in January 2008, the temperature in parts of Minnesota fell from 41 degrees to -13 degrees over a 24 hour period. what was the average temperature change per hour?

In general, a translation:

• in the x-direction by n units is given by: (x, y) → (x + n, y),

• in the y-direction by m units is given by: (x, y) → (x, y + m),

• the combination of both translations is: (x, y) → (x + n, y + m).

In this problem, we want to translate a triangle 2 units up and 5 units to the right, so we want to translate the points of the triangle in the following way:

From the graph we see that the coordinates of point A are:

Making the translation we get:

Answer

(4,4)

From the given table, it is found that:

1. The linear regression equation is: y = 16.96x + 3.

2. The meaning of the slope is that he hiked an average of 16.96 miles a day.

3. In 52 days, Sean had hiked 885 miles.

4. In 22 days, Sean had hiked 377 miles.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

In the context of this problem, the points are given as follows:

(0,0), (19,308), (34, 578), (67, 1070), (91, 1715), (112, 1902), (134, 2200).

Using a calculator, the equation is given as follows:

y = 16.96x + 3.

The input of the function and the output of the function are given as follows:

The slope is the rate of change, that is, change in the output divided by change in the input. Hence the slope of 16.96 means that he hiked an average of 16.96 miles a day.

In 52 days, the number of miles hiked is:

y = 16.96(52) + 3 = 885 miles.

The number of days is took to hike 377 miles is found as follows:

377 = 16.96x + 3

x = 374/16.96

x = 22 days.

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The question states:

Notice that the angle for which its measure is arctan(a/b), is the angle that has "a" as the oposite side, and "b" as the adjacent side , so it is the angle on the bottom right of the triangle.

Then the cosine of that angle, is defined as:

cos(angle) = adjacent/hypotenuse = b / squareroot( a^2+b^2)

which agrees with answer D in the list of possible answers given.

The expressions from least to greatest is (√3)² < 8² < 29².

How to compare expressions with indices?
Expressions with indices are of three types:
(1) when bases are equal and powers are different;
(2) when powers are equal but bases are different;
(3) when both powers and bases are unequal.
To solve an expression of type (1), we compare the powers for the given expressions only to determine the greater number efficiently, no heed needs to be given to the base.
To solve an expression of type (2), we compare the bases for the given expressions only to determine the greater number efficiently, no heed needs to be given to the powers.
To solve an expression of type (3), we reduce the power of an expression until it matches the other, so that for comparison only bases are to be taken into consideration without any heed to powers.

Given the expressions are 29², 3 and 64
The given expressions can be re-written as: 29², (√3)² and 8².
On comparing the expressions with the above literature, they match type (2), thus following the assertions we should compare the bases only to find the greatest number.
Thus, the correct order for expressions is: (√3)² < 8² < 29²

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Function:

A function is a relation in which every input x has a different output value y.

If there is more than 1 outputs for the same input then it doesn't represent a function.

Let us analyze each of the given options.

Option A:

{(2, -1), (4, -2), (6, -3), (8, -4)}

As you can see, each input x has a different output value y.

Therefore, it is a function

Option B:

{(0, 0), (1, 1), (1, 0), (2, 1)}

As you can see, the input (1) has two different outputs (1 and 0)

Therefore, it is not a function.

Option C:

{(3, 3), (3,4),(4,3),(4,4)}

To find the area of the shaded region, we have to find the area of the square first.

Then, we find the area of each yellow triangle inside (up and down). The base of each triangle is 10 inches, and the height of each of them is 7 inches.

Add the area of both triangles.

At last, subtract the area of the triangles from the area of the square.

The strategy is to subtract the area of the yellow triangles (up and down) from the area of the square.

An event can be said to be a set of possible outcomes which results from an experiment.

An individual can be said to create a theory after he observes events.

A theory is said to be a set of ideas that explains the results from an experiment.

Therefore, an individual creates a theory after he observes an event.

ANSWER:

Theory

The main goal is 140 percent i.e., 21 members.

What is meant by percentage?

In mathematics, a percentage (from Latin: percentage , "by a hundred") may be a number or ratio expressed as a fraction of 100. it's often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" also are used. A percentage may be a dimensionless number (pure number); it has no unit of measurement. The term "percent" springs from the Latin per centum, meaning "hundred" or "by the hundred". The Italian word per cento, which means "for a hundred," gradually shrank to become the symbol for "percent." The "per" was often abbreviated as "p."—eventually disappeared entirely. The "cento" was contracted to 2 circles separated by a horizontal line, from which the fashionable "%" symbol is derived.

140 percent of 15 = 15x140/100 = 21 members

Hence, the main goal is 21 members.

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Answer:

4x³

Step-by-step explanation:

substitute x = f(x) into g(x)

(g ￮ f)(x)

= g(f(x))

= g(x³ - 1)

= 4(x³ - 1) + 4

= 4x³ - 4 + 4

= 4x³

Answer:

B

Step-by-step explanation:

(120 - 50 b/m) / 5 b / m^2 = 14 minutes    

The point [tex](-1\frac{3}{4},4\frac{1}{2})[/tex] has been plotted on the coordinate plane.

Given the point [tex](-1\frac{3}{4},4\frac{1}{2})[/tex]

The coordinate plane is used to graph the points, lines and other objects.

First we have to convert the mixed fraction to the simple fraction

[tex]-1\frac{3}{4}[/tex] = -7/4

[tex]4\frac{1}{2}[/tex] = 9/2

Now we have to convert the simple fraction to decimal form

-7/4 = -1.75

9/2 = 4.5

The point is (-1.75,4.5)

Here the condition of axis is given, the horizontal axis is goes from -5 to 5, that is -5 < x < 5, and the vertical axis goes from -5 to 5 that is -5 < y < 8

Plot the points on the coordinate plane  

Hence, the point [tex](-1\frac{3}{4},4\frac{1}{2})[/tex] has been plotted on the coordinate plane.

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Answer

Options C and F are correct.

x² + 6x + 9 = 25

(x + 3)² = 25

are both equivalent to

x² + 6x = 16

Explanation

The equations that are equivalent to x² + 6x = 16 will all have to reduce to this exact equation on simplification.

x² + 6x + 9 = 0

Option A is not correct as this equation isn't equal to the equation given in the question.

x² + 6x + 9 = 16

x² + 6x = 16 - 9

x² + 6x = 7

Option B is not correct as this equation isn't equal to the equation given in the question.

x² + 6x + 9 = 25

x² + 6x = 25 - 9

x² + 6x = 16

This option C is corect as it matches the equation given in the quesion.

(x + 3)² = 0

x² + 6x + 9 = 0

Option D is not correct as this equation isn't equal to the equation given in the question.

(x + 3)² = 16

x² + 6x + 9 = 16

x² + 6x = 16 - 9

x² + 6x = 7

Option E is not correct as this equation isn't equal to the equation given in the question.

(x + 3)² = 25

x² + 6x + 9 = 25

x² + 6x = 25 - 9

x² + 6x = 16

This option F is corect as it matches the equation given in the quesion.

Hope this Helps!!!

Given the formula:

a) Rewrite for b:

First step: Multiply 2 to both sides

Second step: divide both sides by h

B) Rewrite for h:

First step: Multiply 2 to both sides

Second step: divide both sides by b

Using the future value formula, it is found that:

a) You will have $301,355 in the account after 30 years.

b) You will have put $108,000 in the account.

c) You will have earned $193,355 in interest.

The future value formula  is given by:

[tex]V(n) = P\left[\frac{(1 + r)^n - 1}{r}\right][/tex]

In which the parameters are described as follows:

Considering the $300 deposits, the interest rate of 6% and the monthly compoundings for 30 years, the values of the parameters are given as follows:

P = 300, r = 0.06/12 = 0.005, n = 12 x 30 = 360.

Hence the balance of the account after 30 years will be given by:

[tex]V(30) = 300\left[\frac{(1.005)^{360} - 1}{0.005}\right][/tex]

V(30) = $301,355.

The amount placed into the account is given by:

360 x 300 = $108,000.

The remaining amount is earned in interest, hence:

301355 - 108000 = $193,355.

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Answer:

SSS.

Step-by-step explanation:

The text above described the Side-Side-Side Theorem, which states that two triangles are congruent if three sides of one are equal or proportional respectively to three sides of the other (SSS=SSS).

Domain is x values of the set and range is y values of the set.

What is domain and range?

Domain is the set of all first numbers of the ordered pairs in a relation and range is the set of second numbers of the ordered pair in relation.

The domain is the set of independent values, meaning the set of x-coordinates of the ordered pair as x is an independent variable.

The range is set of dependent values, meaning the set of y-coordinates of the ordered pair as y is an independent variable.

For example- we have a set

(1,2) (0,6) (2,3) (4,5)

Domain = {1,0,2,4}

Range = {2,0,3,5}

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The decimal form of this rational number is 0.27, where 27 in decimal is recurring.

What are the steps to solve a rational number?
The steps to solve a rational number problem are:
(a) Let 'a/b' be a rational number. From the sentence, we deduce that denotes the denominator of a rational integer, while represents the numerator. Consequently, is 3 and is 11.
(b) The decimal form is achieved by dividing by, and we described the procedure required to do so:
(i) Ten times the numerator:
Dividend is 30, and the result is known to be zero. Remainder: N/A
ii) Dividend less the dividend multiplied by the divisor by two:
Known outcome: 0.2; residuals: 8
iii) 10 times the residue:
Known outcome: 0.2; residuals: 80
iv) Divide the residue by the divisor and multiply it by 7:
0.27 as known result; 3 as residue
v) Ten times the residue:
0.27 as known result; 30 as residue
vi) Divide the divisor by two and deduct the result from the sum:
Results known: 0.272/Residue: 8
vii) 10 times the residue:
The known outcome is 0.272/Residue: 80.
viii) Divide the divisor by 7 and deduct the result from the sum:
A known outcome is 0.2727/Residue: 3.

Therefore, we can see that is a periodic decimal number in its decimal form.
As a result, we deduce that the decimal representation of this rational number is 0.27, where 27 is a regular integer.

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ANSWER:

D. x = 9/k

STEP-BY-STEP EXPLANATION:

We have the following equation:

We solving for x:

The correct answer is D. x = 9/k

You have the following function for the height respect to the water, Jason has after time t he jumped:

In order to determine the time Jason takes to hit the water, equal h = 0. Thus, you have a quadratic equation and it is necessary to find the zeros of the polynomial:

use the following quadratic formula to find the zeros:

where a,b and c are the coefficients of the polynomial:

a = -16

b = -16

c = 672

replace these values into the formula:

Then, you obtain the following two values:

Select the positive values because negative time does not have physical meaning.

Hence, Jason takes 6 seconds to hit the water.

Answer:

  1) CW 270° or CCW 90°

Step-by-step explanation:

In each case, you want to identify two transformations that will map the preimage to the image.

We note the transformation maps ...

  A(-7, 0) ⇒ A'(0, -7) . . . . . . CCW 90° or CW 270°

  B(-4, -1) ⇒ B'(1, -4)

  C(-7, 3) ⇒ C'(-3, -7)

These can be described by ...

  (x, y) ⇒ (-y, x)

This transformation is equivalent to either of the two transformations ...

As above, rotation about the origin by 90° in one direction is the same as rotation 270° about the origin in the other direction. The attached graph shows the result either way. The two equivalent transformations are ...

The coordinate transformation is ...

  (x, y) ⇒ (y, -x)

Given:-

Answer:

7

Step-by-step explanation:

42 divided by 3 = 14 = total of triangle XYZ

14 divided by 2 = 7

line X/Y = 7

The probability that a sum of 9 on the 2 die will occur at least once is 217/729.

Sum of 9 in a pair of dice can occur in the following 4 ways.

3 + 6

4 + 5

5 + 4

6 + 3

Also, total number of ways = 6*6 = 36

Hence, probability of getting a sum of 9  = 4/36 = 1/9.

We know that,

Probability of getting a sum of 9 + Probability of not getting a sum of 9 = 1

Hence, we can write,

1/9 +  Probability of not getting a sum of 9 = 1

Probability of not getting a sum of 9 = 8/9

Also,

Probability of getting the sum of 9 atleast 1 + probability of getting the sum 9 none of the times = 1

Hence, we can write,

Probability of getting the sum of 9 atleast once =  1 - probability of getting the sum 9 none of the times/

Probability of getting the sum of 9 atleast 1 = 1 - (8/9)*(8/9)*(8/9) = 1 - 512/729 = 217/729.

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The mixed fraction 4 3/8 + 7 3/4 is equivalent to the fraction to 12 1/8

An equation shows the relationship between two or more numbers and variables.

The mixed fraction 4 3/8 is equivalent to the fraction (4 * 8 + 3)/8 = 35/8

The mixed fraction 7 3/4 is equivalent to the fraction (4 * 7 + 3)/4 = 31/4

Hence:

4 3/8 + 7 3/4

Substituting:

= 35/8 + 31/4

Simplifying:

= 97/8 = 12 1/8

4 3/8 + 7 3/4 is equal to 12 1/8

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Answer:

1. 27

2. [tex]\frac{27}{7}[/tex]

Step-by-step explanation:

9 / 7/3

9 * 3/7

9/1 * 3/7

27/7

Answer:

The answer to the first question is:
[tex]27[/tex] groups.

And the second answer is:
[tex]\frac{27}{7}[/tex]

Step-by-step explanation:

Step 1: Analyze the number line

As we can see from the number line, each interval equals to [tex]\frac{1}{3}[/tex].

We can prove this by the fact that at the seventh interval, the value is [tex]\frac{7}{3}[/tex].

So, the value between each intervals would be:

[tex]\frac{7}{3}\div 7\\=\frac{1}{3}[/tex]

Step 2: Solving the first question:

We can see that the number [tex]9[/tex] lies on the [tex]27\text{th}[/tex] interval.

Since the value between each interval is [tex]\frac{1}{3}[/tex], it would take [tex]27[/tex] groups of [tex]\frac{1}{3}[/tex] to equal to [tex]9[/tex].

Step 3: Solving the second question:

From the number line, we can see that it takes four groups of [tex]\frac{7}{3}[/tex] to equal to [tex]\frac{28}{3}[/tex].

And since we are taking [tex]\frac{7}{3}[/tex] as a single group here, each interval in a group of [tex]\frac{7}{3}[/tex] would be [tex]\frac{1}{7}[/tex] of the group.

So, the answer of the division would be: [tex]4[/tex] (the number of groups of [tex]\frac{7}{3}[/tex]needed to reach [tex]\frac{28}{3}[/tex]) minus [tex]\frac{1}{7}[/tex] (the amount of the group that when subtracted, brings the entire answer to [tex]9[/tex]):

[tex]4-\frac{1}{7}\\\\\frac{4\times 7}{7}-\frac{1}{7}\\\\=\frac{28}{7}-\frac{1}{7}\\\\=\frac{28-1}{7}\\\\=\frac{27}{7}[/tex]

04) The complementary angles are the angles whose sum is 90° thus { 26°,54°,48°,29°,22°} will be the corresponding angles.05)The supplementary angles are the angles whose sum is 180° thus {54°,48°,12°,135°,91°} will be the corresponding angles.

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.

If m∠A + m∠B = 90° then A and B will be the complimentary angle.

The complementary of 64° = 90° - 64° = 26°

The complementary angle of 36° = 90° - 36° = 54°

The complementary angle of 42°= 90° - 42° = 48°

The complementary angle of 51°= 90° - 51° = 29°

The complementary angle of 68°= 90° - 68° = 22°

If m∠A + m∠B = 180° then A and B will be the supplementary angle.

The supplementary of   = 180° - 126°  = 54°

The supplementary of   = 180° -  132° = 48°

The supplementary of   = 180° - 178°  = 12°

The supplementary of   = 180° -   45° = 135°

The supplementary of   = 180° -  89°  = 91°

Hence " { 26°,54°,48°,29°,22°} will be the corresponding complementary angle and {54°,48°,12°,135°,91°} will be the corresponding supplementary angles".

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The complex number factors are (x+5i) and (x-5i).

The term a + bi, where a and b are real numbers, can be used to represent any complex number.

The given expression is x² + 25

Now this can be written as :

x² - [(i)²×(5)²] as we know that i² = -1.

Now we use the algebraic form of a²-b² =(a + b)(a - b) to separate it into complex factors.

or , (x+5i)(x-5i)

Therefore the complex number factors are (x+5i) and (x-5i).

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Answer:

  (a) expression: (6 yd)²; area: 36 yd²

  (b) expression: (10 yd)²; area: 100 yd²

  (c) Jones: 18; Evansbee: 50

  (d) Jones: $89.82; Evansbee: $249.50

Step-by-step explanation:

You want the area, number of plants that can be placed, and the cost of plantings for gardens that are 6 yards square and 10 yards square. Each plant takes 2 square yards and costs $4.99.

The formula for the area of a square of side length s is ...

  A = s²

The area of a square garden with a side length of 6 yards is ...

  A = (6 yd)² . . . . . expression for the area

  A = 36 yd² . . . . . the area of the garden

The area of a square garden with a side length of 10 yards is ...

  A = (10 yd)² . . . . . expression for the area

  A = 100 yd² . . . . . the area of the garden

The area used by the plants is the product of their number and the area taken by each.

For Jones' garden, the number of plants that can be placed is ...

  n(2 yd²/plant) = 36 yd²

  n = (36 yd²)/(2 yd²/plant) = 18 plants

Mr. Jones can place 18 plants in his garden.

For Evansbee's garden, the number of plants that can be placed is ...

  n(2 yd²/plant) = 100 yd²

  n = (100 yd²)/(2 yd²/plant) = 50 plants

Mr. Evansbee can place 50 plants in his garden.

At $4.99 each, the cost of plantings will be $4.99 times the number of plants.

Plants for Jones' garden cost 18($4.99) = $89.82.

Pants for Evansbee's garden cost 50($4.99) = $249.50.

The y-intercept of any function is the point where the line intersect with the y-axis, at this point the value of x is zero.

If you look at the graph, the line intersects the y-axis at point (0,3), so the y-coordinate of the y-intercept is 3