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Answer:

[tex]96\ basketballs[/tex]

Step-by-step explanation:

step 1

Find the volume of the cylinder (hollow drum)

The volume is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]h=48\ in[/tex]

[tex]r=24\ in[/tex]

substitute

[tex]V=\pi (24)^{2} (48)[/tex]

[tex]V=27,648\pi\ in^{3}[/tex]

step 2

Find the volume of one basketball

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=6\ in[/tex]

substitute

[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]

[tex]V=288\pi\ in^{3}[/tex]

step 3

Find the maximum number of basketballs that the cylindrical drum contains

so

Divide the volume of the cylinder by the volume of one basketball

[tex]27,648\pi/288\pi=96\ basketballs[/tex]

For this case we have by definition, that if two lines are parallel then their slopes are equal.

We manipulate the equations algebraically to take them to the form y = mx + b.

Equation 1:

[tex]2y = -3x + 8\\y = - \frac {3} {2} x + 4[/tex]

Thus, the slope of this line is [tex]- \frac {3} {2}.[/tex]

Equation 2:

[tex]6x + 2y = 9\\2y = 9-6x\\2y = -6x + 9\\y = \frac {-6x + 9} {2}\\y = -3x + \frac {9} {2}[/tex]

The slope of this line is -3.

As the slopes are not equal, then the lines are not parallel.

Answer:

False

ANSWER

The solution is

(x,y)=(1,-5)

EXPLANATION

The equations are:

1st equation: 6x +5y=-19

2nd equation: 12x-8y=52

Multiply the first equation by 2:

3rd equation: 12x +10y=-38

Subtracy the 2nd equation from the 3rd equations.

12x-12x+10y--8y=-38-52

18y=-90

Divide both sides by 18.

y=-5

Put y=-5 into any of the equations and solve for x.

Preferably, the first equation will do.

6x +5(-5)=-19

6x -25=-19

6x=25-19

6x=6

x=1

The solution is

(x,y)=(1,-5)

Answer:

[tex]\large\boxed{(8\times6)-(4\times2)=48-8=40}[/tex]

The expression (8*2)*2 + 6 + 2 uses the numbers 8, 6, 4, and 2 to equal 40. The question tests knowledge of basic arithmetic operations.

The question involves using the numbers 8, 6, 4, and 2 to create an expression that equals 40. This is a problem dealing with basic arithmetic operations like addition, subtraction, multiplication, and division. The expression can be formed as follows:

So, the expression is: (8*2)*2 + 6 + 2 = 40

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Answer: 10.5 gallons

Step-by-step explanation:

One imperial gallon is approximately 1.2 US gallons. The US gallon is used in the United States and is equal to exactly 231 cubic inches or 3.785411784 liters. The Imperial gallon or UK gallon is used in the United Kingdom and is equal to approximately 277.42 cubic inches. Its exact value is defined as 4.54609 liters.

Answer:

abc is the one that must be a simicircle

Answer:

A. ABC.

Step-by-step explanation:

We have been given an image of a circle. We are asked to choose the arc, which must be a semicircle of our given circle.

Upon looking at our given diagram, we can see that AC divides our given circle into two semicircles ABC and ATC.

From our given choices, we can see that option A is the correct choice.

A line parallel to 2x - 3y = 9 would have the same slope, 2/3, and a different y-intercept, represented as y = (2/3)x + b, where 'b' is any real number.

The equation 2x - 3y = 9 represents a line in a standard form. To find a line that is parallel to it, we need another line with the same slope. The slope-intercept form of the given equation, by isolating y, is y = (2/3)x - 3. A parallel line must have the same slope, which is 2/3 in this case. Therefore, a line parallel to 2x - 3y = 9 could be represented as y = (2/3)x + b, where 'b' is any y-intercept. For example, if b = 5, a parallel line would be given by y = (2/3)x + 5.

Answer:  3

Step-by-step explanation:

Median is the middle number if it is an odd number or if it is even you add the two middle numbers and divide by 2

The median cleanliness rating for Restaurant A is 3.

The median of Restaurant A's cleanliness ratings can be found by arranging the ratings in order from lowest to highest and determining the middle value. In this case, the ratings are 1, 2, 3, 4, and 5. Since there is an odd number of ratings, the median is the middle value, which is 3. Therefore, the median cleanliness rating for Restaurant A is 3.

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Answer:

The 51 and 62 triangle is 67°

The 43 triangle is 47°

Step-by-step explanation:

Angles in a triangle add to 180°

180 - ( 51 + 62 ) = 180 - ( 113 ) = 67°

180 - ( 43 + 90 ) = 180 - 133 = 47°

Answer:

Step-by-step explanation:

The total number of marbles is 24 + 36 + 60 = 120

Red: 24/120 = 1/5

Blue: 36/120 = 6/20 = 3/10

Yellow: 60 / 120 = 1/2

Answer:

160

Step-by-step explanation:

The top right quadrant is 90 and the given is 70, adding them equal 160. It is the only option that is greater than 90 degrees anyway.

Answer: 36ft

Step-by-step explanation: 180*.2=36

Answer:

36 ft

Step-by-step explanation:

to find 20% of 180 ft, multiply 180 ft by 0.20:  0.20(180 ft) = 36 ft

Answer:

You could divide $12 with either method

If you divided 12 by 1/4 you would get $48.

Divided by 1/3, $36.

Answer:

9

i did this question before

Answer:

The value of x is 9.

Step-by-step explanation:

Given equation,

[tex](x+2)^2=a[/tex]

If x = 1 is the solution of this equation,

Then it will satisfy the equation,

[tex]\implies (1+2)^2=a[/tex]

[tex]\implies (3)^2=a[/tex]

[tex]\implies a = 9[/tex]

Hence, the value of x is 9 if x = 1 is the solution of the given equation.

Answer:

x = 8.9 (nearest tenth)

Step-by-step explanation:

6^2 - 4^2 = 36 - 16 = 20

So

x = 2 * (√20)

x = 2 * 4.47

x = 8.94

Answer:

The value of x = 4√5

Step-by-step explanation:

Points to remember

For a right angled triangle

Hypotenuse² = Base² + Height²

To find the value of x

From the figure we can see a right angled triangle with,

hypotenuse = 6 and height = 4

Value of x = 2 * base

we have, Hypotenuse² =  + Height²

Base² = Hypotenuse² - Height²

 = 6² - 4²

 = 36 - 16  = 20

Base = √20 = 2√5

x = 2 * 2√5 = 4√5

The value of x = 4√5

Answer:

x = - 9, x = - 3

Step-by-step explanation:

Given

x² + 12x + 27 = 0

To factorise the quadratic

Consider the factors of the constant term (+ 27) which sum to give the coefficient of the x- term (+ 12)

The factors are + 9 and + 3, since

9 × 3 = 27 and 9 + 3 = 12, hence

(x + 9)(x + 3) = 0

Equate each factor to zero and solve for x

x + 9 = 0 ⇒ x = - 9

x + 3 = 0 ⇒ x = - 3

Answer:

The value of the expression is 100

Step-by-step explanation:

we have

5,200-[40%(300*42.5)]

we know that

(300*42.5)=3*100*42.5=3*4,250=12,750

40%=40/100=0.40

substitute

5,200-[0.40*12,750]

5,200-5,100=100

Answer:

240 units^3

Step-by-step explanation:

To find the volume of a rectangular prism you just multiply length times width times height. So, 8*6*5 which equals 240 units^3.

The dimensions of the prism is given as Length = 8 units, width = 6, Height = 5. Therefore, the volume of the prism is 240 units^3.

Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units,

then its volume is given as:

[tex]V = a\times b \times c \: \: unit^3[/tex]

The dimensions of the prism is given as

Length = 8 units

width = 6

Height = 5

To find the volume of a rectangular prism

[tex]V = a\times b \times c \: \: unit^3[/tex]

V = 8 x 6 x 5

V = 240 units^3.

Therefore, the volume of the prism is 240 units^3.

Learn more about the volume of a right rectangular prism here:

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Answer:

7/9

Step-by-step explanation:

6x^3-8y^3-12x^2y^2+4xy       x=2/3 y=1/2

=6(2/3)^3-8(1/2)^3-12(2/3)^2(1/2)^2+4(2/3)(1/2)

=6(8/27)-8(1/8)-12(4/9)(1/4)+4(1/3)

=(16/9)-1-(4/3)+(4/3)

=(1 7/9)-1

=7/9

Answer:

22

Step-by-step explanation:

The perimeter of the isosceles triangle with a point of tangency that divides one leg into 3 cm and 4 cm segments is 22 cm, having both legs 7 cm each and the base 8 cm.

Given an isosceles triangle with a point of tangency that divides one of the equal legs into segments of 3 cm and 4 cm, we can determine the perimeter of the triangle by first understanding the properties of such a triangle. The two legs are congruent, and by the Theorem 6, the radius from the center to the point of tangency is perpendicular to the tangent and bisects it. Knowing that the point of tangency divides a leg into two parts, we can denote the entire length of one leg as 3 cm + 4 cm, which equals 7 cm.

Since the triangle is isosceles, both legs are equal in length. This means the other leg is also 7 cm. To find the base, we recall the perpendicular from the center bisects it (Theorem 6). Hence, the base is twice one of the segments, either 3 cm or 4 cm. We will choose the longer segment to ensure that the vertex angles remain acute, and hence the base would be 2 * 4 cm = 8 cm.

Now the perimeter (P) of the triangle can be found by adding the lengths of the two legs and the base: P = 7 cm + 7 cm + 8 cm = 22 cm. Therefore, the perimeter of the isosceles triangle is 22 cm.

Answer: 3 yd

Step-by-step explanation: The radius is 3 yards because the diameter is 6 and the radius is d/2. 6/2 is equal to 3.

Hope this helps!

Answer:

I think it is A.

Step-by-step explanation:

Hope my answer has helped you!

The true statement is:

Hence, such points could never form a triangle.

Because a triangle is formed with the help of three non-collinear points.

Hence, the points will be coplanar (i.e. they lie in the same plane)

The answer is:

[tex](g\circ f)(0)=-216[/tex]

To composite functions, we need to evaluate functions in another function(s), for example:

Given f(x) and g(x), if we want to calculate f(x) composite g(x), we need to evaluate g(x) into f(x).

So, we are given the functions:

[tex]f(x)=2x-6\\g(x)=x^{3}[/tex]

And we are asked to calculate g(x) composite f(x), and then evaluate "x" to 0, so, calculating we have:

[tex](g\circ f)(x)=g(f(x))\\\\(g\circ f)(x)=(2x-6)^{3}[/tex]

Now that we have the composite function, we need to evaluate "x" equal to 0, so:

[tex](g\circ f)(0)=(2x-6)^{3}\\\\(g\circ f)(0)=(2*(0)-6)^{3}=(0-6)^{3}=-6*-6*-6=-216[/tex]

Hence, we have that:

[tex](g\circ f)(0)=-216[/tex]

Have a nice day!

Answer:

Step-by-step explanation:216

Answer:

120 square units

Step-by-step explanation:

In triangle PSQ, PS=SQ. Let PS=SQ=x units.

Since SQ-PQ=1, PQ=SQ-1=x-1 units.

The perimeter of the triangle PSQ is 50 units, so

PS+SQ+PQ=50 units.

Substitute PS=SQ=x un. and PQ=x-1 un.

x+x+x-1=50

3x=51

x=17

Hence

PS=SQ=17 units,

PQ=16 units.

Use Heron's formula to find the area:

[tex]A=\sqrt{p(p-a)(p-b)(p-c)},[/tex]

where p is semi-perimeter and a,b,c are lengths of sides.

[tex]p=\dfrac{17+17+16}{2}=25,\\ \\\\A=\sqrt{25(25-17)(25-17)(25-16)}=\sqrt{25\cdot 8\cdot 8\cdot 9}=5\cdot 8\cdot 3=120\ un^2.[/tex]

Answer:

16

Step-by-step explanation:

Exterior angle theorem - the sum of two interior angles (which in this case would be angle R and N) is equal to the measure of the exterior angle.

Answer:

Part 1) The new distance from the water to the top of the tank is [tex]1.979\ in[/tex]

Part 2) The maximum number of balls that can be put into the tank with the tank not overflowing is 95

Step-by-step explanation:

step 1

Find the total volume of the tank

[tex]V=20*10*15=3,000\ in^{3}[/tex]

step 2

Find the volume of the tank if the water level is two inches below the top of the tank

[tex]V=20*10*(15-2)=2,600\ in^{3}[/tex]

step 3

Find the volume of the glass sphere

The volume of the glass sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=1\ in[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]V=\frac{4}{3}(3.14)(1)^{3}[/tex]

[tex]V=4.2\ in^{3}[/tex]

step 4

What is the new distance from the water to the top of the tank?

we know that

[tex]2 in -----> represent (3,000-2,600)=400\ in^{3}[/tex]

so

using proportion

Find how many inches correspond a volume of [tex]4.2\ in^{3}[/tex]

[tex]\frac{2}{400}\frac{in}{in^{3}}=\frac{x}{4.2}\frac{in}{in^{3}}\\ \\x=4.2*2/400\\ \\x=0.021\ in[/tex]

The new distance from the water to the top of the tank is

[tex]2-0.021=1.979\ in[/tex]

step 5

Find how many of these balls can be put into the tank with the tank not overflowing

we know that

The volume of one ball is equal to  [tex]4.2\ in^{3}[/tex]

using proportion

[tex]\frac{1}{4.2}=\frac{x}{400}\\ \\x=400/4.2\\ \\x=95.23\ balls[/tex]

therefore

The maximum number of balls that can be put into the tank with the tank not overflowing is 95

Answer:

Option C

Step-by-step explanation:

we know that

Two angles are complements if their sum is equal to 90 degrees

we have that

∠SWT=50°

so

Its complement must be equal to 40 degrees

we know that

∠USP=40°

∠TSV=40°

therefore

∠USP and ∠TSV are complements to ∠ SWT

ANSWER

An ordered pair that is the solution to the system of equations lies on the y-axis.

The y-coordinate of a solution to the system of equations is 4.

EXPLANATION

The given system has equations:

[tex]y = {x}^{2} + 2x + 4[/tex]

[tex]y = - x + 4[/tex]

We equate both equations to get:

[tex] {x}^{2} + 2x + 4 = - x + 4[/tex]

This implies that,

[tex] {x}^{2} + 2x + x + 4 - 4 = 0[/tex]

[tex] {x}^{2} + 3x = 0[/tex]

[tex]x(x + 3) = 0[/tex]

[tex]x = 0 \: or \: x = - 3[/tex]

When x=0, y=-(0)+4=4

When x=-3, y=-(-3)+4=7

The solutions are: (0,4) and (-3,7)

The true statements about the system of equations are:

The system of equations is given as:

f(x)=−x^2+2x+4

g(x)=−x+4

From the graph of the system of equations (see attachment), we have the following point of intersections

(x,y) = (0,4) and (3,1)

So, the true statements about the system of equations are:

(a), (c), (d) and (e)

Read more about system of equations at:

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Answer:

[tex]-11b^2+8b-4[/tex]

Step-by-step explanation:

We can substitute in our expressions for P and Q to get

[tex]P=-4b^2+6b-9\\Q=7b^2-2b-5\\\\(-4b^2+6b-9)-(7b^2-2b-5)[/tex]

Next, we need to distribute the negative to the values within the parenthesis. Then we can combine like terms in order to get our answer

[tex](-4b^2+6b-9)-(7b^2-2b-5)\\\\-4b^2+6b-9-7b^2+2b+5\\\\-11b^2+8b-4[/tex]

Answer:

-11b^2 + 8b - 4

Step-by-step explanation:

(-4b^2 + 6b - 9) - (7b^2 - 2b - 5) =

Drop the first set of parentheses because it is unnecessary. To drop the second set of parentheses, you must distribute the negative sign. That means you must change every sign inside the second set of parentheses.

= -4b^2 + 6b - 9 - 7b^2 + 2b + 5

Now, group like terms.

= -4b^2 - 7b^2 + 6b + 2b - 9 + 5

Finally, combine like terms.

= -11b^2 + 8b - 4

Answer:

$ 5674.076

Step-by-step explanation:

The question is on compound interest

The formulae = A= P(1+ r/n) ^nt .......where P is the principal amount, r is the rate of interest in decimal, n is number of compoundings per year and t is the total number of years.

Given; P= $4,000.00 , r=12/100=0.12, n=2 and t=3

Substituting values in the equation  A= P(1+ r/n) ^nt

A= 4000 ( 1+0.12/2)^2×3

A=4000(1.06)^6

A=$ 5674.08