Patrick ran from his home to a shop 400m away at an average speed of 2 m per second he walked back to his home at an average speed of 1 m per second find the average speed for the whole journey if he did not stop at the shop​

The equivalent to the statement the price decreased by 1/2% will be 0.995x. Thus, all options are incorrect.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Let the price be 'x'. Then the equivalent to the statement the price decreased by 1/2% is given as,

⇒ (1 - 0.5 / 100) x

⇒ 0.995x

The equivalent to the statement the price decreased by 1/2% will be 0.995x. Thus, all options are incorrect.

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Answer:

Step-by-step explanation:

None of the given equations support the fact that rational numbers are closed under addition, because they all involve irrational numbers or fractions, which are not necessarily rational.

Option (A) involves the irrational number √2.

Option (B) involves adding the irrational number √6 with its negative, which results in a rational number, but it doesn't prove that all additions of rational numbers are also rational.

Option (C) involves the perfect square 9, but the square root of a non-square integer is generally an irrational number.

Option (D) involves the addition of two rational numbers, which is a valid example of the closure property of rational numbers under addition.

Therefore, the correct answer is (D) 1/3+1/3=2/3.

Discrete variables are a subset of variables that have a limited range of values. A variable that counts how many kids a family has, for instance, can only be a whole number, such as 0, 1, 2, etc.

Discrete variables, like integers or categories, are a form of variable that can only take specified, distinct values. For instance, a discrete variable is the number of siblings a person has because it can only be 0, 1, 2, 3, etc.Discrete variables are a subset of variables that have a limited range of values. A continuous variable, on the other hand, can accept any value within a range.Whole numbers like 0, 1, 2, 3, and so forth are frequently used as discrete variables. The number of kids in a household, the number of products in a shopping cart, or the number of individuals in a room are all examples of discrete variables.

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Answer:

(3c - 2)(c - 6)

Step-by-step explanation:

Quadratic Formula:

ax^2 + bx + c

a = 3 and c = 12

a * c --> 3 * 12 = 36

b --> -20

Two numbers that multiply to get 36 and added together get -20 are -18 and -2.

-18(-2) = 36

-18 + (-2) = -20

[tex]\frac{-18}{3c} = \frac{-6}{c}[/tex], [tex]\frac{-2}{3c}[/tex]

(c - 6)(3c - 2) = 3c^2 - 20c + 12

The table of values is

X |f(x)

0 | -45

2 | -35

4 | -25

6 | -15

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

f(x) = -5|x - 9|

We have the x values to be

x = 0, 2 4 and 6

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

f(0) = -5|0 - 9| = -45

f(2) = -5|2 - 9| = -35

f(4) = -5|4 - 9| = -25

f(6) = -5|6 - 9| = -15

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The y- coordinate for the solution to the system of equations is 4

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

8x−4y=−32,

2x+2y=4

Multiply the second equation by 4

So, we have the following representation

8x − 4y = −32

8x + 8y = 16

Subtract the equations

So, we have the following representation

12y = 48

Divide by 12

y = 4

Hence, the solution is y = 4

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The y-coordinate for the solution to the system of equations is equal to 4.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by this ordered pair (-2, 4).

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Sarah's age now is 18.

Ratio is defined as the relationship between two quantities for which it tells how much one quantity is contained in the other.

Normally, the ratio of two quantities a and b is denoted as a : b.

Given in the question that,

The ratio of Sarah's age to her father's age now is 1:3.

Suppose that x is the age of Sarah now.

Then, from the information given, father's age now = 3x

After 6 years,

Sarah's age = x + 6

Father's age = 3x + 6.

Given that, In 6 years' time, the ratio becomes 2:5.

So, numerically,

(x + 6) / (3x + 6) = 2 / 5

Doing the cross multiplication, we get,

5 (x + 6) = 2 (3x + 6)

5x + 30 = 6x + 12

5x - 6x = 12 - 30

-x = -18 or x = 18

Hence now, age of Sarah is x = 18.

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According to the California Board of Accountancy's requirements for CPA license renewal, if the highest level of service provided during the two years prior to the renewal date was a compilation engagement, the CPA must complete 24 hours of continuing education in accounting and auditing subjects.

Here is the breakdown of the requirements for the Accounting and Auditing Education Requirement:

- If the highest level of service provided was an audit, review, or attestation engagement, the CPA must complete 40 hours of continuing education in accounting and auditing subjects.

- If the highest level of service provided was a compilation engagement, the CPA must complete 24 hours of continuing education in accounting and auditing subjects.

- If the highest level of service provided was preparation of financial statements, the CPA must complete 8 hours of continuing education in accounting and auditing subjects.

- If the CPA did not provide any of the above services, they are not required to complete any continuing education in accounting and auditing subjects.

In Brandon's case, since his highest level of service provided was a compilation engagement, he must complete 24 hours of continuing education in accounting and auditing subjects out of the total of 80 continuing education hours required.

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Answer:

B

Step-by-step explanation:

Rise over run should be 4 rise and 5 to the side run

Answer:

Step-by-step explanation:

The last one (placed below)

Just take two random points (x1,y1) and (x2,y2) from the graph and calculate the slope according to the expression:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

The graph placed below, passes through the points (5,4) and (0,0). So if we replace these coordinates within the formula:

[tex]m=\frac{5-0}{4-0}=\frac{5}{4}[/tex]

Answer: 24

Step-by-step explanation: 6*4=24

4+4+4+4+4+4=24

Answer:

she paid $1.50 / 1lb

Step-by-step explanation:

6lbs divided by $4 = 1.50 or $1.50 / 1lb

Step-by-step explanation:

x = number of quarters

y = number of dimes

x + y = 34

therefore, we can say right away

y = 34 - x

0.25x + 0.1y = 4

because a quarter is worth $0.25, and a dime is worth $0.10.

now we are using the first equation in the second :

0.25x + 0.1(34 - x) = 4

0.25x + 3.4 - 0.1x = 4

0.15x + 3.4 = 4

0.15x = 0.6

x = 0.6/0.15 = 4

y = 34 - x = 34 - 4 = 30

the solution is therefore (4, 30).

she has 4 quarters and 30 dimes.

Peng has 4 quarters and 30 dimes.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, Peng has $4 in quarters and dimes. She has 34 coins.

we need to find the number of quarters and dimes, does Peng have,

Let x = number of quarters and y = number of dimes

Therefore, establishing the equations :-

x + y = 34

y = 34 - x...(i)

Since, a quarter is worth $0.25, and a dime is worth $0.10.

Therefore,

0.25x + 0.1y = 4.....(ii)

Therefore,

0.25x + 0.1(34 - x) = 4

0.25x + 3.4 - 0.1x = 4

0.15x + 3.4 = 4

0.15x = 0.6

x = 0.6/0.15

x = 4

Put x = 4 in the eq(i)

y = 34 - x = 34 - 4 = 30

y = 30

Hence, she has 4 quarters and 30 dimes.

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Answer:

140 ° , because it is vertically opp to angle 4 and angle 4 is corresponding 8 .

The sides of the rectangle are

the codes are CFID

The unknown part of the rectangle is solved using division of polynomial and the check is completed by multiplication of the polynomial involved

checking for the correct answers

1. 2(x + 5)(x - 1) = (2x + 10)(x - 1)

2x² - 2x + 10x - 10

2x² + 8x - 10

2. 3(x - 1)(x + 6) = (3x - 3)(x + 6)

3x² + 18x - 3x - 18

3x² + 15x - 18

3. 2(x + 1)(x - 5) = (2x + 2)(x  -5)

2x² - 10x + 2x - 10

2x² - 8x - 10

4. 5(x - 1)(x + 1) = (5x -5)(x + 1)

5x² + 5x - 5x - 5

5x² - 5

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The equation of the line that is perpendicular to this line and passes through the point (5, −1) is y = (9/4)x - (49/4) and the equation of the line that is parallel to this line and passes through the point (5,−1) is y = (-4/9)x + (11/9).

An equation of a line is provided: -4x - 9y = 2

                                       -9y = 4x + 2

                                    y = (-4/9)x - 2/9

The slope-intercept form of the line is y = mx + c

So, the Slope of the line is -4/9

The slope of the perpendicular line is -1/(-4/9) = 9/4

Equation of line with slope 9/4 and containing the point (5, -1):

                                  y - (-1) = (9/4)(x - 5)

                                          y = (9/4)x - (49/4)

Parallel lines have the same slope, so the equation of the line with slope -4/9 and which contains the point (5, -1) is:

                              y - (-1) = (-4/9)(x - 5)

                               y = (-4/9)x + (11/9)

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Answer: $3.32

Step-by-step explanation:

First arrange the given discrete values in ascending order.

$3.26, $3.28, $3.31, $3.31, $3.32, $3.34,$3.35, $3.38, $3.42

we will use the formula 1/2 x (n +1), where n is total number of discrete values which in this case is 9.

This formula doesn't give the answer of the second quartile, it tells which nth term in the arranged set will be the second quartile.

1/2 (9+1) = 5.

Now we will choose the 5th term of the ascending order set.

Second quartile is same as the median, that means you need the mid value.

Answer:3y +=7  

=>3y-7-x

 =>y=(7-x)/3                               Step-by-step explanation:Solve for 'y' means, solve the equation to get the value of y and in terms of ,x means value of y not necessarily in pure constant form,but in the form of x.

The volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot.

So the volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot as a unit of volume equal to a cube with sides that are one foot in length and the quart as a unit of volume in the US customary system.

The quantity of cubic feet can be multiplied by 29.9220779 to get the conversion to quarts. For instance, if you have a container with a 2 cubic foot volume, the quantity of quarts in that container would be:2 cubic feet multiplied by the US liquid quart density of 29.9220779 gives 59.8441558 US quarts. The volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot as a unit of volume equal to a cube with sides that are one foot in length and the quart as a unit of volume in the US customary system.

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Answer:

Option 2 Is Correct

Step-by-step explanation:

The following statements are true about the function and its graph:

The graph of the function is a parabola.

The graph contains the point (0, 0).

The graph does not contain the point (20, -8).

Option 1 is true because the function is a quadratic function, and all quadratic functions have a parabolic graph.

Option 2 is true because the y-intercept of the function is (0,0).

Option 3 is false because the function opens upwards

The true statement is that the y intercept of function A is less than the y intercept of function B.

y intercept is the y coordinate of the point on the line where it touches the Y axis. The x coordinate will be 0 there.

Here we have two functions.

Function A is given in the graph and function B is given in the equation form.

From the graph, the y intercept of function A is the y coordinate of the point touching the Y axis.

Line touches the Y axis at the point (0, -3).

So y intercept of function A = -3.

The equation of function B is the slope intercept form.

In the slope intercept form, y = mx + c, c is the y intercept.

From the equation y = 1/2 x + 4, 4 is the y intercept.

So 4 > -3.

Hence the y intercept of B is greater than that of A.

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The equation AB=BC for [tex]A=BCB^{-1}[/tex].

The solution of AB = BC  for A, assuming that A,B and C are square matrices and B is invertible is

We have to solve the equation

AB = BC given that these all are square matrices and B is invertible.

Write the required Equation:

Multiply both sides by inverse of B

The multiplicative inverse of a matrix is the matrix that gives you the identity matrix when multiplied by the original matrix.

⇒[tex]ABB^{-1} =BCB^{-1}[/tex]

⇒[tex]AI=BCB^{-1}[/tex]

⇒[tex]A=BCB^{-1}[/tex]

Therefore, the solution of AB = BC is [tex]A=BCB^{-1}[/tex].

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The measures of angles in similar triangles are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°

Similar triangles have the same corresponding angle measures and proportional side lengths.

Given that, Triangle ABC is similar to triangle FGH, we need to find the measures of the angles,

The sum of interior angles of a triangle = 180°

Considering Δ ABC,

∠ A + ∠ B + ∠ C = 180°

∠ C = 180°-(22°+75°)

∠ C = 83°

Since, we know that the similar triangles have congruent corresponding angles,

Therefore,

∠ A = ∠ F, ∠ B = ∠  G and ∠ C = ∠ H

Therefore, the measures of angles in Δ FGH are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°

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Answer: The solution of the system of equations is (x, y) = (-1, -2).

Step-by-step explanation:

We can solve this system of equations by using either elimination or substitution method. Here, we'll use elimination:

Adding the two equations, we get:

(3x + 7y) + (-3x + 9y) = -17 - 15

Simplifying the left side and right side:

16y = -32

Dividing both sides by 16:

y = -2

Now we can substitute y = -2 into either of the original equations and solve for x. Let's use the first equation:

3x + 7(-2) = -17

Simplifying:

3x - 14 = -17

Adding 14 to both sides:

3x = -3

Dividing both sides by 3:

x = -1

Answer:

1) 108    2) 72    3) 11

Step-by-step explanation:

1) since the angle of PNM is the same as PLM, then we can simply add 42 and 66 to get 108 degrees

2)since the total angle in parallelogram is 360, we can take away the two angles we do know. Those are PLM and PNM which are 108 each.

360-108-108=144

with the last two corners having the same angle, the remaining degrees are distributed evenly giving us 144/2 = 72

3)since the length of LM and PN are the same then we get the equation

2d = 22 which gives us d = 11

The possible values for radius r and height h of the cone will be 2 and 2.1485 respectively.

What exactly is a cone?

A cone is a shape formed by connecting a single point known as the apex or vertex to all of the points of a circular base using a series of line segments (which does not contain the apex). The distance from the vertex to the base is the cone's height. The circular base's radius has been measured. The slant height is the length of the cone from the peak to any point along the base's perimeter. The height, radius of base, and slant height of the cone in the figure define it.

Volume of cone=1/3πr²h, where r=base radius and h=cone height

Curved surface area=πrL, where L is the slant height.

Now,

Given Volume of cone to hold popcorn=9 inch³

i.e. 1/3πr²h=9

r²h=9*3*7/22

r²h=8.5943

let r=2

then h=8.5943/4

h=2.1485

Hence,

            The possible values for radius r and height h of the cone will be 2 and 2.1485 respectively.

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Answer: 0.20689655

Step-by-step explanation: because you take 12 divided by 58

Answer:

25%

Step-by-step explanation:

x + 0.25x = y

y - 0.25x = x

If the size of a circle increases by 25% and then decreases back down to it's original size it's going to be the same percentage 25%.

Answer:

Step-by-step explanation:

In Stata, you can include fixed effects in a regression by using the "xtreg" command with the "fe" option. The "xtreg" command is used to fit a linear regression model with panel data, and the "fe" option tells Stata to include fixed effects in the model.

Here's an example of how to run a fixed effects regression in Stata:

xtreg y x1 x2 x3, fe

In this example, "y" is the dependent variable, and "x1", "x2", and "x3" are the independent variables. The "fe" option tells Stata to include fixed effects for each individual in the panel data.

Note that the fixed effects in this example are time-invariant, meaning that they are constant for each individual over time. If you have time-varying fixed effects, you can include them in the regression using the "xtreg" command with the "vce(cluster id)" option, where "id" is the variable indicating the individual in the panel data.

If there were 950 countries, we could expect celebrations from 10 countries.

Groundhog Day is a popular North American tradition celebrated on February 2 in the United States and Canada. It is based on the Pennsylvania Dutch superstition that if a groundhog emerges from its burrows on this day and sees its shadow due to clear weather, it will retreat to its burrow and winter will last six weeks longer.

In our calculation, as 2 out of 195 celebrate the day, we need know  how many celebrations we could expect if there were 950 countries.

950 / 195 = 4.87179487179 = 4.87. We will multiply 4.87 by 2 country giving us 9.74, approximately 10 countries.

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The bearing of the bank from the swimming pool is 42 degrees south of west.

What is temperature ?

Temperature is a measure of how hot or cold something is. More specifically, it is a measure of the average kinetic energy of the particles that make up a substance. When the particles in a substance move faster, their kinetic energy increases, and the temperature of the substance goes up.

Temperature is usually measured in degrees Celsius (°C) or degrees Fahrenheit (°F), although in scientific contexts, the International System of Units (SI) unit of temperature is the kelvin (K). The Celsius scale sets the freezing point of water at 0°C and the boiling point at 100°C, while the Fahrenheit scale sets the freezing point of water at 32°F and the boiling point at 212°F. The kelvin scale sets the zero point at absolute zero (-273.15°C or -459.67°F), the theoretical temperature at which all molecular motion ceases.

According to given condition:

The bearing of the swimming pool from the bank is 138 degrees.

The bearing is the angle measured clockwise from the north direction.

Therefore, to find the bearing of the bank from the swimming pool, we need to add 180 degrees to the given bearing of 138 degrees and then subtract 360 degrees (a full circle) to get the bearing within the range of 0 to 360 degrees.

So,

Bearing of bank from swimming pool = (138 + 180 - 360) degrees = -42 degrees

Therefore, the bearing of the bank from the swimming pool is 42 degrees south of west.

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