the question is in the attached file

96% confidence interval for the population mean life of light bulbs produced by the electrical firm to be between 747.63 and 812.37 hours. This can be answered by the concept of standard deviation.

To calculate the confidence interval, we first need to determine the standard error of the mean, which can be calculated using the formula:

Standard Error of Mean = (Standard Deviation of Population) / sqrt(Sample Size)

In this case, the standard deviation of the population is given as 40 hours, and the sample size is 30. Thus, the standard error of the mean can be calculated as:

Standard Error of Mean = 40 / sqrt(30) = 7.32

Next, we need to find the critical value of t for a 96% confidence level with 29 degrees of freedom (n-1). Using a t-distribution table or calculator, we find this to be 2.048.

Using these values, we can calculate the confidence interval using the formula:

Confidence Interval = Sample Mean +/- (Critical Value * Standard Error of Mean)

Substituting the given values, we get:

Confidence Interval = 780 +/- (2.048 * 7.32) = 780 +/- 15.02

Therefore, the 96% confidence interval for the population mean life of light bulbs produced by the electrical firm is between 747.63 and 812.37 hours. This means we can be 96% confident that the true mean life of all light bulbs produced by the firm falls within this interval.

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Answer:

Subtract 15 from both sides

Step-by-step explanation:

To take the given equation to the form (x+b)^2 we do the following:

Therefore, the term that needs to be added is +1.

Answer:14

Step-by-step explanation:You can use distance formula to find the length of each side, and then add them together to approximate the perimeter.

Answer:

30 degrees

Step-by-step explanation:

90 + 60 + x = 180

150 + x = 180

-150 -150

x = 30

Answer: The measure of the acute angle is 30°

Step-by-step explanation:The sum of all triangles is 180° 90+60+30 is 180 and 90 is a right angle

Answer: B, A, C

Step-by-step explanation:

y - 13 > -85

y > -72

Since y is greater than -72, graph B is the correct answer for the first inequality

13 < -85 + y

98 < y

Since y is greater than 98, graph A is the correct answer for the second inequality

y + 13 < -85

y < -98

Since y is less than -98, graph C is the correct answer for the last inequality.

Answer:

0.166667 - Common Ratio

step by step

Formula Used: Common Ratio=First term/Consecutive Term

Calculation: 0.166667=(-14)/(-84)

Answer: 2/4 more pizzia

Step-by-step explanation: Becuse if Mirtra ate 1/4 of the pizzia then you have 3/4 left and alonzo ate 3/4 of the pizza and if you subtract those the differce ends up to be 2/4.

The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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For which population is 636363 wins a legitimate estimate of the average longest streak: Only the top 200200200 longest streaks worldwide in June

Mean = sum of data / Number of data

The 200200200 longest streaks weren't randomly selected from a larger population. They are not representative of all players in the world or Canada, but they are the top 200200200 longest streaks of all players. So,

Only the top 200200200 longest streaks worldwide in June will win.

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Answer: To match the shapes produced by the slice through the triangular prism, we need to consider the orientation of the slice relative to the prism. Here are the matching options:

A. Perpendicular to the base: Rectangle

B. Parallel to the base: Triangle with dimensions equal to the base

C. Diagonal from vertex to vertex: Triangle with unknown dimensions

Answer:

-6/5

Step-by-step explanation:

y-y over x-x

Step-by-step explanation:

Search for questions & chapters

Class 11

>>Maths

>>Trigonometric Functions

>>Trigonometric Equations

>>Solve for x: sin x + sin 2x...

Question

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Solve for x:sinx+sin2x+sin3x=cosx+cos2x+cos3x in the interval 0≤x≤2π.

Medium

Solution

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We write the given equation as

(sinx+sin3x)+sin2x=(cosx+cos3x)+cos2x

or 2sin2xcosx+sin2x=2cos2xcosx+cos2x

or sin2x(2cosx+1)=cos2x(2cosx+1)

or (sin2x−cos2x)(2cosx+1)=0

∴sin2x−cos2x=0 or 2cosx+1=0

If sin2x−cos2x=0, then tan2x=1,

Hence 2x=nπ+π/4

or x=(4n+1)

8

π

.(1)

If 2cosx+1=0, then cosx=−1/2 (2)

∴x=2nπ±

3

2π

or x=

3

6n±2

π

We seek values of x in the interval 0≤x≤2π

In this interval (1) gives

x=π/8,5π/8,9π/8,13π/8. (n=0,1,2,3)

and (2) gives x=2π/3,4π/3. (for n=0,1)

Thus we get the answer

x=π/8,5π/8,2π/3,9π/8,4π/3,13π/8.

Based on the provided question, it seems like you are asking about the most efficient evaluation method, either by hand or using a computer. To determine which method is the most suitable, you need to consider the complexity of the evaluation process and the number of alternatives.

Using a computer is generally faster and more accurate when dealing with large datasets or complex calculations. On the other hand, evaluating by hand may be more suitable for smaller datasets or simpler calculations. It can provide a more hands-on approach, allowing for a deeper understanding of the evaluation process. However, this method is generally more time-consuming and prone to human error.

To select the most appropriate evaluation method, consider the complexity of the task and the available resources. If the evaluation involves a large amount of data or complex calculations, using a computer would likely be the most efficient choice. However, if the task is relatively simple or involves a smaller dataset, evaluating by hand may suffice. In conclusion, the choice between evaluating by hand or using a computer depends on the complexity of the task and the available resources. Consider these factors to determine the most suitable method.

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according to the question

given data in the question,

the type of sample-

random stratified sampling

The usage of satisfied sampling may be required for a variety of distinct features.

The population is first split into two or more strata or subgroups in this kind of random sampling. Beginning with the sampling procedure, each unit is assigned to one stratum based on the unit's historical performance. Following that, separate random samples are chosen using a basic random sampling technique from each stratum, which contains a percentage of the population. that is, they are both mutually and jointly exhaustive.

The traits that we are evaluating are distinct from those of members of another stratum and similar to those of the sample unit stratum.

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the type of sample that proportionately reflects the relevant diversity of opinions in the population from which it is drawn is random stratified sampling

A sample is a condensed, controllable representation of a larger group. It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing.

The sample size in statistics is a measurement of the total number of samples utilized in an experiment. The sample size is 50, for instance, if we are evaluating 50 samples of city dwellers who watch TV. It's also known as sample statistics.

Considering the query

the information in the query

a sample's type-

stratified sampling at random

For a number of unique traits, satisfied sampling may be necessary.

In this type of random sampling, the population is initially divided into two or more strata or subgroups. Each unit is categorized into a stratum at the start of the sampling process depending on its prior performance. A basic random sampling approach is then used to select distinct random samples from each stratum, which represents a portion of the population. they are mutually and jointly exhaustive, in other words.

The characteristics that we are examining are different from those of members of one stratum and comparable to those of the stratum that contains the sample unit.

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Answer:

40

Step-by-step explanation:

Answer:

B. RZ =R BZ

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisectors of both sides. Therefore, CZ and SZ are perpendicular bisectors of AB and ST, respectively.

Option B is true because point R lies on the perpendicular bisector of AB, and therefore RZ = RB.

Answer: vv

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisector of the sides ST and AR.

Therefore, we can draw perpendiculars from point Z to the sides ST and AR, which intersect them at points T' and R', respectively.

Now, let's examine the options:

A. SZ & TZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distance from Z to S and T could be different.

B. RZ = RB: This is true, as point Z lies on the perpendicular bisector of AR, and is therefore equidistant from R and B.

C. CTZ = ASZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of AR, and the distances from Z to C and A could be different.

D. ASZ = ZSB: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distances from Z to A and B could be different.

Therefore, the only statement that must be true is option B: RZ = RB.

The required algebraic expression is 14/2

What is an algebraic expression?

An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.). Terms combine to form expressions.

With the help of integer constants, variables, and the addition, subtraction, multiplication, and division operations in basic arithmetic, an algebraic expression is created. The algebraic statement 5x + 6 is an illustration. In this case, 5 and 6 are fixed values, while x is a variable. Additionally, the variables can be either simple variables with alphabets like x, y, or z or complex variables with names like x², x³, etc. Polynomials are another name for algebraic expressions. Variables (also known as indeterminates), coefficients, and non-negative integer exponents of variables make up a polynomial expression.

Half of 14

=>  (1/2) of 14

=>  14/2

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Answer:

\(y=-\frac{3(x +2)}{2}\)

Step-by-step explanation:

We have an equation, and the question is asking for us to solve y. So to solve, we have to isolate y.

6x - 4y = 12

Subtract 6x from both sides :

-4y = 12 - 6x

Divide both sides by -4 :

\(y=-\frac{3(x+2)}{2}\)

Yes, the given equation is quadratic equation.

Here it has been given that,

3x² - 5x + 9 = x² - 7x + 3

Now, after solving  above equation further we obtain,

2x² + 2x + 6 = 0

From the above equation the factor 2 is taken out as it is common and now the equation looks like : x² + x + 3 = 0

The coefficients of the quadratic equation are compared  and if it meets the criteria then it is quadratic equation otherwise not.

Now as we can see, the above equation clearly represents a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = 1 and c = 3.

Hence, the above given equation is a algebraic quadratic equation.

Which of the following is quadratic equation 3x² - 5x + 9 = x² - 7x + 3 ?

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Answer:

7.5,

Step-by-step explanation:

8 x 15 = 120

So 15 cups

And then since 2 cups equal a pint

15 divided by 2

Which is 7.5 pints

Answer:

13/34

Step-by-step explanation:

subtract the 21 from the 34 and badaboom ya are left with 13 peeps on the bus!

Answer:

13/34

Step-by-step explanation:

34-21=13

13/34

Scientific Notation is EASY.

Just move the decimal to the right if it is positive:

6.2 x 10¹ = 62

6.2 x 10² = 620

6.2 x 10³ = 6,200

6.2 x 10⁴ = 62,000

6.2 x 10⁵ = 620,000

6.2 x 10⁶ = 6,200,000

Move the decimal to the left if it is negative:

6.2 x 10⁻¹ .62

6.2 x 10⁻² = .062

6.2 x 10⁻³ = .0062

6.2 x 10⁻⁴ = .00062

6.2 x 10⁻⁵ = .000062

6.2 x 10⁻⁶ = .0000062

What about about 6.2 x 10⁰?

6.2 It wouldn't change location.

I hope this helps!

Answer: The y intercept is wherever the line crossed the Y axis. I can't see all the graphs but for example graph A would have a Y intercept of -3. Because the line crosses the point (0,-3).

If you update the pic I can give the answer.

Answer:

Number 4

Step-by-step explanation:

Angle CBE is the same thing as angle EBC. The only thing that matters when you're talking about ONE angle is the middle letter.

Answer:

It is number four: ∠CBE

There is a weak negative relationship between essential oils and hormone levels depicted in the scatter plot. So, a better headline for this information can be that "essential oils may disturb hormonal levels".

It is given to us that -

The current news headline claims that "essential Oils Cause Hormone Levels to Drop".

They show a scatter plot displaying a weak negative relationship (r = -0. 13) between essential oil use and hormone levels.

We have to determine a better headline for this information.

We know that a scatter plot is defined as a type of graph that depicts the pairs of data that are plotted as points in the plot.

We also know that, we can use a scatter plot to analyze trends in our data and to help us determine whether or not there is a relationship between two variables.

Again, a scatter plot can represent a positive relationship, a negative relationship, or no relationship.

It can be referred to as a negative relationship between the given variables if the points on the scatter plot form a line that spreads from left to right in the downward direction.

In case of a positive or negative relationship between the variables, we can draw a line that depicts the best fit.

This line depicted through a positive or negative relationship will not pass through each and every point on the scatter plot. However, it will represent the general trend of the available data.

So, it can be concluded that the weak negative relationship between essential oil and hormone levels displayed in the scatter plot suggests that the fact that "essential Oils Cause Hormone Levels to Drop" is not true.

This is because there is weaker relationship between essential oils and the hormone levels which is more of a lesser general trend that doesn't suggest any strong relationship or doesn't represent any stated fact.

Therefore, from the weak negative relationship between essential oils and hormone levels depicted in the scatter plot, a better headline for this information can be that "essential oils may disturb hormonal levels".

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The answer is "Yes". Option (a) and (e) are correct. (a) \((u, v) = UV + 2u²V² + U3V³\) satisfies (u, v) - v, u (e) cu, v) = (u, v) satisfies (v, v) 2 0, and (v, v) = 0 if and only if v = 0.

The given vectors are u = (1, -1) and v = (1,1).

To verify Pythagorean Theorem, we need to check if the square of the magnitude of the vector sum of u and v equals the sum of the squares of the magnitudes of u and v.

Therefore, u+v = (1-1, -1+1) = (0,0).

The square of the magnitude of u is given by |u|^2 = 1^2 + (-1)^2 = 2. The square of the magnitude of v is given by |v|^2 = 1^2 + 1^2 = 2.

The square of the magnitude of u+v is |u+v|^2 = 0^2 + 0^2 = 0. Now, we have:|u|^2 + |v|^2 = 2 + 2 = 4 |u+v|^2 = 0

The condition of the Pythagorean theorem is that |u+v|^2 = |u|^2 + |v|^2. Since, |u+v|^2 ≠ |u|^2 + |v|^2, the given vectors u and v are not orthogonal.

|42-O IV-D = |42-0 IV-D| = |42, -4| = √(42² + (-4)²) = √1760 ≈ 41.89

Since |42-O IV-D| is a non-negative value, it is greater than or equal to 0, so we have verified the condition of the Pythagorean Theorem.

|u, v| = u1v1 + u2v2 = 1(1) + (-1)(1) = 0

Since, |u, v| = 0, we can say that u and v are orthogonal.

Therefore, the answer is "Yes".Option (a) and (e) are correct. (a) \((u, v) = UV + 2u²V² + U3V³\) satisfies (u, v) - v, u (e) cu, v) = (u, v) satisfies (v, v) 2 0, and (v, v) = 0 if and only if v = 0.

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