Drag each set of column entries to the correct location in the augmented matrix. Not all sets of entries will be used.

Mac traveled to three cities on one highway. The total distance one way was 320 miles. The distance from his original location to the first city was 20 miles more than half

the distance from the first city to the second city. The distance from the second city to the third city was 75 miles less than the distance from the first city to the second

city. Let xrepresent the distance from the original location to the first city, y represent the distance from the first city to the second city, and z represent the distance from

the second city to the third city. Place the correct sets of column entries in the augmented matrix that models Mac's situation,

We assume that we have a plot given like the graph attached.

We have n points and we need to find How many of the 9 people listed in the scatterplot have an actual height that differs by more than 3 centimeters from the height predicted by the line of best fit?

So for this case we need to have the predicted value  y^  and the real value y. We are going to put these two values and the difference

    yi                          yi^                       |yi - yi^|

    157                      161.5                        4.5

    163                      163.1                        0.1

    175                      167                           8.0

    171                       170.5                        0.5

    173                      172.5                        0.5

    173                      174.3                        1.3

    172                      176                           4.0

    183                      178                           5.0

    178                      180                           2.0

So as we can see we have 4 points out of the 9 who satisfy the condition

|yi - yi^| >= 3.

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The results of the multiplications are: 1) x²+6x-16 (2) x²+8x+15 (3) x²-2x-63 (4) 6x+x-15 (5) 4x²-17x-15 (5) x²+13x+42

The given equations are

1) (x+8)(x-2)

Opening the brackets to have and collecting like terms  to have

x²-2x+8x-16

x²+6x-16

2) (x+5)(x+3)

Opening the brackets to have and collecting like terms  to have

= x²+3x+5x+15

x²+8x+15

3) (x+7)(x-9)

Opening the brackets to have and collecting like terms  to have

x²9x+7x-63

x²-2x-63

4) (2x-3)(3x+5)

Opening the brackets to have and collecting like terms  to have

6x²+10x-9x-15

6x²+x-15

5) (4x+3)(x-5)

Opening the brackets to have and collecting like terms  to have

4x²-20x+3x-15

4x²-17x-15

6)  (x+7)(x+6)

Opening the brackets to have and collecting like terms  to have

x²+6x+7x+42

x²+13x+42

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The system of the equation is written as

x + y = 428

5x + 3y = 1674

the solution:

adult tickets is 195

students tickets is 233

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

Janine sold 428 tickets for the school play

x + y = 428

Janine’s total ticket sales were $1674

Student tickets were $3 and adult tickets were $5

5x + 3y = 1674

The simultaneous equation

x + y = 428

5x + 3y = 1674

solving the equation  by elimination method

x + y = 428 * 3

3x + 3y = 1284

5x + 3y = 1674

subtraction gives

-2x = -390

x = 195

substitute x = 195 into x + y = 428

195 + y = 428

y = 428 - 195

y = 233

hence adult tickets is 195, while students tickets is 233

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The values of n for the given expression such that -15< 3n < 6 is -5 < n < 2.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The given expression is:

-15< 3n < 6

Divide all the sides of the equation with 3 to isolate the value of n.

-15 / 3 < 3n/3 < 6/3

-5 < n < 2

Hence, the values of n for the given expression such that -15< 3n < 6 is -5 < n < 2.

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For the given time taken to cover 20 miles from upstream and downstream the rate of Rick paddles in still water is 6.5mph and rate of current is 1.5mph.

Let us consider 'x' be the rate at which Rick paddles in still water

'y' be the rate of the current

Distance covered while going in upstream = 20 miles

Time taken while going 20 miles upstream = 4 hours

Rate of upstream = 20 / 4

⇒ x - y = 5 miles /hours    ___(1)

Distance covered while going in downstream = 20 miles

Time taken while going 20 miles downstream = 2.5hours

Rate of downstream = 20 / 2.5

⇒ x + y = 8 miles /hours    ___(2)

Solve (1) and (2) we get,

x - y = 5

x + y = 8

2x = 13

⇒ x = 6.5miles per hour

y = x - 5

⇒ y = 1.5 miles per hour

Therefore, the rate of the Rick paddles in the still water is 6.5mph and the rate of the current is 1.5mph.

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Throughout the solar system, solar energy is continuously emitted by the sun. The Earth is warmed by solar energy, which also affects the weather, the wind, and the survival of plant and animal life. Electromagnetic radiation, which is a kind of energy, heat, and light, is released from the sun (EMR).

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As per the asked equation the value of P(x<6) will be c=1

The probability of an event is always between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

Given the information provided, P(x-1)=0.178, P(x>1)=0.822, it's not possible to calculate P(x<6) because the information provided doesn't give us the complete picture of the probability distribution function, also we don't know the type of distribution used to calculate the probabilities. So we can't infer anything about P(x<6) from the information given.

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The light travels 3.784 x 10 ^13 kilometers in 4 years .As Given that, light travels 1 meter in 1/299,772,458 of a second.

In 4 years how many kilometers it will travel?

covert 4 years into seconds.

since it is given that 1 year = 365.25 days.

           4 years in seconds = 4 x 365.25 x 24 x 60 x 60

                                            = 126230400 sec

          1 m in 1/299,772,458 sec

          x km in 126230400 sec

(let x be the distance travelled)

          x = 126230400 x 299,772,458

             = 3.784 x [tex]10^13\\[/tex] km.

Therefore , The light travels 3.784 x 10 ^13 kilometers in 4 years .

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The complete question :

if light travels exactly 1 meter in 1/299,772,458 of a second, how many kilometers does it travel in 4.00 years? for this question,

1 year = 365.25 days.

The table that represents the proportional relationship would be table A. Option A

In this table we can see that in option A, there is a constant for which the values of the y are gotten. This is common on all of the values in A

For instance 2² = 4

3² = 9

4² = 16

0² = 0

The power of 2 is the constant that when applied on the values it gives the corresponding solution.

This shows the constant proportional relationship that is in existence between the values in x and the y solution

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The transformation represented by the figure is (c) translation

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

The figure

On the figure, we have the following

A figure and its translated image

When a shape is translated to form another, then the transformation is a translation

Hence, the transformation is translation

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Answer:

Equation is   x-5 = 37

Reason:

x = starting temperature

We start with x degrees, and decrease by 5 degrees.

We go from x to x-5

The x-5 is now 37 degrees

Therefore, we arrive at the equation x-5 = 37

To solve this equation, add 5 to both sides and you'll get x = 42

Nice work on getting the correct value of 42.

The solutions of the system of inequalities are the points on the purple region, one example of a solution is (-2, -2)

When we have a system of inequalties (so we have 2 or more inequalities) the solutions are the points (x, y) that are solutions of both inequalities at the same time.

Here we can see the graph of a system, such that the solution set of one of the inequalities is represented by the red shaded area, and the solution set of the other inequality is represented by the blue shaded area.

The solution set of the system is represented by the intersection between the areas, which is the purple area.

So any point on that region is a solution to the system, for example, the point (-2, -2) is a solution.

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The expression 4× 4 × 5 × 10 = 800 in the field of math.

Algebra is a branch of mathematics that is used to manipulate symbols and equations in order to solve problems. Algebra helps to solve problems involving unknown quantities and to develop relationships between different variables. It is a powerful tool that can be used to solve and analyze a variety of mathematical problems and equations.

Algebra can be used to solve equations, simplify expressions, and find solutions to linear and quadratic equations. Through algebra, we can also find the slope of a line, the area of a triangle, and the volume of a cube. Algebra is an invaluable tool that is useful in many areas of mathematics and science.

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The distance of Naudia from starting point based on distance travelled is 13 miles.

The distance travelled by Naudia and distance from starting point will form right triangle. Distance between Naudia and her final destination is the straight line or hypotenuse.

So, the expression will be -

Distance of South² + distance of East² = Distance from starting point

Distance form starting point = 2² + 3²

Distance form starting point = 4 + 9

Distance form starting point = 13 miles

Thus, the required distance is 13 miles.

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The mean height of the members of the football club is 163.4 to rounded to 1 decimal place.

The mean height It is calculated by summing up all the data values and dividing by the total number of data points. The mean can also be represented by the point at which the frequency polygon would balance if it were a physical object.

The values with their corresponding frequencies are:

height: 120 × frequency: 8 = 960

height: 140 frequency: 11 = 1549

height: 160 frequency: 17 = 2720

height: 180 frequency: 18 = 3240

height: 200 frequency: 10 = 2000

sum frequency = 64

sum of all data values = 10460

mean height = 10460/64

mean height = 163.4375

Therefore, the mean height of the members of the football club is 163.4 to rounded to 1 decimal place.

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Answer:

21v

Step-by-step explanation:

Since it is the same variable you would just add them!!

10+11=21

10v+11v+21v

Answer:

1.  5 inches in 2 days

2.  y = (5/2)x. where y is rainfall and x is days.

3.  Yes

4.  (5/2)

5.  2.5"/day

6.  37.5 Inches

Step-by-step explanation:

See attached worksheet

.

We should administer 2.05 ml/hr.

A sort of neurotransmitter and hormone is dopamine. It affects a variety of vital bodily processes, such as mobility, memory, rewarding pleasure, and motivation. Dopamine levels are linked to a number of neurological and mental health conditions.

To determine the ml/hr to administer, we first need to calculate the dose of dopamine in mg/kg/min. We can use the following formula:

dose (mg/kg/min) = 4 mcg/kg/min x 10^-3 (to convert from mcg to mg)

dose (mg/kg/min) = 0.004 mg/kg/min

Next, we need to calculate the total dose in mg/min. We can use the following formula:

dose (mg/min) = dose (mg/kg/min) x weight (kg)

dose (mg/min) = 0.004 mg/kg/min x 64 kg = 0.256 mg/min

Now we need to convert the dose from mg/min to ml/hr, using the following formula:

ml/hr = dose (mg/min) x weight (kg) / concentration (mg/ml) x 60 min/hr

ml/hr = 0.256 mg/min x 64 kg / 400 mg/250 ml x 60 min/hr

ml/hr = 2.048 ml/hr

To round to the nearest tenth, we will round 2.048 to 2.05 ml/hr. Therefore, we should administer 2.05 ml/hr.

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When a figure is rotated and reflected, the new figure will be congruent to the original one, but different coordinate axis. When a figure is translated, reflected and dilated the image will be similar, but the scales will be different.

The original figure we transform is the pre-image and after transformation it is called image. Rotation is the transformation of an image when it is rotated through the Centre of axis. Reflection creates a mirror image of the original figure/ pre-image. Translation means the image is moved to a certain distance in the coordinate axis. Dilation is making an image bigger or smaller, the sides will be in ratio and thee will be a scale factor.

So if a image is rotated, reflected and translated, there will be changes in the coordinate plane, but no change in the size of the image. During dilation the size is varied.

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(x,y) = (1, -1). Option (c) is the correct answer.

Given equations:

5x + 2y = 3   ..(1)

4x - 8y = 12   ..(2)

Solving using the elimination method:

so, 4x = 8y + 12 or x = 2y + 3   ..(3)

Now, substituting the x in equation(1) from equation(3)

so we get,

5(2y+3) + 2y = 3

10y + 15 + 2y = 3

12y = -12

y = -1

Putting the value of y in equation(3)

x = 2(-1) + 3 = 1

x = 1

Therefore, (x,y) = (1, -1)

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Answer: Option C, (-1,1)

Step-by-step explanation:

The expression of the statement is 3x² - 8

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

A mathematical statement

The mathematical statement is given as

Three times the square of a number minus eight

Represent the number with x

So, we have

Three times the square of x minus eight

Express as squares and numbers

This gives

3 * x² minus 8

So, we have

3x² - 8

hence. the expression is 3x² - 8

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Answer: Volume of a right prism = BH where B is the area of the base and H is its height.

So Volume = 16 × 12 = 192 cm^3

Step-by-step explanation:

The probability that the first bar Iesha selects will be lemon and the second will be raisin= 2/45.

What is probability ?

Probability can be defined as the ratio number of favourable outcomes and total number of outcomes.

Note this selection is done without replacement hence after each selection sample size will reduce

Given data,

Samples 3 chocolate chip bars,

2 peanut butter bars,

1 lemon bar, and

4 raisin bars

Sample size S= [3+2+1+4]= 10

Probability that first selection is lemon = 1/10

Probability that second selection is raisin = 4/9

Hence the probability that the first bar Iesha selects will be lemon and the second will be raisin= 1/10*4/9 = 4/90= 2/45

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The graph of a line passing through the points (2, -4) and (0, 0). The correct answer would be an option (A).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The table represents a linear relationship.

x: −1   0    1    2

y:  2   0  −2  −4

As per the points, the graph has been attached below

Here we can see that the shown graph of a line passing through the points (2, -4) and (0, 0)

So the attached graph shows this relationship.

Hence, the correct answer would be option (A).

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The box plot given by the number of students read 8 books is the centre quartile which is 5.

Three values called quartiles divide sorted data into four equal portions with the same amount of observations in each. One kind of quantile is a quantile.

Thus, for the stated question.

The box plot given by the number of students read 8 books is the centre quartile which is 5.

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The assertion that 997 is the largest 3-digit prime number is correct.

What is a prime number?

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. In other words, it is a number that is divisible by only 1 and itself. To determine if a number is prime, one common method is to check if any positive integer less than or equal to the square root of the number divides the number.

In the case of the assertion that 997 is the largest 3-digit prime number, we know that 997 is a 3-digit number (999 being the largest) and we can check if any positive integer less than or equal to the square root of 997 divides 997. Since 997 is a prime number, it is not divisible by any positive integer less than or equal to 31 (the square root of 997). Therefore, we can conclude that 997 is a prime number and the largest 3-digit prime number.

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The square root of 224 in long division is 14.96

The term square root in math is defined as  a factor of a number that, when multiplied by itself, gives the original number

Here we know that we need to find the square root of √224.

In order to solve this one we have to do the following steps,

Here we have to start dividing the digits from the right side into pairs of two by drawing a line on top of them. In the case of 224, then we have two pairs 24 and 2.

And then we have to find a number(z) whose square is ≤ 2.

Then the value of z will be 1 as 1 × 1 = 1 ≤ 2.

Here we get the value of quotient and the remainder as 1 and now we have to add the divisor z with itself and get the new divisor 2z (2).

And then we have to drag down the next pair and find a number (n) such that 2n × n ≤ 124 here we have the value of n comes out to be 4.

Finally we have to add a decimal in the dividend (224) and quotient (14) simultaneously.

Here we have to add 2 pairs of zero in the dividend after the decimal  and repeat the above step for the remaining three pairs of zero.

Complete Question:

Finale the square root of √224 and go step by step to reduce the radical.

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The weight of the hedgehog in grams is 281 grams

The first step is to determine the unit of conversion of pounds to grams.

1 pound = 453.592 grams

In order to convert the weight of the hedgehog to grams, multiply the unit of conversion by the weight of the hedgehog in pounds. Multiplication is the product of two or more numbers,

Weight of the hedgehog in grams = 0.62 x 453.592 grams = 281 grams

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Answer:

there is 30 ways

Step-by-step explanation:

There are 6 people who can be president x 5 other people who can be vice president. so there is 30 ways

The statement that is true about the 2 functions, in which the relationship between the x and y-values in the table of values for both functions is a linear relationship is presented as follows;

A linear relationship is a relationship that when plotted on the coordinate plane, produces a linear graph.

The first difference of the y-values in the data contained in the table for Function A are the same and equal to 6, therefore, the data for Function A is a linear relationship.

The slope of the graph of the values in Function A, [tex]m_A[/tex] is found as follows;

Slope of Function A, [tex]m_A[/tex] = (18 - 12)/(3 - 2) = 6

The slope of the graph of A is 6

The equation representing the relationship in function A in point-slope form is therefore;

y - 12 = 6·(x - 2)

y - 12 = 6·x - 12

y = 6·x - 12 + 12 = 6·x

The equation in slope-intercept form, y = m·x + c, where c is the y-intercept is therefore; y = 6·x

The value c in the equation is 0 (c = 0). The y-intercept intercept of the graph of Function A is therefore, c = 0

The y-intercept of the graph of Function A is 0

The first difference of the data in the table of Function B is also a constant

The slope of Function B, [tex]m_B[/tex] = (5 - 1)/(1 - 0) = 4

The slope of the graph of B is 4

From the values in the table, the y-value at the y-intercept, which is the point where x = 0, is y = 1

The y-intercept of the graph of Function B is 1

The true statement is therefore;

The y-intercept of the graph of A is less than the y-intercept of the graph of B

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