how many significant figures are in the measurement 0.00001 meters?

The sum of the 25th term of the AP 3, 10, 17 is 171.

The sum of the 25th term of an arithmetic progression (AP) 3, 10, 17 can be found using the formula for the nth term of an arithmetic progression, which is:
aₙ = a₁ + (n - 1) d
where aₙ is the nth term, a₁ is the first term, d is the common difference, and n is the number of terms.

In this case, a₁ = 3, d = 10 - 3 = 7, and n = 25. Plugging in these values into the formula, we get:
a₂₅ = 3 + (25 - 1) 7
a₂₅ = 3 + 168
a₂₅ = 171

Therefore, the sum of the 25th term of the AP 3, 10, 17 is 171.

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x=12

L||M means L will be parallel to M.

Two lines are parallel if their corresponding angles are the same.

Corresponding angles are shown below.

As the two angles given are corresponding, L||M when x+5 = 2x-7.

x+5 = 2x-7

x = 12

Therefore, the value of x which makes L||M is 12.

Answer:

x = 12

Step-by-step explanation:

Now we have to,

→ find the required value of x.

Forming the equation,

→ x + 5 = 2x - 7

Then the value of x will be,

→ x + 5 = 2x - 7

→ x - 2x = -7 - 5

→ -x = -12

→ [ x = 12 ]

Hence, the value of x is 12.

answer: 55

Step-by-step explanation:

angle apg is eqal to angle pgr (being alternate angles)

x + pgr is equal to 120 (exterior angle of a triangle is equal to opposite interior angle)

Solution:

Let "E" denote the top right angle. (Refer to image). Then ∠E and ∠R are a linear pair.

⇒ ∠E + ∠R = 180

⇒ ∠E + 120 = 180

⇒ ∠E = 180 - 120

⇒ ∠E = 60°

Line AB forms a straight line which is a measure of 180°.

⇒ 65 + ∠E + x = 180

⇒ 65 + 60 + x = 180

⇒ 125 + x = 180

⇒ 125 - 125 + x = 180 - 125

⇒ ∠x = 55°

If (6*1.33) - 8 equals anything, it's -0.02

If you want your answer to be 16, X must equal 4

The number of ways a team can win the World Series is 56 ways. Therefore, the correct option is B.

A team needs to win 4 games to win the World Series. Let's look at the possible scenarios using combination concept:

1. The series ends in 4 games (4-0): There is only 1 way for this to happen (winning all 4 games).

2. The series ends in 5 games (4-1): There are 4 ways to arrange the wins and losses (e.g., WWLWW, WLWWL, LWWWW, etc.).

3. The series ends in 6 games (4-2): There are 5C2 ways to arrange the wins and losses, which is 10 ways (choosing 2 losses out of 5 games).

4. The series ends in 7 games (4-3): There are 6C3 ways to arrange the wins and losses, which is 20 ways (choosing 3 losses out of 6 games).

Now, add all the ways together: 1 + 4 + 10 + 20 = 35 ways for one team. Since there are two teams, we have to multiply the result by 2: 35 x 2 = 56 ways for a team to win the World Series which corresponds to option B.

Note: The question is incomplete. The complete question probably is: A baseball team wins the World Series if it is the first team in the series to win four games. Thus, a series could range from four to seven games. For example, a team winning the first four games would be the champion. Likewise, a team losing the first three games and winning the last four would be champion. In how many ways can a team win the World Series? a. 5 b. 56 c. 15 d. 94 e. 35.

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Answer:

18 units^2

Step-by-step explanation:

Formula for Area of trapezoid:    ( base 1 + base 2 / 2) * height

(3 + 9 / 2) * 3 = (12 / 2) * 3 = 6 * 3 = 18 units^2

I hope this helps

Answer:

18²

Step-by-step explanation:

Formula for a trapezium:

Area = base1 + base2/2 × height

3 + 9/2 × 3

= 12/2 × 3

18²

Answer:

C

Step-by-step explanation:

Given

\(\frac{-m}{2}\) - \(\frac{5}{4}\) ≤ \(\frac{5m}{12}\) - \(\frac{7}{6}\)

Multiply through by 12 to clear the fractions

- 6m - 15 ≤ 5m - 14 ( subtract 5m from both sides )

- 11m - 15 ≤ - 14 ( add 15 to both sides )

- 11m ≤ 1

Divide both sides by - 11, reversing the symbol as a result of dividing by a negative quantity

m ≥ - \(\frac{1}{11}\) → C

Answer:

y=5x+5

Step-by-step explanation:

Answer:

Y=5x-5

Step-by-step explanation:

-3y=-15x+15

3y=15x-15

Y=5x-5

Answer:

18 eggs

Step-by-step explanation:

Answer:

\(\frac{35}{48}\)

Step-by-step explanation:

Put the value of r in the equation.

\(\frac{1}{4}\) × r + \(\frac{7}{12}\)  = \(\frac{1}{4}\) × \(\frac{7}{12}\) + \(\frac{7}{12}\)

Evaluate.

\(\frac{1}{4}\) × \(\frac{7}{12}\) + \(\frac{7}{12}\) = \(\frac{7}{48}\) + \(\frac{7}{12}\)

Make them have the same denominator by multiplying the denominator of the second fraction by 4 so their denominators are 48.

\(\frac{7}{48}\) + \(\frac{7}{12}\) = \(\frac{7}{48}\) + \(\frac{28}{48}\)

Evaluate.

\(\frac{7}{48}\) + \(\frac{28}{48}\) = \(\frac{35}{48}\)

A D. simple random sample is a sample in which every member of the population has an equal chance of being chosen.

A. Systematic: In a systematic sample, the population is first ordered or arranged in some systematic way, such as by alphabetical order or numerical sequence. Then, a starting point is randomly selected, and subsequent members are chosen at regular intervals from the ordered list. This method ensures that every member of the population has an equal chance of being selected.

B. Probability: The term "probability sample" is a general concept that encompasses various sampling methods. It refers to any sample in which each member of the population has a known nonzero probability of being selected. Probability sampling methods include simple random sampling, stratified sampling, cluster sampling, and systematic sampling.

C. Stratified: In stratified sampling, the population is divided into distinct subgroups or strata based on specific characteristics or attributes. Then, a random sample is taken from each stratum in proportion to its representation in the overall population. This method ensures that the sample is representative of the population across different subgroups or strata.

D. Simple random: A simple random sample is a sampling method where each member of the population has an equal and independent chance of being selected. It involves selecting individuals randomly and without any specific pattern or grouping. This method ensures that each member of the population has an equal probability of being chosen, leading to unbiased estimates and generalizability to the larger population.

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a. the probability that a stone taken at random will have a diameter greater than 18mm is approximately 0.7977 or 79.77%. b. the stones should be rejected if their diameter is below approximately 17.628mm.

(a) To find the probability that a stone taken at random will have a diameter greater than 18mm, we can use the properties of the normal distribution.

First, we need to standardize the value of 18mm using the formula: z = (x - μ) / σ, where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

z = (18 - 19.5) / 1.8 ≈ -0.83

Next, we need to find the probability corresponding to this standardized value in the standard normal distribution table. Since we want the probability that the diameter is greater than 18mm, we need to find the area under the curve to the right of z = -0.83.

Using the standard normal distribution table or a calculator, we find that the area to the right of z = -0.83 is approximately 0.7977.

Therefore, the probability that a stone taken at random will have a diameter greater than 18mm is approximately 0.7977 or 79.77%.

(b) To determine the size of the holes in the sieve, we need to find the cutoff value below which the smallest 15.15% of the stones will be rejected.

Since the distribution of stone sizes is normally distributed, we can use the standard normal distribution table to find the corresponding z-score.

We need to find the z-score that corresponds to a cumulative probability of 0.1515. Looking up this value in the standard normal distribution table, we find that the z-score is approximately -1.04.

Next, we can use the z-score formula to find the actual diameter value corresponding to this z-score:

z = (x - μ) / σ

-1.04 = (x - 19.5) / 1.8

Solving for x, we have:

x - 19.5 = -1.04 * 1.8

x - 19.5 ≈ -1.872

x ≈ 19.5 - 1.872

x ≈ 17.628

Therefore, the stones should be rejected if their diameter is below approximately 17.628mm.

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The distance covered is. 90 miles

Speed is the distance an object travels in a given time.

This is represented as

Speed = Distance ÷ Time

We can also use the speed formula to calculate the distance or time by substituting the known values in the formula for speed and further evaluating,

Distance = Speed × Time or,

Time = Distance/Speed

To find the distance covered, we find the total speed

= 5 + 10(twice as fast on the trip back)

= 15

Distance = speed x time

= 15mph x 6hours

= 90miles

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Answer:

the answer is 10 :)

Since the park is isosceles trapezoid-shaped, the two sides, AB and CD, that make up the parallel sides of the trapezoid are of equal length.

An isosceles triangle is a type of triangle with two sides of equal length. It has two equal angles opposite of the two equal sides, and the third angle is usually different. Isosceles triangles are named after the Greek term isoskelēs, which means “equal legs”. They are very common in geometry and are used in many applications, including architecture and engineering.

We can then use the midpoints of the adjacent sides of the trapezoid, E and F, to form a rhombus. Since the rhombus is formed from the midpoints of the two parallel sides, we know that the two sides AE and CF of the rhombus are of equal length. Similarly, the two sides BE and FD of the rhombus are also equal in length. This means that the trail, if constructed in the shape of the rhombus, will have all sides of equal length, satisfying the criteria set by the Parks Commission.

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The value of g in terms of f is:

\(x^{4} -20x^{2} +100\)

\(x^{9} -2\)

\(-x^{4} -12x^{2} -34\)

\(8-||X|+4|\)

\(|-|x|+5|+7\)

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

Finding g in terms of f, given:

g(x)=\(x-10^{2}\),f(x)= \(x^{2}\)

g(x)=g(f(x))

f(x)=    \(x^{2}\) =g(  \(x^{2}\))

g(  \(x^{2}\)): \((x^{2} -10)^{2}\)

Expanding \((x^{2} -10)^{2}\) : \(x^{4} -20x^{2} +100\)

Finding g in terms of f, given:

g(x)=\(-x^{3} -2\),f(x)= \(x^{3}\)

g(x)=g(f(x))

f(x)=    \(x^{3}\) =g(  \(x^{3}\))

g(  \(x^{3}\)): \(x^{9} -2\)

Finding g in terms of f, given:

g(x)=\(-(x-6)^{2} +2\) ,f(x)= \(x^{2}\)

g(x)=g(f(x))

f(x)=    \(x^{2}\) =g(  \(x^{2}\))

g(  \(x^{2}\)): \(-x^{4} -12x^{2} -34\)

Finding g in terms of f, given:

g(x)=\(8-|x+4|\) ,f(x)= \(|x|\)

g(x)=g(f(x))

f(x)=    \(|x|\) =g(  \(|x|\) )

g(  \(|x|\) ): \(8-||X|+4|\)

Finding g in terms of f, given:

g(x)=\(|-x+5|\) ,f(x)= \(|x|\)

g(x)=g(f(x))

f(x)=    \(|x|\) =g(  \(|x|\) )

g(  \(|x|\) ): \(|-|x|+5|+7\)

\(|-|x|+5|+7\)

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The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. Therefore, the correct answer is C.

A pivot column is a column of the matrix that has a non-zero entry in the pivot position and all entries below the pivot are zero. In row echelon form, every row below a pivot column has a zero in the corresponding position. The pivot columns correspond to the linearly independent columns of the original matrix and the number of pivot columns determines the rank of the matrix.

The rank of a matrix is defined as the number of linearly independent columns or rows in the matrix. If the columns of a matrix span Rn, then the rank of the matrix must be equal to n. This means that the matrix must have n linearly independent columns. To ensure that the columns of A span R5, A must have at least 5 pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have a non-trivial solution, meaning that the columns of A would not be linearly independent and would not span R5.

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a) To solve the differential equation 4" – y = xe^(x/2) using variation of parameters, we first find the general solution of the associated homogeneous equation by solving the characteristic equation, which is r^2 - 4 = 0.

The roots are r = ±2, so the general solution of the homogeneous equation is y_h(x) = c_1 e^(2x) + c_2 e^(-2x).

Next, we assume that the particular solution has the form y_p(x) = u_1(x) e^(2x) + u_2(x) e^(-2x), where u_1(x) and u_2(x) are functions to be determined. We then substitute this into the differential equation and solve for u_1(x) and u_2(x) using the method of undetermined coefficients.

After finding the particular solution, we add it to the general solution of the homogeneous equation to obtain the general solution of the differential equation. Finally, we use the initial conditions y(0) = 1 and y'(0) = 0 to determine the values of the constants in the general solution.

b) To solve the differential equation 2y" + y' – y = x + 1 using variation of parameters, we first find the general solution of the associated homogeneous equation by solving the characteristic equation, which is 2r^2 + r - 1 = 0. The roots are r = (-1 ± sqrt(3))/4, so the general solution of the homogeneous equation is y_h(x) = c_1 e^((-1 + sqrt(3))x/4) + c_2 e^((-1 - sqrt(3))x/4).

Next, we assume that the particular solution has the form y_p(x) = u_1(x) e^((-1 + sqrt(3))x/4) + u_2(x) e^((-1 - sqrt(3))x/4), where u_1(x) and u_2(x) are functions to be determined. We then substitute this into the differential equation and solve for u_1(x) and u_2(x) using the method of undetermined coefficients.

After finding the particular solution, we add it to the general solution of the homogeneous equation to obtain the general solution of the differential equation. Finally, we use the initial conditions y(0) = 1 and y'(0) = 0 to determine the values of the constants in the general solution.

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Answer:

25 weeks

Step-by-step explanation:

I did the work so you can see if you need the explanation just ask and I'll comment it

Answer:

i think it is 25

Step-by-step explanation:

i 900÷36 × the answer which is 25

Answer:

19

Step-by-step explanation:

Answer:

The width would be 3 1/3 inches or 3.333 repeating

Step-by-step explanation:

Since you divide the length by 3, you would also have to divide the width by 3. 10 divided by 3 is 3 1/3 or 3.333 repeating (whichever one you choose).

Answer:

3 1/3

Step-by-step explanation:

Answer:

d-p

Step-by-step explanation:

In substraction the numbers/ letters are reversed.

I hope this helps.

Answer:

There are $\boxed{3}$ paths from $A$ to $B.$

Answer:

A. yes

Step-by-step explanation:

The contestant has a 60% chance of winning because they could either spin 1, 3, or 5.

However, unless there's another player who can only spin evens, it's not fair, because the contestant who spins odds has a 60% chance, while this player will only have a 40% chance.

Answer

r → (p ∨ q)

Step-by-step explanation:

The given statement is False. A test statistic based on point estimation is not used to construct the decision rule which defines the rejection region.

In hypothesis testing, a test statistic is calculated using sample data and a specific hypothesis to assess the strength of evidence against the null hypothesis. The decision rule, which determines whether to reject or fail to reject the null hypothesis, is based on the test statistic's distribution under the null hypothesis, rather than the point estimate itself.

The construction of the decision rule involves selecting a significance level (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The rejection region is determined based on the chosen significance level and the distribution of the test statistic. If the calculated test statistic falls within the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.

Point estimation, on the other hand, is used to estimate an unknown parameter of interest, such as the population mean or proportion, based on sample data. It involves calculating a single value (point estimate) that represents the best guess for the parameter value. The point estimate is not directly involved in constructing the decision rule or defining the rejection region in hypothesis testing.

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False. A test statistic based on point estimation is not used to construct the decision rule that defines the rejection region.

The process of hypothesis testing involves constructing a decision rule to determine whether to accept or reject a null hypothesis based on sample data. The decision rule is typically defined using a critical region or rejection region, which is a range of values for the test statistic.

Point estimation, on the other hand, is a method used to estimate an unknown population parameter based on sample data. It involves calculating a single value (point estimate) that serves as an estimate of the population parameter.

While point estimation and hypothesis testing are both important concepts in statistics, they serve different purposes. Point estimation is used to estimate population parameters, whereas hypothesis testing involves making decisions based on sample data.

The decision rule for hypothesis testing is typically constructed based on the significance level (alpha) and the distribution of the test statistic, such as the t-distribution or the standard normal distribution. The test statistic is calculated using sample data and compared to critical values or calculated p-values to determine whether to reject the null hypothesis.

Therefore, the statement that a test statistic based on point estimation is used to construct the decision rule defining the rejection region is false.

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i. Range (A): The space spanned by the columns of matrix A. It represents all possible linear combinations of the columns of A.

ii. Null (A): The set of all vectors x such that Ax = 0. It represents the solutions to the homogeneous equation Ax = 0.

iii. Row (A): The space spanned by the rows of matrix A. It represents all possible linear combinations of the rows of A.

iv. Null (A): The set of all vectors y such that ATy = 0. It represents the solutions to the homogeneous equation ATy = 0.

The equation Ax = b has a solution only when b is in the Range (A). It has a unique solution only when the Null (A) contains only the zero vector.

The equation ATy = d has a solution only when d is in the Row (A). It has a unique solution only when the Null (A) contains only the zero vector.

Assuming the size of A is m × n:

When Ax = b has a unique solution, the space Null (A) must be equal to Rn. This means there are no non-zero vectors that satisfy Ax = 0, ensuring a unique solution.

When ATy = d has a unique solution, the space Null (AT) must be equal to Rm. This means there are no non-zero vectors that satisfy ATy = 0, ensuring a unique solution.

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The limit of √x - 2 as x approaches 1 is -1.

The limit of -4√x + 25 - 5x as x approaches 0 is 25.

To solve the given limits, we can simplify the expressions and evaluate them. Let's solve each limit step by step:

√x - 2 as x approaches 1:

We can simplify this expression by plugging in the value of x into the expression. Therefore, we have:

√1 - 2 = 1 - 2 = -1

The limit of √x - 2 as x approaches 1 is -1.

-4√x + 25 - 5x as x approaches 0:

Again, let's simplify this expression by plugging in the value of x into the expression. Therefore, we have:

-4√0 + 25 - 5(0) = 0 + 25 + 0 = 25

The limit of -4√x + 25 - 5x as x approaches 0 is 25.

In summary:

The limit of √x - 2 as x approaches 1 is -1.

The limit of -4√x + 25 - 5x as x approaches 0 is 25.

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Answer:

No solution

Step-by-step explanation:

=> \(\frac{1}{4} (20-4a) = 6-a\)

=> \(\frac{1}{4} *4(5-a) = 6-a\)

=> \(5-a=6-a\)

Adding a to both sides

=> \(5-a+a=6-a+a\)

=> 5 ≠ 6

So, this equation has no solution.

If \(MU_{x}/P_{x}\)=30 and \(MU_{y} /P_{y}\)=40 then the consumer should buy the commodity y to maximise utility.

Given that \(MU_{x}/P_{x}\)=30 and \(MU_{y} /P_{y}\)=40 of commodities x and y.

Marginal utility is the additional utility that a consumer gets from consuming additional units of commodity. For maximising the utility of the consumer,the ratio of marginal utilities must be equal to the ratio of the products.

There can be two situations in our case:

Because \(MU_{x}/P_{x}\)<\(MU_{y} /P_{y}\)

So to equalise the ratio we need to reduce \(MU_{y} /P_{y}\). To reduce the utility of y the consumer needs to increase the consumption of y because as the consumption of commodity y increase it decreases the utility of commodity y.

Hence if \(MU_{x}/P_{x}\)=30 and \(MU_{y} /P_{y}\)=40 then the consumer should buy the commodity y to maximise utility.

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