A line passes through the points (-8, – 7) and (-6, – 3). What is its equation in slope-intercept form?

The confidence interval for the average age of the population would be (18.8, 25.2).

What is the confidence interval?

In frequentist statistics, a confidence interval is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used.

Given that,

Point estimate = sample mean = [tex]\bar x[/tex] =22

sample standard deviation = s = 6

sample size = n = 16

Degrees of freedom = df = n - 1 = 16 - 1 = 15

At 95% confidence level

[tex]\alpha[/tex] = 1 - 95%

[tex]\alpha[/tex] =1 - 0.95 =0.05

[tex]\alpha/2[/tex] = 0.025

[tex]t_{\alpha/2},df[/tex] = t 0.025 , 15 = 2.131

Margin of error = E = [tex]t\alpha/2,df * \frac{s}{\sqrt n}[/tex]

                              =2.131  * (6 / √16)

Margin of error = E = 3.20

The 95% confidence interval estimate of the population mean is,

= [tex]\bar x \pm E[/tex]

= 22  ± 3.20

= (18.8, 25.2)

Hence, the confidence interval for the average age of the population would be (18.8, 25.2).

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An equation for the nth term of the arithmetic sequence is 2 + 0.5n.

What is an arithmetic sequence?

An arithmetic sequence is a set of integers where each term (except the first) is created by adding a fixed amount to the term before it.

Given, initial distance = 2 miles

Let n be each day on which he jogs one-half (1/2 = 0.5) mile.

Then, according to the question,

nth term = 2 + 0.5n

Hence, an equation for the nth term of the arithmetic sequence is 2 + 0.5n.

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Rate of change of y =[tex]\frac{5}{4}x +1[/tex]  is 5/4.

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.

Given that the expression, y =[tex]\frac{5}{4}x +1[/tex] .

To find the rate of change,

first we make the equation in standard form.

Slope intercept form ;

(y₂ - y₁) =m (x₂ -x₁) + c

Comparing the expression to the standard form;

Here, x intercepts: ( -4/5 , 0) and y intercepts: (0,1)

Rate of change = (y₂ - y₁) / (x₂ -x₁)

Rate of change = 5/4

Therefore, rate of change of y =  is 5/4.

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The values of x that make the expression undefined are 0 and 2

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

Volume = 5 - x

Width = x - 2

Height = 5 - x/x(x -2)

Introduce brackets to the height expression to differentiate between the numerator and the denominator

So, we have

Height = (5 - x)/x(x -2)

The question implies that we calculate the domain

Set the denominator to 0

This gives

x(x - 2) = 0

So, we have

x = 0 or x - 2 = 0

Solve for x

x = 0 or x = 2

This means that the undefined height value of x are 0 and 2

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The value of piecewise function at x = -1 is f(-1) = 11, and the value of piecewise function at x = 9 is f(9) = 1.

what is piecewise function?

A piecewise-defined function in mathematics is one that is composed of several smaller functions, each of which has a specific interval of the domain it applies to. Instead of being a property of the function itself, piecewise definition is a way to express the function.

We have to evaluate the piecewise function for x = -1 and x = 9.

Let, function has value for x = -1 in the domain x ≤ 5 which is 11.

And function has value for x = 9  in the domain 6 < x which is 1.

⇒  f(-1) = 11 and f(9) = 1

Hence, the value of piecewise function at x = -1 is f(-1) = 11, and the value of piecewise function at x = 9 is f(9) = 1.

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The p-value of the hypothesis test in this problem is given as follows:

0.075.

The first step in calculating the p-value of the test is obtaining the test statistic, which is given by the equation presented as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which the parameters are defined as follows:

The values of these parameters in this problem are given as follows:

[tex]p = 0.35, n = 500, \overline{p} = \frac{156}{500} = 0.312[/tex]

Hence the test statistic is of:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.312 - 0.35}{\sqrt{\frac{0.35(0.65)}{500}}}[/tex]

z = -1.78.

Now we have to consider that we have a two-tailed test, as we are testing if the mean is different of a value.

Using a z-distribution calculator, with a two-tailed test and z = -1.78, the p-value of the test is given as follows:

0.075.

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The width of the shape is 4.2 units

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

Surface Area = 54 square units

Length = 2 units

Height = 3 units

The surface area of the shape can be calculated using the following formula

Surface Area = 2 * (Length * Width + Length * Height + Width * Height)

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

2 * (2 * Width + 2 * 3 + Width * 3) = 54

Divide both sides by 2

So, we have

2 * Width + 2 * 3 + Width * 3 = 27

Subtract 6 from both sides

2 * Width + Width * 3 = 21

This gives

Width * 5 = 21

Divide both sides by 5

Width = 4.2

HEnce, the width is 4.2 units

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If the 12 inch pizza is cut into 8 (equal) slices, the number of calories in one slice is 2440/8 = 305.

"Information available from the question"

In the question:

A 6 inch personal pizza has 610 calories, with 240 of those from fat. A 12 inch pizza is cut into 8 slices.

Estimate the number of calories in one slice of a 12 inch pizza.

Now, According to the question:

The 6 inches and 12 inches are  the diameters of the two pizzas.

Consider the two pizzas as similar figures with a ratio of similarity of 2:1. By a basic geometric principle, the ratio of the areas of the two pizzas is the square of that ratio. So the area of the 12 inch pizza is 2^2=4 times the area of the 6 inch pizza.

The number of calories in the 6 inch pizza is 610.

The number of calories in the 12 inch pizza is 610 x 4  = 2440.

Hence, If the 12 inch pizza is cut into 8 (equal) slices, the number of calories in one slice is 2440/8 = 305.

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The sum of two interior angles other than the adjacent angle of extended length will be equal to the external angle of extended length thus m∠PQR will be 18°.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus. The identical endpoint of the two rays known as the vertex is referenced as an angle's sides.

In any triangle, the sum of two interior angles other than the adjacent angle of extended length will be equal to the external angle of extended length.

In the given triangle,

m∠PQR = m∠OPQ + m∠POQ

4x - 10 = x + 9 + x - 5

4x - 10 = 2x + 4

2x = 14

x = 7

So,

m∠PQR = 4(7) - 10 = 18°

Hence the measure of m∠PQR will be 18° for the given triangle.

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Answer:

[tex]\frac{4(8-1)}{6}[/tex]

6

Step-by-step explanation:

[tex]\frac{4(8 + 1) }{6}[/tex]

[tex]\frac{4(9)}{6}[/tex]

[tex]\frac{36}{6}[/tex]

6

Answer:

The expression is:

4(8+1)/6

Simplify:

= 6

Step-by-step explanation:

The expression is:

4(8+1)/6

Simplify:

= 4(9) / 6

= 36/6

= 6

Equation s/12 = 6 represents the equation on how many stones were used for the order. On solving we get 72 stones.

How to form an equation for a word problem?

Follow these steps:

Understand the problem. Understand all the words used in stating the problem. Understand what you are asked to find.

Translate the problem to an equation. Assign a variable (or variables) to represent the unknown.

Carry out the plan and solve the problem.

According to the given question:

Leslie's most recent order included a total of 6 bracelets.

It takes 12 stone to make one bracelet.

Let the total number of stones be s.

If one bracelet requires 12 stones then 6 bracelets requires 12 x 6 stones

Therefore, s = 12 x 6 or s/12 = 6

On solving to get value of s we get 12 x 6 = 72 stones.

Hence s/12 = 6 represents the equation on how many stones were used for the order. On solving we get 72 stones.

Complete question:

Leslie creates designer bracelets with gemstones. Her most recent order included a total of 6 bracelets. It takes 12 stone to make one bracelet.

Write and solve an equation that represents how many stones were used for the order.

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For instance, we might simply show the following conditional statement:

1. Return true if the array's size is zero or one.

2. Verify the last two members of the array; if they are sorted, call n-1 times in a recursive fashion; otherwise, return false.

In the given question, we have to state true or false for the given statement.

In our programs, we frequently want to be able to "conditionally" execute certain actions, i.e., "if this is true, then do X, but if this other thing is true, then do Y." It's similar to how we dress when we get out of bed: "If it's sunny, I wear sunglasses, but if it's raining, I take an umbrella." In our programs, we can use if statements, if/else statements, and conditional expressions to do things conditionally.

If a condition is true, an if statement instructs the computer to run a certain piece of code. Only if x is bigger than 0 do we output a message in the following code:

We would be able to see the message on the canvas since x is 5, which is bigger than 0. If we modified x to -1, the message wouldn't appear at all because x wouldn't be greater than 0.

A conditional expression is one that can only be evaluated as either true or false, and the x > 0 qualifies as one. A boolean value is one that can only be either true or false (as opposed to a number or a string). For instance, we might simply show the following conditional statement:

1. Return true if the array's size is zero or one.

2. Verify the last two members of the array; if they are sorted, call n-1 times in a recursive fashion; otherwise, return false.

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The right question is:

State in predicate calculus that an array of int, say a, is sorted. You may use the Java expression syntax (e.g., a.length, a[i], ==, and <) and logical operators (&&).

No, the expression ( x - 1 ) as required to be checked is not a factor of the given polynomial function g ( x ) = -2x⁴ + 4x³ - x + 9.

It follows from the task content that the expression ( x - 1 ) is required to be checked if it's a factor of the given polynomial function.

Since the given factor can be equated to 0 so that we have; x - 1 = 0; x = 1.

On this when g (1) is evaluated, the result must be zero in order to confirm ( x - 1 ) is a factor of g ( x ) = -2x⁴ + 4x³ - x + 9.

Hence; g ( 1 ) = -2 ( 1 )⁴ + 4 ( 1 )³ - 1 + 9.

g (1) = -2 + 4 - 1 + 9

g (1) = 10

Ultimately, since g (1) ≠ 0; the expression ( x - 1 ) is not a factor of the given expression; g ( x ) = -2x⁴ + 4x³ - x + 9.

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The positive integers that meet the requirement that the product of their digits be 120 are: 1546, 1564, 1456, 1465, 1654, 1645, 6145, 6154, 6451, 6415, 6541, 6514, 4156, 4165, 4561, 4516, 4651, 4615, 5146, 5164, 5461, 5416, 5614, and 5641.

To find the integer numbers that meet the aforementioned requirement that the product of its digits be 120, we must take a positive 4-digit integer number and multiply its digits until obtaining the result of 120.

In this case, the four digits would be 1456. So, we must find all the four-digit numbers that are made up of these numbers, the numbers are shown below:

1546, 1564, 1456, 1465, 1654, 1645, 6145, 6154, 6451, 6415, 6541, 6514, 4156, 4165, 4561, 4516, 4651, 4615, 5146, 5164, 5 4161, and 5 614, and 4

Finally, we can check it with any of the numbers and the result will be 120 because the order of the factors does not change the result.

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If the triangle ABC is an equilateral triangle having the length as (4x - 3) , and perimeter as 63 in , then the value of x is 6 .

The triangle having all the sides of equal measure is termed as Equilateral triangle.

The triangle ABC is equilateral triangle,

The measure of length of side of triangle ABC is = 4x - 3 ;

The perimeter of the triangle is = 63

So, According to the question,

(4x - 3) + (4x - 3) + (4x - 3) = 63

12x - 9 = 63

12x = 63 + 9

12x = 72

x = 72/12

x = 6

Therefore, the value of x in the given triangle  is 6.

-- The given question is incomplete, the complete question is

"Find the value of x, if the triangle ABC is an equilateral triangle with length of each side as (4x - 3), and the perimeter of the equilateral triangle ABC is 63 inches." --

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Answer:

26.74

Step-by-step explanation:

add the money John spends on the week days(13.75) to 12.99 and you get your answer

Answer: 32% probability of going to the beach given the information provided in the weather forecast.

Step-by-step explanation:

The probability of going to the beach is equal to the probability of it not raining times the probability of going to the beach if it does not rain. Therefore, the probability of going to the beach is equal to (1 - 0.6) * 0.8 = 0.4 * 0.8 = 0.32.

The graph of the system of equations -2x - y = -2 and 13x - y = -2 is attached and the solution is

(0, 2)

Graphs are plotted using the input values in the x coordinates and the output in the y coordinate

assuming an input of -4 0 4 we calculate the output for the graphs as

-2x - y = -2

y = -2x + 2

For x = -4, y = -2 * -4 + 2 = 10

For x = 0, y = -2 * 0 + 2 = 2

For x = 4, y = -2 * 4 + 2 = -6

table of values

x     y

-4   10

0     2

4     -6

13x - y = -2 rearranging gives y = 13x + 2

y = 13x + 2

For x = -4, y = 13 * -4 + 2 = -50

For x = 0, y = 13 * 0 + 2 = 2

For x = 4, y = 13 * 4 + 2 = 54

table of values

x     y

-4   -50

0     2

4     54

The point of intersection of the two line is the solution and this is (0, 2)

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The average rate of change from 1992 to 2000 is -1.025 percent per decade.

What is the average rate of change?

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

the average rate of change :

A(x) = 34.5 - 42.7 / 2000 - 1992

A(x) = -8.2 / 8

A(x) = -1.025

Hence, the average rate of change from 1992 to 2000 is -1.025 Percent per decade.

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a) 270° counter clockwise rotation of figure 1

b) The image of point (-3,-4) is (3,4).

c) The new image of point (7,8) is (8,-7) after 90° degree clockwise rotation.

d) The new image of point (7,8) is (-8,7) after 90° degree anticlockwise rotation

e) The fig. abcd will moves to second quardent after 90° counter clockwise rotation.

f) The rotation angle of figure is 270° , in the counterclockwise direction about origin.

A rotation is an isometric transformation that turns every point of a figure through a specified angle and direction about a fixed point.

To describe a rotation, you need three things:

Direction (clockwise or counterclcokwise.

90 Degree Rotation:

When rotating a point 90 degrees counterclockwise about the origin of a point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.

180 Degree Rotation :

When we rotating a point 180 degrees counterclockwise about the origin a point A(x,y) it becomes A'(-x,-y). So all we do is make both x and y negative.

We have given that,

a) The given figure is rotated aoround 90° clockwise or 270° counter clockwise.

b) A point (-3,-4) is rotated around the origin 180 degrees , then the new point or position after the rotation is (3,4).

c) Rotate the point (7 , 8) around the origin 90 degrees , the new point or image of (7,8) is ( 8,-7).

d) If a point (7,8) is rotate around the origin 90 degrees counterclockwise then new point is (-8,7).

e) If you were to rotate abcd 90 degrees counterclockwise then the image of figures abcd will enter in quadrent 2nd with all coordinate changes.

f) when a figure is rotated in counterclockwise rotation about the origin the angle of rotation is 270 degrees.

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The diagonals are congruent and the median is parallel to the bases in isosceles trapezoid .

What is an isosceles trapezoid?

An isosceles trapezoid is trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal.

In any isosceles trapezoid, two opposite sides (the bases) are parallel, and the two other sides (the legs) are of equal length (properties shared with the parallelogram). The diagonals are also of equal length.

The diagonals are congruent because if the diagonals are congruent the at least to of its legs (probably the vertical ones) are congruent. and the median is parallel to the bases in isosceles trapezoid  because parallelism indicates that heights (vertical legs) are accurately congruent .

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The probability that such cuts would be supported by at least 155 persons in a survey of 250 people is 0.62.

Probability is a branch of mathematics that deals with numerical descriptions of the likelihood of an event occurring or a statement being true. The probability of an occurrence is represented by a number between 0 and 1, where 0 signifies the event's impossibility and 1 denotes its certainty.

Assume 60% of the public favors huge government budget cutbacks.

We must determine the likelihood that, in a poll of 250 persons, at most 155 respondents approve such reduction.

As a result, the chance is 155/250 = 0.62.

Hence, probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.

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The percentage of 35 percent of 80 is 28

In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number (pure number); it has no unit of measurement.

For example, 45% (read as "forty-five per cent") is equal to the fraction

45/100, the ratio 45:55 (or 45:100 when comparing to the total rather than the other portion), or 0.45. Percentages are often used to express a proportionate part of a total.

The percentage of 35 percent of 80 is

= [tex]\frac{35}{100}[/tex]× 80

=28

The percentage of 35 percent of 80 is 28

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The unknown number which is added to the number 32.6 will be 3.54.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that when adding 32.6 to a certain number, the sum is 36.14. The unknown number will be calculated as,

32.6 + N = 36.14

N = 36.14 - 32.6

N = 3.54

Therefore, the unknown number which is added to the number 32.6 will be 3.54.

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Answer:

Step-by-step explanation:

2 and 2 equal 5

Answer:

9 pound

Step-by-step explanation:

We know

The new puppy's weight has increased by 32% since her last vet visit.

100% + 32% = 132%

First, we have to find 1%

12 divided by 132% = 0.09 pound

Then we take

0.09 times 100% = 9 pounds

So, the puppy weighs 9 pounds on her last visit.

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Answer:

The answer to the problem is 9 pounds.

Step-by-step explanation:

100+32=132

12/132=.09

.09x100= 9

I know my explanation wasn't very detailed, but I know sometimes people learn by just seeing it instead of having a long drawn out explanation so I wanted to give you that option incase it works better for you.

Calculating interest on the principal borrowed as well as any prior interest. $6,000 for six years at a daily compounded rate is None of these. No option is correct. The amount is $991.15.

Annual interest compounding adjective finance. If you borrow $100,000 at 5% interest compounded annually, you would owe $5,250 after the first year on a principal of $105,000. This method involves calculating and adding interest to an investment or loan once a year rather than for a longer period.

The formula to determine how much an investment will grow to overtime when it is placed in an account for years during which it generates dollar-compound interest is:

A = P(1 +r/m) m t

The values for each of these variables are provided as follows, presuming that a year has 365 days: m =365 t=6r  8.5% = 0.085The investment's worth is then computed after six years, as illustrated below.

A =991.15

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Answer:

Side h and side

Answer:

  -1

Step-by-step explanation:

You want to evaluate (8x -5) for x = 1/2.

Put the value where x is in the expression, then do the arithmetic.

  8x -5 = 8(1/2) -5

  = 4 -5

  = -1

The value of the expression is -1.

By simplifying the equation we can get 5y²+2y+0.4.

An equation is said to be a formula that express the equality of two expressions. These two expressions on either side of the equal sign are called the "left side" and "right side" of the equation. We usually assume that the right-hand side of the expression is zero. This can be compensated for by subtracting the right side formula from the two side formulas, so there is no loss of generality.

The equation is representing direct proportion is, by the commenting them with equal sign.

4y²+4.1+7y-3.7-5y+y²

Reorder and gather like terms-

(1.4y²+y²)+(4.1-3.7)-(7y-5y)

Collect coefficients of likes terms

(1.4+1)y²+(4.1-3.7)-(7y-5y)×y

Calculate the sum or difference we can get

2.4y²+0.4+2y

Rewrite the expression

2.4y²+2y+0.4

Thus this is the correct answer .

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