The ratio of boys to girls in a class is 2:3 if there are 48 pupils in the class.How many boy and girls are there?

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The number of quarts in 12 L is 12.684 qt.

Given that, 12 L to qt.

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

Here,

There are 1.057 quarts in a liter, and there are 0.946 liters in a quart.

Now, 12 L=12×1.057

= 12.684 qt

Therefore, the number of quarts in 12 L is 12.684 qt.

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a. The numeric value at Thursday -> x = 4 is of 32 degrees, which agrees with the graph.

b. A numeric value of 35 degrees Fahrenheit is obtained on Monday and on Thursday, also agreeing with the graph.

To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

In this problem, the function is defined as follows:

f(x) = 3x² - 18x + 56.

Giving the temperature in degrees Fahrenheit in x days after Sunday.

The day that represents Thursday is given by:

x = 4.

Hence the temperature is the numeric value of the function at x = 4, replacing both instances of x on the function by 4, hence:

f(4) = 3(4)² - 18(4) + 56 = 32 ºF.

Which agrees with the graph, as the Thursday's bar is a value slightly above 30, which can be interpreted as 32.

The numeric value is of 35 when:

3x² - 18x + 56 = 35

The solutions to the quadratic equation are:

x = 1.6, x = 4.4.

Hence the days are:

Monday and Thursday.

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Answer:

the perimeter is 129 inches

Step-by-step explanation:

4x² + 8x + 3x² - 5x + 20 + 7x + 30 + 31 =

= 7x² + 10x + 81

x = 2

= 7(2²) + 10(2) + 81

= 7(4) + 20 + 81

= 28 + 101

= 129

Answer: 129 in.

The image of (12, -12) after a dilation by a scale factor of 1/4 ​centered at the origin would have these coordinates (3, -3).

In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object based on the scale factor applied, but not its shape.

Next, we would dilate the coordinates of the preimage (12, -12) by using a scale factor of 1/4 centered at the origin (0, 0) as follows:

Coordinate A (12, -12) → Coordinate A' (12 × 1/4, -12 × 1/4) = Coordinate A' (3, -3).

In conclusion, the coordinates of the image after a dilation by using a scale factor of 1/4 are (3, -3).

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Answer:

-3/8

Step-by-step explanation:

3(x+6)+5(x-3)

3x+18+5x-15

8x+3

8x=-3

x= -3/8

Using prime factorization, the LCM and GCF of numbers are

1) For 46 and 4

GCF = 2

LCM = 92

2) For 2 and 34

GCF = 2

LCM = 34

3) For 32 and 4

GCF = 4

LCM = 32

A natural number other than 1 with just the number 1 and itself as factors is known as a prime factor. Actually, 2, 3, 5, 7, 11, and so on are the first few prime numbers. For numbers, we may now also employ what is known as prime factorization, which really involves utilizing factor trees.

When a number is expressed as the product of its prime factors, this is known as prime factorization.

1) The factors of the numbers are

46 = 2 × 23

4 = 2 × 2

GCF = 2

LCM = 2 × 2 × 23

= 92

2) The factors of 34 are

34 = 2 × 17

GCF = 2

LCM = 2 × 17

=34

3) The factors of the numbers are

32 = 2 × 2 × 2 × 2 × 2

4 = 2 × 2

GCF = 2 × 2

= 4

LCM = 2 × 2 × 2 × 2 × 2

= 32

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Answer:

A the scale factor is 2 from LMN to CDF (or 1/2 from CDF to LMN).

Step-by-step explanation:

shadows are similar, when they have the same angles, abd if there is one scale factor for all sides and other lengths from one shape to the other.

8×2 = 17

15×2 = 30

17×2 = 34

The vertex is (-2, 11), then the vertex form of the quadratic is:

f(x) = 5*(x + 2)^2 - 11

A quadratic equation with a leading coefficient a and a vertex (h, k) can be written in vertex form as:

y = a*(x - h)^2 + k

And for a quadratic equation of the form:

y = a*x^2 + b*x + c

The vertex is at:

h = -b/2a

In this case, our equation is:

f(x) =5x^2 + 20x + 9

Then:

h = -20/2*5 = -2

Evaluating in x = -2 we get:

f(-2) = 5*(-2)^2 + 20*-2 + 9

f(-2) = 5*4 - 40 + 9

f(-2) = 20 - 40 + 9 = -20 + 9 = -11

The vertex is (-2, -11), and the leadin coefficient is a = 5, then the vertex form is:

f(x) = 5*(x + 2)^2 - 11

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Answer:

9x+28

Step-by-step explanation:

7(2x+4)_5x

14x+28-5x

9x+28

The speed of the current is 9 miles per hour

Given that: the motorboat maintained a constant speed of 11 miles per hour relative to the water in going 10 miles upstream and then returning.

Total time = 5.5 hours

Let s = speed of the current

speed downstream relative to land =  11 + s

speed upstream relative to the land = 11 - s

speed = distance/time

time = distance/speed

upstream time + downstream time = total time

10/11-s  + 10/11+s = 5.5      (find LCM of 11-s and 11+s)

10(11+s) + 10(11-s) /(11-s)(11+s)  = 5.5

110+10s+110-10s /(11-s)(11+s)  = 5.5

220 = 5.5(11-s)(11+s)

220 = 5.5(121 - 11s + 11s - s²)

220 = 5.5(121 - s²)

220 = 665.5 - 5.5s²

5.5c² = 665.5 - 220

5.5c² = 445.5

s² = 445.5/ 5.5

s² = 81

s = √81 = 9

Therefore, the speed of the current is 9 miles per hour

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Answer:

1/3

Explanation:

Imagine you repeat the experiment 100 times.

It is expected that half of the times (50) you take the fair coin and half of the times (50) the trick coin.

When you take the fair coin, half of the times you get heads, that is 25 times from 100 you “get the fair coin AND you get heads with the fair coin”.

When you take the trick coin, all the times you get heads, that is 50 times from the original 100 you “get the trick coin AND you get heads with the trick coin”.

In total, it is expected you get heads 75 times. And from those, 50 times will be with the trick coin and 25 times with the fair coin.

Now, if you get one of those at random, what’s the likelihood it was the fair coin?

Well, you have 25 cases it was the first coin and 50 cases it wasn’t, so it is 25 from a total of 75 and that is 25/75 = 1/3. That is, about 33.33%

Also, with probability theory:

Bayes’ Theorem:

P(B|A) = P(A ∩ B) / P(A)

P(A|B) = P(A ∩ B) / P(B)

So: with just the definitions I prove Bayes:

P(B|A) = P(A|B) * P(B) / P(A)

In our case:

P(Fair| Heads) = P(Heads|Fair) * P(Fair) / P(Heads)

p = P(Fair | Heads) = 0.5 * 0.5 / P(Heads)

What is P(Heads) ??

We can apply this:

Heads = (Heads ∩ Fair) U (Heads ∩ Trick)

And those in the union are disjoint (mutually exclusive), so:

P(Heads) = P(Heads ∩ Fair) + P(Heads ∩ Trick) =

= P(Heads|Fair) * P(Fair) + P(Heads|Trick) * P(Trick) =

= 0.5 * 0.5 + 1.0 * 0.5 = 1/4 + 1/2 = 3/4

Then:

p = P(Fair | Heads) = 0.5 * 0.5 / P(Heads) = 1/4 / (3/4) = 1/3

By graphing, the solution of the system of equations is: (-4, 1).

The solution to the system of equations can be solved by graphing both lines of each equation on a coordinate plane, then find the coordinates of the point where both lines intersect each other.

Given the following equations:

y = 1/4x + 2

y = -2x - 7

The graph for y = 1/4x + 2 will intercept the y-axis at 2 and also has a slope of 2. The line for this equation is the red line.

The graph of y = -2x - 7 will also have a slope of -2. Its y-intercept would be -7. The line of the equation is the blue line.

The graph below shows the lines of both equations which intersect at (-4, 1), The solution is, (-4, 1).

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Answer: 1253.33

Step-by-step explanation:

The BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3 is 2 so option A is correct.

Given:

1 ≤ x ≤ 3

we know x is between 1 and 3 so the best estimate is 2 even though the answer could also be 3 but that will be skewed.

1 ≤ 2 ≤ 3 is the best estimate.

Therefore the BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3 is 2 so option A is correct.

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Answer:

Any Integer less than 20 ( ex. 19 , 18 , 17 , 16 , ........)

Step-by-step explanation:

Solve the Inequality to find the Integers that satisfy the Inequality

x - 4 < 16

add 4 for both terms

x - 4 + 4 < 16 + 4

x < 20

So any Integer less than 20 will make the Inequality True

Answer:

Step-by-step explanation:

We know that:

Then 6 gallons is:

Add 3 quarts to get total:

Answer:

27 quarts

Step-by-step explanation:

Now we have to,

→ find how many quarts does 6 gallons 3 quarts of paint measure.

Formula we use,

→ 1 gallon = 4 quarts

Now the required solution will be,

→ (6 × 4) + 3

→ 24 + 3

→ 27 quarts

Hence, the answer is 27 quarts.

Earned income is said to be $35,000, Base tax amount at that level is $4386, The amount over $31850 is  $3150, Line 3 is multiplied by 25% is $787.50, The sum of lines 2 and 4 is $5173.50 and This amount divided by 12 is $431.13.

Two or more expressions with an Equal sign is called as Equation.

Given,

The given Federal Income Tax Table Single: Over But not over The tax is $0 $7,825 10% of the amount over $0 $7,825 $31,850 $788 + 15% of the amount over $7,825 $31,850 $77,100 $4,386 + 25% of the amount over $31,850 $77,100 $160,850 $15,699 + 28% of the amount over $77,100 $160,850 $349,700 $39,149 + 33% of the amount over $160,850 $349,700 And Over $101,469 + 35% of the amount over $349,700

Earned income is said to be $35,000.

Base tax amount at that level is $4386.

The amount over $31850 is $35000-31850 = $3150

Line 3 is multiplied by 25%: $3150×0.25 = $787.50

The sum of lines 2 and 4 is $4386 +787.50 = $5173.50

This amount divided by 12 is ... $5173.50/12 ≈ $431.13

Hence, Earned income is said to be $35,000, Base tax amount at that level is $4386, The amount over $31850 is  $3150, Line 3 is multiplied by 25% is $787.50, The sum of lines 2 and 4 is $5173.50 and This amount divided by 12 is $431.13.

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An equation of this line shown in the graph in slope-intercept form is y = 0.75x + 5 or 3x/4 + 5.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

From the graph of this line, we have the following parameters:

Point (x, y) = (60, 50)

Point (x, y) = (20, 80)

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (80 - 50)/(20 - 60)

Slope, m = 30/40

Slope, m = 3/4 or 0.75

At point (60, 50), the intercept is given by:

y = mx + c

50 = 0.75(60) + c

50 = 45 + c

Intercept, c = 50 - 45

Intercept, c = 5.

Now, we can write the equation of this line in slope-intercept form as follows:

y = 0.75x + 5 or 3x/4 + 5.

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The best interpretation of the function v(2) = 8 is that the volume of a cube with side length of 2 units is 8 cubic units

Function notations are the representation of a function using expressions such as g(x), f(x), etc

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

v(2) = 8

From the question, we have the following representation

v(s)

This means that the volume of a cube of side length s is v(s)

When the above function is compared to v(2) = 8, we have the following comparison

s = 2 and v(s) = 8

This means that a cube of side length 2 has a volume of 8

The above represents the best interpretation of v(2) = 8

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Kurt spent a total amount of $22.68 a month on movie streaming services.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, or operations such as multiplication and division.

These operations are used from the unit rates, as when we have an amount over some time, then the amount per unit of time is the total amount divided by the total time.

We have been given the important parameters are;

The total amount = is $96.39.

The time is a mixed number, 4 and 1/4 months, hence it will be 4.25 months,

Therefore, his monthly spending is given by the unit rate as;

96.39/4.25 = $22.68 a month.

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The distance to the point is less than c=10, so the point is inside the circle.

Given that, (a, b) = (5, –2) and c = 10.

The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively. For example, if the relation is, R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then:

Domain = the set of all x-coordinates = {1, 2, 3, 4}

Range = the set of all y-coordinates = {2, 3}

Part A:

Use of the Pythagorean theorem gets you to the equation for a circle in essentially one step:

Sum of squares of sides = square of hypotenuse

(x -a)²+(y -b)² = c² circle centered on (a, b) with radius c.

Part B:

The circle will be defined for values of x in the domain f ± c, and for values of y in the range b ± c.

domain: 5 ± 10 = [5, -5]

Range: -2 ±10 = [8, -11]

Part C:

The distance from point (10, 2) to (a, b)=(5, -2) is

c² = (10-5)² +(-2-2)²

c² = 25+16

c² = 41

c=√41

c=6.4

The distance to the point is less than c=10, so the point is inside the circle.

Therefore, the distance to the point is less than c=10, so the point is inside the circle.

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The probability that the sample proportion of the number of people using the courier will differ from the population proportion by greater than 0.03 is 0.0504

The probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of variables

mean, μ  = p = 0.05

sample size, n = 202

standard deviation, σ

= √{(p(1 - p)) / n}

= √{(0.05(1 - 0.05)) / 202}

= √{(0.05 * 0.95) / 202}

= 0.01533

The probability

differ from the population proportion by less than 3%

|X - 0.05| > 0.03

X < 0.02 OR X > 0.08

P(z < 0.02) + P(z > 0.08 )

z score for z < 0.02

z = (0.02 - 0.05) / 0.01533

= -1.9569

p value for z < -1.9569 = 0.02518

z score for z > 0.08

z = (0.08 - 0.05) / 0.02196

= 1.9569

p value for z > 1.9569 = 1 - 0.9748 = 0.02518

The probability required = 0.02518 + 0.02518 = 0.0504 = 5.04%

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The quantity of sugar required to make 78 cookies is 8.1 cups.

Given that, you need 1.25 cups of sugar to make 1 dozen cookies.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here,

The quantity of sugar to make 1 cookie

= 1.25/12

= 0.10417

The quantity of sugar to make 78 cookies

= 78×0.10417

= 8.1 cups

Therefore, the quantity of sugar required to make 78 cookies is 8.1 cups.

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-4 2/3 ,-3 2/3, -1 2/3 2/3

Step-by-step explanation:

5.

xnew = 205 = 2×xold + 5

200 = 2×xold

xold = 100

the old city machine can produce 100 copies per hour.

6.

2 cups of milk relate to 6 1/4 cups of flour.

such recipes represent a direct dependency of one variable on the other. one variable is always the other variable multiplied by a constant factor.

m = cups of milk

f = cups of flour

m = n×f

2 = n×(6 1/4) = n×(6×4 + 1)/4 = n×25/4

8 = 25n

n = 8/25

now, f = 43 3/4 = (43×4 + 3)/4 = 175/4

so,

m = 8/25 × 175/4 = (8×175)/(25×4) = 2×7 = 14

you will need 14 cups of milk.

Answer:

Step-by-step explanation:

I think the slope and the y is not 1/x because 2 is not part of the slope, im not sure

Answer:

k=44

Step-by-step explanation:

1 + 2 + 3 + 4......+ k = 990

Arithmetic sequence  with  d = 1    a1 = 1

1   +   1+ 1    +   1 +2 ...... 1+ (k-1) = 990    

ak = a1 + (k-1)     <====formula for sequence

Sum of a sequence formula =   Sk = k ( a1+ak)/2

990 = k ( 1 + (1 + k-1) /2

1980 = k^2 + k

 k^2 + k - 1980 = 0       Use quadratic formula   a = 1   b = 1   c = - 1980

       to find k = 44