{(1, 2), (1, 3), (1, 4), (1,5), (1, 6)}

To calculate the value of the test statistic, we need to use the sample results provided: d-bar = 6.9, sD = 7.8, and n = 10. The value of the test statistic is approximately 1.983.

Given:

Sample mean difference (d-bar) = 6.9

Sample standard deviation of the differences (sD) = 7.8

Sample size (n) = 10

To calculate the test statistic, we can use the formula for the t-statistic:

t = (d-bar - μD) / (sD / sqrt(n))

where d-bar is the sample mean difference, μD is the hypothesized mean difference under the null hypothesis, sD is the sample standard deviation of the differences, and n is the sample size.

In this case, the null hypothesis (H0) states that μD is less than or equal to 2. Since the alternative hypothesis (HA) is μD > 2, this is a one-tailed test.

Plugging in the values into the formula:

t = (6.9 - 2) / (7.8 / sqrt(10))

t = 4.9 / (7.8 / 3.162)

t = 4.9 / 2.471

t ≈ 1.983

Therefore, the value of the test statistic is approximately 1.983.

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Answer:

Step-by-step explanation:

my answer is attached in the photo below

The volume of a hemisphere with a radius of 44.9 m, rounded to the nearest tenth of a cubic meter, is approximately 222,232.7 cubic meters.

To calculate the volume of a hemisphere, we use the formula V = (2/3)πr³, where V represents the volume and r is the radius. In this case, the radius is 44.9 m. Plugging in the values, we get V = (2/3)π(44.9)³. Evaluating the expression, we find V ≈ 222,232.728 cubic meters. Rounding to the nearest tenth, the volume becomes 222,232.7 cubic meters.

The explanation of this calculation lies in the concept of a hemisphere. A hemisphere is a three-dimensional shape that is half of a sphere. The formula used to find its volume is derived from the formula for the volume of a sphere, but with a factor of 2/3 to account for its half-spherical nature. By substituting the given radius into the formula, we can find the volume. Rounding to the nearest tenth is done to provide a more precise and manageable value.

Therefore, the volume of a hemisphere with a radius of 44.9 m is approximately 222,232.7 cubic meters.

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Answer:

-4

Step-by-step explanation:

Number of nails to finish the project by buying are required = 2964 units

1 package of nails contains per unit  = 52 units

To find the no. of packages we have to simply divide the total no. of nails required by the total of no. of nails of unit given in the one package of nails.

So,

Number of package required to the builder

= Total number of nails required to buy by the builder / no. of nails provided  per package

=2964/52

=57 packages

Therefore, No. of packages required by the builder to buy to complete the project

=57 packages needed.

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Answer: 57

Step-by-step explanation:

Just plug it into a calculator.

2964/52 = 57

He needs to buy 57 packages

Answer:

31

Step-by-step explanation:

although we cannot see the whole graph, I assume it would be 31 because

2010-1979 is 31

and the x values are years after 1979

Check the picture below.

y=-2x+5

First of all we need to determine the slope of the line perpendicular to y = 1/2x - 5 .

The slopes of perpendicular lines are opposite reciprocals.

So we take 1/2 , turn it over , and change it's sign :

\(^1/_2\:\:\:--- > ^2/_1\:\:\:--- > 2\:\:\:--- > -2\)

The slope of the line perpendicular to y = 1/2x-5 is -2 .

Since we're also given a point that the line crosses , we can write the line's equation in point - slope form :

y-y₁=m(x-x₁)

y-7=-2(x-(-1)

y-7=-2(x+1)

Now convert to slope intercept :

y-7=-2x-2

add 7 on both sides :

\(\footnotesize\text{hope\:helpful}\)

According to the rules of significant figures:



1.25 × 200 = 300

the answer is

TRue

The solution to the differential equation D²y(t) + 12 Dy(t) + 36y(t) = 2 \(e^{(-5t)}\), with initial conditions y(0) = 1 and Dy(0) = 0, is \(y(t) = (1 + 6t) e^{(-6t)}\).

To solve the given differential equation using the classical method, we can assume a solution of the form \(y(t) = e^{(rt)}\) and find the values of r that satisfy the equation. We then use these values of r to construct the general solution.

Using the classical method:

Substitute the assumed solution \(y(t) = e^{(rt)}\) into the differential equation:

D²y(t) + 12 Dy(t) + 36y(t) = \(2 e^{(-5t)}\)

This gives the characteristic equation r² + 12r + 36 = 0.

Solve the characteristic equation for r by factoring or using the quadratic formula:

r² + 12r + 36 = (r + 6)(r + 6)

= 0

The repeated root is r = -6.

Since we have a repeated root, the general solution is y(t) = (c₁ + c₂t) \(e^{(-6t)}\)

Taking the first derivative, we get Dy(t) = c₂ \(e^{(-6t)}\)- 6(c₁ + c₂t) e^(-6t).\(e^{(-6t)}\)

Using the initial conditions y(0) = 1 and Dy(0) = 0, we can solve for c₁ and c₂:

y(0) = c₁ = 1

Dy(0) = c₂ - 6c₁ = 0

c₂ - 6(1) = 0

c₂ = 6

The particular solution is y(t) = (1 + 6t) e^(-6t).

Using the Laplace transform method:

Take the Laplace transform of both sides of the differential equation:

L{D²y(t)} + 12L{Dy(t)} + 36L{y(t)} = 2L{e^(-5t)}

s²Y(s) - sy(0) - Dy(0) + 12sY(s) - y(0) + 36Y(s) = 2/(s + 5)

Substitute the initial conditions y(0) = 1 and Dy(0) = 0:

s²Y(s) - s - 0 + 12sY(s) - 1 + 36Y(s) = 2/(s + 5)

Rearrange the equation and solve for Y(s):

(s² + 12s + 36)Y(s) = s + 1 + 2/(s + 5)

Y(s) = (s + 1 + 2/(s + 5))/(s² + 12s + 36)

Perform partial fraction decomposition on Y(s) and find the inverse Laplace transform to obtain y(t):

\(y(t) = L^{(-1)}{Y(s)}\)

Simplifying further, the solution is:

\(y(t) = (1 + 6t) e^{(-6t)\)

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The appropriate calculator function to use in determining the percentage of sumo wrestlers who are predicted to weigh more than 700 lbs is the "percentage" function.

A percentage is a decimal or a fraction written as a percentage with a percentage sign. For example, 50% is equal to 0.5 or 1/2 as a decimal or fraction. The concept of a percentage is utilized in a variety of calculations, including finance, science, and everyday life.

To calculate percentages, divide the number you want to convert by the total amount and multiply by 100. The following are the steps to follow:Divide the number you want to convert by the total amount. Multiply by 100 to obtain the percentage.

As an example: 20/100 = 0.2, 0.2*100 = 20%. To determine the percentage of sumo wrestlers predicted to weigh more than 700 lbs, you'll need to use the "percentage" function.

Here are the steps to follow:Begin by determining the number of sumo wrestlers who are expected to weigh more than 700 lbs.Divide the number of sumo wrestlers predicted to weigh more than 700 lbs by the total number of sumo wrestlers (100%).Multiply by 100 to obtain the percentage.

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The correct answer is D. 50% long-tailed cat with long whiskers, 50% short-tailed cat with short whiskers.

This is because the long-tailed cat with long whiskers is homozygous for the recessive allele for tail length (ww) and homozygous for the dominant allele for whisker length (TT), while the short-tailed cat with short whiskers is homozygous for the dominant allele for tail length (TT) and homozygous for the recessive allele for whisker length (ww). Therefore, all the offspring will inherit one copy of the dominant allele for tail length (T) from each parent, making them all long-tailed, but half will inherit the recessive allele for whisker length (w) from each parent, making them short-whiskered.

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The frequency of revision times is given by the product of the frequency

density value and the class width.

Correct response:

The estimate of the number of students who revised for less than 45

minutes is given by the area, A, under the histogram to the left of the 45

minute mark as follows;

Frequency, f = Frequency density × Class width

Number of students = ∑f

Therefore;

A = 5 × 2 + 10 × 2.2 + 20 × 1.6 + 10 × 0.8 = 72

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Research has shown that competent communicators achieve effectiveness by adjusting their behaviors to the person and situation (option e).

Effective communication involves being adaptable and responsive to the specific context, individual preferences, and the needs of the situation.

Competent communicators recognize that different people have different communication styles, preferences, and expectations. They understand the importance of tailoring their communication approach to effectively connect and engage with others.

This may involve using appropriate language, tone, non-verbal cues, and listening actively to understand the needs and perspectives of others.

By adapting their behaviors, competent communicators can build rapport, foster understanding, and promote effective communication exchanges. They are mindful of the social and cultural dynamics at play, and they strive to communicate in a way that is respectful, inclusive, and conducive to achieving mutual goals.

In summary, competent communicators understand that effective communication is not a one-size-fits-all approach. They adjust their behaviors to the person and situation, demonstrating flexibility and adaptability in order to enhance communication effectiveness.

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Competent communicators achieve effectiveness mostly by adjusting their behaviors to suit the person they are communicating with and the situation they find themselves in. While other factors, like having a broad vocabulary or giving feedback, play a part in effective communication, the former is considered the most crucial.

Research suggests that competent communicators achieve effectiveness mostly through adjusting their behaviors depending on the person they are communicating with and the situation they are in. This is option e. of your question. Communicating effectively involves behaviors like active listening, understanding the other person's point of view, being able to express thoughts and ideas clearly, and being polite and respectful. While a broad vocabulary (option b.) can be useful, it is not as crucial as adapting your behavior to fit the situation. Moreover, giving feedback (option d.) is a part of effective communication but not the sole defining factor. Apologizing when offending others (option c.) is also important but it doesn't necessarily make one a competent communicator. Using the same type of behavior in various situations (option a.) might not always work, as different situations and individuals require different communication styles.

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\(m\angle E=\sin \dfrac{\sqrt{10}}{2\sqrt5}=\sin \dfrac{\sqrt2}{2}=45^{\circ}\)

Answer:

Step-by-step explanation:

Answer:

about  $2442.42

Step-by-step explanation:

1985 - 1980 = 5 years

B = Initial Value

r = rate of change

t = time

A = B(1 + r)^t

2245(1 + 0.017)^5 = 2442.42428756

2442.42428756 = 2442.42

Therefore , the solution of the given problem of function comes out to be f(x) = -4.5199 * (1.5546)ˣ

The mathematics class covers  a broad variety of subjects, such as mathematics, numbers and their subsets, as well as expressions  building, construction, and both real and imagined geographic locations. The relationships between various components that all cooperate to create the same outcome are covered by a work. A utility is comprised of several unique parts that work together to produce unique outcomes for each input.

Here,

We can see from the table that:

When x = -3, f(x) = -2.999.

f(x) equals -2.99 when x is two.

At x = 1, f(x) equals -2.9.

If x = 1, then f(x) = 7.

F(x) = 97 when x = 3.

x = 5 when f(x) = 997.

We can write: since f(x) is an exponential function.

f(x) = a + bˣ

Using the specified numbers for x and f(x), we obtain:

=> -2.999 = a * b⁻³

=> -2.99 = a * b⁻²

=> -2.9 = a * b⁻¹

=> 7 = a * b¹

=> 97 = a * b³

=> 997 = a * b⁵

Any two sets of the aforementioned equations can be used to find the values of a and b. By splitting the fourth equation by the third equation, for instance, we obtain:

7 / (-2.9) = (a * b^(1)) / (a * b⁻¹)

-2.4138 = b²

=> b ≈ -1.5546 or b ≈ 1.5546

Using b = 1.5546 as a replacement in the third equation, we obtain:

=> -2.9 = a * (1.5546)⁻¹

=> a ≈ -4.5199

Consequently, the exponential function's general form is as follows:

=> f(x) = -4.5199 * (1.5546)ˣ

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hello

to solve this question, we should let the unknown number be represented by x

the first number (x) is equal to 11, we can find the other number.

from the calculations above, the numbers are 11 and 22

Answer:

y = -1/2x - 8

Step-by-step explanation:

You are looking for the equation in the form of y=mx + b, so you need y on the left hand side without x. Subtract x from both sides.

2y = -x - 16

Now you want 1y instead of 2y. So divide everything by 2.

y = -1/2x - 8

Answer:

\(=x^3-x^2-30x+72\)

Step-by-step explanation:

Distribute parentheses:

\(=xx^2+x\left(-7x\right)+x\cdot \:12+6x^2+6\left(-7x\right)+6\cdot \:12\)

Apply minus - plus rule:

\(=x^2x-7xx+12x+6x^2-6\cdot \:7x+6\cdot \:12\)

Simplified:

\(=x^3-x^2-30x+72\)

Its complicated but..

Step-by-step explanation:

( x + 6 ) ( x^2 - 7x + 12 )

x ( x^2 - 7x + 12) + 6 ( x^2 - 7x + 12 )

x^3 - 7x^2 + 12x + 6x^2 - 42x + 72

x^3 + 6x^2 + 12x - 42x - 7x^2 + 72

19x - 49x + 72

30x + 72

x = 72/30

x = 2.4

Answer:

The mass of the piece of granite with volume of 75 cm^3 is 202.5 grams.

Step-by-step explanation:

Let

m = the mass of a piece of granite whose volume is: 40 + 35 = 75 cm^3 (greater by 35 cm^3)

Since Density = Mass / Volume and we are talking about pieces of the same material (same density) we can write:

m/75 = 108/40

m = 202.5 g

f(x) = -2x and g(x) = 4x - 8, find h(x) = f(x) + g(x).

Replace f(x) and g(x) with their given values:

h(x) = -2x + 4x -8

Combine like terms:

h(x) = 2x -8

To find the missing value of x in a triangle, subtract the sum of the two angles from 180 degrees.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. Having three edges and three vertices, a triangle is a polygon. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C.

Subtract the sum of the two angles from 180 degrees. The sum of all the angles of a triangle always equals 180 degrees. Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X.

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Answer:

£134.2 more

Step-by-step explanation:

Divide 1342 by 100

Then you get 13.42

Times that by 10 and £134.2 is 10%

The relation will not be a function if you complete the table with:

x = 8

x = 6

or

x = -9

A relation maps elements from one set called the domain (represented with the variable x), into elements of another set called the range (represented with the variable y)

A relation is only a function if every element in the domain is mapped into only one element of the range.

So, if we repeat any of the values of the domain that already are in the table (8, 6, -9) then the relation will not be a function, so you can choose any of these 3 values.

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The opposite of being short $4.28 would be having $4.28 or more. That is a surplus or extra of $4.28.

Surplus refers to an amount or quantity that is left over or in excess of what is needed or used. It can refer to various things, such as:

In finance, a surplus refers to an excess of revenue over expenses, or an excess of assets over liabilities. It means having more of something than is necessary or expected.

Therefore, the opposite of being short $4.28 would be having $4.28 or more. This is often referred to as having a surplus or extra of $4.28.

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