If AB = 12 and BC = 19,
then what does AC equal?

Answer: the probability of selecting the first urn and then drawing two white balls from the first urn is 0.027.

Step-by-step explanation:

Let's call the event of selecting the first urn "A" and the event of drawing two white balls from the selected urn "B". The probability we want to find is P(A and B), which can be found using the formula for the intersection of two events:

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

where P(B|A) is the probability of drawing two white balls from the first urn given that the first urn was selected.

First, let's find P(A):

P(A) = 0.3

Next, let's find P(B|A):

P(B|A) = (3/10) * (3/10) = 9/100

Finally, let's find P(A and B):

P(A and B) = P(A) * P(B|A) = 0.3 * 9/100 = 0.027

So the probability of selecting the first urn and then drawing two white balls from the first urn is 0.027.

Let's assume the width of the rectangular pool is w. According to the problem, the length of the pool is 12 feet shorter than the width, so the length can be represented as w - 12.

The area of a rectangle is given by the formula A = L x W, where A is the area, L is the length, and W is the width. We know that the area of the pool is 640 square feet, so we can set up the equation:

A = L x W

640 = (w - 12) x w

Simplifying the equation:

640 = [tex]w^{2}[/tex] - 12w

[tex]w^{2}[/tex] - 12w - 640 = 0

We can solve for w by using the quadratic formula:

w = [-(-12) ± [tex]\sqrt{-12}^{2}[/tex]- 4(1)(-640))] / (2 x 1)

w = [12 ± [tex]\sqrt{(12^{2}+2560)[/tex]] / 2

w = [12 ± [tex]\sqrt{2596}[/tex]] / 2

w = [12 ± 51] / 2

We can ignore the negative solution, so:

w = (12 + 51) / 2

w = 31.5

Therefore, the width of the pool is 31.5 feet. We can use this value to find the length:

L = w - 12

L = 31.5 - 12

L = 19.5

Therefore, the length of the pool is 19.5 feet.

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Answer:

[tex]x > 7[/tex]

Step-by-step explanation:

Given the inequality

[tex]x+4 > 11[/tex]

Lets solve the inequality for [tex]x[/tex].

Subtract [tex]4[/tex] from both sides of the inequality.

[tex]x > 11-4[/tex]

Evaluate [tex]11-4[/tex].

[tex]x > 7[/tex]

[tex]x[/tex] is greater than 7

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The inequality which describes the problem about the pot of stew Finn made is x/6 > 2.5

Number of bowls= 6

Quantity of stew in each bowl > 2.5

Quantity of stew Finn made = x

The inequality

Quantity of stew Finn made / Number of bowls > Quantity of stew in each bowl

x/6 > 2.5

Therefore, x divided by 6 greater than 2.5 is the inequality which describes the situation.

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The amount of money Abdoulaye would have saved in w weeks is given by the equation A = 10w + 70 and in 9 weeks Abdoulaye saved $ 160

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the initial amount of money Abdoulaye saved be = $ 70

The amount of money Abdoulaye saves each week = $ 10

Let the number of weeks be w

So , the amount of money Abdoulaye saved w weeks is = ( amount of money Abdoulaye saves each week x w ) + initial amount of money Abdoulaye saved

Substituting the values in the equation , we get

The amount of money Abdoulaye saved w weeks is A = 10w + 70

Now , when w = 9 weeks

Substitute the value of w = 9 , we get

A = 10w + 70

A = 10 ( 9 ) + 70

A = 90 + 70

A = $ 160

Hence , the equation is A = 10w + 70

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Answer: His debts to income ratio is 35.29%

Step-by-step explanation:

His debts to income ratio is 35.29% ($2,400 / $6,800 = 0.3529).

The area of a rectangle with side lengths 5/8ft. and 1/3 ft is: D. 5/24 ft².

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Substituting the given points into the area of rectangle formula, we have the following;

Area of rectangle = 5/8 × 1/3

Area of rectangle = 5/24 square feet.

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The percentage change in the price is 15.78% decrease.

What is the percentage?

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. Per 100 is what the term percent signifies. The sign "%" represents it.

Here are some percentage examples:

Now,

Initial price=4.1

Final price=3.5

Change=3.5-4.1= -0.6 , minus means decrease in price

final value + initial value

then

percentage change by midpoint approach = (final value-initial value) / ((final value + initial value)/2) *100

=0.6/3.8*100

=0.1578*100

=15.78%

hence,

         The percentage change in the price is 15.78% decrease.

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sum of two complementary angle is 180•

[tex]180 - 49 = y = 131[/tex]

Answer:

∠1 = ∠2 = 135

Step-by-step explanation:

We know that the sum of the interior angles of a polygon of n sides = (n – 2) × 180° = 3 x 180°= 540°. Hence, the sum of interior angles of a pentagon is 540°.

so ∠1 + ∠2 + 3(90°) = 540°

since ∠1 = ∠2

∠1 + ∠1 + 3(90) = 540

2∠1 + 270 = 540

2∠1 = 540 - 270

2∠1 = 270

∠1 = 270/2 = 135

Answer:

The set of all numbers less than 17 and greater than or equal to -8 can be expressed in set builder notation as:

{x | -8 <= x < 17}

Step-by-step explanation:

Set builder notation is a way of expressing a set of elements in mathematical terms. The syntax of set builder notation is {x | <condition>}, where x represents an element in the set and the condition specifies the properties that the element must satisfy to be included in the set.

In this case, the set consists of all numbers less than 17 and greater than or equal to -8. The condition for the set is -8 <= x < 17, where x is a real number. This means that x must be greater than or equal to -8 and less than 17 in order to be included in the set.

Therefore, the set of all numbers less than 17 and greater than or equal to -8 can be expressed in set builder notation as:

{x | -8 <= x < 17}.

Find the total distance that Ramesh ran is 23km. His average running speed for the whole journey is 3 5/6 km/h.

To find the average speed,

We find the total distance and divide it by the total time.

During the first part of the run, she ran 3 hours at a speed of 7 km/h.  

To find the the distance she ran, multiply the speed times the time:  3 x 7 = 21 km.

From the second part of the run, she ran 2km.

So the total distance he ran is 21 + 2 = 23km.

The total time was 6 hours.

To find the the average speed;  

Divide 23 by 6 to get the average speed, which comes to 3 5/6 km/h.

hence, the average speed is 3 5/6 km/h.

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The length of

KL = 7.8units

LM = 7.1 units

MN = 8.5 units

NK = 7.8units

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²).

KL = √1-(-4)²+3-(-3))²

KL = √5²+6²

KL = √ 25+36

KL = √ 61 = 7.8 units

To find the length KN

KN = √ 1-7)²+ 3(-2)²

KN = √ 6²+5²

KN = √ 36+ 25

KN = √ 61 = 7.8 units

to find LM

LM = √-4-1)²+-3(-8)²

LM = √25+25

LM = √50

LM = 7.1 units

to find MN

√ 7-1)²+ -2-(-8)²

MN= √ 6²+6²

MN = √ 36+36

MN=√ 72

MN = 8.5 units

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The system of equations that can be used to find the length of each workout and the duration of each workout are as follows;

(a) 5·x + 3·y = 10

2·x + 6·y = 10

(b) Length of each Plan A workout: 1.25 hours

Length of each Plan B workout: 1.25 hours

A linear system of equation consists of two or more linear equations that share common variables.

(a) The number of Plan A workouts Mary trained on Wednesday = 5

Number of Plan B workouts she trained on Wednesday = 3

The total time (in hours) Mary trained both workouts on Wednesday = 10

Where x represents the length (in hours) of each of the Plan A workout, and B represents the time in hours of each of the Plan B workout, we get;

5·x + 3·y = 10

Similarly, the number of Plan A workouts trained on Thursday = 2

Number of Plan B workout trained on Thursday = 6

The duration of training of all workouts on Thursday = 10 hours

Therefore, we get;

2·x + 6·y = 10

The system of equations that could be used to find the length (in hours) of each type of workout can be presented as follows;

(b) The first equation from the system of equations indicates that we get;

5·x + 3·y = 10

3·y = 10 - 5·x

Plugging the value of y above into the second equation from the system of equations, we get;

2·x + 6·y = 10

2·x + 6 × ((10 - 5·x)/3) = 10

2·x + 2·(10 - 5·x) = 10

2·x + 20 - 10·x = 10

20 - 8·x = 10

8·x = 20 - 10 = 10

x = 10/8 = 1.25

y = (10 - 5·x)/3,

x = 1.25, therefore;

y = (10 - 5 × 1.25)/3 = 1.25

y = 1.25

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The expression for its distance d (measured in feet) from the intersection t seconds later is d = x + 79200 t (feet)

Since the balloon is moving due east, we only need to consider its horizontal motion, ignoring its vertical motion at a constant altitude of 95 feet.

Let's call the initial distance of the balloon from the intersection x. The distance of the balloon from the intersection t seconds later can be found using the formula for distance traveled at a constant speed:

d = x + vt

where v is the speed of the balloon (15 miles per hour) and t is the time elapsed (in hours). To convert the speed from miles per hour to feet per second, we can multiply by the conversion factor of 5280 feet per mile:

d = x + (15 miles/hour) * (5280 feet/mile) * (t hours)

d = x + (15 * 5280) t feet

d = x + 79200 t feet

So the expression for the distance of the balloon from the intersection t seconds later is:

d = x + 79200 t (feet)

Note: In this expression, x represents the initial distance of the balloon from the intersection, which is unknown.

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On solving the provided question, we can say that  In decimals r = 3.8799 and d = 7.7598

Integer and non-integer numbers are οften expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded tο include non-integer values. Decimal notation is the name fοr the method used to represent numbers in the decimal system.

A decimal is a number with a whοle and a fractional component. Decimal numbers, which are in between integers, are used tο express the numerical value οf full and partially whole amounts.

the lengths (in inches) οf the radius and the diameter οf a circle with area 47.25 in'.

Area  = πr²

47.25 = 3.14 × r × r

r × r = 15.0541401274

In decimals

r = 3.8799

d = 7.7598

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Answer:

x=6

Step-by-step explanation:

the two dashes show that the two lines are parallel, so 23=3x+5; subract 5 from both sides to get 18=3x, so x=6

−26am^2 + 26am + 37a

Answer: Let's call the number of hours it takes for Rayna and Desi to build the fence together as "h". During this time, Rayna will build 10h feet of fence line, and Desi will build 2h feet of fence line.

Together, they will build 10h + 2h = 12h feet of fence line in h hours.

To build 80 feet of fence line, they will need h hours such that:

12h = 80

So,

h = 80 / 12 = 6.67 hours

So it will take Rayna and Desi 6.67 hours to build 80 feet of fence line together.

Step-by-step explanation:

The perimeter of the given figure is: 36 +16√5 ft ≈ 71.777 ft

The area of the figure is: 288 ft²

Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly. Then summing all those pieces' area gives us the area of the main big region.

We know that the perimeter is the total length of all the sides. The length of the horizontal sides is; 8 ft + 10 ft = 18 ft.

The length of the slant sides can be found by the Pythagorean theorem.

For side length s, we have;

s^2 = 8^2 + 16^2

 s^2 = 64 +256 = 320

 s = √320 = 8√5

Then the perimeter;

 P = 2(8√5 + 18) = 36 +16√5 ≈ 71.777 . . . feet

Area,  A = bh

where b is the base and h is the height.

 A = (18 ft)(16 ft) = 288 ft²

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The equation that we want to write is:

193n - 242 = 131

Here we want to write the sentence:

"242 fewer than the quantity 193 times n equals 131"

As an equation.

The first part means that we need to take a number n, multiply it by 193, and then subtract 242.

193n - 242

And that must be equal to 131, then the equation is:

193n - 242 = 131

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Answer:

Q(x) = 15x^2 + x - 2.

Step-by-step explanation:

To find the height of the water in a pool when both hoses are on, we need to add the values of the two functions, F(x) and P(x), at a given x value. The new function, Q(x), that determines the height of the water in the pool can be expressed as follows:

Q(x) = F(x) + P(x) = 9x^2 + 3x - 5 + 6x^2 - 2x + 3 = 15x^2 + x - 2

So the height of the water in the pool is determined by the function Q(x) = 15x^2 + x - 2.

By using the substitution method, the value of a is equal to 10 and the value of b is equal to -1.

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

2a + 7b = 13      .......equation 1.

8b = 2 - a          .......equation 2.

From equation 2, we have:

a = 2 - 8b         .......equation 3.

By using the substitution method to substitute equation 3 into equation 1, we have the following:

2(2 - 8b) + 7b = 13

4 - 16b + 7b = 13

4 - 9b = 13

9b = 4 - 13

9b = -9

b = -1

a = 2 - 8b

a = 2 - 8(-1)

a = 2 + 8

a = 10.

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Answer:

f-g= 3x²+1-(1-x)

3x²+1-1+x

3x²+x=0

x(3x+1)=O

x=0, 3x+1=0

So, x=0 or -1/3

Note that the Polynomial Expression for to represent the total surface area of the two drums is: 4πrh + 4hr².

A polynomial expression is any expression that consists of variables, constants, and exponents and is combined using mathematical operators such as addition, subtraction, multiplication, and division.

According to the number of terms in the expression, polynomial expressions are classed as monomials, binomials, or trinomials.

Given that the total surface area of one cylinder is:

2πrh + 2πr²,

The total surface area of two drums will therefore be:

(2πrh + 2πr²) * 2

⇒ 4πrh + 4hr²

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Answer:

c) [tex]10x<7z[/tex]

Step-by-step explanation:

[tex]5x<3y \implies 10x<6y \\ \\ \therefore 10x<6y<7z \implies 10x<7z[/tex]

D because none of the inputs (x) are repeated. All the others have the same input with two or more different outputs.

➡ There are 22 hundredths. That is enough to make a tenth.

What is the arithmetic operations?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional  operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms,[disputed – discuss] which are highly important to the field of mathematical logic today.

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

To find the total volume of the slime, we need to add 1.5 and 0.72:

1.5 + 0.72 = 2.22

There are 22 hundredths, which is enough to make a tenth.

Hence, the answer is:

➡ There are 22 hundredths. That is enough to make a tenth.

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(a) The height after t years is given by

h(t) = 0.6t² + 3t + 11

(b) The shrubs are 38 centimetres tall when they are sold.

The growth rate of the shrubs during the first year of growth can be determined by setting t = 1 in the given differential equation dh/dt = 1.2t + 3. This gives us dh/dt = 1.2(1) + 3 = 4.2 centimeters per year.

Therefore, during the first year of growth, the shrubs will grow at a rate of 4.2 centimeters per year. This rate of growth is expected to increase as the shrubs age and reach the end of the 5-year growth period before they are sold by the nursery.

(a) To find the height after t years, we integrate the growth rate function with respect to t:

∫dh/dt dt = ∫(1.2t + 3) dt

h(t) = 0.6t² + 3t + 11

(b) The shrubs are sold after 5 years, so we plug in t = 5 into the function we found in part (a):

h(5) = 0.6(5)² + 3(5) + 11

= 38 cm

Therefore, the shrubs are 38 centimetres tall when they are sold.

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