Ms. Michaels surveyed her class on whether they preferred free time at the beginning of class or at the end of class. If the ratio of students who prefer free time at the beginning of class to students who prefer free time at the end of class is 12 over 19, what does the ratio 12 over 19 represent?

A19 students prefer free time at the beginning of class, and 12 students prefer free time at the end of class.
B 19 students prefer free time at the beginning of class, and 31 students prefer free time at the end of class.
C 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.
D 31 students prefer free time at the beginning of class, and 12 students prefer free time at the end of class.

The scale factor that was used in the dilation is 1.6.

A change called dilation lets you resize an object. Dilation is a method for enlarging or contracting objects. The result of this alteration is a picture with the exact same shape as the original. The form, however, has a size difference.

Now,

Scale factor = Dimension of the new shape/Dimension of the original shape

We have △R′S′T′ is the image of △RST under a dilation through point C. Also, given that RS=5 and R′S′=8.

So, the scale factor is,

Scale factor = Dimension of the new shape/Dimension of the original shape

Scale factor = R′S′ / RS

                    = 8/5

                     = 1.6

Hence, the scale factor that was used in the dilation is 1.6.

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Answer:

x ≈ 41.7 ° (a)

Step-by-step explanation:

b² = a² + c² - 2ac × cosβ

~~~~~~~~~~~

25² = 32² + 37² - 2(32)(37)cosx

625 = 2,393 - 2,368 cosx

cosx = [tex]\frac{-2393+625}{-2368}[/tex] ≈ 0.74662162

x ≈ 41.7 ° (a)

Answer: x= -9

Step-by-step explanation:

Add like terms excluding x in: x+59+80+50=180

= x+189=180

[Transposing 189 to RHS]    x=180-189

So x= -9

Each share of the tech company cost is $1 and 18 more shares can Josh buy with the remainder of his savings.

Given:

Josh spends of his savings to buy 48 4/5 shares in a cech company. He has $18 left.

Let x be the total savings

4/5 x = 48

x = 48*5/4

= 240/4

= $60

= 4/5*60

= 240/5

= $48.

Part A:

The cost of each share of the tech company = 48/48

= $1

Part B :

He has 18 so he can buy =18*1

= 18 shares .

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Answer:

Step-by-step explanation:

 y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis)

try this it works

The value of w in Angle  (w + 1)°  is 88

Given,

Angle (w + 1)°

Angle 91°

We have to find the value of w.

Here,

Linear pair of angles;

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.

Then,

Here the given angles are linear pair.

So,

(w + 1)° + 91 = 180

w + 1 + 91 = 180

w + 92 = 180

w = 180 - 92

w = 88

Then,

Angle (w + 1)° = 88 + 1 = 89°

Therefore,

The value of w in Angle  (w + 1)°  is 88

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a) After 1 day, the revenue for each item is the same.

b) Graph is shown in the attachment.

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

M(d) = 2x² + 8x - 4

R(d) = 2x + 4

a) Find x by taking y=M(d)=R(d). ( same revenue=y)

     y= 2x² + 8x - 4

     y= 2x + 4

This shows that right-side expressions are equal.

 2x² + 8x - 4 = 2x + 4

 2x² + 8x - 4 - 2x - 4=0

2x² +6x-8=0

Find the factors

2(x-1)(x+4)=0

x-1=0,  x+4=0

x= 1, x=-4

consider positive value for days

So, after 1 day, the revenue for each item is the same

b)  The equations:

 y= 2x² + 8x - 4

     y= 2x + 4

By taking some random values for x and finding the corresponding y values, we get the ordered pairs in the form of (x,y).

By plotting and joining those points, we get the graph as shown in the attachment.

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Answer: y=-2x+7

Step-by-step explanation:

we know that equation is y=mx+b

b=y intercept

x=the x coordinate

m=slope

y=y coordinate

then you can just fill it in from there . hope this helps

The expression we get from the given functions h for all real numbers x.

h(-3)= 8

Given that,

All real numbers x are defined by the functions h.

h(x)= -x+5

We have to find the expression

h(-3)

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.

Take the functions,

h(x)= -x+5

Now, Take

h(-3) =-(-3)+5 = 3+5= 8

Therefore, The expression we get from the given functions h defined for all real numbers x.

h(-3)=8

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The parabola has a minimum value of 5.75.

From the question, we have

f(x)=x^2-x+6

a=1, b=-1, c=6

Δ=b^2-4ac

=1-24

=-23<0

So f(x)=0 has no solution.

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

f(1/2)=1/4-1/2+6

=23/4  is the minimum

=5.75

The parabola has a minimum value of 5.75.

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer:

The x-intercept is the point where the graph crosses the x-axis; it can be found by setting y = 0 and solving for x.

The y-intercept is the point where the graph crosses the y-axis; it can be found by setting x = 0 and solving for y.

1) g(x) = (x + 5)⁴

2) f(x) = 7 - x⁴

3) h(x) = ¼(x - 3)⁴

The graphs are labeled below.

Answer:

The average rate of change is 2

Step-by-step explanation:

First set divide your data into 2 sets of separate data:

Independent Data= Day 3        

Dependent Data   = 10 points

Independent Data= Day 6

Dependent Data   = 16 points

Then subtract your two independent data: 6-3=3

Then subtract your two dependent data:  16-10=6

Next divide: difference in dependent/ difference in independent

6/3=2

So, your rate of change is 2.

Answer:

1

Step-by-step explanation:

3(2)-5/4(4)

6-20/4

6-5

1

Answer:

========================

We observe on the graph that:

All the above helps us to conclude that:

Answer:

Reflection through the x-axis, f(x) → -f(x).

Step-by-step explanation:

On comparison of the dotted red line with the solid blue line, it is apparent that the x-coordinates do not change, yet the y-coordinates are negatives of each other.

This suggests a reflection in the x-axis.

(Note: If the function was reflected in the y-axis, the y-coordinates would not change, yet the x-coordinates would be negatives of each other).

Mapping rule for reflection in the x-axis:  

Therefore, as y → -y then f(x) → -f(x).

So the correct answer that describes how the dotted line relates to the solid line f(x) is:

Answer:

1.9

2.3

3.6

4.5

5.20

Step-by-step explanation:

hope it helps

The expanding the expression y^2 - 3y^3 x^-1) 2m^0 y^-2 using distributive property is 2y² + 1 - 6y³ + 2x⁻¹ + x⁻¹y⁻²

We need to expand the expression (y² - 3y³ + x⁻¹) (2m⁰ + y⁻²)

The distributive property allows to multiply a sum by multiplying each term separately and then add all of the products together.

y²(2m⁰ + y⁻²) - 3y³(2m⁰ + y⁻²)  + x⁻¹(2m⁰ + y⁻²)

2(1)y² + y²⁻² - 3y³2(1) - 3y³⁻² + x⁻¹2(1) + x⁻¹y⁻²

2y² + 1 - 6y³ + 2x⁻¹ + x⁻¹y⁻²

Therefore, the expanding the expression y^2 - 3y^3 x^-1) 2m^0 y^-2 using distributive property is 2y² + 1 - 6y³ + 2x⁻¹ + x⁻¹y⁻²

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The volume of the jar is 1130.4 cubic inches and the number of marbles that can fit is 56.

In geometry, it is defined as a three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

[tex]\rm V = \pi r^2 h[/tex]

It is given that:

A cylindrical jar has a radius of 6 inches and a height of 10inches.

The volume:

V = π(6)²(10)

V = (3.14)(6)²(10)

V = 1130.4 cubic inches

Number of marbles = 1130.4/20 = 56.52 = 56 marbles

Thus, the volume of the jar is 1130.4 cubic inches and the number of marbles that can fit is 56.

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The function for motorboat's distance from the shore is y = -4x + 50.

A function is a formula, rule, or law that specifies how one variable (the independent variable) and another variable are related. The linear equation is of the form Ax+By+C=0.

Where A and B are the coefficient and C is the constant.

After 9 minutes, boat is 14 km from the shore, so finding the rate of change,

Rate of Change [tex]=\frac{14-50}{9}\\[/tex]

[tex]=\frac{-36}{9}\\ =-4[/tex]

So, the rate of change of distance is 4 km / minutes.

Now, finding the function,

The function for the distance of motorboat from the shore will be,

y = -4x + 50

Where y will be the final distance and x is the minutes.

Therefore, the function for motorboat's distance from the shore is y = -4x + 50.

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It takes them approximately 1.8 hours to paint the house together

Given,

Sam can paint a house in 5 hrs.

and, Gary can do it same work in 3 hrs.

To find the how long it will take the two working together?

Sam can paint a house in 5 hours. This means that Sam's unit rate of working is 1/5

Gary can paint the same house in 3 hours.

This means that Gary's unit rate of working is 1/3

If they work together, it would take them lesser time because they are working simultaneously. This means that their unit rates are additive. Combining their unit rates, it becomes

1/5 + 1/3 = 8/15

Assuming that if they work together, it will take them t hours. Therefore, Their unit rate of working will be 1/t.

Therefore,

8/15 = 1/t

8t = 15

t = 15/8  = 1.875

Hence, It takes them approximately 1.8 hours to paint the house together.

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Answer:

y = x + 2

Step-by-step explanation:

Use any two points.

For example, let's use (-3, -1) and (1, 3).

First, we find the slope.

slope = m = (-1 - 3)/(-3 - 1) = -4/(-4) = 1

We have slope = m = 1.

Now we use the equation:

y = mx + b

We plug in the slope we found above.

y = 1x + b

y = x + b

Now we use one of the given points to find b.

We'll use point (1, 3).

3 = 1 + b

b = 2

Now that we know m and b, we write the equation:

y = x + 2

Answer:

h(2) = 0

Step-by-step explanation:

1) 2 * 2 = 4

2) 4 * 3 = 12

3) 5 * 2 = 10
4) 12 - 10 - 2 = 0

The time taken for 14g of the radioactive isotope to remain is 25.70 years.

We know that the half life is the time that it would take for us to have only half of the number of the original radioactive isotopes in the sample still remaining in the sample.

We have the following information;

Half life of the sample = 11 years

Amount of the sample initially present = 70 grams

Amount of the sample after time t = 14 grams

Given that;

N/No = (1/2)t/[tex]t_{\frac{1}{2} }[/tex]

N = amount of radioatve isotpe at time t

No = amount of radioactive isotope initially present

t = time taken

[tex]t_{\frac{1}{2} }[/tex] = half life

14/70 = (1/2)^t/11

0.2 = (1/2)^t/11

ln 0.2 = t/11 ln0.5

t/11  = ln 0.2/ ln0.5

t = 11 *  ln 0.2/ ln0.5

t = 11 * (-1.61/-0.69)

t = 25.70 years

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Answer: 2.5

Step-by-step explanation:

got it right

The amount of money that Malachy get is £123 .

In the question ,

it is given that ,

£410 is divided between Gordon, Malachy and Paul .

also given that Malachy gets three times as much as Paul ,

let the amount that Paul get = x .

So , the amount that Malachy get = 3x

it is given that Gordon gets twice as much as Malachy ,

that means , the amount that Gordon get = 2(3x) = 6x

given the total amount is £410 ,

So, equation representing the total amount is

x + 3x + 6x = 410

4x + 6x = 410

10x = 410

x = 410/10

x = 41

So , the amount that Paul get = £41 ,

amount that Malachy get = 3(41) = £123

amount that Gordon get = 6(41) = £246

Therefore ,  The amount of money that Malachy get is £123 .

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Answer:

x = 7

x = 2

√ 3x − 5 = x − 3

or

3x − 5 = ( x − 3 ) 2

or

3x − 5 = x 2 − 6x + 9

or

x 2 − 9x + 14 = 0

or

x 2 − 7x − 2x + 14 = 0

or

x(x − 7) − 2(x − 7) = 0

or

(x − 7) ( x − 2) = 0

or

x − 7 = 0

or

x = 7

Ans

1

or

x − 2 = 0

or

x = 2

Ans

2

The average for the price of the stock for the end of day 7 is 57.28

Given,

The stock of 8 days;

Day 1 - 62. 00

Day 2 - 56. 00

Day 3 - 50. 00

Day 4 - 60. 00

Day 5 - 59. 00

Day 6 - 55. 00

Day 7 - 59. 00

Day 8 - 63. 00

We have to find the average for the price of the stock for the end of day 7.

Here,

Average = Total sum / Number

Then,

Average =  (day 1 + day 2 + day 3 + day 4 + day 5 + day 6 + day 7) / n

= (62 + 56 + 50 + 60 + 59 + 55 + 59) / 7

= 401/7

= 57.28

Therefore,

The average for the price of the stock for the end of day 7 is 57.28

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Rewriting the expression |3r-15| without using absolute value bars gives

3r < 15 for r < 5

Absolute value do not give negative values it gives only the positive value

The given expression is |3r-15|

|3r - 15| < 0

|3r| < |-15|

3r < 15

If r < 5 then  say 4

|3r - 15|

|3 * 4 - 15|

|12 - 15|

|-3| = 3

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The probability of rolling a yahtzee on the first round is calculated to be  6/46656 or 1/7776

Given that,

A dice is rolled for one time .

To find : The probability that a yahtzee will be rolled on the first round.

Your first die will be one of the 6 possible results 6/6 times

That will match on the second die 1/6th of the time.

The third, fourth, and fifth dice all share this characteristic.

Multiplying the all probabilities that the first die will be a yahtzee which is

P( yahtzee will be rolled on the first round) = Product of all possible outcomes of each time a dice is rolled.

6/6*1/6*1/6*1/6*1/6*1/6=6/46656 or 1/7776

Therefore, probability that a yahtzee will be rolled on the first round is 1/7776.

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Answer:

It does not have an answer because the square root of any number cannot be negative

Yes, the equation √z= -7 does not have a solution.

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.

here, we have,

given that,  the equation √z= -7

now, we know, that the equation √z= -7 does not have a solution.

because, we know,

It does not have an answer because the square root of any number cannot be negative.

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