Decide whether b = (-10, 13, –4, 9) is in the Span of S = {(10, -6, 4, 12), (-5, 4, -2, -3), (-10, 14, −4, 12)}. If so, express b in the simplest possible way and check directly that your answer is correct. Then express b using V₁ and v3 only.

Yes, larger sample sizes do increase the certainty of a statistical test. This is because as the sample size increases, the sample becomes more representative of the population, leading to more accurate results.

larger sample sizes generally increase the certainty of the statistical test. This is because larger samples provide more information and reduce the likelihood of chance variations affecting the results. The estimated parameter becomes more stable and accurate with a larger sample size. Additionally, larger sample sizes allow for the detection of smaller effect sizes and greater statistical power. However, it is important to note that sample size alone does not guarantee the validity of the statistical test. Other factors such as sampling methods, data quality, and appropriate statistical analysis must also be considered.
Yes, larger sample sizes do increase the certainty of a statistical test. This is because as the sample size increases, the sample becomes more representative of the population, leading to more accurate results. Additionally, larger sample sizes decrease the margin of error and increase the statistical test's power, allowing for better detection of true differences or relationships in the population. Overall, larger sample sizes lead to more reliable and valid conclusions in statistical tests.

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Answer: -27/8

Step-by-step explanation:

\(\left(-\frac{1}{2}\cdot \:3\right)^3\)

\(\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=-a^n,\:\quad \mathrm{if\:}n\mathrm{\:is\:odd}\)

\(\left(-\frac{1}{2}\cdot \:3\right)^3=-\left(\frac{1}{2}\cdot \:3\right)^3\)

\(=-\left(\frac{1}{2}\cdot \:3\right)^3\)

\(\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n\)

\(\left(\frac{1}{2}\cdot \:3\right)^3=\left(\frac{1}{2}\right)^3\cdot \:3^3\)

\(=-\left(\frac{1}{2}\right)^3\cdot \:3^3\)

\(=-\frac{1}{8}\cdot \:3^3\)

\(=-\frac{1}{8}\cdot \:27\)

\(=-\frac{27}{8}\)

RS = SP - 7, PQ = RS = QR = SP Perimeter of ▱PQRS = 124We are supposed to find the length of each side of ▱PQRS under the given conditions. Therefore, let us use the formula of the perimeter of a polygon (quadrilateral) to find the length of each side of the polygon.

The formula of the perimeter of a polygon is given by: P = a + b + c + d Where P is the perimeter and a, b, c, and d are the length of each side of the polygon. Let's substitute the given values in the above formula and solve it: P = PQ + QR + RS + SP124 = PQ + QR + RS + SP... (Equation 1)Now, we know that: PQ = RS = QR = SP We can rewrite the equation 1 as follows:124 = PQ + PQ + PQ - 7 + PQ + PQ - 7

Simplifying, we get;124 = 5PQ - 14Adding 14 on both sides;124 + 14 = 5PQ138 = 5PQDividing by 5 on both sides;138/5 = PQPQ = 27.6Now, we know that; PQ = RS = QR = SP We can substitute the value of PQ in any of the above equations. Let's use the equation PQ = RS. Then; RS = 27.6Using the equation; PQ = SPSP = 27.6QR = 27.6Using the equation; RS = SP - 7SP = RS + 7SP = 27.6 + 7 = 34.6Therefore, the length of each side of ▱PQRS is: PQ = 27.6, QR = 27.6, RS = 27.6, SP = 34.6

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(a) The product of 39 and -45 using the Booth multiply algorithm is -56.

(b) The product of -53 and -43 using the Booth multiply algorithm is -17.

(a) To compute the product of 39 and -45 using the Booth multiply algorithm, follow these steps:

1. Convert the numbers to binary representation:

  - 39: 00100111

  - -45: 11010011 (2's complement representation)

2. Set up the algorithm with the following initial values:

  - A = 00100111 (39 in binary)

  - Q = 11010011 (-45 in binary, 2's complement representation)

  - Q(-1) = 0 (initial value)

  - M = 11010011 (-45 in binary, 2's complement representation)

3. Perform the Booth multiply algorithm steps:

  Iteration 0:

  - Check the least significant bit (LSB) of Q and Q(-1). Since Q0 = 1 and Q(-1) = 0, perform subtraction.

  - A = A - M = 00100111 - 11010011 = -1010110

  - Q0 = Q(-1) = 1

  Iteration 1:

  - Shift A and Q right by 1 bit:

    - A = 11101011 (arithmetically shifted right)

    - Q = 11101001 (arithmetically shifted right)

  - Check the new LSB of Q and Q(-1). Since Q0 = 1 and Q(-1) = 1, perform addition.

  - A = A + M = 11101011 + 11010011 = 101001010

  - Q0 = Q(-1) = 1

  Iteration 2:

  - Shift A and Q right by 1 bit:

    - A = 11010101 (arithmetically shifted right)

    - Q = 11110100 (arithmetically shifted right)

  - Check the new LSB of Q and Q(-1). Since Q0 = 0 and Q(-1) = 1, perform addition.

  - A = A + M = 11010101 + 11010011 = 101100000

  - Q0 = Q(-1) = 0

  Iteration 3:

  - Shift A and Q right by 1 bit:

    - A = 11101000 (arithmetically shifted right)

    - Q = 11111010 (arithmetically shifted right)

  - Check the new LSB of Q and Q(-1). Since Q0 = 0 and Q(-1) = 0, no operation is required.

4. The final result is obtained by combining the value of A and Q:

  - A = 11101000 (in binary, which is -56 in decimal)

  - Q = 11111010 (in binary, which is -42 in decimal)

Therefore, the product of 39 and -45 is -56.

(b) To compute the product of -53 and -43 using the Booth multiply algorithm, follow the same steps as in part (a) with the respective binary representations of the numbers and perform the necessary calculations.

The product of -53 and -43 is -17.

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Answer:

1/4, 4/10, 3/7, 24/50 are all less than 1/2.

Step-by-step explanation:

C) The ordered pair that represents the initial value of the function is of (0,3840), meaning that the graph of the function crosses the y-axis at the value of y = 3840.

D) The rate of change of the equation is of -128, meaning that when x increases by one, y is decreased by 128.

The following is the definition of a linear function's slope and intercept:

y = mx + b.

In which:

m is the slope, representing the rate of change, that is, by how much y changes when x is increased by one.

The value of y at x=0 is represented by the intercept, b. Hence the ordered pair is of (0,b).

The function is defined as follows for this problem:

y = -128x + 3840.

The slope and intercept are therefore given as follow:

m = -128, b = 3840.

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The 95% confidence interval for population mean is (19.8, 22.2).

The confidence interval for population mean using the Student's t-distribution is:

CI = x ± \(t_{\frac{\alpha }{2}, (n -1) }\) \(\frac{s}{\sqrt{n} }\)

Given:

x = 22

s = 3

n = 27

α = n - 1 = 26

The critical value of t for α = 0.05 and degrees of freedom, (n - 1) = 19 is:

\(t_{\frac{\alpha }{2} , (n -1)}\) = \(t_{\frac{0.05}{2,19} }\)

            = 2.093

Compute the 95% confidence interval for population mean as follows:

   CI = X + \(t_{\frac{\alpha }{2}, (n -1) }\frac{s}{\sqrt{n} }\)

⇒ CI = 21± 2.093 × 3/√27

        = 21 ± 1.20

        = (22.2, 19.8)

Thus, the 95% confidence interval for population mean is (19.8, 22.2).

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Answer: A on Edge

Step-by-step explanation:

f(x) = (x –1)2 – 7

Answer:

A

Step-by-step explanation:

Alice paid $25 for her pair of jeans, and Jeff paid $4 for the steaks.

Let's calculate the final amount paid by Alice and Jeff for their purchases.

Alice:

Jeff:

So, Alice paid $25 for her pair of jeans, and Jeff paid $4 for the steaks.

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Answer:

That's ️ ️ ️

Answer:

3h+4.50=15

We know that she skates for 3 hours, but we don't know the cost per hour so is the "h". He pays a start up $4.50 for the ice skates. And he spend $15 in total for ice skating.

Hopefully that helps. Have a great night! Or day!

Answer:

$40 and $72, see below :)

Step-by-step explanation:

One way we can do this is to add the total ratios and then divide that from 112.

10x + 18x = 28x = 112

28x = 112

x = 4

That means, for every ratio, you just have to multiply the amount by 4.

so for example, 10 is just 10 * 4 = 40

So, your answer would be you share the money into $40 and $72

Step-by-step explanation:

If you mean 7⁶, the exponent is 6. (A)

When written as a^m, a is a number and m is the exponent.

Answer:

y = 4x - 9

Step-by-step explanation:

Take 2 points:

(0,-9) and (4,7)

Find the slope:

(7 - (-9))/(4 - 0)

16/4 = 4

so we have y = 4x + b

Now find b:

Insert a point for y and x:

7 = 4(4) + b

7 = 16 + b

b = -9

y = 4x - 9

The greatest number of groups Jessica can display is 2

From the question, we have the following parameters that can be used in our computation:

Photos = 62

Drawings = 68

Next, we expand the numbers

This gives

Photos = 2 * 21

Drawings = 2 * 2  * 17

The common factor in the above products is

Common factor = 2

This means that the greatest number is 2

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The answer of the given question based on the trigonometry is , to calculate YZ, we should use the cosine function with the angle 35.5°.

The sine function is a mathematical function that relates the ratios of the lengths of two sides of a right triangle with the measure of one of its non-right angles. Specifically, the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse.

To use trigonometry to calculate YZ, we need to find a trigonometric ratio that involves the given side XZ and the angle opposite the requested side, which is angle YXZ. We don't have the measure of this angle, but we know that it is supplementary to the given angle 35.5°, so it must measure:

180° - 35.5° = 144.5°

We can use this angle and the given side XZ to find the length of YZ using the sine or cosine function.

In this case, the length of the opposite side is YZ, the length of the hypotenuse is XZ, and the measure of the angle is 144.5°. So we can write:

sin(144.5°) = YZ / XZ

Solving for YZ, we get:

YZ = XZ * sin(144.5°)

On the other hand, the cosine function , this case, the length of the adjacent side is YZ, the length of the hypotenuse is XZ, and the measure of the angle is 35.5°. So we can write:

cos(35.5°) = YZ / XZ

Solving for YZ, we get:

YZ = XZ * cos(35.5°)

Therefore, to calculate YZ, we should use the cosine function with the angle 35.5°.

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We discuss what are similar polygons and their relationship with scale factors through the given questions.

What are similar polygons?

Two polygons that are similar in shape but not in size are called similar polygons. Identical polygons have congruent corresponding angles and proportional corresponding sides. There will always be similar varieties of triangles, quadrilaterals, and polygons. For instance, squares and equilateral triangles are both similar shapes. We know the lengths of corresponding sides are proportional if two polygons are similar to one another.

1) a) When two polygons are similar, we calculate the ratio of the lengths of the two corresponding sides of given polygons to determine the scale factor. The polygons are similar if the ratio is the same for all corresponding sides.

b) Using the scale factor, we can find the length of the corresponding sides of the new polygon and hence this is how we draw a similar polygon.

2) a) The scale factor between two similar polygons tells us about the ratio of the corresponding sides of the polygons.

  b) A scaled polygon's perimeter can be calculated by multiplying the original polygon's perimeter by the scale factor.

c) The area of the scaled polygon can be found by multiplying the square of the scale factor with the original polygon's area.

d) The angles of two similar polygons are congruent. So scale factor does not affect the angles of similar polygons.

Therefore similar polygons are related by scale factor as discussed above.

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The scenario that is an example of simple random sampling is option C: "A supermarket wants to study the buying habits of its customers. They choose every 20th customer entering the supermarket to fill out the survey."

Simple random sampling is a method of selecting a sample from a population in which every member of the population has an equal chance of being chosen.

In option C, the supermarket chooses every 20th customer entering the store, which ensures that each customer has an equal chance of being selected. Therefore, this is an example of simple random sampling.

Options A, B, and D do not meet the criteria for simple random sampling, as they involve selecting specific regions, asking for opinions from readers, or mailing questionnaires to students, which does not ensure that every member of the population has an equal chance of being selected.

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Answer:252

Step by step explanation:

db

Answer:

5 blue and 5 white tiles per row

Step-by-step explanation:

80/8 =(10-this is the amount per row)then divide 10 by 2 to factor in your different different tiles)

Work Check:

80/8rows=10/2colors=5 this means 5 blue and 5 white per row

Answer: stop spamming

Step-by-step explanation:

answer is c

sorry if incorrect

The distance between 1.5 and any point,n,on a number line is |1.5 - n|

From the question, we have the following parameters that can be used in our computation:

Points = n and 1.5

The distance between these points is the absolute difference between them

This is represented with the following equation

Distance = |1.5 - n|

Hence, the distance is |1.5 - n|

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The worth of a $300 investment at an annual interest rate of 8% per year after 30 years can be calculated using the compound interest formula. The worth of the investment after 30 years will be approximately $1,492.22.

1. Start with the initial investment amount: $300.

2. Calculate the interest rate as a decimal: 8% = 0.08.

3. Use the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial investment), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

4. Plug in the given values into the formula:

  A = 300(1 + 0.08/1)^(1*30)

  A = 300(1 + 0.08)^30

  A ≈ 300(1.08)^30

5. Calculate the final amount using a calculator or spreadsheet:

  A ≈ 300 * 5.1847055

  A ≈ $1,555.41

Therefore, the worth of the $300 investment after 30 years at an annual interest rate of 8% will be approximately $1,492.22.

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Answer:

x² + 2x + 3

Step-by-step explanation:

(f + g)(x) = f(x) + g(x), thus

f(x) + g(x)

= 4x + 5 + x² - 2x - 2 ← collect like terms

= x² + 2x + 3

Answer:

A' (9,4)

B' (8,-1)

C' (5,1)

Answered by GAUTHMATH

Answer:

A' = 9,4

B' = 8,-1

C' = 5,1

Step-by-step explanation:

Answer:

its the  firs one

Step-by-step explanation:

The way that errors can be introduced are;

Giving the questionnaire to all participants when they arrive for their appointment does not follow the protocol;

The participant could fill out the questionnaire before experiencing the therapy session.

Statistical errors are defined as errors that describe the difference that exists between a value obtained from a data collection process and the 'true' value for the population. Thus, the greater the error, the less representative the data will be of the population.

There are two main errors in this case which are type I error and type II error.

A type I error is called false-positive and it occurs if an investigator rejects a null hypothesis that is actually true in the population.

A type II error is called false-negative and it occurs if the investigator fails to reject a null hypothesis that is actually false in the population.

Now, from the question, since the data collection protocol alls for a questionnaire to be administered to patients having knee replacement surgery after the third physical therapy appointment, then we can introduce an error by;

Giving the questionnaire to all participants when they arrive.

The participant could fill out the questionnaire before experiencing the therapy session.

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Giving a questionnaire to all par-ticipants follows the timing of theprotocol.

BReading the questionnaire to par-ticipants with poor reading skillsfollows the timing of the protocol.

CGiving the questionnaire to allparticipants when they arrive fortheir appointment does not fol-low the protocol; the participantcould fill out the questionnairebefore experiencing the therapysession.

DGiving the questionnaire to theparticipants after the appoint-ment to be completed while theyhave a snack follows the timingof the protocol.