60% of the marbles in a container are red and the rest are black. After another 9 black
marbles are added, the ratio of red and black marbles becomes 4: 3. How many black marbles
are there now?

Answer: 1 and 26

Step-by-step explanation:

The lowest common denominator for 4/21, 3/7, 4/9 is 63.

Lowest common denominator is the lowest number that is divisible by the denominators of the set of fractions.

Step 1:  we will write down the prime factors of all the denominators.

[tex]21=7^{1} *3^{1}[/tex]

[tex]7=7^{1}[/tex]

[tex]9=3*3=3^{2}[/tex]

Step 2 : write down highest power of each prime number.

[tex]7^{1} ,3^{2}[/tex]

Step 3 : Multiply the values

7x9=63

Therefore , The lowest common denominator for 4/21, 3/7, 4/9 is 63.

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Answer:

A) It can be represented using the formula f(x + 1) = 6/5(f(x)) when f(1) = 10/3.

C) It can be represented using the formula f (x) = 10/3(6/5)/\x-1

What is sequence?

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given:

10/3, 4, 24/5, 144/25, ...

From the above sequence we can generate the formula,

f (x) = 10/3

Also, for f(x+1) we can have

x=1,

f(1)= 10/3

f(2)= 4

So, f(x + 1) = 6/5(f(x))

Step-by-step explanation:

In proportion , 13 ft is the actual length of a room.

What in mathematics is a proportion?

A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

0.25 inches       8.5 inches

----------------   = --------------

 5 ft                   x ft

Using cross products

0.25x = 8.5 * 5

Divide each side by 0.25

0.25x/0.25 =  8.5  * 5/0.25

x = 13

x = 13 ft

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The solution to the system of equation is (7/5, 22/5)

Given the system of equation as shown below;

4x + y = 10 * 2

3x - 2y = 13 * 1

_____________

8x + 2y = 20

3x - 2y = 13

Subtract

8x - 3x = 20 - 13

5x = 7

x = 7/5

Substitute the value of x into any of the equation

4x + y = 10

4(7/5) + y = 10

28/5 + y = 10

y = 10 - 28/5

y = 22/5

Hence the solution to the system of equation is (7/5, 22/5)

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Answer: 99,999

Step-by-step explanation:

The accurately captures a system's gravitational potential energy:

ME = KE + GPE.

Gravitational potential energy is the energy that an object possesses or acquires as a result of a change in its position when it is in a gravitational field. In layman's terms, gravitational potential energy is energy that is tied to gravitational force or gravity.

The energy held in an object due to its height above the ground is known as gravitational potential energy. It is determined by the object's mass, the gravitational acceleration caused by the Earth, and the object's height. Kinetic energy is the energy that an object possesses as a result of its motion.

An object's mechanical energy is equal to the sum of its kinetic energy and potential energy. If ME is mechanical energy and KE is kinetic energy, then PE is its potential energy.

ME = PE + KE

KE = (1/2) mv^2

PE = ME - KE

PE = ME - 1/2(mv²)

PE = ME - 1/2(mv²)

PE = ME - KE

ME = KE + GPE

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Answer:

B

Step-by-step explanation:

ME equals the sum of KE and GPE

The only set of elements that satisfied the equation 2x-1= -13 is {-6}.

A set is a combination of specific quantities in which the meaning of each variable must be the same.

For example {1,2,3,4,5,6...} is a set of natural numbers in which each variable is representing a natural number so the overall meaning is the same among all.

Another example could be a set of whole numbers like that.

Given the equation,

2x-1= -13

By taking -1 right-hand side

2x = -13 + 1 = -12

By dividing 2

x = -6

Hence "The only set of elements that satisfied the equation 2x-1= -13 is {-6}".

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A sample of n = 100 scores has a mean of 5. A second sample has n = 25 scores and m = 7. if the two samples are combined, the sample mean for the combined sample will be 5.4.

We are given the sample mean of n = 100, is 5. Therefore, the sum of 100 observations is 100 x 5 = 500

The sample mean of n = 25, is 7. Therefore, the sum of 25 observations is

25 x 7 = 175

The sum of two samples is 500 + 175 = 675.

And the sum of two sample size is 100 + 25 = 125

Now, the combined mean is:

675125=5.4

A dataset's mean(also known as the arithmetic mean, which differs from the geometric mean) is calculated by dividing the sum of all values by the total number of values. It is frequently referred to as the "average" and is the most widely used measure of central tendency.

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Answer:

3/9  3/8  3/7

Step-by-step explanation:

The higher the denominator, the higher number of times  a number will be divided which means, the number will become smaller.

The acres of vacant land that the county have now will be 144 acres.

Since 36% has been used, the remaining percentage will be:

= 1 - 36%

= 64%

Therefore, the acres of vacant land that the county has now will be:

= 64% × 225

= 64/100 × 225

= 0.64 × 225

= 144

Therefore, the acres of vacant land that the county have now will be 144 acres.

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Answer:

$2.61

Step-by-step explanation:

So, We have $5.22 for 6 pounds of Bananas.

If we need to find the cost for 3 pounds, we would divide $5.22 by 2 because 6/2=3

In order to do this, we need to turn 5.22 into a whole number, so we multiply by 100

5.22*100=522

Now we divide

522/2 = 261

Now we divide 261 by 100, since we multiplied by 100 earlier.

261/100 =2.61

So our answer is $2.61 for 3 pounds of bananas .

Hope this helps! ^^

Answer:$2.61 for 3 pounds  

Thank for the  brainliest

Step-by-step explanation:first you divided $5.22/6  because the money always goes on the top and you get 0.87, you multiply 0.87 by 3 which is $2.61

Answer: Hi The Answer is 3 (the third one)

Step-by-step explanation: Am not sure if this is correct am taking the test right now

Answer:

all real numbers

Step-by-step explanation:

Florida

Part(A) Leslie's initial investment was $500 and

Part(B) The quarterly interest rate is 10.4 %

What is compound interest?

Compound interest is the interest calculated on the principal amount , which also considers all the accumulated interest of previous periods of deposit or loan.

If P is the principal amount and rate of compound interest is r  then after t years of time , the present amount (if the interest is compounded annually) will be = P(1+(r/100))^n

If the interest is compounded quarterly, then the present amount be A

Where A = [tex]P (1+\frac{r/4}{100} )^{4t}[/tex]

Given that Leslie invests in a bank that earns interest quarterly , and account balance after t years is given as 500(1.026)^(4t)

A= [tex]P (1+\frac{r/4}{100} )^{4t} = 500(1.026)^{4t\\[/tex]

Comparing both sides we get P = 500

And 1+(r/400)=1.026

(r/400)=1.026-1

(r/400)=.026

r=400(0.26) = 10.4 %

Therefore , Leslie's initial investment was $500 and the quarterly interest rate is 10.4 %

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The values a = 1/3 and b = 1/6.

Given function is, f(x) =  

                                       [tex]\frac{x^2-4}{x-2}\ \ \ if\ x < 2 \\ax^2-bx+3 \ \ \ if\ 2\leq x < 3\\2x-a+b\ \ \ if\ x\geq 3[/tex]

The interval in which the function is defined is broke down into three. They are: x<2, 2≤x<3 and x≥3.

Now the function [tex]\frac{x^2-4}{x-2}[/tex] is continuous except at x = 2. But this function is defined in the interval x>2. The other two function are defined as polynomial, so are continuous any way.

So for the whole function f(x) to  be continuous, we need to check the continuity at x = 2, x = 3.

When x = 2,  [tex]\frac{x^2-4}{x-2}[/tex] =[tex]\frac{(x+2)(x-2)}{x-2}=x+2 = 4[/tex]  and [tex]ax^2-bx+3[/tex] = 4a-2b+3

⇒  4a-2b+3 = 4

⇒4a- 2b-1 = 0, for the function to be continuous at x = 2.

When x = 3,  [tex]ax^2-bx+3[/tex] = 9a-3b+3 and 2x-a+b = 6-a+b

⇒ 9a-3b+3 = 6-a+b

⇒ 10a -2b-3 = 0, for the function to be continuous at x = 3.

On solving   4a-2b-1 = 0 and 10a -2b-3 = 0 by subtracting the two,

we get, -6a+2 = 0

⇒ a = 1/3 and therefore, b = 1/6

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Answer:

3.64

Step-by-step explanation:

collect like terms

divide both sides by x coefficient

Answer:

x=51/14

Step-by-step explanation:

28x-2=100

+2. +2

28x=98

28x/28=102/28

×=51/14

Answer:

26%

Step-by-step explanation:

Number of seats by 6th graders / Number of seats in total × 100% = Percentage of seats by 6th graders

442/1700 × 100% = 26%

Hope this helps! ^^

Answer:

your answer is $2.55

The length between the two points is 9.2 units.

Given points are:

Q(1,₋5)

P(₋5,2)

Let the two points be denoted as

Q(1,₋5) as (x₁,y₁)

P(₋5,2) as (x₂,y₂)

Distance between two points is calculated as:

d = √(x₂ ₋ x₁)² ₊ (y₂ ₋ y₁)²

d = √(₋5 ₋ 1)² ₊ (2 ₋ (₋5))²

d =  √(₋6)² ₊ (7)²

d =  √36 ₊ 49

d =  √85

d = 9.2

Hence the length of QN is 9.2 units.

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We have to draw the model for 5 divide 1/7 . In order to draw the model we use below steps.

Draw 1/7 boxes to represent 1/7 groups.

Assume 5 as the number which represents the total of these 1/7 groups.

Put a question mark at the first box.

Attached is the model to represents 5 divide 1/ 7 .

5/(1/7)

5*7

35

In the question mark we should put 35.

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The 80th percentile is 125.37.

It is required to find the solution.

A part of a whole expressed in hundredths a high percentage of students attended. Also the result obtained by multiplying a number by a percent the percentage equals the rate times the base.

Given:

The weights (in pounds) of seven people:

100, 115, 135, 140, 180, 197, 230.

We have to find the 80th percentile first we have to find the mean of seven people.

Mean=100+ 115+135+140+ 180+197+ 230/7

Mean=156.71

100 percent=156.71

80  percent=156.71*80/100

80  percent=125.37.

Therefore, the 80th percentile is 125.37.

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Answer:

The terms are 2, 6 and 12

The sum  is 20

Step-by-step explanation:

n      n + 1            n(n+1)
--      -------           ---------
1         2               1 x 2 =  2
2        3               2 x 3 =  6
3         4               3 x 4 = 12
The terms are 2, 6 and 12
The sum  is 2 + 6 + 12 = 20

The rate of change of elevation is 0.32.

An easy-to-remember equation for finding change in elevation as a decimal is “rise over run,” meaning the rise (the change in vertical distance) divided by the run (the change in horizontal distance).

So the problem wants to ask to calculate the rate of change of the elevation if x=2 in the function f(x) = 0.32x. So base on that, the rate of change of elevations can be get through the formula of slope intercept form and the answer would would 0.32 is the rate of change in disregard of the value of x.

Hence, The rate of change of elevation is 0.32.

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Answer:

B

Step-by-step explanation:

The y coordinate tells us when we are going up for down.  So the rule would be (x, y + 5)  So, the x coordinate stays the same and the y goes up 5.

(1,2)  The 2 is the y coordinate. It will increase by 5 and become (1,7)

(3,2)  The 2 is the y coordinate.  It will increase by 5 and become (3,7)

(3,4)  The 4 is the y coordinate.  It will increase by 5 and become (3,9)

(1,4) The 4 is the y coordinate.  It will increase by 5 and become (1,9)

Answer:

Hello,

Step-by-step explanation:

[tex]u_2=u_1*r\\u_3=u_1*r^2\\u_4=u_1*r^3\\\\\dfrac{u_4}{u_3} =r=\dfrac{-56}{28} =\boxed{-2}\\\\u_1=\dfrac{u_3}{r^2} =\dfrac{28}{(-2)^2} =\dfrac{28}{4}=\boxed {7}\\\\\\\displaystyle\ s=\sum_{i=1}^6\ u_i\\\\=u_1*\sum_{i=1}^6\ r^{i-1}\\\\=7*\dfrac{(-2)^6-1}{-2-1} \\\\=-7*\dfrac{65}{3} \\\\\\\boxed{s=-\dfrac{455}{3} }\\[/tex]

The area of the triangle is 1200√5 cm².

Given that, the sides of the triangle are 70cm,80cm and 90cm.

We need to find the area of a triangle using Heron's formula.

As per Heron's formula, the value of the area of any triangle having lengths, a, b, c, perimeter of the triangle, P, and semi-perimeter of the triangle as 's' is determined using the below-given formula:

Area of triangle = √s(s-a)(s-b)(s-c), where s = Perimeter/2 = (a + b + c)/2

Now, semi perimeter = (70+80+90)/2=120

Area of triangle=√120(120-70)(120-80)(120-90)

=√120×50×40×30

=√40×3×2×25×40×30

=40×5√3×2×3×2×5

=40×5×3×2√5

=1200√5 cm²

Therefore, the area of the triangle is 1200√5 cm².

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