Plot the points (-3, 8) and (5, -8) on the plane below. Determine the slope-intercept form of the equation of the line
through these points.

Answer:7 3/4

Step-by-step explanation:

(5*8+1)/8+(8*2+5)/8=41/8+21/8=62/8=7 6/8=7 3/4

Answer:

25

Step-by-step explanation:

Let's assume the number of boys in the class is "x". Then, according to the problem, the number of girls in the class is 2.5 times the number of boys, which can be expressed as:

number of girls = 2.5 * number of boys

We also know that the total number of students in the class is 35. Therefore, we can write an equation in terms of "x" as follows:

x + 2.5x = 35

Simplifying the above equation, we get:

3.5x = 35

Dividing both sides by 3.5, we get:

x = 10

This means that there are 10 boys in the class. To find the number of girls, we can use the equation we derived earlier:

number of girls = 2.5 * number of boys

number of girls = 2.5 * 10 = 25

Therefore, there are 25 girls in the class.

Answer:

≅20.9%

Step-by-step explanation:

To find the percent decrease, we need to calculate the difference between the old value (349) and the new value (276), divide that by the old value, and then multiply by 100 to express it as a percentage.

The formula for percent decrease is:

percent decrease = ((old value - new value) / old value) x 100%

Substituting the given values, we get:

percent decrease = ((349 - 276) / 349) x 100%

percent decrease = (73 / 349) x 100%

percent decrease = 20.92%

Rounding to the nearest tenth of a percent, we get:

percent decrease ≈ 20.9%

Therefore, the percent decrease in the number of petty crimes this year is [approximately 20.9%.]

The expression when evaluated is 1.25

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

1.25*0.9-1.25*0.3+1.25*0.4

Evaluate the products in the expression

So, we have the following representation

1.25*0.9-1.25*0.3+1.25*0.4 = 1.125 - 0.375 + 0.5

Evaluate the like terms

1.25*0.9-1.25*0.3+1.25*0.4 = 1.25

Hence the solution is 1.25

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Multiplying a whole number by a proper fraction results in a product which is lesser than the whole number.

Proper fractions are fractions in which the value of the numerator is less than the value of the denominator.

For example, 1/4, 3/4, 3/8, are all proper fractions.

4/3, 5/2, are all improper fractions.

So, from the definition, it is clear that, proper fractions are all less than 1.

When a whole number is multiplied by 1, we get the number itself.

So logically, when we multiply an whole number with fractions less than 1, then the resulting number will always be less than the whole number.

For example, consider 3 × [tex]\frac{3}{4}[/tex]

Multiplication of fraction is by multiplying numerators together and the denominators together.

3 × [tex]\frac{3}{4}[/tex] = [tex]\frac{3}{1}[/tex] × [tex]\frac{3}{4}[/tex] = [tex]\frac{9}{4}[/tex] = 2.25 < 3

Hence the multiplication of a whole number with a proper fraction is always less than the whole number.

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The population after 4 years is 1982.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have.,

Current population = 1652 people

The population triples every 10 years.

This means,

We can make a function for the number of population after m years.

y = 1652 x 3(m/10)

Where M is the number of years.

Now,

Substitute m = 4.

y = 1652 x 3(m/10)

y = 1652 x 3 (4/10)

y = 1652 x 3 x 2/5

y = 1982.4

y = 1982

Thus,

1982 is the population after 4 years.

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Answer: Shown in screenshot.

Step-by-step explanation: First, let's start at 7. We are adding 2 to seven, so we move to the right two places. When we do so, we get to 9. So, 9 is the answer.

This answer will probably get taken down like SO MANY of my answers for no reason when literally WRONG answers stay on the website.

9 is the answer .When using a number line and you need to add you go to the right or forward

The original number in the given question solved by algebra is 39/7.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

The number is divided 5 times by 7 more than that number.

Let the number be x

Then,

x+7/5x = 8

x+7=40x

7=39x

x=39/7

Therefore, by algebra the answer will be 39/7.

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Therefore , the solution of the given problem of  test statistic comes out to be  Using a t-table or calculator, with 66 degrees of freedom (df = n1 + n2 - 2), we find the p-value to be approximately 0.039.

The Z-statistic has been the test statistics for anything resembling a Z-test and it confirms that the ordinary standard neutral hypothesis is true. Consider doing two separate X-y tests with a 0.05 level of significance and getting a 2.5 R-t value from your data (also referred as a Z-value). The p-value associated with this Z-value is 0.0124.

Here,

The hypotheses are:

Null hypothesis: There is no significant difference in punishment between those who smiled and those who remained neutral during a court proceeding.

Alternative hypothesis: There is a significant difference in punishment between those who smiled and those who remained neutral during a court proceeding.

To test this claim, we can use a two-sample t-test since we are comparing the means of two independent samples.

The formula for the test statistic is:

t = (x1 - x2) / sqrt((s1² / n1) + (s2² / n2))

where:

x1 = sample mean of those who smiled

x2= sample mean of those who remained neutral

s1 = sample standard deviation of those who smiled

s2 = sample standard deviation of those who remained neutral

n1 = sample size of those who smiled

n2 = sample size of those who remained neutral

Substituting the given values, we get:

t = (4.9 - 4.1) / sqrt((1.7² / 34) + (1.5² / 34))

t ≈ 2.116

Using a t-table or calculator, with 66 degrees of freedom (df = n1 + n2 - 2), we find the p-value to be approximately 0.039.

Since the p-value (0.039) is less than the significance level (0.10), we reject the null hypothesis. Therefore, we have sufficient evidence to conclude that there is a significant difference in punishment between those who smiled and those who remained neutral during a court proceeding.

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Amplitude a = none

Period = π

Phase shift = none

Vertical shift = -2

Let the functions f(x) and g(x) be two real functions.

And g (x) = f (x) + k, where k is real numbers.

The function can be sketched by shifting f (x), k units vertically.

The direction of shift can be found by the value of k:

if k > 0, the base graph shifts k units up, and

if k < 0, the base graph shifts k units down.

Given:

A function,

f(x) = 3 sec 2θ - 2.

The standard form of the function is,

a sec(bx - c) + d.

Here, c is a phase shift and d is a vertical shift.

So, by comparison, we get,

Amplitude a = none

Period = π

Phase shift = none

Vertical shift = -2

Therefore, the graph is given in the attached image.

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The speed of the slower plane is 125 mph and the speed of the faster plane is 175 mph.

Let's call the speed of the slower plane "x" and the speed of the faster plane "x+50".

When two planes are flying in opposite directions, the distance between them increases at a rate equal to the sum of their speeds. So, we can set up the following equation:

2(x + x+50) = 600

Simplifying this equation, we get:

2(2x+50) = 600

4x + 100 = 600

4x = 500

Divide

x = 125

Therefore, the speed of the slower plane is 125 mph and the speed of the faster plane is x+50 = 175 mph.

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Refer to the attached image.

Southeast Washington State has a long history of seasonal dust storms. In October 1991, levels of dust particles in the air were six times greater than the Environmental Protection Agency's standard.

Several researchers conducted studies at three community hospitals to examine the relationship between the amount of dust particles in the air during the storms and the number of emergency room visits for respiratory disorders. Using the methods of correlation and regression, they were able to determine the effect of these dust storms on local residents.

In this module, you will write a short statistical report based on your linear regression analysis of data collected for two interesting variables that you believe could be linearly correlated. Your report should be supported by a scatter plot of the data and a least squares regression line.

To begin, you should collect your own data or use data that has already been collected. You may find data in the exercises at the end of sections 10.2 and 10.3 of your course text. Use at least 5 pairs of data.

Once you have collected your data, you should create a scatter plot of the data and a least squares regression line. You should also calculate the correlation coefficient and the equation of the regression line.

In your report, you should discuss the relationship between the two variables and the strength of the correlation. You should also discuss the equation of the regression line and how it can be used to make predictions.

Finally, you should conclude your report by discussing the implications of your findings and any limitations of your study.

Overall, your statistical report should be factually accurate, professional, and concise. You should also be sure to cite any sources that you use in your report.

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The area of the shaded region is 104 m².

What is a Triangle ?

The intersection of the two sides of a triangle's three sides, which are known as the vertex, is a sort of polygon. Between two sides, an angle forms. This is among geometry's crucial components.

We know that Area of a triangle = 1/2 × base × height

The area of Big triangle = 1/2 × 30 × 13

                                        = 15 × 13

                                       = 195 m²

Area of Small triangle = 1/2 × 14 × 13

                                    = 91 m²

So, Area of the shaded region

        =  Area of big triangle - Area of small triangle

        = 195 - 91

        =  104 m²

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The data described, the numbers of cases of flu treated at a certain hospital in different years, are quantitative data.

Quantitative data is any data that can be measured or expressed in numerical terms. In this case, the data is expressed as the number of cases of flu treated at the hospital in different years. This type of data can be analyzed using mathematical and statistical methods to obtain insights and patterns.

The information provided, specifically the numbers of flu cases treated at a certain hospital in various years, is quantitative information because it is expressed numerically.

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The probability that the basketball player makes 0 shots out of 3 is 0.343, or 34.3%. This can be calculated by using the binomial probability formula.

To calculate the probability of any outcome of a binomial experiment, use the formula: P(x) = nCx * px * (1-p)n-x, where n is the number of trials, x is the number of successes, and p is the probability of success in any one trial.

The Binomial Probability formula is

In this case, n = 3, x = 0, p = 0.39, and (1-p) = 0.61. Plugging these values into the formula, we get

P(x) = 3C0 * [tex]0.39^0[/tex] * 0.61³

= 0.343.

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Answer:

n = 14

Step-by-step explanation:

Theorem:

In a triangle, the measure of an exterior angle equals the sum of the measures of the two remote interior angles.

12n - 8 = 8n - 4 + 52

4n = 56

n = 14

The volume of the sno-cone is approximately 774.9 cm³.

The volume of a hemisphere is the amount of space that a hemisphere (a half-sphere) takes up. A hemisphere is a three-dimensional shape that is half of a sphere, and it is created by cutting a sphere in half along a plane that passes through the center of the sphere.

The formula for the volume of a hemisphere is given by:

V = (2/3)πr³

Where V is the volume of the hemisphere, π is the mathematical constant pi (approximately 3.14), and r is the radius of the hemisphere.

To use this formula, you simply need to know the radius of the hemisphere. To find the radius, measure the distance from the center of the sphere to the edge of the hemisphere. Then, plug this value into the formula and simplify to find the volume.

The volume of the sno-cone can be calculated by finding the volume of the hemisphere and the volume of the cone separately and then adding them together.

Volume of the hemisphere = (2/3)πr³

where r is the radius of the hemisphere

Given r = 5 cm, the volume of the hemisphere is

(2/3)π(5)³ = (500/3)π ≈ 523.6 cm³

Volume of the cone = (1/3)πr²h

Given r = 5 cm and h = 9.6 cm, the volume of the cone is

(1/3)π(5)²(9.6) ≈ 251.3 cm³

The volume of the sno-cone is the sum of the volume of the hemisphere and the volume of the cone, which is

523.6 + 251.3 ≈ 774.9 cm³

Therefore, the volume of the sno-cone is approximately 774.9 cm³.

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Answer:

f/ 3 4 5 6

b/ 8 10 12 14

Step-by-step explanation:

the 4th wall has 6×3-4=14

so the relationship is

f/ 3 4 5 6

b/ 8 10 12 14

Answer:

3.

a.4 feet

b.77 feet

c.8 seconds

Step-by-step explanation:

We can start by noting that the given equation, d(p) = 1/4p^2 - 2p, represents the depth (in feet) at a given point in time as you swim underwater, where p is the time in seconds since you started swimming.

a. To find the deepest point underwater, we need to find the maximum of the function d(p). We can do this by finding the vertex of the parabola. The formula for the x-coordinate of the vertex of a parabola in the form y = ax^2 + bx + c is given by x = -b/2a. In this case, a = 1/4 and b = -2, so the x-coordinate of the vertex is:

x = -b/2a = -(-2)/(2(1/4)) = 4

So the deepest point underwater occurs at p = 4 seconds. To find the depth at this point, we can substitute p = 4 into the equation:

d(4) = 1/4(4)^2 - 2(4) = -4 feet

Therefore, the deepest point underwater is 4 feet below the surface.

b. To find the depth when you have held your breath for 22 seconds, we need to evaluate the function d(p) at p = 22. We can round our answer to the nearest foot.

d(22) = 1/4(22)^2 - 2(22) = 77 feet

Therefore, the depth when you have held your breath for 22 seconds is approximately 77 feet below the surface.

c. To find how long you hold your breath to make the swim, we need to find the time it takes to swim from one side of the pool to the other. We can do this by finding the roots of the equation d(p) = 0, which represent the times when you reach the other side of the pool (i.e., when the depth is zero). We can use the quadratic formula to solve for p:

p = (-b ± sqrt(b^2 - 4ac))/2a

In this case, a = 1/4, b = -2, and c = 0, so the formula becomes:

p = (-(-2) ± sqrt((-2)^2 - 4(1/4)(0)))/(2(1/4)) = 8 or 0

The root p = 0 corresponds to the start of the swim, so the time it takes to make the swim is:

p = 8 - 0 = 8 seconds

Therefore, you hold your breath for 8 seconds to make the swim from one side of the pool to the other.

The measure of angle m2 is 65°, the reason is interior opposite angles.

For a regular polygon of any number of sides, the sum of its exterior angle is 360° (full angle).

Exterior angle is an measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended. Also, due to polygon being regular, let it be having 'n' sides, all the exterior angles are of same measure, and therefore, their measure is (360/n)°.

We are given that;

The measure of angle 1= 65°

Now,

By interior opposite angle property

Angle 1 = Angle 2

Substituting the value of angle 1

65°= angle 2

Therefore, by interior angle property the answer will be 65°.

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The solution to the inequality is any value of X that is less than or equal to -36

What is Inequality?

An inequality is a relationship that compares two numbers or other mathematical expressions that are not equal. It is most commonly used to compare the sizes of two numbers on a number line.

The inequality X/(-3) ≥ 12 can be solved as follows:

We begin by multiplying both sides of the inequality by -3, which will reverse the direction of the inequality since we are multiplying by a negative number. This gives:

X ≤ -36

Therefore, the solution to the inequality is any value of X that is less than or equal to -36.

In interval notation, we can write the solution as:

(-∞, -36]

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The evaluation of the two more bids Bruno received, and the equations, table and graph obtained from the bids are as follows;

x = The number of books

y = The total charge based on the pricing

The equations are;

Bid 7: y = 15·x + 3

Bid 8: y = 10·x + 40

Please find the completed table in the following explanation part

Part B;

Please find attached the graph of the two equations, created with MS Excel

An equation is a mathematical statement indicating that the quantity, magnitude or values of two expressions are the same.

The amount Bid 7 charges per book = $15

Amount paid upfront for Bid 7 = $5

Amount Bid 8 charges upfront = $40

Amount Bid 8 charges per book = $10

The variables are;

The equations are;

The table of values can be presented as follows;

                   Bid 7               [tex]{}[/tex]        Bid 8

x             [tex]{}[/tex] y = 15·x + 5              y = 10·x + 40

0               [tex]{}[/tex]       5               [tex]{}[/tex]          40

3               [tex]{}[/tex]       50               [tex]{}[/tex]        70

5               [tex]{}[/tex]       80               [tex]{}[/tex]        90

7               [tex]{}[/tex]       110               [tex]{}[/tex]        110

10               [tex]{}[/tex]     155               [tex]{}[/tex]       140

Part B;

Please find attached the required graph of the two equations, showing the legend and the scale for the x and y axis created with MS Excel.

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Answer:

Below

Step-by-step explanation:

1/81    *    27^5   =

1/(3^4)   *   (3^3)^5 =

3^-4    *    3^(3 *5)

3^-4    *   3^15

3^(-4 + 15)

3^11

The expression  1/81 * 27⁵ can be written as a power of 3 as 3¹¹.

Exponents are the method of writing numbers, especially large numbers, in terms of a base and an exponent, which is written as the power of base.

Given expression is,

1/81 × 27⁵

We have to write the expression as a power of 3.

Write each term as a power of 3.

81 can be written as 3⁴.

27 can be written as 3³.

1/81 × 27⁵ = (1 / 3⁴) × (3³)⁵

We can use two rules here, 1/aᵇ = a⁻ᵇ and (xᵃ)ᵇ = xᵃᵇ.

1/81 × 27⁵ = 3⁻⁴ × 3¹⁵

Multiplication rule of exponent states that xᵃ × xᵇ = xᵃ⁺ᵇ.

1/81 × 27⁵ = 3⁻⁴⁺¹⁵

                = 3¹¹

Hence the expression can be written as 3¹¹.

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The required real diameter of the tin is 250 mm.

Diameter is a measurement of the length of a straight line that passes through the center of a circular object, such as a circle or a sphere. It is the distance between two points on the object's edge that are furthest from each other and that pass through the center of the object.

Here,
If the diameter of the tin in the picture is 10 cm, then the actual diameter of the tin can be calculated as:

Actual Diameter = 2.5 x Picture Diameter
Actual Diameter = 2.5 x 10 cm
Actual Diameter = 25 cm

To convert the actual diameter to millimeters (mm), we can multiply by 10:

Actual Diameter in mm = Actual Diameter x 10
Actual Diameter in mm = 25 cm x 10
Actual Diameter in mm = 250 mm

Therefore, the real diameter of the tin is 250 mm.

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Answer:

⁷

Step-by-step explanation:

questions 1 and

Answer:

Find the ninth term rule for the sequence 3, 4, 7, 12, 19

28, 39, 52, 67

(the term number) nth term is +increasing odd numbers (+1, +3, +5, +7, etc)

Step-by-step explanation:

You're welcome.

The measure of the largest exterior angle of the polygon in discuss is; 100°.

It follows from the task content that the measure of the largest exterior angle of the polygon be determined.

Since the sum of all exterior angles of a polygon is equal to 360°;

x° + 4x° + 5x° + 7x° + 9x° + 10x° = 360°

36x° = 360°

x = 10

Therefore, it follows that the measure of the largest exterior angle is; 10x° = 10(10)° = 100°.

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