In the 6th grade classes there are 4 girls for every 3 boys if there are 24 girls how many boys are there?

Answer:

C

Step-by-step explanation:

The line has a positive slope which means it slopes upwards from left to right

A and B  slope downwards so can be excluded

C and D have the correct upward slope but C has the y-intercept of - 3

Thus C is the required line

Answer:

The volume of the cone is [tex]27cm^3[/tex]

Step-by-step explanation:

We know that formulas

Volume of cylinder is

[tex]V_1=\pi r^2 h[/tex]

Volume of cone is

[tex]V_2=\frac{1}{3}\pi r^2 h[/tex]

we are given

A cone and cylinder have the same height and the same base radius

So, both will have same radius and height

now, we can find ratios

[tex]\frac{V_2}{V_1}=\frac{\frac{1}{3}\pi r^2h }{\pi r^2h}[/tex]

now, we can simplify it

[tex]\frac{V_2}{V_1}=\frac{1}{3}[/tex]

we are given

the volume of the cylinder is 81 cm^3

so, [tex]V_1=81[/tex]

now, we can plug it and solve for V2

[tex]\frac{V_2}{81}=\frac{1}{3}[/tex]

[tex]81\times \frac{V_2}{81}=81\times\frac{1}{3}[/tex]

[tex]V_2=27[/tex]

So, the volume of the cone is [tex]27cm^3[/tex]

The volume of the cone, which has the same height and base radius as the cylinder with a volume of 81 cm³, is one-third that of the cylinder, equating to 27 cm³.

For a cone with the same height and base radius as the cylinder, the volume formula is V = ⅓πr²h, which is one-third of the volume of the cylinder. Given that the volume of the cylinder is 81 cm³, the volume of the cone can be found by dividing this value by 3, resulting in a volume of 27 cm³ for the cone. Therefore, the correct answer is B) 27 cm³.

Answer: 1

Step-by-step explanation:

Method #1: Using the log rules (+ → x and - → ÷)

  log₂4 + log₂16 - log₂32

= log₂[tex](\frac{4*16}{32})[/tex]

= log₂[tex](\frac{64}{32})[/tex]

= log₂2

= 1

Method #2: Using log rules to simplify each expression

log₂4 = x              log₂16 = x                  log₂32 = x

      4 = 2ˣ                    16 = 2ˣ                       32 = 2ˣ

      2² = 2ˣ                   2⁴ = 2ˣ                       2⁵ = 2ˣ

        2 = x                      4 = x                          5 = x

log₂4 = 2               log₂16 = 4                 log₂32 = 5

             2     +                      4       -                        5     =     1

35/23 is an improper fraction because the numerator is larger than the denominator.

To convert to a mixed number, use long division to find 35 into 23 goes in exactly one whole time (quotient) and there is 12 leftover (remainder)

You can see it through doing it like this

35/23 = (23+12)/23 = 23/23 + 12/23 = 1 + 12/23 = 1 & 12/23

So in short, 35/23 = 1 & 12/23

1 & 12/23 is a mixed number with 1 as the whole part and 12/23 as the fractional part.

---------------------

Real life example: if you had 35 cookies and 23 friends, then each friend would get 1 whole cookie. There would be 12 cookies left over.

The question involves understanding improper fractions, specifically 35/23. This fraction is already improper as the numerator is larger than the denominator and it cannot be simplified further.

The student's question pertains to converting an improper fraction, which in this case is 35/23. To clarify, an improper fraction is one where the numerator (the top number) is larger than the denominator (the bottom number). This type of fraction represents a quantity greater than one whole. The student's example already is an improper fraction.

There is no further calculation needed unless the goal is to convert it to a mixed number or to its simplest form, which cannot be done in this case since 35 and 23 have no common factors besides 1.

Answer:

divide 100 ml and 1.2 liter

Step-by-step explanation:

You will get the answer in percent

Answer:

10

Step-by-step explanation:

Answer:

None of the above

Step-by-step explanation:

x-1/3 = k

We know that k=3, so we can substitute that into the equation

x-1/3 = 3

Add 1/3 to each side

x-1/3 + 1/3 = 3+1/3

x = 3 1/3 or as an improper fraction 10/3

Answer:

5000.

Step-by-step explanation:

1000 milliliter is one liter. So if you have 5 liters 5 x 1000 can fit inside.

Answer:

4

Step-by-step explanation:

Only one plane can be drawn perpendicular to plane B through point A in three-dimensional space. The correct answer is option 1) that is One.

The question at hand involves geometric concepts, specifically the relationship between planes and lines in three-dimensional space. If point A lies in plane B, then there can be one and only one plane drawn perpendicular to plane B through point A; this is because in three-dimensional space, a point defines a line and only one perpendicular plane can contain that line.

This principle is similar to how any three points not on a single straight line determine a plane and how two lines intersect at a single point or not at all. The perpendicular plane would form a 90-degree angle along every line in plane B that passes through point A.

The correct answer is option 1) that is One

Answer:

16.6%

Step-by-step explanation:

Answer: $9.83

Step-by-step explanation:You need to calculate

($880/month)(.1665)(1/12) = $12.21

($880/month)(.0325)(1/12) = $2.38

Difference = $12.21 - $2.38 = $9.83

The Interest does your friend save at the end of the first month by Paying you instead of Credit Card is dollar 9.83.

What is Simple Interest?

''Simple Interest is a fee paid for borrowing money. The amount borrowed is called Principal the interest is expressed as a Percentage Rate of  the Interest".

What is Rate of  the Interest?

"Rate of  the Interest is the amount a lender charges a borrower and is a Percentage of the Principal - the amount loaned".

According to the question

Credit Balance is taken as Principal(P) = $880.00

Rate of Interest = 16.65%

Number of years = [tex]\frac{1}{12}[/tex]

Formula for Simple Interest = [tex]\frac{pnr}{100}[/tex]

Simple Interest=  [tex]\frac{(880)(1)(16.65)}{(12)(100)}[/tex]

=  12.21

Friend Pay you of Rate of Interest = 3.25%

Formula for Simple Interest is= [tex]\frac{pnr}{100}[/tex]

=[tex]\frac{(880)(1)(3.25)}{(12)(100)}[/tex]

= 2.38

In order to find the saving money make if Difference between Simple Interest paid at rate of interest 16.65% and Simple Interest paid at rate of Interest 3.25%

=  12.21 - 2.38

=  9.83

Hence, the Interest save at the end of the first month by paying you instead of the credit card $9.83.

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A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.

(2, 0), (-3, 3), (9, 1), (-3, 5)  NOT

(9, 1), (-3, 4), (2, 1), (9, 2)     NOT

(2, 4), (-3, 2), (9, 1), (-7, 2)     YES

(2, 4), (-3, 6), (2, 3), (-7, 2)     NOT

The sum represented by the notation [tex]\sum\limits^{10}_{i=3} {2i - 9[/tex] is 32

How to determine the sum represented by the notation

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

[tex]\sum\limits^{10}_{i=3} {2i - 9[/tex]

This means that we determine the value of the expression from i = 3 to i = 9 and then add them up

So, we have

2(3) - 9 = -3

2(4) - 9 = -1

2(5) - 9 = 1

2(6) - 9 = 3

2(7) - 9 = 5

2(8) - 9 = 7

2(9) - 9 = 9

2(10) - 9 = 11

Evaluate the sum

Sum = -3 - 1 + 1 + 3 + 5 + 7 + 9 + 11

Sum = 32

Hence, the sum represented by the notation is 32

Question

Find the sum of [tex]\sum\limits^{10}_{i=3} {2i - 9[/tex]

Answer:

Sue // 6 More blocks

Step-by-step explanation:

Sue has more blocks because 34>28.

34-28 is 6 so sue has 6 more.

Answer:

Do not qualify

Step-by-step explanation:

Yearly income = $58000

Monthly income = [tex]\frac{58000}{12}[/tex] = $4833.33

Median annual income = $47778

Monthly expenses = $4600

Income < Median Income ? 58000 < 47778 -> No

x = (Monthly income - expenses) * 60

  = (4833.33 - 4600) * 60

  = 233.33 * 60

  = 13999.8

x < 10000 ? 13999.8 < 10000 -> No

So, Do not qualify

Answer:

The family does not qualify for bankruptcy

Step-by-step explanation:

Expenses=$4,600

Yearly income=$58,000

Monthly income=Yearly income / 12

Monthly income=$58,000/12

Monthly income=$4,833.333333

Rounded to the nearest cent:

Monthly income=$4,833.33

Flowchart

                                                           No

                                                                  Mean test. Calculate

Income=$58,000<$47,778=Median  →   (Monthly income - expenses)*60

                                              Income       ($4,833.33-$4,600)*60

                                                                 ($233.33)*60

                                                                  $13,999.80

                                                                  Call this number X.           No

                                                                  X=$13.999.80 < $10,000   →  Do not

                                                                                                                   qualify

The family does not qualify for bankruptcy

Answers:

f(-3) = -1

f(-1) = 2

f(3) = 5

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

Explanations:

Draw a vertical line through -3 on the x axis. Make sure this vertical line crosses the orange graph. Mark this point of intersection and then draw a horizontal line from this point to the y axis. You should find that it touches -1 on the y axis. Check out the attached image to see this process in action.

Those steps basically say that x = -3 leads to y = -1. Since y = f(x), this means f(-3) = -1

Through similar steps, you should find that f(-1) = 2 and f(3) = 5

Note that the open hole/circle does not count. So if you land on an open hole, just keep going until you hit a closed circle on the other piece of the graph.

A) f (–3) = -1

B) f (–1) = 2

C) f (3) = 5

Straight-line equations are mathematical equations that are described in the plane of cartesian coordinates

General formula

or

y = mx + c

Where

m = straight-line gradient which is the slope of the line

x1, y1 = the Cartesian coordinate that is crossed by the line

c = constant

The formula for a gradient (m) between 2 points in a line

m = Δy / Δx

or we can use:

[tex]\rm \dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}[/tex]

Piecewise Functions: functions that have different equations based on the input (x) value

We look for 3 pieces of function from the graph

1. graph 1 is a straight line that passes through 2 points : (-4.0) and (-1, -3) so that the straight line equation:

[tex]\rm \dfrac{y-0}{-3-0}=\dfrac{x+4}{-1+4}\\\\\dfrac{y}{-3}=\dfrac{x+4}{3}\\\\3y=-3(x+4)\\\\3y=-3x-12\\\\y=-x-4\Rightarrow \:for\:x<-1[/tex]

2. graph 2 is a straight line with the equation: \

[tex]\rm y=2\Rightarrow \:for\:-1\leq x<3[/tex]

3. graph 1 is a straight line that passes through 2 points,  (3.5) and (5.1) so that the straight line equation  :

[tex]\rm \dfrac{y-5}{1-5}=\dfrac{x-3}{5-3}\\\\\dfrac{y-5}{-4}=\dfrac{x-3}{2}\\\\2(y-5)=-4(x-3)\\\\2y-10=-4x+12\\\\2y=-4x+22\\\\y=-2x+11\:\Rightarrow for\:x\geq 3[/tex]

A function made up of 3 pieces:

a solid dot means "including",

an open dot means "not including"

[tex]\rm y=-x-4\:for\:x<-1[/tex]

[tex]\rm y=2\:for\:-1\leq x<3[/tex]

[tex]\rm y=-2x+11\:for\:x\geq 3[/tex]

A) f (–3) =

Because -3 <-1, the function used is y = -x-4, so

f (-3) = - (- 3) -4

f (-3) = 3-4

f (-3) = -1

B) f (–1) =

Because x = -1, the function used y = 2, so

f (-1) = 2

C) f (3) =

Because x = 3, the function used is = -2x + 11, so

f (3) = -2 (3) +11

f (3) = -6 + 11

f (3) = 5

Piecewise Functions

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the inverse of the function

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domain of the function

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The property in expression is Associative property.

The characteristics of addition specify the possible methods for adding the given integers. One of the fundamental arithmetic operations in mathematics is "addition." The process of adding items together is called addition. The "+" symbol is used to add the two numbers together. The numbers we will add are referred to as "addends," and the outcome will be referred to as "sum." Any two or more digit numbers, known as addends, are used in the addition process.

Given expression

(m + 7.3) + 4.1 = m + (7.3 + 4.1)

this shows

(A + B) + C = A + (B + C)

this is associative property,

According to this property or law, the addition of three integers yields the same result regardless of how the numbers are arranged. It means that even if the order of the addends is modified while adding three or more numbers, the total or sum will remain the same.

Hence the expression follows associative property.

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Answer:

m=1

Boys: Girls

2:1

Step-by-step explanation:

To find the slope from 2 point we use the formula

m = (y2-y1)/(x2-x1)

m = (-13--10)/(3-6)

  = (-13+10)/(3-6)

   = -3/-3

   = 1

Boys: Girls

16:8

We can divide each number by 8

16/8: 8/8

2:1

Boys: Girls

2:1

Answer:

The y intercept is -1

Step-by-step explanation:

y-14=6(x-2.5)

We need to get the equation in the form y = mx+b where b is the y intercept

Distribut the 6

y-14 = 6x -15

Add 14 to each side

y-14+14 = 6x-15+14

y = 6x-1

The y - intercept is -1

Answer:

(0, -1)

Step-by-step explanation:

y-14=6(x-2.5)

Distributive property:

y-14 = 6 * x - 6*2.5

y-14= 6x-15

Add 14 on each side:

y-14+14=6x-15+14

Simplify:

y=6x-1

In the form y=mx+b (slope-intercept form, as shown above), the y-intercept is (0, b). b is -1.

Answer:

23/44 < 33/64

Step-by-step explanation:

if you don't want to  get common denominators multiply the denominator of the second fraction by the numerator of the first (1,427) and the denominator of the first one to the numerator of the second (1,452) the bigger number is greater. 1,427 < 1,452

By converting both fractions into decimals (23/44 becomes 0.5227; 33/64 becomes 0.5156), it is clear that 23/44 is greater than 33/64.

To compare which fraction, 23/44 or 33/64, is greater, you need to find a common denominator and then compare the numerators. The calculation can be simplified by converting these fractions into decimals. To do so, divide the numerator by the denominator. Therefore, 23/44 becomes 0.5227 and 33/64 becomes 0.5156. Therefore, 23/44 is greater than 33/64.

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Answer: C

Step-by-step explanation:

Makes sense

Answer: C. 3* (5*4)

Step-by-step explanation:

(3*5)*4=60

(3+5)*4=32

3*(5*4)=60

(3*5)+(3*4)=27

(3*5)+4=19

3*(5*4)=60=(3*5)*4

Answer:

UV =2

Step-by-step explanation:

From the diagram

TV = x+14

TV = TU + UV

x+14 = 9+ 8+2x

Combine like terms

x+14 = 17+2x

Subtract x from each side

x-x+14 = 17+2x-x

14 = 17+x

Subtract 17 from each side

14-17 = 17+x-17

-3 =x

But we are not asked to solve for x, but for UV

UV = 8+2x

Substitute x=-3

UV = 8+2(-3)

UV  = 8-6

UV =2

Answer:

0<_g <_ 14 or A. If it’s the same paper

Step-by-step explanation:

Answer:

[tex]0\leq g\leq 14[/tex]

Step-by-step explanation:

The function is defined as [tex]m(g)[/tex], that is, the independent variable represents gallons, and the dependent variable represents miles, depending on the gallons of gas, the car will move certain number of miles.

Knowing the relation between the variables of the function, we also can know that the fuel tank holds 14 gallons, that is, the independent variable holds 14 units, and the independent variable is [tex]g[/tex].

Remember that the domain is the set that represents all valid values that the independent variable can take. In this case

[tex]0\leq g\leq 14[/tex]

Which means that the fuel tank can hold a maximum of 14 gallons and a minimum of 0 gallons. Therefore, the domain is

[tex]0\leq g\leq 14[/tex]

Answer: x = 5

Step-by-step explanation:

1 = -4 + x

We have to isolate x, and remember, what we do to one side we do to the other.

1 + 4 = -4 + 4 + x

5 = x

Check:

-4 + 5 = 1

1=1

Answer:

With a number line with two points opposite from each other on a number line, the middle of it is always going to be 0.  Therefore, both points are the same distance away from 0 just in opposite directions. That means point Q is always going to equal the negative of point P. An example of this is if point p equals 5, point p equals -5.

This method only works when it is specifically stated that the two points are opposite from each other.

Hope this helps!

xx,

myara

The location of Point Q on the number line is the opposite of the location of Point P. If Point P is at +a, then Point Q is at -a, and vice versa.

In order to determine the location of Point Q, we first need to know the location of Point P on the number line. If we assume that point P is positive and located at +a, then Point Q, being the opposite of Point P, would be located at -a on the number line. Conversely, if Point P was negative and located at -a, the opposite, Point Q, would be on the +a location on the number line. The important thing to remember here is that opposite points on a number line are simply reflection of each other with respect to the origin (0).

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