On a​ team, 3 girls and 2 boys scored a total of 27 points. The difference between the number of points scored by the 3 girls and the number of points scored by the 2 boys is 15. Each girl scored the same number of points, and each boy scored the same number of points. Find the number of points scored by each girl and each boy.

(a)The class width = 3

(b) The class midpoint of the first class = 51

(c) The class boundaries of the first class =  (49.5, 52.5)

Consider the frequency distribution in the following image.

We know that in  frequency distribution the class width is nothing but the distance between the lower limits of consecutive classes.

Whereas the range is the difference between the maximum and minimum data entries.

The smallest number is 50, and the largest is 62.

So the range is 62 - 50 = 12

We know that the formula for the class width:

Class width= upper limit – lower limit +1

So, the class width = 52 - 50 + 1

                               = 3

The formula for the midpoint of each class:

midpoint = (lower limit of class + upper limit of class)/2

Let us assume that m be the midpoint of the first class.

Using above formula of midpoint:

m = (50 + 52)/2

m = 51

We know that the class boundaries are nothing but the end points of an open interval which contains the class interval.

So, the class boundaries of the first class = (49.5, 52.5)

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The length of the base is 2√15 units. The median of an isosceles triangle divides the triangle into two equal parts.

What is an isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be specified as having exactly two equal-length sides or at least two equal-length sides, with the latter definition including the equilateral triangle as an exception.

A median in a triangle is a line that runs from one corner (or vertice) to the centre of the other side. Triangle congruence makes it easy to demonstrate an isosceles triangle's property that the median to the base is perpendicular to the base.

According to the Pythagorean theorem,

AD² + BD² = AB²

7² +  BD² = 8²

BD² = 64 - 49

BD² = 15

BD = √15

The median divides the base into two equal parts.

The length of the base is 2√15.

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A graph is said to represent a function if a vertical line drawn anywhere on the graph of a relation only intersects the graph once by  Slope of 3.75b + 5: 3.75

Example:

F(b) = 3.75b + 25

Axis interception points of 3.75b + 25:

X intercepts :(-20/3).

Y intercepts :(0.25)

Slope of 3.75b + 5:

3.75.

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The two previous terms of 248 are 64 and 18.

A term-to-term rule is a rule that will describe calculating the following terms of a sequence given by the previous term.

In the given problem, the rule is to subtract 2 and multiply by 4.

Considering that the third term is 248. we can utilize the rule to figure out the subsequent term.

248 = (4 * (x - 2))

248 = 4x - 8

256 = 4x

x = 64

So the subsequent term is 64.

To find the initial term, we can utilize a similar rule once more

64 = (4 * (x - 2))

64 = 4x - 8

72 = 4x

x = 18

So the initial term is 18.

Therefore, the two previous terms of 248 are 64 and 18.

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Answer:

2048

Step-by-step explanation:

Find out what [tex]16^{3}[/tex] is:

16x16x16 =

4096.

Now lets divide it by 2:

4096/2 =

2048.

2048 would be your answer to your problem.

There was a 125% change in the price of the house.

The answer can be deduced to be above 100% because the revised price represented an increase from the initial 100,000.

Tom's house cost $100000 in the year 2000.

In 2008 he sold his house for $125000.

Whatever the case, in order to solve this problem,

you must divide 100,000 by 125,000 to discover the answer. 125,000/100,000=1.25.

Then 1.25 can be converted to 125%.

So, There was a 125% change in the price of the house.

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Answer:

Step-by-step explanation:

honolululuulu

The volume of file cabinet is equal to 26 / 3 cubic feet.

The statement let us infer that file cabinet has the form of right prism with rectangular base, whose formula is shown below:

V = b · h · l

Where:

If we know that b = 2 1 / 6 ft (13 / 6 ft), h = 1 1 / 2 ft (3 / 2 ft) and l = 2 2 / 3 ft (8 / 3 ft), then the volume of the file cabinet is:

V = (13 / 6 ft) · (3 / 2 ft) · (8 / 3 ft)

V = 26 / 3 ft³

Statement present an anomalous character "2", correct statement is introduced below:

A locker measurement at the bottom as 2 1 / 6 ft wide, 1 1 / 2 ft high and 2 2 / 3 ft long.

Picture is missing but question can be solved by inferential approach.

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The value of x from the given proportion is given as x = 10 after scalling both side of the equation.

A ratio is a divisional comparison of two quantities, and a proportion is the equality of two ratios. A ratio is often read as "x is to y" but may also be written as "x: y" or "x/y." The proportion equation, on the other hand, states that two ratios are equal.

The equality of two ratios is referred to as proportion. There is never a difference between two comparable ratios. The ratio sign (::) is used to express proportions, which aid in solving problems with ambiguous amounts. To put it another way, a percentage is an equation or a claim that shows the equality of two ratios or fractions. If a: b = c: d, then four non-zero values, a, b, c, are said to be in proportion. Let's now compare the two ratios, 3:5 and 15:25. In this case, 3:5 and 15:25 may both be written as 3:5 = 3/5 and 0.6, respectively. We may argue that these two ratios are proportionate because they are both equal.

There are two types of proportions :

The proportion is given by ,

x/12 = 15/18

⇒ multipling both side with 12 we get ,

x = (12*15)/18

⇒ x = 5 * 2 = 10

The value of x from the given proportion is given as x = 10.

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The value of x from the given proportion is given as x = 10 after scalling both side of the equation.

What is meant by equation?

There are two types of proportions :

==>Direct Proportion

==>Inverse Proportion

The proportion is given by ,

x/12 = 15/18

⇒ multipling both side with 12 we get ,

x = (12*15)/18

⇒ x = 5 * 2 = 10

The value of x from the given proportion is given as x = 10.

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The simplified form of the expression 4hk/20h²k is 1/5h.

Given the expression in the question;

4hk / 20h²k

To simplify, first cancel out the common factor of 4 and 20.

4hk / 20h²k

4(hk) / 4(5h²k)

hk / 5h²k

Next, cancel out the common factor of h and h²

h(k) / h(5hk)

k / 5hk

Now, cancel out the common factor of k

k(1) / k(5h)

1/5h

Therefore, the simplified form is 1/5h.

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Yes, 3 apple pies divided among 5 people

Now, According to the question:

"Information available from the question"

Apple shared equally

Portion of each person = 3/5

A possible way that shows how the pies were shared.

7/5 is the ration of the pie to each individual (Jerry and his friends).

Provided that each individual got equal ration....

The ration can be divided into two

The numerator = 3

The denominator = 5.

The numerator shows the number of things that were shared.

Hence, 3 apples were shared.

The denominator shows the number of people involved.

Hence, 5 people were involved.

So, we can conclude that 3 apples were divided among 5 people.

Hence, 3 apple pies divided among 5 people.

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The bearing of point A from point O is 256°.

In mathematics, a bearing is the angle in degrees measured clockwise from north. Bearings are usually given as a three-figure bearing. For example, 30° clockwise from north is usually written as 030°.

Given that, angle x= 076° and angle y = 111°.

Now, the bearing of point A from point O is

180°+ 076°

= 256°

Therefore, the bearing of point A from point O is 256°.

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The expression represents the :

40% of 118 = Answer - Regular price

The sale price is = $70.8

Now, According to the question:

"Information available from the question"

The regular price is $118,

but the online store is having a 40% off sale.

To find the sale price.

Now, 40% of 118 = 47.2

And the sale price will be:

$118 - $47.2

= 70.8

The expression represents the :

40% of 118 = Answer - Regular price

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Answer:

Step-by-step explanation:

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Answer:

See explanation below.

Step-by-step explanation:

1. (-1, -1) and (2, -2)

  m = -2+1 / 2+1

  m = -1/3

2. (-1, -4) and (0, -1)

  m = -1+4 / 0+1

  m = 3/1

  m = 3

3. (-4, 0) and (-2, -3)

  m = -3-0 / -2+4

  m = -3/2

4. (2, 0) and (0, -3)

  m = -3-0 / 0-2

  m = -3/-2

  m = 3/2

5. (-1, 2) and (-4, -3)

  m = -3-2 / -4+1

  m = -5/-3

  m = 5/3

6. (4, 3) and (1, -4)

  m = -4-3 / 1-4

  m = -7/-3

  m = 7/3

The area of the circle, as a function of x, will be:

A(x) = 3.14*(3ft + 2x)²

We know that for a circle of radius R, the area is:

A = pi*R²

Where pi = 3.14

In this case we have a circular plot of land with a diameter of 6ft, then the radius (half of that) is:

R = 6ft/2 = 3ft

And then we have a walkway with a width of 2x, then the radius of the circle that includes the walkway is:

R' = 3ft + 2x

Replacing that in the area equation we will get:

A(x) = 3.14*(3ft + 2x)²

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Any p-value less than 0.05 is a cause to reject the null hypothesis.

What is Null Hypothesis?

The statement "The null hypothesis is a claim about population parameter that is assumed to be false until it is declared false" is false. The null hypothesis is denoted by H0 assumes that the claim you are trying to prove did not happen. It is a claim about a population parameter that is assumed to be true until it is declared false.

In this case, 0.015 is the only option for p-value that would lead to a rejection of the null hypothesis (if the level of significance for the test is 0.05).

Any p-value less than 0.05 is a cause to reject the null hypothesis.

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Answer:

There is no real solution set for this equation

Step-by-step explanation:

We have

[tex]\sqrt{2x-1}+7=4[/tex]

Move 7 to the right side:

[tex]\sqrt{2x-1}+7-7=4-7\\\\\sqrt{2x-1}=-3\\\\[/tex]

If we treat 2x - 1 as a function f(x) then we are getting

[tex]\sqrt{f(x)} = -3\\\\[/tex]

But the square root of a function cannot be negative for real values of x

Hence there is no real solution set

The measure of x is 105° and the measure of y is 45°.

A square is a quadrilateral with four equal sides. There are many objects around us that are in the shape of a square. Each square shape is identified by its equal sides and its interior angles that are equal to 90°.

The given quadrilateral is square.

The diagonals of a square are angle bisectors. Therefore, the diagonals split the right angles of the square into two 45° angles.

Here, y°=45°

Here, a+60° =180°

a=120°

In quadrilateral y°+x°+a°+90°=360°

45°+x°+120°+90°=360°

x°+255°=360°

x°=105°

Therefore, the measure of x is 105° and the measure of y is 45°.

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The cost of the wings per dollar is 1.2 wings per dollar ($15 / 18 wings = $0.83 per wing). The cost of 18 wings is $15. To calculate the cost of the wings per dollar, divide the total cost of the wings ($15) by the number of wings (18).

1. Divide the total cost of the wings ($15) by the number of wings (18).

2. The result of this calculation is the cost of each wing ($15 / 18 = $0.83).

3. Divide 1 by the cost of each wing ($1 / $0.83 = 1.2 wings per dollar).

The cost of 18 wings is $15. To calculate the cost of the wings per dollar, divide the total cost of the wings ($15) by the number of wings (18). This calculation will give the cost of each wing ($15 / 18 = $0.83). To find the number of wings per dollar, divide 1 by the cost of each wing ($1 / $0.83 = 1.2 wings per dollar). This means that for every dollar spent, 1.2 wings can be purchased.

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Answer:

Mixed Number: [tex]\frac{7}{2}[/tex]

Regular [tex]3\frac{1}{2}[/tex]

Explantion \/ \/

Answer:

126 cans in total / 6 cans per row

126/6 = 21 rows of cans

4x−2y=14

Step-by-step explanation:

Answer:

The solution to the system of linear equations is x = 4, y = 1.

Step-by-step explanation:

Given system of linear equations:

[tex]\begin{cases}4x-2y=14\\y=\dfrac{1}{2}x-1\end{cases}[/tex]

To solve the system of linear equations by the method of substitution, substitute the second equation into the first equation:

[tex]\implies 4x-2\left(\dfrac{1}{2}x-1\right)=14[/tex]

Solve the equation for x:

[tex]\implies 4x-x+2=14[/tex]

[tex]\implies 3x+2=14[/tex]

[tex]\implies 3x=12[/tex]

[tex]\implies x=4[/tex]

Substitute the found value of x into the second equation and solve for y:

[tex]\implies y=\dfrac{1}{2}(4)-1[/tex]

[tex]\implies y=2-1[/tex]

[tex]\implies y=1[/tex]

Therefore, the solution to the system of linear equations is:

The linear function relating S to N is given as follows:

S(n) = 1800 + 60n.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

The parameter values for this problem are given as follows:

m = 60, b = 1800.

Hence the function is defined as follows:

S(n) = 1800 + 60n.

The function is graphed on the image given at the end of the answer.

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So, the probability that you see at least one shooting star in the period of an hour is 59.04%.

The probability of seeing at least one shooting star in a 15-minute interval is 20%, so the probability of not seeing a shooting star in that interval is 80%. The probability of not seeing a shooting star in an hour-long period is the product of the probability of not seeing a shooting star in each of the four 15-minute intervals, which is 0.8 * 0.8 * 0.8 * 0.8 = 0.4096 or 40.96%. Therefore, the probability of seeing at least one shooting star in an hour-long period is 1 - 0.4096 = 59.04%.

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The size of angle x = 46 degree.

Now, According to the question:

A triangle in which at least two sides are equal is called an isosceles triangle. Following this fact, if two sides of a triangle are equal, then the angles opposite to those sides are also equal.

"Information available from the question"

Since Δ ABC is equilateral then interior angles = 60°

Since CE = DE then Δ CDE is isosceles and the base angles are congruent,

So,

∠ ECD = [tex]\frac{180-32}{2}[/tex] = [tex]\frac{148}{2}[/tex] = 74 degree

BCD is a straight line, then the 3 angles on it sum to 180°, that is

60° + 74° + x = 180°

134° + x = 180° ( subtract 134° from both sides )

Hence, The size of angle x = 46°

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Answer:

Third choice: (1, -3); (2, 2); (3, 7)

Step-by-step explanation:

There are two ways to solve this

The easiest way to solve this is to understand that the inverse of a function f(x), denoted by f⁻¹(x) is nothing but a reflection of the function about the line y = x

What that means is that if (x, y) is a specific point on the line, then the inverse point will be (y, x). Basically we are swapping the x, y values

The 3 points on f(x) and the corresponding points on f⁻¹(x) are given below:

f(x)                f⁻¹(x)
------             --------
(-3, 1)             (1, -3)
(2, 2)             (2, 2)
(7, 3)             (3, 7)

From the options given we see that the 3rd choice gives the correct values

So answer:
Third choice: (1, -3); (2, 2); (3, 7)

I have not taken the trouble of finding the equation for the line and finding the inverse of that equation since it is not needed in this question

The width of the leftover brass is 18 1/2 inches.

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

Initial length = 36 inches

Length of each piece = 8 3/4 inches

The width of the leftover brass is then calculated as

Width = Initial length - 2 * Length of each piece

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

Width = 36 - 2 * (8 3/4)

Evaluate

Width = 18 1/2

hence, the width is 18 1/2 inches

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The GDP using value added approach is $3.50

GDP using value added approach is calculated by obtaining the sum total of value added by each production unit.

Value added by Farmer Fred = Price of output - Cost of inputs = $0.50 - $0 = $0.50

Value added by Baker Bob = Price of output - Cost of inputs = $1.50 - $0.50 = $1.00

Value added by Trucker Tom = Price of output - Cost of inputs = $2.25 - $1.50 = $0.75

Value added by Retail Rob = Price of output - Cost of inputs = $3.50 - $2.25 = $1.25

GDP = Value added by Farmer Fred + Value added by Baker Bob + Value added by Trucker Tom + Value Added by Retail Rob

GDP = $0.50 + $1.00 + $0.75 + $1.25

GDP = $3.50

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The required simple interest would be the amount of 1,170€ on a 4500€ principal deposited for four years at a rate of 6.5%

We have been given data as:

Principal (P) = 4500€

Rate of Interest (R) = 6.5% = 6.5/100 = 0.065

Time (T) = 4 years

⇒ Simple interest  = P × R × T

Substitute the value of P, R, and T in the above formula,

⇒ Simple interest  = 4500 × 6.5% × 4

⇒ Simple interest  = 4500 × 6.5/100 × 4

⇒ Simple interest  = 4500 × 0.065 × 4

Apply the multiplication operation, and we get

⇒ Simple interest  = 1,170€

Therefore, the required simple interest would be the amount of 1,170€.

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