41/17 rounded to the nearest hendreth

The Chi-square test is a statistical test used to determine if there is a significant difference between observed and expected frequencies in categorical data. In this example, the test is used to assess whether there is a significant difference in the mean breaking strengths of two types of cables.

The Chi-square test of significance is employed when dealing with categorical or nominal data. It compares the observed frequencies with the frequencies that would be expected if the variables were independent. In this case, the breaking strengths of the two cables are the variables of interest.

To perform the test, the first step is to define the null hypothesis (H0) and the alternative hypothesis (Ha). In this example, H0 assumes that there is no difference in the mean breaking strengths of the two cables, while Ha suggests that there is a difference.

Next, the test statistic, denoted by X2 (chi-square), is calculated using the formula X2 = Σ[(O - E)²/E], where O represents the observed frequencies and E represents the expected frequencies under the assumption of independence.

To determine the expected frequencies, we need to estimate the means and variances of the breaking strengths. Here, x = 1925 and sigma = 40 for the first cable, and x = 1905 and sigma = 30 for the second cable.

Once the test statistic is calculated, it is compared to a critical value from the Chi-square distribution with degrees of freedom equal to (r - 1)(c - 1), where r is the number of rows and c is the number of columns in the contingency table. The significance level of 0.01 determines the critical value.

If the calculated X2 value is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to indicate a difference in the mean breaking strengths of the two cables. Conversely, if the calculated X2 value is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is no significant difference.

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Answer:

$3.23

Step-by-step explanation:

1.71 ÷ 18 = 0.095 = 9.5%

9.5% × 34 = 3.23

The equation of each line in slope intercept form y = 2x + 3,x = 4

The equation of a line in slope-intercept form (y = mx + b), the slope (m) and the y-intercept (b). The slope-intercept form is a convenient way to express a linear equation.

Equation of a line with slope m and y-intercept b:

y = mx + b

Equation of a vertical line:

For a vertical line with x = c, where c is a constant, the slope is undefined (since the line is vertical) and the equation becomes:

x = c

An example for each case:

Example with given slope and y-intercept:

Slope (m) = 2

y-intercept (b) = 3

Equation: y = 2x + 3

Example with a vertical line:

For a vertical line passing through x = 4:

Equation: x = 4

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Answer:

y=mx+b

Step-by-step explanation:

On solving the provided question, we can say that here in this rhombus,

angle 1 is 106 and  angle 2 and 3 are 37 each

A rhombus is an equal-sided quadrilateral in Euclidean plane geometry. The term "equilateral triangle" also refers to a quadrilateral whose sides are of the same length. A parallelogram has a unique variation known as a rhombus. In a rhombus, the opposite sides and angles are parallel and equal. A rhombus's diagonal is split in half by a right angle, and each of its sides is the same length. Rhombic diamonds and diamonds are other names for rhombuses. The length of every side is the same. Diagonals are equal in a rhombus. At a 90° angle, parallel lines split in half. 180 degrees is the sum of adjacent angles.

here in this rhombus,

angle 1 is 106

other two side are 360-106-106 = 148

148/2 = 74

so angle 2 and 3 are 37 each

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A common everyday counting unit that is used to mean 12 of an object is a Dozen

Dozen is derived from the Old French word "douzaine" which means twelve each. In most situations, a dozen is used to refer to a group of twelve items. The term dozen is also used in informal situations to refer to a very large number of objects. For example, one might say "I have dozens of friends!" to mean that they have a lot of friends.

Dozen is a useful term when counting items. It allows for large numbers to be easily broken down into manageable groups. For example, if you have 120 pencils, you could easily count them by saying that you have 10 dozen pencils. It can also be useful when talking about fractions. For example, instead of saying "one and a half of an item," one could say "one and a half dozen of an item."

Dozen is a common everyday counting unit that is used to mean 12 of an object. It is a useful term when counting items and when talking about fractions, and can be used in both formal and informal settings.

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Answer:

8x2 – 25x + 7

Step-by-step explanation:

its A

Answer:

its A

Step-by-step explanation:

or 8x2 – 25x + 7

Answer:

144%

Step-by-step explanation:

I hope this helps you

Answer:

900 L

Step-by-step explanation:

after 10 hours : 10*10=100 liters

1000-100=900 liter

is the answer I recived

My work is below:

Next after 10 hours (10*10=100 liters )

1000-100=900 liter

Hope this helps you learn what to do in similar probles

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From the line plot, we can see that:

A. The greatest value with a dot above it is 8.

B. There will be a total of 31 dots.

C. There will be 3 more dots above 7 than above 8.

D. There will be 6 dots above 7.

A line plot is a type of graph that shows the frequency of data along a number line. It is also known as a dot plot. In a line plot, each data point is represented by a dot above the number on the number line that corresponds to its value. The dots are stacked above each other for data points that have the same value, so that the height of the stack indicates the frequency of that value. Line plots are often used to visualize small to medium-sized data sets and can be useful for quickly identifying patterns or outliers in the data.

Here,

None of the statements in the given options are true based on the given table. However, we can create a line plot using the data from the table. The line plot would have numbers from 3 to 8 on the horizontal axis and dots representing the number of teams with that many people on the vertical axis. The line plot would look something like this:

|        o

|        o

|        o

|        o

|     o  o

|  o  o  o

|  o  o  o

|  o  o  o

|  o  o  o

|_ o  o  o

 3  4  5  6  7  8

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The given statement, "The nullspace of a nonzero 4 x 4 matrix cannot contain a set of four linearly independent vectors" is False.

Explanation: Null space is a linear algebra term used to refer to the set of all vectors that are mapped to the null vector. The solution of Ax=0 is also referred to as the null space or kernel of A. Since the matrix is of size 4x4 and non-zero, it must have at least one non-zero eigenvalue. Any non-zero vector multiplied by this non-zero eigenvalue will result in a non-zero vector, even if it is in the nullspace of the matrix. Because of this, a non-zero 4 x 4 matrix's nullspace can have four or fewer linearly independent vectors.

Hence, the statement "The nullspace of a nonzero 4 x 4 matrix cannot contain a set of four linearly independent vectors" is false.

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Hey there! I'm happy to help!

We see that if you add 5% to the original cost, we have $168 as our cost. This means that 105% of the original cost is 168. Let's set up an equation to find the original cost. Let's call our original cost c.

To turn a percent into a decimal, you divide by 100.

1.05c=168

We divide both sides by 1.05.

c=160

Therefore, the original cost was $160.

Have a wonderful day! :D

If the sample size is large enough, the normal sampling distribution can be used to test the claim about the population proportion p at the given level of significance. If the sample size is not large enough, we can use the binomial distribution instead.

The general rule of thumb is that if both np and n(1 - p) are greater than or equal to 10, then the normal sampling distribution can be used, where n is the sample size and p is the hypothesized proportion.

If np and n(1 - p) are both less than 10, we should use the binomial distribution instead. If only one of them is less than 10, we can still use the normal sampling distribution, but it may not be as accurate.

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Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

The probability distribution is a) discrete, with b) a mean of 1.23, the standard deviation is c) 0.6458, d) the probability that an American will take 3 or more trips is 0.04, e) the probability that an American will take 2 or less trips is 0.96 and, f) the probability to take at least one trip is 0.94

It is given that the probability distribution of the no. of trips an American adult takes that lasts 5 nights or more

x              probability

0                  0.06

1                   0.70

2                  0.20

3                  0.03

4                  0.01

a)

Here we can see that all the values are isolated and there is no continuity between them. The distribution clearly has breaks between them.

Hence, we can say that the distribution is discrete.

b)

The expected value of any probability

E(X) = ∑xp(x)

where,

x is the random variable

p(x) is the probability of the corresponding random variable hence we get

E(X) = 0 × 0.06  +  1 × 0.70  +  2 × 0.20  +  3 × 0.03  +  4 × 0.01

= 0  +  0.7  +  0.4  +  0.09  +  0.04

= 1.23

Hence the expected value is 1.23

c)

The standard deviation is √σ²

Where σ² = variance of the distribution

σ² = E(X²) - {E(X)}²

{E(X)}² = 1.23²

= 1.5129

E(X²) = ∑x²p(x)

= 0 × 0.06  +  1 × 0.70  +  4 × 0.20  +  9 × 0.03  +  16 × 0.01

= 0.7  +  0.8  +  0.27  +  0.16

= 1.93

Therefore,

σ² = 1.93  -  1.5129

= 0.4171

Therefore

σ = 0.6458

d)

The probability to take 3 or more trips is

P(X≥3)

= P(X = 3)  +  P(X = 4)

= 0.03 + 0.01

= 0.04

e)

The probability of an American taking 2 or less trips is

1 - P(X≥3)

= 1 - 0.04

= 0.96

f)

The probability that an American will take at least one trip is

P(X≥1)

= 1 - P(X = 0)

= 1 - 0.06

= 0.94

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The amount Connor and Ashley need to make to have the same amount saved is $144

Let

Ashley:

1/4x + 11

Connor:

3/8x - 7

1/4x + 11 = 3/8x - 7

11 + 7 = 3/8x - 1/4x

18 = (3x-2x) / 8

18 = 1/8x

x = 18 ÷ 1/8

x = 18 × 8/1

x = $144

Therefore, the amount Connor and Ashley need to make to have the same amount saved is $144

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The recursive formula that represents the same sequence of numbers as the explicit formula an = 3n + 4 is an = an-1 + 3, with the initial term a1 = 7.

A recursive formula defines a sequence by expressing each term in terms of previous terms. In this case, the explicit formula an = 3n + 4 gives us a direct expression for each term in the sequence.

To find the corresponding recursive formula, we need to express each term in terms of the previous term(s). In this sequence, each term is obtained by adding 3 to the previous term. Therefore, the recursive formula is an = an-1 + 3.

To complete the recursive formula, we also need to specify the initial term, a1. We can find the value of a1 by substituting n = 1 into the explicit formula:

a1 = 3(1) + 4 = 7

Hence, the complete recursive formula for the sequence is an = an-1 + 3, with the initial term a1 = 7. This recursive formula will generate the same sequence of numbers as the given explicit formula.

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Answer:

x= 7

Step-by-step explanation:

add (12x+1) and (5x-3) which becomes 17x-2 and then set that equal to 117 and solve. move the 2 to the right side of the equation which becomes 17x=119 and then divide 119 by 17 which x equals 7.

plug in 7 for x to make sure you get 117

An algebraic representation which best describes this transformation is: C. (x, y) → (5x/2, 5y/2).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

By critically observing the graph, we can logically deduce the following vertices:

In this scenario, the transformation rule is given by this algebraic representation:

Q (x, y)                      →               Q' (x, y)

Coordinate Q = (2, 0)   →  Coordinate Q' = ((5/2 × 2), (5/2 × 0)) = Coordinate Q' = (5, 0).

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Answer:

1.  X= 4

2.  X= 1

3. X= 3

4. X= 5

5. X= 7

6. X= -3/4

7. X= 6

8. X= 5

Step-by-step explanation:

Answer:

Look below :)

Step-by-step explanation:

1.x=4

2.×=1

3.x=3

4.x=5

5.x=7

6.x=-0.75

7.x=6

8.x=5

Hope this helps :)

Answer:

∠ 2 = 40°

Step-by-step explanation:

∠ 1 and ∠ 2 are corresponding angles and congruent, thus

∠ 2 = ∠ 1 = 40°

Answer:

  A)  7/5

Step-by-step explanation:

An exponential equation like this can be solved by using logarithms, or by rewriting the bases so they are the same.

  3^(2h-1) = 27^(-h+2)

Using 27 = 3^3, we can write the equation in terms of powers of 3:

  3^(2h-1) = (3^3)^(-h+2)

  3^(2h -1) = 3^(-3h +6)

Equating exponents gives ...

  2h -1 = -3h +6

  5h = 7 . . . . . . . . . add 1+3h

  h = 7/5 . . . . . . . divide by 5

__

Additional comment

When solving this using a graphing calculator, it is often convenient to write the equation in such a way that the solution is an x-intercept. Here, we can do that by subtracting the right-side expression from both sides:

  3^(2h-1) -27^(-h+2) = 0

The solution is h = 1.4 = 7/5.

Answer:

h=7/5

hope this helps!

Answer:

(3, 3) (1, -1)

Step-by-step explanation:

Answer:

(1, - 1) , (3, 3 )

Step-by-step explanation:

Given the 2 equations

3 + y - 2x = 0 → (1)

3x² + 2y² - 4xy = 9 → (2)

In (1) subtract 3 - 2x from both sides

y = 2x - 3 → (3)

Substitute y = 2x - 3 into (2)

3x² + 2(2x - 3)² - 4x(2x - 3) = 9 ← distribute and simplify left side

3x² + 2(4x² - 12x + 9) - 8x² + 12x = 9

3x² + 8x² - 24x + 18 - 8x² + 12x = 0

3x² - 12x + 18 = 9 ( subtract 9 from both sides )

3x² - 12x + 9 = 0 ( divide through by 3 )

x² - 4x + 3 = 0 ← in standard form

(x - 1)(x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 3 = 0 ⇒ x = 3

Substitute these values into (3) for corresponding values of y

x = 1 : y = 2(1) - 3 = 2 - 3 = - 1 ⇒ (1, - 1 )

x = 3 : y = 2(3) - 3 = 6 - 3 = 3 ⇒ (3, 3 )

The facts about the quotient expression p(x) / (2x+5)

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

The expression p(-5/2) = 0 means that

The divisor is a factor of the polynomial

This statement represents the first fact

The second fact in the expression p(x) / (2x+5) is that p(x) has a zero at x = -5/2

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Neither of these generations are typically associated with multitasking and instant gratification to the same extent as Millennials.

Based on the generational categories commonly used, it is most likely that Meg is a Millennial.

Millennials are known for their proficiency in multitasking and their preference for instant gratification. They have grown up with technology and are comfortable with constant communication through various channels. The Baby Boomer and Gen X generations, on the other hand, did not have the same level of exposure to technology from a young age, and may not prioritize instant gratification in the same way.

Baby Busters is a less common term for the generation born between the late 1950s and mid-1960s, and Golden Boomers typically refer to the leading edge of the Baby Boomer generation (born between 1946 and 1955). Neither of these generations are typically associated with multitasking and instant gratification to the same extent as Millennials.

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Answer:

caca

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

(0)(8)(3+1−4)

=0(3+1−4)

=0(4−4)

=(0)(0)

=0

The researcher should use a sample size of approximately 312 middle school students to conduct the research.

To determine the sample size needed for the researcher to create a 95% confidence interval with a margin of error of 0.5 days, we can use the formula:

\(\[ n = \left(\frac{Z \cdot \sigma}{E}\right)^2 \]\)

Where:

- \(\( n \)\) is the sample size

- \(\( Z \)\) is the z-score corresponding to the desired confidence level (for 95% confidence, Z is approximately 1.96)

- \(\( \sigma \)\) is the known standard deviation of the population

- \(\( E \)\) is the desired margin of error

Plugging in the values, we get:

\(\[ n = \left(\frac{1.96 \cdot 4.5}{0.5}\right)^2 \]\)

To solve the equation for the required sample size, we can substitute the given values into the formula:

\(\[ n = \left(\frac{1.96 \cdot 4.5}{0.5}\right)^2 \]\)

Calculating this expression gives us:

\(\[ n = \left(\frac{8.82}{0.5}\right)^2 \]\)

\(\[ n = (17.64)^2 \]\)

\(\[ n \approx 311.1696 \]\)

Therefore, the researcher should use a sample size of approximately 312 middle school students to conduct the research.

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A. To find the position vector of point C:

c = a + b = (21 + 2 + k) + (i + j - 4k)

  = 21i + (2 + 1)j + (1 - 4)k

  = 21i + 3j - 3k

B. To show that OACB is a rectangle:

Firstly, we need to prove that the opposite sides of the quadrilateral are parallel and of equal length.

Since we already have the position vectors of points A, B and C we will calculate the vectors.

Side OA:

Vector OA = a - o = (21 + 2 + k) - (0 + 0 + 0)

= 21i + 2j + k

Side CB: Vector CB = b - c = (i + j - 4k) - (21i + 3j - 3k)

= -20i - 2j - k

Since OA and CB are parallel  they have the same direction (proportional vectors) but in opposite directions.

Also, the magnitudes of OA and CB are equal, which means that the opposite sides are also of equal length. Therefore, we can prove that OACB is a rectangle.

The area of the rectangle OACB can be found by:

Area = |OA x OB|

OA x OB = |21i + 2j + k x i + j - 4k|

        = |(2 × (-4) - k × 1)i + (k × 1 - 21 × (-4))j + (21 × 1 - 2 × 1)k|

        = |-8i + (k + 84)j + 19k|

        = -8i + (k + 84)j + 19k

The area of the rectangle is therefore -8i + (k + 84)j + 19k.

C. The point of intersection between diagonals AB and OC is the midpoint of both diagonals.

Since we know the position vectors of points A and B, we can also find the midpoint by averaging their position vectors:

Position vector of point D = (a + b) / 2

= ((21 + 2 + k) + (i + j - 4k)) / 2

= (21 + i + 2 + j - 3k) / 2

= (23 + i + j - 3k) / 2

Therefore, the position vector of point D is (23 + i + j - 3k) / 2.

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Answer:

4 9/10

Step-by-step explanation:

Answer:

a) 8/20 = 8 is the total of the girls and 20 is the total of the kids

b)2/20 = 2 is the total of girls that are left handed and 20 is the total of the kids

The percentage error in measuring the line segment is 4%. The correct option is (4)4%.

The actual length of the line segment is 5 cm, but it was measured as 5.2 cm, which is 0.2 cm more than the actual length.

The percentage error in measuring the line segment can be calculated as follows:

Percentage error = (Error / Actual value) x 100%

where Error = Measured value - Actual value

Substituting the given values, we get:

Error = 5.2 cm - 5 cm = 0.2 cm

Actual value = 5 cm

Percentage error = (0.2 cm / 5 cm) x 100% = 4%

Therefore, the percentage error in measuring the line segment is 4%.

Hence, the correct option is (4)4%.

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