A part manufactured at a factory is known to be 12.05 cm long on average, with a standard deviation of 0.350. One day you suspect that that the part is coming out a little longer than usual, but with the same deviation. You sample 14 at random and find an average length of 12.20. What is the z-score which would be used to test the hypothesis that the part is coming out longer than usual?

The linear inequality for the graph in this problem is given as follows:

y ≥ 2x/3 + 1.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by 3, y increases by 2, hence the slope m is given as follows:

m = 2/3.

Then the linear function is given as follows:

y = 2x/3 + 1.

Numbers above the solid line are graphed, hence the inequality is given as follows:

y ≥ 2x/3 + 1.

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Answer: 20.76

Step-by-step explanation:

Since you're given the hypotenuse and need to find the opposite side, use sine.

sin53 = x/26

x = 26sin53

x = 20.76

The graph of x vs. t^2 for an object falling from rest should be a curve with a positive y-intercept and a decreasing slope.

If you plot x vs. t^2 for an object falling from rest (assuming down to be positive), the graph should be a curve with a decreasing slope. Here's why:

When an object is falling freely under the influence of gravity, its position (x) can be described by the equation:

x = 1/2 * g * t^2

Where g is the acceleration due to gravity.

If we plot x vs. t^2, we can rewrite the equation as:

x = (1/2) * g * (t^2)

Comparing this equation with the standard form y = mx + b, we can see that the graph represents a curve with a positive y-intercept (b) and a decreasing slope (m).

The y-intercept (at t = 0) is positive because the object starts from rest at a positive height (assuming down to be positive).

The slope of the curve decreases because as time increases, the object accelerates due to gravity, but at a constant rate. Therefore, the displacement (x) increases, but at a decreasing rate.

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Answer:

$27/month

Step-by-step explanation:

300-220=80

100%= 300

1%= 300÷100

= 3

10%= 3×10

= 30

300-30=270

270÷10= $27

Answer:

C) it will get narrower

Step-by-step explanation:

Answer:

how many blanks are their

Step-by-step explanation:

Answer: Even though an image was not provided, I would continue with 96, 100, 104, 108, 112, 116, and so on.

Step-by-step explanation:

92 + 4 = 96 + 4 = 100 + 4, and so on.

There's not really anything else to this.

Roger has enough stainless steel pipe to replace the chimney liner, with a slight surplus remaining.

To determine if Roger has enough stainless steel pipe for the chimney liner, we need to convert the given measurements to a consistent unit of measurement. Since the length of the liner required is given in feet, we need to convert the 400 inches of stainless steel pipe to feet.

There are 12 inches in a foot, so 400 inches is equal to 400/12 = 33.33 feet (approximately).

Comparing this converted length of the stainless steel pipe (33.33 feet) with the length of the liner required (33 feet), we can see that Roger does indeed have enough pipe. In fact, he has slightly more than required.

Since the length of the liner required is 33 feet and Roger has 33.33 feet of stainless steel pipe available, there is a surplus of approximately 0.33 feet (about 4 inches) of pipe. This additional length is more than enough to cover any potential measurement errors or adjustments needed during the installation process.

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Answer:

See explanation

Step-by-step explanation:

The answer is either 2r+3 or 2 r + 3

I'm a bit confused because they're kinda the same thing but one of them is spaced out. I don't know if that space means anything.

Anyway if he's scores 3 more than 2 times the points ray scores, that means that he scores twice the amount that ray scores plus 3.

The following financial assets that has the historically  largest standard deviation is option A. Common stock.

Common stocks, also known as equities, have historically exhibited the largest standard deviation among the listed financial assets. Standard deviation is a statistical measure of the volatility or variability of returns.

Common stocks are considered to be riskier investments compared to other financial assets due to their higher volatility. The prices of common stocks can fluctuate significantly over time, influenced by various factors such as market conditions, economic performance, company-specific news, and investor sentiment. These fluctuations result in a larger standard deviation, indicating a higher level of risk associated with common stock investments.

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The total rainfall at station D for that particular year was approximately 1028 cm Total precipitation recorded by A, B and C = 1125 + 1057 + 1003 = 3185 cm.

Mean precipitation = (Total precipitation recorded by A, B and C) / 3

Mean precipitation = (3185) / 3 = 1061.67 cm (approx.)

The total annual precipitation of four rainfall gauges in a particular catchment is given. In a particular year, one station becomes inoperative. Using the data recorded by the other three stations, we have to find the total rainfall at station D. It can be done by using the arithmetic mean method.

So, let's calculate the mean precipitation of the three operational stations.


Now, we have to estimate the total rainfall at station D. We can use the arithmetic mean of the four stations to estimate this.

Arithmetic mean precipitation \(= (1120 + 1088 + 1033 + 972) / 4 = 1053.25 cm (approx\).)

Now, we can use this arithmetic mean and the mean precipitation of the three operational stations to estimate the total rainfall at station D.

Total precipitation at all four stations = (Arithmetic mean precipitation) × 4

Total precipitation at all four stations = 1053.25 × 4 = 4213 cm

Total precipitation at D = Total precipitation at all four stations – (Total precipitation recorded by A, B and C)

Total precipitation at \(D = 4213 – 3185 = 1028 cm\)

Therefore, . We used the arithmetic mean method to estimate the total precipitation at station D because the normal annual precipitation at each of the four stations was known, and this method uses the averages to estimate the missing value.

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The discrete random variables from the given options are: 1, 2, 4, and 5.

The number of CDs that a college student owns: This is a discrete random variable because the number of CDs can only be a whole number. You cannot have a fractional or continuous value for the number of CDs.

The number of dogs you own: This is a discrete random variable because you can only own a whole number of dogs. You cannot own a fractional or continuous number of dogs.

Number of 6s you get when you throw 5 number cubes: This is a discrete random variable because the number of 6s can only be a whole number from 0 to 5. You cannot have a fractional or continuous value for the number of 6s obtained.

The number of dog sleds that a competitor uses in an annual sled dog race: This is a discrete random variable because the number of dog sleds can only be a whole number. You cannot have a fractional or continuous value for the number of dog sleds used.

On the other hand, the following option is not a discrete random variable:

The amount of gas in your car: This is a continuous random variable because the amount of gas can be any non-negative real number. It can have fractional or continuous values, such as 10.5 liters or 20.25 gallons. Option 1,2,3,4 and 5

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Answer:

(6, 1)

Step-by-step explanation:

Answer:

centre = (6, 1 )

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² - 12x - 2y + 12 = 0

Collect the x and y terms together and subtract 12 from both sides

x² - 12x + y² - 2y = - 12

To obtain the equation in standard form use completing the square

add ( half the coefficient of the x/ y term )² to both sides

x² + 2(- 6)x + 36 + y² + 2(- 1)y + 1 = - 12 + 36 + 1

(x - 6)² + (y - 1)² = 25 ← in standard form

with centre = (6, 1 ) and radius = \(\sqrt{25}\) = 5

Answer:

C=1

Step-by-step explanation:

5/6=5/6c which is 1.

The margin of error for the 90% confidence interval is 5.84

To find the margin of error for a 90% confidence interval, we will use the given information and the z-score table provided.

1. Identify the z-score for a 90% confidence level: Since the confidence level is 90%, there is 10% left in the tails. Divide this by 2 to find the area in each tail, which is 5%. Look for the z-score associated with 0.05 in the table provided. The z-score is 1.645.

2. Find the standard error: The standard error is calculated as the population standard deviation (σ) divided by the square root of the sample size (n). In this case, σ = 21 and n = 35.

Standard Error (SE) = σ / √n = 21 / √35 ≈ 3.55

3. Calculate the margin of error: The margin of error (ME) is calculated by multiplying the z-score by the standard error.

ME = z-score * SE = 1.645 * 3.55 ≈ 5.84

4. Round the final answer to two decimal places: 5.84

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.

Answer:

x= 0,5

Step-by-step explanation:

You have to move all the terms to the left side and set them equal to zero. Then set each factor equal to zero.

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Answer:

5x

Step-by-step explanation:

3x+2x

Combine like terms

x(3+2)

x(5)

5x

Answer:

5x

Step-by-step explanation:

3x + 2x

Step 1 :- Calculate like terms by adding their coefficient.

Step 2 :- Combine like terms.

Step 3 :- Multiply ; 5 times x.

Answer:

The 61st term is -52

Step-by-step explanation:

A standard subdivision consists of subdivisions with four or fewer parcels.

In a standard subdivision, the number of parcels is limited to four or fewer. This means that each subdivision within the standard subdivision will have a maximum of four parcels.

So, if you are looking for a standard subdivision, you can expect to find subdivisions with four or fewer parcels.

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The sampling procedure that is being used in this case is simple random sampling.

What is sampling?

Sampling refers to the method of choosing a subset of individuals from a population to represent the whole population, with the aim of making inferences or conclusions about the population. The different types of sampling are random, stratified, cluster, and systematic, among others. Simple random sampling, as well as its variants, is the most basic and common method of random sampling.

What is simple random sampling?

Simple random sampling is a probability sampling technique in which every item in the sampling frame has an equal probability of being selected. This means that every element in the population has an equal chance of being included in the sample. The researcher first creates a sampling frame, which is a list of all the elements in the population, and then selects individuals for the sample at random.

The selection of each item is independent of the selection of the others, so the sample is representative of the population and free from bias. In this scenario, each individual's name in the sampling frame list has an equal chance of being picked, thus making it simple random sampling.

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Answer:

turn 3% into decimal by diving 3 by 100

3/100=0.03

0.03X3460=103.80

3460-103.80=3356.20

3356.20-100=3256.2

He made $112 each week

The total amount earned in three weeks before his weekly earning was doubled = $168

The amount earned each week before his weekly earning was doubles = $168/3

The amount earned each week before his weekly earning was doubled = $56

If his weekly earning was doubled:

The amount earned each week = 2 x $56

The amount earned each week = $112

We have proved the trigonometric expression cos A + cos 2 A + cos 5 A = cos 2 A (1 + 2 cos 3 A) by using C/D formula.

We are given the expression:

cos A + cos 2 A + cos 5 A = cos 2 A (1 + 2 cos 3 A)

We need to prove the expression.

We know that:

Cos C + Cos D = 2 cos ( C + D / 2) cos ( C - D / 2)

Using this identity, we get that:

= cos 5 A + cos A + cos 2 A = cos 2 A (1 + 2 cos 3 A)

= 2 cos ( 5A + A / 2) cos ( 5A - A / 2) + cos 2 A = cos 2 A (1 + 2 cos 3 A)

= 2 cos 3 A cos 2 A + cos 2 A = cos 2 A (1 + 2 cos 3 A)

= cos 2 A ( 2 cos 3A + 1) = cos 2 A (1 + 2 cos 3 A)

= cos 2 A (1 + 2 cos 3 A) = cos 2 A (1 + 2 cos 3 A)

LHS = RHS

Hence proved.

Therefore, we have proved the trigonometric expression cos A + cos 2 A + cos 5 A = cos 2 A (1 + 2 cos 3 A) by using C/D formula.

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The probability of rolling a sum of 7 or 11 when rolling both dice is approximately 0.111 or 11.1%.

The probability of rolling a sum of 7 or 11 with two 6-sided dice, we can first calculate the total number of possible outcomes when rolling both dice.

Each die has six possible outcomes, so the total number of possible outcomes when rolling both dice is 6 x 6 = 36.

To count the number of outcomes where the sum is 7 or 11.

There are two ways to roll a sum of 7:

(1, 6) and (6, 1).

There are also two ways to roll a sum of 11:

(5, 6) and (6, 5).

There are four possible outcomes that result in a sum of 7 or 11.

Thus, the probability of rolling a sum of 7 or 11 is:

4/36

= 1/9

≈ 0.111

The total number of outcomes while rolling both dice in order to determine the likelihood of rolling a sum of 7 or 11 using two 6-sided dice.

Rolling both dice, there are a total of six possible results for each die, for a total of 36 options in all.

to determine how many possibilities there are where the total is 7 or 11. Rolling a 7, there are two possible outcomes: (1, 6) and (6, 1).

Additionally, there are two methods to roll an 11: (5, 6) and (6, 5).

There are four events that can lead to a total of either 7 or 11.

As a result, the likelihood of rolling a 7 or 11 is 4/36 = 1/9 0.111.

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Answer:

it would be x>-18

Step-by-step explanation:

Answer:

x > −18

Step-by-step explanation:

Move all terms not containing xx to the right side of the inequality.

−2x<36-2x<36

Divide each term by −2-2 and simplify.

x>−18x>-18

The result can be shown in multiple forms.

Inequality Form:

x > −18

The expression that has the element of A*B*B is Option A - (b,2,3)

Sets are groups of clearly defined objects or elements in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.

The "elements" of a set are the objects that make up the collection. Sets are equal if and only if they have the same elements, therefore a = A denotes that 'a' is one of A's elements. For sets, repetition and order are irrelevant.

Given, A={a.b} and B=[1,2,3]

Since the required expression was supposed to have the element of A*B*B the correct option would be A since it has elements b from A, 2 from B, and 3 from B, fulfilling all the required elements.

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Given :

Lin has a pet German shepherd that weighs 38 when measured in one unit and 84 when measured in a different unit.

To Find :

Which measurement is in pounds, and which is in kilograms.

Solution :

We know, mass in kg and pounds are related as :

\(m_P = 2.2m_{kg}\)

Putting, \(m_{kg}=38\) and \(m_P=84\) , we get :

LHS = 84

RHS = 2.2 × 38 = 83.6 ≈ 84

Since, LHS = RHS .

Therefore, 38 units is Kg and 84 units in Pounds.

Hence, this is the required solution.

The twelfth term of the arithmetic sequence is -12.

To find the twelfth term of an arithmetic sequence, we can use the formula:

term = first term + (n - 1) * common difference

In this case, the first term (a) is 32 and the common difference (d) is -4. We want to find the twelfth term, so n = 12.

Plugging the values into the formula, we have:

term = 32 + (12 - 1) * (-4)
    = 32 + 11 * (-4)
    = 32 + (-44)
    = -12

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Answer:

The number of packages of gift wrap and greeting cards sold is 181 and 44 respectively

Step-by-step explanation:

The computation of the number of packages of gift wrap and greeting cards sold is as follows:

Let us assume the number of packages of gift wrap be x

And, for greeting cards be y

The equation are as follows

x + y = 225 ..................(1)

We can write as

y = 225 - x

4x + 10y = $1,164 ............(2)

Now put the y value in the equation 2

4x + 10 (225 - x) = $1,164

4x + $2,250 - 10x = $1,164

-6x = $1,164 - $2,250

-6x = -$1,086

x = 181

And, y = 225 - 181

= 44