hypotenuse, using the law of sines which will end up being 12 inches approximately then you can use law of sines again but this time for the 1st triangle on the left. Giving you an answer of 15 inches for the whole side on the top of the triangle, but then you must subtract 8 inches, giving you the FINAL answer of 7 inches.

Answer: 2280 more

Step-by-step explanation:

We need to first find out how much Dani spends to make one treat bag:

1520/2 = 760

Now we can find out how much it would cost to make 5 more bags:

760 x 5 = 3800

Therefore, Dani would have to spend 3800 - 1520 = 2280 more to make 5 more similar bags.

Based on the information provided, Maxine needs to buy a total of 6 cups of flour.

The total of flour can be calculated by adding the numbers provided; however, to make it easier let's simplify the numbers:

Chocolate cake: 1 3/4 = 1.75

Chocolate chip cookies: 2 1/3 = 2.33

Brownies: 1 2/3 = 1.66

Now, let's add the amounts given:

1.75 + 2.33 + 1.66 = 5.74 which can be rounded as 6 cups, which means she will need to buy a 6 or 7-cup bag.

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100 is the common difference of the given sequence

An ordered collection of objects that allows repetitions is referred to as a sequence. It has members, just like a set does. The length of the sequence is the number of elements.

Given the sequence below

8, 108, 208, 308...

The nth term of an arithmetic sequence is given as Tn = a + (n-1)d

The common difference is the difference between the preceding and the succeeding term.

First term = 12

Second term = 20

Common difference = 108 -8 = 208 - 108

Common difference = 100

Hence the common difference of the sequence is 100

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The Good Fruit stand needs to sell 180 baskets of cherries and 240 baskets of blueberries to reach their daily sales goal of $720.

1 cherry = $4

1 blueberry = $3

60 cherry basket:

60 × 4

= 240

Goal amount = $720

Bw day selling blueberry basket

Money:

= 720 - 240

= 480

Blueberry basket = 480 ÷ 3

Cherry = 60

Blueberry = 160

Sales goals are measurable objectives that sales reps and teams use to guide them through their day-to-day sales activities and help them make big-picture strategic decisions. Sales goals are usually based on KPIs and specific sales metrics.They are data-driven and are meant to provide a blueprint for sellers and organizations on how to achieve new levels of success. Sales goals bring clarity and control to the sales process while also mitigating risk.

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Question:

The Good Fruit stand sells baskets of cherries for $4 and baskets of blueberries for $3. Its daily sales goal is $720. Write and graph the linear equation that describes the problem. Use the graph to find how many baskets of blueberries it must sell to reach its goal if 60 baskets of cherries are sold.

Answer:

The correct answer is 3) an.

In a geometric sequence, the term can be calculated by the formula an = a1 × r^(n–1).

In this case, the first term (a1) is 4, the common ratio (r) is 2, and the 15th term (n) is 15. Therefore, replacing an with 27, we get 27 = 4 × 2^(15–1). Solving for the 15th term (n), we get n = 27/4 × 2^(-14). The 15th term is 27.

The value of P(A and B) is 0.24.

What is Conditional probability?

Conditional probability is a type of probability that describes the likelihood of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the joint occurrence of both events by the probability of the occurrence of the event that has already occurred.

More formally, if we have two events A and B, the conditional probability of event A given event B is denoted by P(A|B) and is defined as:

P(A|B) = P(A and B) / P(B)

We are given :

P(A)=0.6, P(B)=0.4, and P(B|A)=0.4

We can use the formula for conditional probability to solve :

P(B|A) = P(A and B) / P(A)

We can write it as :

P(A and B) = P(B|A) * P(A)

Now, Substituting in the given values, we get:

P(A and B) = 0.4 * 0.6 = 0.24

Therefore, the probability of both events A and B occurring is 0.24.

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Alfonzo can mow at most 4 lawns if he works at least 14 hours. And we used the "less than or equal to" symbol because Alfonzo may not be able to mow a fraction of a lawn.

What is an Inequality ?

An inequality is a mathematical statement that describes a relationship between two values or expressions that are not necessarily equal.

Let's start by determining how many lawns Alfonzo can mow in 1 hour:

1 hour = 4/4 hours

Lawns mowed in 1 hour = 1 / (3/4) = 4/3

Now, let L be the number of lawns Alfonzo can mow if he works at least 14 hours. Since he works 8 hours without a lunch break, he has (14 - 8 - 1/2) = 5.5 hours left to work after his lunch break. Therefore, we can set up the following inequality to find L:

4/3(L) ≤ 5.5

Multiplying on both sides by 3/4, we get:

L ≤ 5.5 x 3/4

L ≤ 4.125

Therefore, Alfonzo can mow at most 4 lawns if he works at least 14 hours. Note that we used the "less than or equal to" symbol because Alfonzo may not be able to mow a fraction of a lawn.

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Leah should multiply her current balance by 1.08 to find her total balance in one year.

To find Leah's total balance in one year, we can use the simple interest formula:

Simple Interest = Principal x Rate x Time

where:

Principal is the amount of money invested

Rate is the interest rate per year

Time is the time period in years

In this case, we know that Leah's account pays a simple interest rate of 8% per year, and no money will be added or removed from the account during the year. Hence, we may condense the formula to:

Total Balance = Principal + Simple Interest

Total Balance = Principal + (Principal x Rate x Time)

Total Balance = Principal x (1 + Rate x Time)

So to find Leah's total balance in one year, she should multiply her current balance by (1 + 0.08 x 1), which simplifies to 1.08:

Total Balance = Current Balance x 1.08

For example, if Leah currently has 1,000 in her account, her total balance in one year would be:

Total Balance = 1,000 x 1.08

Total Balance = 1,080

So Leah should multiply her current balance by 1.08 to find her total balance in one year.

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When x is equal to 5, the value of y is equal to 9/11. When x is equal to 0, y is equal to -1/6 and when x is equal to -6, y is undefined since the denominator of the fraction is equal to 0.

Every function that can be expressed as the ratio of two polynomial functions is referred to as rational. A rational function, then, has the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomial functions and q(x) is not equal to 0. All real numbers fall inside a rational function's domain, with the exception of x values that cause the denominator to be equal to 0. A rational function's graph may include vertical and horizontal asymptotes, or lines that the graph approaches when particular values of x are approached.

The given equation of y is y=(2x-1)/(x+6).

Substituting the given values of x we have:

When x = 5:

y = (2(5) - 1)/(5 + 6) = 9/11

When x = 0:

y = (2(0) - 1)/(0 + 6) = -1/6

When x = -6:

y = (2(-6) - 1)/(-6 + 6) = undefined

Hence, when x is equal to 5, y is equal to 9/11. When x is equal to 0, y is equal to -1/6 and when x is equal to -6, y is undefined since the denominator of the fraction is equal to 0.

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Area is a measure of the size of a two-dimensional surface or region. It is typically measured in square units, such as square meters or square feet. The area of a shape is found by multiplying the length and width of the shape in most cases, although the formula for finding the area may vary depending on the shape.

In the given question,

To find the unit rate in terms of the number of squirrels per square mile, we need to divide the total number of squirrels by the total area of the park.

Total number of squirrels = 20 + 32 + 128 = 180

Total area of the park = 5 + 8 + 32 = 45

Note: The last blank can be filled with 40, as shown above.

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Answer:

1. 4

2. 512

3. 81

Step-by-step explanation:

After answering the provided question, we can conclude that As a result, probability the correct answer is C) A• The expected point value is 0.13, so guessing is advantageous.

Probability of how likely an event is to occur. It is represented by a number is for both 0 and 1, with 0 representing an unlikely event and 1 representing an unavoidable event. Shifting a fair coin and coin flips has a probability of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probability theory is a mathematical discipline that investigates random events instead than their properties. It is applied in many fields, including facts and figures, finance, scientific knowledge, and engineering.

After eliminating one of the six possible answers, the remaining five options are equally likely to be correct, so the probability of correctly guessing is now 1/5 and the probability of incorrectly guessing is 4/5.

Point value expected = (probability of gaining points x point value) - (probability of losing points x point value)

(1/5 x 1) is the expected point value. - (4/5 x 1/6)

1/5 - 1/30 = expected point value

5/30 - 1/30 = expected point value

4/30 is the expected point value.

The expected point value is 0.13. (rounded to two decimal places)

It is advantageous to guess because the expected point value is positive.

As a result, the correct answer is C) A• The expected point value is 0.13, so guessing is advantageous.

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Answer:

rar

Step-by-step explanation:

rar

Answer: 666

Step-by-step explanation:

Changing the value of 'a' changes the shape, position, and concavity of the graph of the function.

In mathematics, a function is a rule that assigns to each element in a set (called the domain) a unique element in another set (called the range or codomain).

Stretching or compressing the graph: If 'a' is greater than 1, the graph of the function will be stretched vertically, making it thinner and taller. If 'a' is between 0 and 1, the graph will be compressed vertically, making it wider and shorter. If 'a' is negative, the graph will be upside down.

Shifting the graph: If 'a' is positive, the graph will be shifted up or down depending on the value of 'a'. If 'a' is negative, the graph will be shifted down or up.

Changing the concavity of the graph: The graph of the parent function G(x) is an upward-facing parabola, which means it has a positive concavity. If 'a' is positive, the graph of the function will also have a positive concavity. If 'a' is negative, the graph of the function will have a negative concavity, which means it will be a downward-facing parabola.

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The village will require 14 bundles of mosquito nets to be brought by the government.

There are 12 households in the village with a total of 12 members. To determine the number of mosquito nets needed, we first need to calculate the total number of individuals who require a net:

2 + 3 + 4 + 5 + 3 + 7 + 9 + 8 + 11 + 12 + 8 + 10 = 82 individuals

Since each package contains an equal number of nets of six, we can calculate the number of packages required by dividing the total number of individuals by six:

82 individuals ÷ 6 = 13.67

Since we cannot have a fractional number of packages, we need to round up to the nearest whole number:

14 packages

Therefore, the government will need to take 14 packages of mosquito nets to the village.

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Answer:

$1.92

Step-by-step explanation:

We take

23 / 12 = $1.92 per flower

So, it costs $1.92 per flower.

The economy size is more economical, as you will get 2kg for $3.15, which comes out to be $1.58 per kg, while the regular size will cost you $0.65 per gram.

To determine which option is more economical, we need to calculate the cost per unit of weight for each detergent.

For the economy size, the cost per kilogram is:

Cost = $3.15

Weight = 2 kg

Cost per kilogram = Cost / Weight = $3.15 / 2 kg = $1.575/kg

For the regular size, the cost per kilogram is:

Cost = $0.60

Weight = 920 g = 0.92 kg

Cost per kilogram = Cost / Weight = $0.60 / 0.92 kg = $0.652/kg

Therefore, the regular-size detergent is more economical as it has a lower cost per kilogram.

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Answer: $91.25

Step-by-step explanation:

We know that

Vintage movie = $28.5

Rock = $29.75

Rap = $19.5

For the total cost, we get

(2 × 28.5) + (2 × 29.75) + (1 × 19.5) = $136

Recalling that he has a $35 gift card as well as the 1/2 off coupon on rap posters,

136 - 35 - ½(19.5)

$91.25