The ratio of girls to boys in a class is 3:2. There are 25 students in this class. How many are girls and how many are boys?

Answer: 4r-8+4y

Step-by-step explanation: Distribution is when you multiply every term inside the parantheses by the outside term. So 4(r-2+y)=4(r)+4(-2)+4(y). This is the same as 4r-8+4y. Since none of these are like terms we have the fewest symbols possible.

Answer:-4

Step-by-step explanation:

The 65-th percentile is  approximately 83.8 ounces.

A number at or below which a particular percentage falls in its frequency distribution, or a score below which a given percentage falls, is known as the k-th percentile in statistics. The 50th percentile, for instance, is the score at or below which 50% of the distribution's scores can be found.

The percentile can be calculated by using the formula

Percentile Value = μ + zσ  where

z is the z-score , μ is the mean and σ is the standard deviation.

Here the percentile that is to be calculated is 65.

So we take the value that is closest to 0.65 from the z-table.

We get the value of the data to be 0.39

Now putting the values in the equation we get:

Percentile Value = μ + zσ  

or, Percentile Value = 83 + (0.39 × 2)

or, Percentile Value = 83.78

or, Percentile Value ≈ 83.8

Hence the 65th percentile value of the function is given by 83.8  .

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Answer:

#3: -2 = 2y - 8

#7: 3 = y

#8: y = 3

#4: Angle1 + Angle2 = Angle ABC

#6: Angle 1 and Angle 2 are supplementary

Step-by-step explanation:

6y - 2 = 8y - 8

 8 - 2 = 8y - 6y

     6/2 = 2y/2

       3 = y

       y = 3

If A is between B and C, and AB=x+2, BC=4x-7 and AC=2x-1,  then the x=8 and AC=15 units.

Given,

That A is between B and C.

AB= x+2

BC= 4x-7

AC= 2x-1

Then,

BC = AB+AC

4x-7= x+2+2x-1

4x-7= 3x+1

4x-3x=1+7

x=8

Then the length of the line AC is

AC= 2x-1

AC= 2×8-1 =15 units

Hence, If A is between B and C, and AB=x+2, BC=4x-7 and AC=2x-1,  then the x= 8 and AC= 15 units

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The 8th term of the geometric sequence is 13122x^22

The explicit form of a geometric sequence is expressed according to the equation;

Tn = ar^n-1

where

r is the common ratio

a is the first term

n is the number of terms

Given the sequence below;

6x,18x^4,54x^7

r = 18x^4/6x

r = 3x^3

a = 6x

n = 8

Substitute to have:

T8 = 6x(3x^3)^8-1

T8 = 6x (3x^3)^7

T8 = 13122x^22

Hence the 8th term of the geometric sequence is 13122x^22

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Answer: c=[tex]\sqrt{A/\pi}[/tex]

Step-by-step explanation:

πc²=A​

c²=A/π

c=[tex]\sqrt{A/\pi}[/tex]

Considering the definition of an equation and the way to solve it, the number of points Carlos scored in the last game is 19.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Being:

and knowing that in the last game, Fabio had 7 points less than 2 times as many points as Carlos, the equation to determine the number of points Carlos scored in the last game is:

2C - 7= F

Fabio scored 31 points in the game. So you get:

2C - 7= 31

Solving:

2C= 31 + 7

2C= 38

C= 38 ÷ 2

C=19

Finally, the number of points Carlos scored in the last game is 19.

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The length and the widths are 420.031 yards and 0.031 yards if a rectangular parking lot has a length that is 420 yards greater than the width.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

Let L be the length and W be the width of the rectangle.

From the question:

L = 420 + W (based on the data given in the question)

LW  = 13

(420 + W)W = 13

W² + 420W - 13 = 0

After solving the above quadratic equation:

W = 0.031, W = -420.03 (width cannot be negative)

W = 0.031 yards (which is not practical but from a mathematical point of view it can be considered)

L = 420 + 0.031 = 420.031 yards

Thus, the length and the widths are 420.031 yards and 0.031 yards if a rectangular parking lot has a length that is 420 yards greater than the width.

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Answer:

8. Supplementary means that two angles add up to 180 degrees (straight line). For the justification, I would simply write "def. of supplementary angles."

9. Equilateral means that all sides equal. For the justification, I would simply write "def. of equilateral triangle."

10. In a circle, all radiuses equal in length. TC and ZC are both radiuses. For the justification, I would simply write "def. of radius."

11. A midpoint divides a line segment in half. For the justification, I would simply write "def. of midpoint."

Answer:3 5/7

Step-by-step explanation:

Answer:   A ----------------3 5/7

[tex] \frac{f(x)}{g(x)} = \frac{x + 5}{ \sqrt{3x + 1} } [/tex]

[tex]x ∈ \: \: ] \frac{ - 1}{3} ,∞[[/tex]

[tex]f(x) - g(x) = x + 5 - \sqrt{3x + 1} [/tex]

[tex]x ∈ \: \: [ \frac{ - 1}{3} ,∞[[/tex]

when multiplicity is removed, you get 2^(2n+1)/2 members, which is 2^(2n).

Take the power set. It has 2^(2n+1) members.

Replace any member which has n+1 or more elements with its complements.

Now the power set has members, which have n or fewer elements, and each such member appears twice.

Therefore, when multiplicity is removed, you get 2^(2n+1)/2 members, which is 2^(2n).

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The required answer would be 3.7×10¹⁰ which is written in the form of scientific notation.

Scientific Notation is a way of writing down in the easy form of very large or very small numbers.

We have been given that expression as:

⇒ (7×10⁹)(5.3×10²)

⇒ 7×5.3 ×10⁹×10²

We have to add exponents of tens and apply the multiplication operation between 7 and 5.3,

⇒ 37 ×10⁹⁺²

⇒ 3.7×10⁻¹ ×10¹¹

⇒ 3.7×10¹⁰

Hence, the required answer is 3.7×10¹⁰ which is expressed in scientific notation.

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Answer:

number 2. A
number 3. C

number 4. B

Step-by-step explanation:

if the answer's are correct then comment or like

The linear equation for the remaining Federal Helium Reserves, r(t) = 20 -1.9t

There is 20 billion cubic feet of Helium in 2010. Helium is depleted by about 1.9 billion cubic feet each year.

Let 'r' denotes the remaining Federal Helium Reserves in billions of cubic feet.

Let 't' denotes the number of years since 2010.

We have to find a linear equation to represent the depletion of Helium through years since 2010. A linear equation will have two variables, one dependent and one independent variable. Here, let 'r' be the dependent variable and 't' be the independent variable.

Then the amount of Helium depleted in 't' years = 1.9t

So, the remaining Helium in the Federal Helium Reserve since 2010 = 20 - 1.9t.

Thus, r(t) = 20 - 1.9t

This is a linear equation because it depends on only one variable, 't'.

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The cost of 15 carnival tickets is 37.5 dollars.

The equation y = 2.50x determines the total cost, y, of buying x carnival tickets.

where

Therefore, according to the equation, the cost of 15 carnival ticket can be calculated as follows:

y = 2.50x

where

x = 15

Hence,

y = 2.50 × 15

y = 37.5 dollars

Therefore, the cost of 15 carnival tickets is 37.5 dollars.

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The solution of the of the expression is as follows:

Three less than the quotient of a number and two has a result of thirteen.

Therefore,

let

the number = x

The quotient of the number and two  = x / 2

Therefore,

x  / 2 - 3 = 13

add 3 to both sides

x  / 2 - 3 = 13

x  / 2 - 3 + 3 = 13 + 3

x / 2 = 16

cross multiply

x = 2 × 16

x = 32

Therefore, the solution of the of the expression is as follows:

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Answer:

0.4761

Step-by-step explanation:

It is in the 10ths place making it bigger than 0.04761 and 0.04671

Then in the hundreths place for 0.4761  7 is bigger than the 6 in in the hundreths place of 0.4671, so the answer is

0.4761

The sum of the first twenty terms of the given AP is 1380.

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Answer:

-4

Step-by-step explanation:

Let's solve this step by step:

-7 + 14 = 7
7 + 10 = 17

17 - 21 = -4

Your answer would be -4

Answer:

-1/4 ,-(-1/-4) and 1/-4 are the answers please

The data is qualitative one.

Qualitative Data:

Qualitative data consists of Labels, Attributes, Descriptions

This type of data is observed not measured

Examples: Colors, categories, appearances, dogs, etc.

Basically it considers the qualities of the data.

Quantitative Data:

Quantitative data Consists of numbers or counts in the data.

This type is mainly focused on the measurement. Which means it only consider the quantities.

Examples: Length, height, area, speeds, dollar amounts, ages, etc.

Given,

The colors of automobiles on a used car lot.

Here we need to determine the given data is qualitative or quantitative.

Based on the definition of the qualitative or quantitative,

We conclude that the given data is qualitative.

Because it describe the quality of the car.

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Answer:

160

Step-by-step explanation:

180 (a straight angle's degrees) /9 = 20

20 * 8 = 160

Check:

160 + 20 = 180

Answer:

128°

Step-by-step explanation:

The three INTERIOR angles of the triangle are 90  38 and 52°  ( they sum to 180 °)    

   52 °  and 'x'  form a straight line = 180 °    so x = 128°

Answer:

128

Step-by-step explanation:

Add the two farthest angles, 90 and 38, so that's 128

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The remainder when polynomial function is divide by linear function is 773.

Given that the polynomial functon f(x)=3x⁴+5 and the linear function is x+4.

As it is given that we have to find the remainder the polynomial

f(x)=3x⁴+5 is divided by the linear expression g(x)=x+4.

f(x)=3x⁴+5    .......(1)

g(x)=x+4       .......(2)

We know the remainder theorem that when a polynomial f(x) is divided by a linear expression (x−a), the remainder will be f(a).

From equation (2), we have a linear expression.

Now, on simplifying equation (2) to obtain the zero of g(x), we get

g(x)=x+4=0

x+4=0

Now, on comparing (x+4) and (x−a), we get

a=-4      ......(3)

Here, we have to get the value of f(a).

Now, using the remainder theorem, we can say that to get the remainder when the polynomial f(x)=3x⁴+5 is divided by g(x)=x+4, we have to replace x by -4 in the polynomial f(x)=3x⁴+5, we get

f(-4)=3(-4)⁴+5

f(-4)=3(256)+5

f(-4)=768+5

f(-4)=773

Therefore, the remainder when the polynomial f(x)=3x⁴+5 is divided by the linear expression g(x)=x+4 is 773.

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We need to know about domain and range of a graph to solve this problem. The domain is (-∞,5) and the range is (-∞,2).

The domain of a function is the input values that the function can take. The range is the set of values that can be the possible output of the function. The domain of a graph are the values that are on the x-axis and the range is on the y-axis. The arrow means that the graph goes on till infinity, a solid sphere means that the graph ends at that point and the ending point is included in the function, a hollow sphere means the graph ends at that point and the ending point is not included in the function. In the graph in the question, along x-axis the values on left goes on till negative infinity and on right the domain is open at 5. For range along y-axis, the range on the left side goes on till negative infinity and on the right it is open at 2.

Therefore we see that the domain of the graph is (-∞,5) and the range is (-∞,2).

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Answer:

x= -9/5

Step-by-step explanation:

I hope this helps!