The table shows the temperature (y) at different altitudes (X). This is a linear relationship.

The explicit formula for calculating the sum is

\(S_N=\frac{n(n-1)}{2} \cdot\frac{n(n+1)}{2}\)

The sum of the nth term of a sequence is expressed as;

\(S_n=\frac{n}{2}(2a+(n-1)d)\)

a is the first term

d is the common difference

n is the number of terms

For the sequence  0 + 1 + 2 + 3  +...

\(S_n=\frac{n}{2}(2(0)+(n-1)1)\\S_n= \frac{n}{2}(n-1)\\S_n= \frac{n(n-1)}{2}\)

Similarly for the sequence:

1 + 2+ 3 + 4+...

\(S_n=\frac{n}{2}(2(1)+(n-1)1)\\S_n= \frac{n}{2}(2+n-1)\\S_n= \frac{n(n+1)}{2}\)

Taking the product of the sum to get the explicit formula for calculating the sum

\(S_N=\frac{n(n-1)}{2} \cdot\frac{n(n+1)}{2}\)

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True 6. If the obtained sample data (test statistic value) falls inside the critical region, it provides support for the researcher's hypothesis.

True 7.  When the Z-test statistic, obtained from the sample data, falls inside the critical region, it indicates that the observed result is unlikely to have occurred by chance alone under the assumption of the null hypothesis. Therefore, we reject the null hypothesis and accept the alternative hypothesis.

True 8. If the obtained sample data (test statistic value) is not in the critical region, it means that the observed result is likely to have occurred by chance under the assumption of the null hypothesis. hypothesis.

True 9. Failing to reject the null hypothesis means that the data do not provide sufficient evidence to conclude that the treatment or independent variable had a significant effect on the dependent variable.

True 10.  Whenever the statistical decision is to fail to reject the null hypothesis, there is a possibility of making a Type I error.

6. The critical region is determined based on the desired level of significance and contains the extreme values that would lead to rejecting the null hypothesis.

7. When the Z-test statistic, obtained from the sample data, falls inside the critical region, it indicates that the observed result is unlikely to have occurred by chance alone under the assumption of the null hypothesis. Therefore, we reject the null hypothesis and accept the alternative hypothesis.

8. In this case, we do not have sufficient evidence to reject the null hypothesis, and the correct statistical decision is to "fail to reject" the null

9. It does not necessarily mean that the treatment had no effect, but rather that the evidence in the sample is not strong enough to support such a claim.

10. Type I error refers to rejecting the null hypothesis when it is actually true. The probability of committing a Type I error is denoted by the significance level (usually denoted as alpha) and is predetermined before conducting the statistical test.

In summary, the statements are all true. The critical region plays a crucial role in hypothesis testing, and the decisions made based on the test statistic falling inside or outside the critical region determine whether the null hypothesis is rejected or failed to be rejected.

Failing to reject the null hypothesis does not provide sufficient evidence to support the researcher's hypothesis and there is always a possibility of making a Type I error when conducting hypothesis tests.

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Answer:

The sample size is   \(n =326 \)

Step-by-step explanation:

From the question we are told that

  The rough estimate of the standard deviation is  \(\sigma = 0.14\)

   The interval width is  \(w = 0.04\)

Generally the margin of error is mathematically represented as

          \(E = \frac{w}{2}\)

=>       \(E = \frac{0.04}{2}\)

=>       \(E = 0.02\)

From the question we are told the confidence level is   99% , hence the level of significance is    

      \(\alpha = (100 - 99 ) \%\)

=>   \(\alpha = 0.01\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  2.58\)

Generally the sample size is mathematically represented as

    \(n = [\frac{Z_{\frac{\alpha }{2} } *  \sigma }{E} ] ^2\)

=>   \(n = [\frac{ 2.58 *  0.14 }{0.02} ] ^2\)

=>   \(n =326 \)

The required value of the sum of the decimal values is 0.5536. Option c is correct.

Given that,
0.4 + 0.143 + 0.3706 =

It is defined as a decimal number that only consists of repeating digits after a certain interval after the decimal. For example, 94.642642642..., 213.569569... etc.

Here,
To simplify 0.4 + 0.143 + 0. 3706 we transform it into
= 0.0400 + 0.1430 + 0.3706
= 0.1830 + 0.3706
= 0.5536

Thus, the required value of the sum of the decimal values is 0.5536. Option c is correct.

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Answer:

3/90

Step-by-step explanation:

1 slot  is 1/30

2 slot is 1/30

3 slot is 1/30

this gives you that 3/90 when you had them

Answer:

D)  1/(30×30×30) = 1/27000 = 0.00003 or 0.003%

Step-by-step explanation:

The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

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Answer:

1.) she will spend $13.60 in two weeks

2.) $3,174.75 because 22.5 x 34 x 4.15 = 3,174.75

3.) 1003.75 miles. Explanation: if we know that there's 365 days in a year and Eric wants to walk 2.75

Step-by-step explanation:

Answer:

A=0.51

B=0.73

C=0.41

D=A student taking algebra II is dependent on whether they prefer it and a student being in 10th grade is dependent on their age

Step-by-step explanation:

These answers are all in fractions btw

A)5/255+20/245+65/225+90/725=0.514267 which rounds to 0.51

B)100+65=165

165/225=0.73

C)100/245=0.41

Hope it helps !

Answer: B

Step-by-step explanation: there are 1760 yards in one mile

9.  The stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. The stamp duty payable on a property with a purchase price of K150,000 is K7,500.

To calculate the stamp duty payable on properties with a purchase price of K45,000 and K150,000, we need to apply the corresponding rates of stamp duty based on the given information.

Given:

Value of Property:

Up to K35,000: Stamp Duty Rate - 2%

K35,000 to K70,000: Stamp Duty Rate - 3%

K70,000 to K140,000: Stamp Duty Rate - 4%

Over K140,000: Stamp Duty Rate - 5%

9. Calculate the stamp duty payable on properties whose purchase price is K45,000:

Since the purchase price of K45,000 falls within the range of K35,000 to K70,000, the stamp duty rate applicable is 3%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K45,000 * 3%

= K45,000 * 0.03

= K1,350

Therefore, the stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. Calculate the stamp duty payable on properties whose purchase price is K150,000:

Since the purchase price of K150,000 is above K140,000, the stamp duty rate applicable is 5%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K150,000 * 5%

= K150,000 * 0.05

= K7,500

Therefore, the stamp duty payable on a property with a purchase price of K150,000 is K7,500.

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Answer:

I am not exactly sure but it is around 170p

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the unit rate

Answer:

-1.5

negative and negative

Step-by-step explanation

the number line shows 3 * -1.5 = -4.5

the number line shows three groups of a negative number, which results in a negative.

Answer:

-1.5,

the number line shows three groups of a negative number, which results in a positive

Answer:

1711

Step-by-step explanation:

\(4\cdot(14+8)^2-9\cdot(9-4)^2\\=4\cdot(22)^2-9\cdot(5)^2\\=4(484)-9(25)\\=1936-225\\=1711\)

Make sure to follow order of operations!

Answer: 1280 fluid ounces.

Step-by-step explanation:

Using the Pythagoras theorem, the longest leg has the length of 24 feet.

Given that,

A ladder of length (2x+6) feet is positioned x feet from a wall.

Height of the ladder = (2x + 6) feet

Distance of ladder from the wall = x feet

Height of the wall that the ladder is placed = (2x + 4) feet

These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.

Longest leg is (2x + 4) feet

Using the Pythagoras theorem,

(2x + 6)² = (2x + 4)² + x²

4x² + 24x + 36 = 4x² + 16x + 16 + x²

4x² + 24x + 36 = 5x² + 16x + 16

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2

x = 2 is not possible.

So x = 10

Longest leg = 2x + 4 = 20 + 4 = 24 feet

Hence the length of the longest leg is 24 feet.

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Answer:

see below

Step-by-step explanation:

To graph this equation, start at the origin (0,0) since there is not y-intercept.

Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.

Because the rise (up and down, numerator) is 1, we know that we will go up one unit.

The run (side to side, denominator) is 4, so we will go to the right 4 units.

This makes the first point (4, 1).

Continue doing this until you get an idea of the line and connect the points to get the graph

Answer:

Info down in Explaination

Step-by-step explanation:

To graph this equation, start at the origin (0,0) since there is not y-intercept.

Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.

Because the rise (up and down, numerator) is 1, we know that we will go up one unit.

The run (side to side, denominator) is 4, so we will go to the right 4 units.

This makes the first point (4, 1).

Continue doing this until you get an idea of the line and connect the points to get the graph

A researcher's design of an experiment is to make clearer already known

facts, or to discover new knowledge.

The responses are:

Reasons:

The aim of the experiment is to determine if self-check out is faster than

regular checkout.

The number of customers sent to one of the checkout options = 100

The experimental units are the subject of the experimental treatment.

Therefore;

An explanatory variable is the manipulated variable in an experiment. An explanatory variable is known as an independent variable.

Treatments are the levels of the explanatory variable available in the experiment, or a combination of the levels. The treatment is what the experimental units are subjected to.

The response variable, is also known as the dependent variable, that depends on the treatment an experimental unit is subjected to.

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Answer:

a) m = 4/5, b = -3

y = (4/5)x - 3---slope-intercept form

b) The original line has slope 4/5, so a perpendicular line will have slope -5/4.

An equation for this line is y = (-5/4)x + c, where c is any constant. For example, if

c = 0, then y = (-5/4)x.

To graph y = (-5/4)x:

Start at the origin. Go up 5 units, then left 4 units. Plot the point (-4, 5). Draw a straight line that goes through these two points.

We proceed as follows;

The formula we have to use is the formula for z-scores as follows;

a) Probability that the board is greater in length than 93.11

Since there is no number of samples, then n will be 1

We have this as;

We will have to use standard normal distribution table for P (z > 0.22) = 0.4129

b) A sample of 42 boards

We have it as;

So, we use the standard normal distribution table to calculate the P (z > 1.43)

From the table, we have the answer as 0.0764

Answer:

Yes these two triangles are similar I know this because all of the angles are the same.  But the only differenc is the size one is bigger one is smaller.

Hope this answers your question!

Answer:

The triangles are similar due to the Angle-Angle Similarity Postulate

Step-by-step explanation:

Use the triangle-sum postulate to figure out the missing angle measurements by subtracting the given info for each triangle.

angle E: 180 -60-53 = 67, corresponds with angle H.

angle G: 180-60-67= 53, corresponds with angle D.

Since all of the angles have corresponding measurements with the other triangle, the triangles are similar.

a)Lucy's acceleration during the last 6 seconds is 1/3 m/s².

b) Lucy's speed at the end of the 80-meter race is 6.67 m/s.

Acceleration is a physical quantity that measures the rate at which the velocity of an object changes with time. It is defined as the rate of change of velocity (v) with respect to time (t), and is usually denoted by the symbol "a".

a) Let's assume that Lucy's speed increases at a constant rate "a" during the last 6 seconds. Then we can use the following kinematic equation to find her speed at 16 seconds:

v = u + at

where "v" is her final speed at 16 seconds,

"u" is her initial speed at 10 seconds,

"a" is her acceleration during the last 6 seconds,

and "t" is the time interval of 6 seconds.

v = u + 2

Substituting these values into the equation above, we get:

u + 2 = u + 6a

Simplifying and solving for "a", we get:

a = 1/3 m/s²

Therefore, Lucy's acceleration during the last 6 seconds is 1/3 m/s².

b) Let's first find Lucy's average speed during the entire 16 seconds:

average speed = total distance / total time

The total distance is 80 meters and the total time is 16 seconds, so:

average speed = 80 / 16 = 5 m/s

Now, we can use the following kinematic equation to find Lucy's final speed "v":

v² = u² + 2as

where "u" is her initial speed at 0 seconds,

"a" is her average acceleration during the entire 16 seconds,

"s" is the total distance of 80 meters,

and "v" is her final speed at 16 seconds.

We can rearrange this equation to solve for "v":

v = √(u²+ 2as)

her speed at 10 seconds is:

u = at = (a)(10) = 10a

Substituting these values into the equation above, we get:

v = √((10a)² + 2a(80))

Simplifying and substituting the value of "a" that we found in part a), we get:

v = 6.67 m/s

Therefore, Lucy's speed at the end of the 80-meter race is 6.67 m/s.

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A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

\( \frac{45}{10} - \frac{19}{10} = \frac{26}{10} \)

Using it's concept, it is found that the probability of selecting a boy or a blond-haired person is of 0.7407 = 74.07%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that there are 27 people, of which 5 + 15 = 20 have at least one of the desired characteristics, hence the probability is given by:

p = 20/27 = 0.7407.

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