The length of four rivers in Africa is shown in the table below.
How is the length of the Zambezi river written in scientific notation?
Move the correct answer to each box. Not all answers will be used.

The mean and standard deviation of the sampling distribution include the following: C. mean = 64, standard deviation = 2.5.

In Mathematics and statistics, the Central Limit Theorem states that the sampling distribution of means would always be normally distributed, as long as the sample size is large enough.

This ultimately implies that, the sampling distribution of means would always be normally distributed as the sample size gets larger in accordance with the Central Limit Theorem.

Mathematically, the standard deviation of a sampling distribution can be calculated by using this mathematical expression:

Standard deviation, σy = σ/√n

Where:

Substituting the given parameters into the formula, we have;

Standard deviation, σy = 10/√16

Standard deviation, σy = 10/4

Standard deviation, σy = 2.5.

In conclusion, the mean of an original population is expected to be equal to the mean of the sampling distribution of means i.e 64.

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A reaction that acts to amplify or reinforce an initial change is termed a positive feedback.

The positive-feedback mechanism is used in climatic change, any effect that acts to reinforce the initial change.

In Asian philosophy, yin and yang are viewed as forces that interact and are connected to one another and are crucial parts of a dynamic system. Positive and negative feedbacks function something like yin and yang in the Earth system; they are integral parts of the total system that eventually help to maintain a more or less stable state. While negative feedback mechanisms stabilize a system and keep it from reaching extreme states, positive feedback mechanisms increase or magnify an original change. The evolution of Earth's climate system can be viewed in many ways as a kind of conflict between these two feedback mechanisms.

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Eric typed 15 words more than Dae per minute.

Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line. A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.

To find the amount of words typed in 1 minute for both;

Dae = 333/9

Dae = 27 words per minute

Eric = 252/6

Eric = 42 words per minute

Therefore 42 - 27 = 15 words per minute

Eric typed 15 more words per minute.

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A bi-weekly visit to your favorite restaurant. Say on average you spend $25 each visit.

You will spend an average of $50 a week at this restaurant.

The equation of the regression line is y = 4 + x and the regression analysis of the given data need not be done.

Straight line equation is y = a + bx.

The normal equations are

∑y = a·n + b ∑x ∑ xy = a ∑x + b∑x² Hence the regression analysis of the data :

The values are calculated using the following table

x y x²             x⋅y

58 62 3364 3596

47 51 2209 2397

84 88 7056 7392

62 66 3844 4092

57 61 3249 3477

72 76 5184 5472

69 73 4761 5037

hence :

∑x = 449

∑y = 477

∑x² = 29667

∑x⋅y = 31463

Substituting these values in the normal equations

7a+449b=477

449a+29667b=31463

Solving these two equations using Elimination method,

7a+449b=477

and 449a+29667b=31463

7a+449b=477→(1)

449a+29667b=31463→(2)

equation(1)×449

⇒3143a+201601b=214173

equation(2)×7

⇒3143a+207669b=220241

Substracting

⇒-6068b = -6068

⇒6068b = 6068

⇒b = 1

Putting b = 1 in equation (1), we have

7a+449(1) = 477

⇒7a = 477  - 449

⇒7a = 28 or a  = 4.

Now Estimate y for x=50

y = a + bx , we get

y = 4 + 1×50

y = 4 + 50

y = 54

At x equals 50 we get the value of y as 54 .

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Answer:

≈20.35°

Step-by-step explanation:

height = 8

hypotenuse =23

angle is x

sin(x) =8/23

[tex]sin^{-1} (\frac{8}{23} )[/tex] ≈20.35°

x is about ≈20.35°

The ramp makes an angle of approximately 20.86 degrees with the ground.

Given that there is a truck with a ramp at a height of 8 feet the size of the ramp is 23 feet,

we need to find the angle ramp make with the ground.

To find the angle that the ramp makes with the ground, we can use the sine function.

The sine of an angle is equal to the opposite side divided by the hypotenuse in a right triangle.

In this case, the opposite side is the height of the ramp (8 feet), and the hypotenuse is the length of the inclined portion of the ramp (23 feet).

Let's calculate the angle:

sin(angle) = opposite/hypotenuse

sin(angle) = 8/23

To find the angle, we need to take the inverse sine (or arcsine) of both sides of the equation:

angle = arcsin(8/23)

We can find the approximate value of the angle:

angle ≈ 20.86 degrees

Therefore, the ramp makes an angle of approximately 20.86 degrees with the ground.

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Answer:

-11

Step-by-step explanation:

4c - 3   Substitute -2 for c

4(-2) - 3

-8 - 3

-11

Answer:

-11

Step-by-step explanation:

We are given the value of c, so we just need to plug it in. We can do this by replacing "c" with "-2" in our given expression.

4c - 3 ⇒ 4(-2) - 3

Now, we can simplify this.

-8 - 3 = -11

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The expression [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]

What is algebraic expression ?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

According to question

⇒     [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex]

⇒   taking LCM of 4, 5 = 20

now [tex]\[\frac{4(4+6a)-5(1+3a)}{20}[/tex]

⇒ (16 +24a - 5 - 15a)/20

⇒ ((24a - 15a) - (16-5))/20

⇒ (9a - 11)/20

hence, the expression  [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]

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Option a) 90% confidence interval for the population proportion of successes = 0.402

Option b) 90% confidence interval for the population proportion of failures = 0.598

According to the question given,

Critical values of Standard deviations are to be used to construct the proportions for the confidence interval.

The formula of a confidence interval that we will be using for the solution will be,

p = [tex]z_{a} * \sqrt{\frac{p(1-p)}{n} }[/tex]

In the above expression,

p = observed population.

n = sample size

[tex]z_{a}[/tex] = critical value of confidence interval

Now the given observations in question = 115

That result in success = 46

The resultant sample proportion = [tex]\frac{46}{115}[/tex]

⇒ 0.40 and it is for both success and failure

Here we can see that the answer for both parts will be identical.

The critical value of z at 90% confidence = 1.64

a) Lower bound = [tex]0.4 - 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]

⇒ 0.402

b) Upper bound = [tex]0.4 + 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]

⇒ 0.598

Confidence interval = 0.402 to 0.598

Therefore,

Option a) 90% confidence interval for the population proportion of successes = 0.402

Option b) 90% confidence interval for the population proportion of failures = 0.598

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Answer: $2,275.94

Step-by-step explanation: First, we need to find how much he pays for the stocks alone. So, we would use this equation:

41.09(55)

41.09 x 55

That would get us to $2,259.95. Now, we have to add the $15.99, bc he had to pay a fee. So $2,259.95 + 15.99 = $2,275.94. I hope this helped!

Answer: NO

Step-by-step explanation:

This is not a function, since there are multiple outputs for ONE input.

Answer:

no

Step-by-step explanation:

to be a function, the x's can only have one partner. Here, 7 has two partners (7 goes to 20 and also to 18) and the 11 has two partners also. This relation is not a function.

Answer:

Below

Step-by-step explanation:

If you turn it sideways and use the y-axis portion as the base (4)  , you can see height = 5

Area = 1/2 * b * h =    1/2 *  4 *5 = 10 units^2

The horizontal and vertical asymptotes for the function f(x) =6/(-2x +1) is equal to y = 0 and x = 1/2 respectively.

Graph is attached.

As given in the question,

Given function is :

f(x) =6 /(- 2x +1)

f(x) = y

Degree of the numerator is zero

Degree of the denominator is 1.

Degree of denominator is greater than the degree of numerator.

Function represent the horizontal asymptotes for y =0

To get the vertical asymptotes equate denominator equals to zero

(- 2x +1) = 0

⇒2x = 1

⇒x = 1/2

Vertical asymptotes is given by x =1/2.

Graph is attached.

Therefore , the horizontal and vertical asymptotes for the given function is equal to y=0 and x =1/2 respectively.

The above question is incomplete, the complete question is:

Graph the rational function. f(x) =6 /(- 2x +1) Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button X.

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The 95% confidence interval for the mean reduction in cholesterol level is given as follows:

(51.3, 96.7).

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 8 - 1 = 7 df, is t = 2.3646.

From the image given at the end of the answer, the sample of the differences is given as follows:

37, 72, 86, 78, 60, 47, 124, 88.

Hence the parameters are given as follows:

[tex]\overline{x} = 74, s = 27.1, n = 8[/tex]

Then the lower bound of the interval is of:

74 - 2.3646 x 27.1/square root of 8 = 51.3.

The upper bound of the interval is of:

74 + 2.3646 x 27.1/square root of 8 = 96.7.

The table is given by the image shown at the end of the answer.

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The information needs to be divided into class intervals in order to make a histogram. Following that, make a tally to display the frequency (or relative frequency) of the data within each interval.

Histogram Illustration

135  137   136  137  138  139

140  139   137  140  142  146

148  145    139  140  142  143

144   143   141  139   137  138

139   136   133   134  132  132

Her weight should be a histogram.

Answer

131.5-133.5

133.5-135.5

135.5-137.5

137.5-139.5

139.5-141.5

141.5-143.5

143.5-145.5

145.5-147.5

147.5-149.5

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The measures of angles x, y and z are 40°, 50° and 130° and measures of the segments are AY = 16, IY = 9, FG = 30, AP = 24

Centroid is the point in a triangle where all the medians of the triangle intersects.

Given are two triangles, in first we have to find the missing angles and in the second one we need to find the asked segments,

1) We know that, in a right triangle, one angle is 90° and the sum of other two sides is 90°,

Therefore, 40°+y = 90°

y = 50°

x+y = 90°

x = 90°-50°

x = 40°

z = 180°-50° (linear pair)

z = 130°

2) we know that, the centroid divides the medians into 2:1

AY = 2YP

AY = 16

IY = TY/2

IY = 9

FG = GY+YF   (segment addition postulate)

GY = YF/2

GY = 10

FG = 10+20 = 30

PA = AY+YP  (segment addition postulate)

PA = 8+16

PA = 24

Hence. the measures are x, y and z are 40°, 50° and 130° and  AY = 16, IY = 9, FG = 30, AP = 24

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Answer: To solve this problem, we need to set the two equations equal to each other and solve for the number of text messages that were sent by each person. We know that the cost of Jack's plan is c = 0.30t + 9 and the cost of Jill's plan is c = 0.60t. To find the number of text messages they each sent, we can set these two equations equal to each other and solve for t:

0.30t + 9 = 0.60t

0.30t = 0.60t - 9

0.30t = 0.60t - 9

-0.30t = -9

t = 30

Therefore, if Jack and Jill paid the same amount for their text plans, they each sent 30 text messages.

The number of hours it will take the student to complete the project is 5 / 6 hours.

A student completes ⅘ of a math project in ⅔ hour. If the student continues at the same rate,  the time it will take the student to complete the project can be calculated as follows:

Therefore,

let

x = time it will take the student to complete the project

Hence

if 4 / 5 x = 2 / 3 hours

x = ? hours

cross multiply

Therefore,

number of hours to complete the whole math project = x × 2 / 3 ÷ 4 / 5 x

number of hours to complete the whole math project = 2 / 3 x × 5 / 4x

number of hours to complete the whole math project = 10x / 12x

number of hours to complete the whole math project = 10 / 12

number of hours to complete the whole math project = 5 / 6 hours

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A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.

In the given question, a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa.

We have to calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints.

Sample size: n = 13

Sample mean: x’ = 8.52 mps

Sample standard deviation: s = 0.78 mps

95% lower confidence bound for the true average proportional limit stress of all such joints

Level of Significance (α) = 1-95% = 5% = 0.05

α/2 = 0.025

So the value of t(α/2) = 1.8

The confidence interval = x’± t(α/2)*s/√n

Now putting the value:

The confidence interval = 8.41± (1.8)*(0.78)/√12

The confidence interval = 8.41± (1.8)*(0.226)

The confidence interval = 8.41± 0.4068

The confidence interval = (8.41- 0.4068, 8.41+ 0.4068)

The confidence interval = (8.01, 8.82)

A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.

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The right question is:

A sample of 12 joint specimens of a particular type gave a sample mean proportional limit stress of 8.41 mpa and a sample standard deviation of 0.78 mpa.

Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.)

Complete Question :

An application is using a two-dimensional list defined as follows: 1. Write a statement that creates an empty two-dimensional list named values with 4 rows and 3 columns. 2. Write nested loops that get an integer value from the user for each element in the list, for example: values= [[1, 2, 3], [10, 20, 30], [100, 200, 300],[1000, 2000, 3000]] 3. Write a function named row_values that accepts values as argument and returns the sums of each row and displays the result as a list named row 4. Write a function named column_values that accepts values as arguments and returns the sums of each column and displays the result as a list named column 5. Write a function called sum_values that sums all the elements of the array and displays the result.

Sum of rows : [ 6, 60, 600, 6000 ]

Sum of columns : [ 1111, 2222, 3333]

Sum of all elements : 6666

The nested loops are :

Enter a number at row 0, and column 0 : 1

Enter a number at row 0, and column 1 : 2

Enter a number at row 0, and column 2 : 3

Enter a number at row 1, and column 0 : 10

Enter a number at row 1, and column 1 : 20

Enter a number at row 1, and column 2 : 30

Enter a number at row 2, and column 0 : 100

Enter a number at row 2, and column 1 : 200

Enter a number at row 2, and column 2: 300

Enter a number at row 3, and column 0 : 1000

Enter a number at row 3, and column 1 : 2000

Enter a number at row 3, and column 2 : 3000

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The length of segment AY is 16.7 ft if the length of segment BC is 16.7 ft

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

BC = 16.7 ft

The measures of the angles are not given

However, the marks on the side lengths imply that:

Using the above as a guide, we have the following:

AY = BC

This is because these segments are parallel segments

Recall that parallel segments are equal segments

Substitute the known values in the above equation, so, we have the following representation

AY = 16.7

Hence, the length of AY is 16.7 ft

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[tex]340.11[/tex] or [tex]\frac{32651}{96}[/tex].

[tex]\frac{(\frac{309*317}{9-4+7})}{8x3}[/tex]

[tex]\frac{(\frac{309*317}{9-4+7})}{24}[/tex]

[tex]\frac{(\frac{309*317}{12})}{24}[/tex]

[tex]\frac{(\frac{97953}{12})}{24}[/tex]

[tex]\frac{(8162.75)}{24}[/tex]

[tex]340.11[/tex] or [tex]\frac{32651}{96}[/tex].

The graph (created with MS Excel) of the height the box is lifted to the number of times Brennan turns the crank to lift the box which is the graph of the proportional relationship, y = x, is attached.

A proportional relationship is one in which one variable (the output variable) is a constant multiple of the another variable known as an input variable.

The number of times Brennan turns the crank = x

The height to which the box is lifted = y

The points on the graph are; (15, 15), and (45, 45)

The ratio of the y-values to the x-values is 15/15 = 45/45 = 1, which indicates that the relationship is a proportional relationship

A point on the graph of a proportional relationship is the point (0, 0), therefore, the points on the graph are; (0, 0), (15, 15), and (45, 45)

Please find attached the graph of the proportional relationship between the number of times Brennan turns the crank to the height to which the box is lifted created with MS Excel

The relationship between the variables x and y is; y = x

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The probability that their mean length is less than 17.4 inches is 28.26%

Given :

A manufacturer knows that their items have a normally distributed length, with a mean of 19.7 inches, and standard deviation of 4 inches , If 25 items are chosen at random .

z = ( X - μ ) / σ, where X = date , μ = mean , σ = standard deviation .

substitute the values

z = 17.4 - 19.7 / 4

= -2.3 / 4

= -0.575

P - value at z = -0.575 is 0.2826

Converting into percentage :

= 0.2826 * 100%

= 28.26 %

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A total of 3 cups of vinegar goes into 27 total cups

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

1/4 cups of vinegar

2 cups of water

So, we have

Water : Vinegar = 2 : 1/4

Rewrite as

Water : Vinegar = 8 : 1

Multiply by 3

Water : Vinegar = 24 : 3

The sum of 24 and 3 is 27

So, we have

Vinegar = 3

Hence, the number of cups of vinegar is 3

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Step-by-step explanation:

Hope u get it x=3×3

x=9

It didn't include in the photo

The 2 3/4 is greater than 1 5/6, hence 1 1/4 × 2 1/5 > 5/6 × 2 1/5

An algebraic inequality is a mathematical statement that uses the inequality sign to connect an expression to a value, a variable, or another expression.

Relationships between two expressions that aren't equal to one another are known as inequalities. Inequalities are represented by the symbols, >,,, and. has the connotation "7 is greater than" (or "is less than 7," when read left to right).

Given the incomplete expression

1 1/4 × 2 1/5 _ 5/6 × 2 1/5

We are to fill it with the necessary inequality sign

For the expression:

1 1/4 × 2 1/5 = 5/4 * 11/5

1 1/4 × 2 1/5 = 55/20

1 1/4 × 2 1/5 = 2 3/4

For the expression 5/6 × 2 1/5

5/6 × 2 1/5 = 5/6 * 11/5

5/6 × 2 1/5 = 55/30

5/6 × 2 1/5 = 1 25/30

Since 2 3/4 is greater than 1 5/6, hence 1 1/4 × 2 1/5 > 5/6 × 2 1/5

The complete question is : Select the correct symbol to compare the expressions below.

1 1/4 × 2 1/5 _ 5/6 × 2 1/5

Symbols: <, >, =

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The p-value for the z-distribution table is 0.4854.

What is  z-distribution?

A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardise it. Z scores provide the number of standard deviations from the mean that each value falls within.

Given that the z statistic to be 2.19 standard deviation above the population mean.

2.19 can be written as 2.1 + 0.09

Z₂.₁₉ = Z₂.₁₊₀.₀₉ =  0.4854

Therefore p-value is  0.4854.

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