The figure is made up of a cylinder, a cone, and a half sphere. The radius of the half sphere is 3 inches. What is the volume of the composite figure?

Answer:

The value of discriminant is 384

There are two different real roots for the equation

Step-by-step explanation:

* Lets explain what is the discriminant

- In the quadratic equation ax² + bx + c = 0, the roots of the

 equation has three cases:

1- Two different real roots

2- One real root or two equal real roots

3- No real roots means imaginary roots

- All of these cases depend on the value of a , b , c

∵ The rule of the finding the roots is  

   x = [-b ± √(b² - 4ac)]/2a

- The effective term is b² - 4ac to tell us what is the types of

 the roots

# If the value of b² - 4ac is positive means greater than 0

∴ There are two different real roots

# If the value of b² - 4ac = 0

∴ There are two equal real roots means one real root

# If the value of b² - 4ac is negative means smaller than 0

∴ There is no real roots but the roots will be imaginary roots

∴ We use the discriminant to describe the number and type of roots

* Now lets solve the problem

∵ -3x² - 18x + 5 = 0

∴ a = -3 , b = -18 , c = 5

∵ Δ = b² - 4ac ⇒ (Δ is the discriminant symbol)

∴ Δ = (-18)² - 4(-3)(5) = 324 - (-60) = 324 + 60 = 384

∴ The value of discriminant is 384

∵ The value of discriminant greater then 0

∴ There are two different real roots for the equation

Answer: Third option

[tex]-u-v = <-2, -3>[/tex]

Step-by-step explanation:

We have the vector u and the vector v. We must perform the operation [tex]-u-v[/tex].

To perform this operation multiply the vector u by -1 and multiply the vector v by -1.

If u = (-5,6)

So

-1u = (5, -6)

If v = (7, -3)

So

-1v = (-7, 3)

Then the sum of both vectors is done by adding the components of u with the components of v.

[tex]-u-v = (5, -6) + (-7,\ 3)\\\\-u-v = (5-7\ ,\ -6 + 3)\\\\-u-v = (-2,\ -3)[/tex]

The answer is:

The correct option is:

A) Jeff, 4.5 hours; Julia 9 hours.

To solve the problem, we need to write two equations using the given information.

So, writing the first equation we have:

We know that Jeff can weed the garden twice as fas as his sister Julia, so:

[tex]JeffRate=2JuliaRate[/tex]

Also, from the statement we know that they can weed the garden in 3 hours, so, writing the second equation we have:

[tex]JeffRate+JuliaRate=\frac{1garden}{3hours}[/tex]

Then, we need to substitute the first equation into the second equation in order to isolate Julia's rate, so, solving we have:

[tex]JeffRate+JuliaRate=\frac{1garden}{3hours}[/tex]

[tex]2JuliaRate+JuliaRate=\frac{1garden}{3hours}[/tex]

[tex]2JuliaRate+JuliaRate=\frac{1garden}{3hours}[/tex]

[tex]3JuliaRate=\frac{1garden}{3hours}[/tex]

[tex]JuliaRate=\frac{1garden}{3hours*3}=\frac{1garden}{9hours}[/tex]

We have that Julia could weed the garden by herself in 9 hours.

So, calculating how long will it take to Jeff, we have:

[tex]JeffRate=2*JuliaRate\\\\JeffRate=2*\frac{1garden}{9hours}=\frac{2garden}{9hours}=\frac{1garden}{4.5hours}[/tex]

We have that Jeff could weed the same garden by himself in 4.5 hours.

Hence, the correct option is:

A) Jeff, 4.5 hours; Julia 9 hours.

Have a nice day!

Answer:

A

Step-by-step explanation:

Answer:

The volume of cone B is equal to [tex]256\pi\ ft^{3}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

The scale factor is equal to the ratio of its diameters

so

16/8=2

step 2

Find the volume of cone B

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z -----> the scale factor

Vb ----> volume of cone B

Va ----> volume of cone a

[tex]z^{3}=\frac{Vb}{Va}[/tex]

we have

[tex]z=2[/tex]

[tex]Va=32\pi\ ft^{3}[/tex]

substitute

[tex]2^{3}=\frac{Vb}{32\pi}[/tex]

[tex]Vb=(8)(32\pi)=256\pi\ ft^{3}[/tex]

The volume of cone B that is similar to cone A is calculated as: 256π ft³.

Volume of Solid A/volume of solid B = a³/b³, where a and b are the corresponding linear measures of both solids.

32π/B = 4³/8³

B(4³) = (8³)(32π)

64(B) = 16,384π

B = 16,384π/64

Volume of cone B is: 256π ft³

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Answer:

Sur. area = 360 area unit , vol = 54√3 volume unit

Step-by-step explanation:

Sur. area = 6×(6×10)

Volume= (n/4)X² (cot(180/n)) , n is number of sides and X is side length

Find the exact value of each one:

5^2 = 25

2^4 = 16

3^3 = 27

1^8 = 1

Now you can list them in order from smallest to largest:

1^8, 2^4, 5^2, 3^3

Answer:

Step-by-step explanation:

5²=25

2^4=16

3^3=27

1^8=1

1<16<25<27

so 1^8<2^4<5^2<3^3

Answer:

Add the equations to eliminate x

Step-by-step explanation:

Let's go through each of these statements

1) Add the equations to eliminate x

   y = x + 10

+

   y = -x + 3

   _______

  2y = 13

This works!

Answer:

Add the equation to eliminate x.

Step-by-step explanation:

Add the equation to eliminate x.

Let's actually do the work!  

y = x + 10

y = −x + 3

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

2y = 13, so y = 6.5.

Subbing 6.5 for y in either of the equations above lets us calculate y.  For example, in the second equation, 6.5 = -x + 3, or 3.5 = -x, or x = -3.5.

The solution is (-3.5, 6.5).

2 pounds total!

3/6 * 4 cans = 2 pounds

Answer:

The weight of 4 cans of peaches will be 2 pounds if one can of peaches weigh 3/6 pound.

Step-by-step explanation:

We need to find the weight of 4 cans of peaches altogether.

Weight of 1 can of peaches = 3/6 pounds

Weight of 4 cans of peaches = 3/6 * 4

                                                = 12 / 6

                                                = 2 pounds.

So, The weight of 4 cans of peaches will be 2 pounds if one can of peaches weigh 3/6 pound.

3q - 2p; all you are doing is simplifying straight across. I think you got confused by the parentheses unwrapped around 6p - 9q. Well, it is STILL the same process.

Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, - 3)

m = [tex]\frac{-3-0}{0+1}[/tex] = - 3

note the line crosses the y- axis at (0, - 3) ⇒ c = - 3

y = - 3x - 3 ← in slope- intercept form

Add 3x to both sides

3x + y = - 3 ← in standard form → C

Hello There!

[tex]\frac{18}{20}[/tex] as a decimal is 0.9

You can first reduce this fraction by dividing both the numerator and denominator by the Greatest Common Factor of 18 and 20 using 2.

18 ÷ 2 ≈ 9

20 ÷ 2 ≈ 10

We now have the fraction [tex]\frac{9}{10}[/tex]

Finally, we divide 9 by 10 and we get a quotient of 0.9

The equivalent value of the decimal is A = 18/20 = 0.9

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the numerator of the fraction be p

where the value of p = 18

Let the denominator of the fraction be q

where q = 20

Now , the fraction is A = p/q

On simplifying the expression , we get

So , the left hand side of the equation is equated to the right hand side by the value of p/q

A = 18/20

A = 9/10

On further simplification , we get

A = 0.9

So , the decimal number is A = 0.9

Therefore , the value of A = 0.9

Hence , the expression is A = 0.9

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Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given a number n then the multiplicative inverse is [tex]\frac{1}{n}[/tex]

The product of a number and it's multiplicative inverse = 1

Given 2, then multiplicative inverse is [tex]\frac{1}{2}[/tex]

Answer:

12

Step-by-step explanation:

we can see that the base's size is doubled, from that we can find that 6 will be doubled to twelve.

Answer: 12

Step-by-step explanation: The Answer is 12. This is because the numbers on the left are 2x less than on the right.

Answer:

Step-by-step explanation:

8.8 laps because of the concepts of molecular osmosis used to provide a detailed explanation to kermit. Thereby omitting the theory of dark matter into the universe and thus replacing it with the new compulsive theory of 50 % growth of human anatomical secretory sections.

Answer:

D) 8.8 laps.

Step-by-step explanation:

We have been given that each player on the football team is required to run 1.5 miles in less than 15 minutes. One lap around the field is 300 yards.

We know that 1 mile equals 1760 yards.

First of all, we will convert 1.5 miles into yards by multiplying 1.5 by 1760.

[tex]\text{1.5 miles}=\text{1.5 miles}\times \frac{\text{1760 yards}}{\text{Mile}}[/tex]

[tex]\text{1.5 miles}=1.5\times \text{1760 yards}[/tex]

[tex]\text{1.5 miles}=2640\text{ yards}[/tex]

We have been given that one lap around the field is 300 yards. To find the number of laps a player must run, we will divide 2640 by 300.

[tex]\text{Number of laps a player must run}=\frac{2640\text{ yards}}{300\text{ yards}}[/tex]

[tex]\text{Number of laps a player must run}=8.8[/tex]

Therefore, a player must run 8.8 laps to meet the requirement.

C. Expression

An inequality must contain a sign relating magnitude.

An equation must contain an equal sign.

An expression cannot have an equal sign or any symbols of inequality.

A fraction must contain a bar representing division.

Hope this helps!!

The values of 12C4 and 11P4 are 495 and 7920, respectively

The expressions are illustrations of permutation and combination, and they are calculated using:

[tex]^nC_r = \frac{n!}{(n -r)!r!}[/tex]

and

[tex]^nP_r = \frac{n!}{(n -r)!}[/tex]

So, we have:

[tex]^{12}C_4 = \frac{12!}{(12 -4)!4!}[/tex]

Evaluate the difference

[tex]^{12}C_4 = \frac{12!}{8!4!}[/tex]

Evaluate the factorials

[tex]^{12}C_4 = \frac{479001600}{967680}[/tex]

Divide

[tex]^{12}C_4 = 495[/tex]

Also, we have:

[tex]^{11}P_4 = \frac{11!}{(11 -4)!}[/tex]

Evaluate the difference

[tex]^{11}P_4 = \frac{11!}{7!}[/tex]

Evaluate the quotient

[tex]^{11}P_4 = 7920[/tex]

Hence, the values of 12C4 and 11P4 are 495 and 7920, respectively

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Answer:

Part 1)  [tex]f^{-1}(x)=3(x+17)/2[/tex] ----> [tex]f(x)=\frac{2x}{3}-17[/tex]

Part 2) [tex]f^{-1}(x)=x+10[/tex] -----> [tex]f(x)=x-10[/tex]

Part 3) [tex]f^{-1}(x)=\frac{x^{3}}{2}[/tex] ----> [tex]f(x)=\sqrt[3]{2x}[/tex]

Part 4) [tex]f^{-1}(x)=5x[/tex] ----> [tex]f(x)=x/5[/tex]

Step-by-step explanation:

Part 1) we have

[tex]f(x)=\frac{2x}{3}-17[/tex]

Find the inverse

Let

y=f(x)

[tex]y=\frac{2x}{3}-17[/tex]

Exchange the variables, x for y and y for x

[tex]x=\frac{2y}{3}-17[/tex]

Isolate the variable y

Adds 17 both sides

[tex]x+17=\frac{2y}{3}[/tex]

Multiply by 3 both sides

[tex]3(x+17)=2y[/tex]

Divide by 2 both sides

[tex]y=3(x+17)/2[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

so

[tex]f^{-1}(x)=3(x+17)/2[/tex]

Part 2) we have

[tex]f(x)=x-10[/tex]

Find the inverse

Let

y=f(x)

[tex]y=x-10[/tex]

Exchange the variables, x for y and y for x

[tex]x=y-10[/tex]

Isolate the variable y

Adds 10 both sides

[tex]y=x+10[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

so

[tex]f^{-1}(x)=x+10[/tex]

Part 3) we have

[tex]f(x)=\sqrt[3]{2x}[/tex]

Find the inverse

Let

y=f(x)

[tex]y=\sqrt[3]{2x}[/tex]

Exchange the variables, x for y and y for x

[tex]x=\sqrt[3]{2y}[/tex]

Isolate the variable y

elevated to the cube both sides

[tex]x^{3}=2y[/tex]

Divide by 2 both sides

[tex]y=\frac{x^{3}}{2}[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

so

[tex]f^{-1}(x)=\frac{x^{3}}{2}[/tex]

Part 4) we have

[tex]f(x)=x/5[/tex]

Find the inverse

Let

y=f(x)

[tex]y=x/5[/tex]

Exchange the variables, x for y and y for x

[tex]x=y/5[/tex]

Isolate the variable y

Multiply by 5 both sides

[tex]y=5x[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

so

[tex]f^{-1}(x)=5x[/tex]

The inverse of a function is shown in the picture we can calculate by interchanging the value of f(x) and x.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

Functions are shown in the picture.

We have to find the inverse of a function.

[tex]\rm f(x) = \dfrac{2x}{3}-17[/tex]

To find the inverse of a function plug in the place of f(x)→x and x→f(x) ⁻¹

[tex]\rm x = \dfrac{2f^-^1(x)}{3}-17[/tex]

f(x) ⁻¹ = 3(x + 17)/2

Similarly, we can find the rest of the inverse of the function as follows:

f(x) = x - 10

f(x) ⁻¹ = x + 10

f(x) = ∛2x

f(x) ⁻¹ = x³/2

f(x) = x/5

f(x) ⁻¹ = 5x

Thus, the inverse of a function is shown in the picture we can calculate by interchanging the value of f(x) and x.

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Answer:

The values of theta where cos(theta) is 0 is equal to π/2 or 3π/2 so, the value of tan(theta) will be zero.

Step-by-step explanation:

As we know,

tan(theta) = sin(theta)/ cos(theta)

tan(theta) will be undefined whenever cos(theta) = 0

as anything divided by zero is undefined.

We need to find the values of theta where cos(theta) is 0.

cos(0) = 1

cos (π/2) = 0

cos(π) = 1

cos(3π/2) = 0

The values of theta where cos(theta) is 0 is equal to π/2 or 3π/2 so, the value of tan(theta) will be zero.

using the composition of the functions [tex]\(f\)[/tex] and [tex]\(g\)[/tex] as defined by the table, we get that [tex]\((f \circ g)(1) = 17\).[/tex]

To find [tex]\((f \circ g)(1)\)[/tex], we need to first find  and then find the value of [tex]\(f\)[/tex] at that result.

1. Identify [tex]\(g(1)\)[/tex]: We need to evaluate the function [tex]\(g\)[/tex] at [tex]\(x = 1\)[/tex]. Looking at the table under the row for [tex]\(g(x)\)[/tex] and the column where \(x = 1\), we find that [tex]\(g(1) = 6\).[/tex]

2. Evaluate [tex]\(f\)[/tex] at [tex]\(g(1)\)[/tex]: Now that we have that [tex]\(g(1) = 6\)[/tex], we need to evaluate the function [tex]\(f\)[/tex] at [tex]\(x = 6\)[/tex]. Looking at the table under the row for [tex]f(x)\)[/tex] and the column where [tex]\(x = 6\)[/tex], we find that [tex]\(f(6) = 17\).[/tex]

3. **Combine the results**: We have [tex]\(f(g(1)) = f(6)\)[/tex]. Since we found out that [tex]\(f(6) = 17\)[/tex], we can conclude that [tex]\((f \circ g)(1) = 17\).[/tex]

So, using the composition of the functions [tex]\(f\)[/tex] and [tex]\(g\)[/tex] as defined by the table, we get that [tex]\((f \circ g)(1) = 17\).[/tex]

Answer:

-480

Step-by-step explanation:

If f varies directly as g, and inversely as h, then we can write the variation equation:

[tex]f=\frac{kg}{h}[/tex], where k is the constant of variation.

If g=56 when h=-2 and f=-7, then we substitute these values into the formula to find the value of k.

[tex]-7=\frac{k(56)}{-2}[/tex]

[tex]-7\times -2=56k[/tex]

[tex]k=\frac{14}{56}=\frac{1}{4}[/tex]

The equation now becomes:

[tex]f=\frac{g}{4h}[/tex]

if f=10 and h=-12, then;

[tex]10=\frac{g}{-48}[/tex]

[tex]g=-48\times 10=-480[/tex]

The correct answer is B.

To find g when f = 10 and h = -12, use the formula for direct variation: f = kg. Substituting the given values, we can solve for g.

We are given that f varies directly as g, and f varies inversely as h. To find g when f = 10 and h = -12, we can use the formula for direct variation: f = kg, where k is the constant of variation. So, f/g = k. Substituting the given values, we have 10/g = k. To find k, we need to find g when f = -7 and h = -2. Using the same formula, we have -7/g = k. Since k is the same constant in both cases, we can equate the two equations: 10/g = -7/g. Solving for g, we get g = -70/10 = -7.

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Answer:

In logic, statements and are logically equivalent if they have the same logical content. That is, if they have the same truth value in every model. The logical equivalence of and is sometimes expressed as, or. However, these symbols are also used for material equivalence. Proper interpretation depends on the context.

Step-by-step explanation:

Answer:

they have the same logical content

Step-by-step explanation:

that is if they have the same truth

Answer:

A = 90 - x

Step-by-step explanation:

The square on the lower right means the two line segments form a right angle.

If B = x

and C = 90

the A = 180 - x - 90    (Every triangle has 180 degrees -- no exceptions).

A = 90 - x

Answer:

17) Ф = 57.99 ≅ 58°

18) Ф = 20.10 ≅ 21°

Step-by-step explanation:

* Lets revise the trigonometry functions

- In any right angle triangle:

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

- For angle A

# sin(A) = opposite/hypotenuse

∵ The opposite to ∠A is BC

∵ The hypotenuse is AC

∴ sin(A) = BC/AC

# cos(A) = adjacent/hypotenuse

∵ The adjacent to ∠A is AB

∵ The hypotenuse is AC

∴ cos(A) = AB/AC  

# tan(A) = opposite/adjacent

∵ The opposite to ∠A is BC

∵ The adjacent to ∠A is AB

∴ tan(A) = BC/AB

* Now lets solve the problems

17) In Δ ACB

∵ m∠C = 90°

∵ BC = 16 units ⇒ opposite to angle Ф

∵ AC = 10 units ⇒ adjacent to angle Ф

∵ tanФ = opposite/adjacent

∴ tanФ = BC/AC

∴ tanФ = 16/10 = 8/5

- To find angle Ф find the inverse of tan (tan^-1)

∴ Ф = tan^-1 8/5 = 57.99 ≅ 58°

18) In Δ ACB

∵ m∠C = 90°

∵ BC = 5.6 units ⇒ opposite to angle Ф

∵ AC = 15.3 units ⇒ adjacent to angle Ф

∵ tanФ = opposite/adjacent

∴ tanФ = BC/AC

∴ tanФ = 5.6/15.3 = 56/153

- To find angle Ф find the inverse of tan (tan^-1)

∴ Ф = tan^-1 56/153 = 20.10 ≅ 21°

Answer:

17).  θ = 57.99°

18).  θ =20.10°

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ  = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = Opposite side/Adjacent side

Question (17).

From the figure we can write,

Tan θ = Opposite side/Adjacent side

= BC/AC = 16/10 = 1.6

θ = Tan⁻¹ (1.6) = 57.99°

Question 18)

From the figure we can write,

Tan θ = Opposite side/Adjacent side

= BC/AC = 5.6/15.3 = 0.366

θ = Tan⁻¹ (0.366) = 20.10°

Answer:

Step-by-step explanation:

It's the parallelogram. The formula of an area of a parallelogram:

A = bh

b - base

h - height

We have b = 11 ft, h = 6.1 ft. Substitute:

A = (11)(6.1) = 67.1 ft²

Answer:

All real numbers

Step-by-step explanation:

This equation is well defined for all real values of x, hence

domain : x ∈ R

Answer:

similar triangles

Step-by-step explanation:

did it on usatestprep

Similar triangles are triangles with congruent angles and proportional sides.

In mathematics, triangles with congruent angles and proportional sides are called similar triangles.

Similar triangles have the same shape, but their sides may have different lengths. Two triangles are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional.

For example, if angle A in triangle ABC is congruent to angle X in triangle XYZ, and the ratio of the length of AB to XY is equal to the ratio of the length of BC to YZ, then triangle ABC is similar to triangle XYZ.

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To find out how many tickets were sold at the gate, we can set up and solve a system of equations. From equation 1, we can express x in terms of y: x = 600 - y. Substituting this expression into equation 2, we get 1.00(600 - y) + 1.50y = 700. Simplifying the equation, we find 600 - y + 1.50y = 700. Combining like terms, we have 0.50y = 100. Dividing both sides by 0.50, we get y = 200.

The question provides information about the cost of tickets for a school football game. Before the day of the game, tickets cost $1.00, while tickets bought at the gate cost $1.50 each. The total number of tickets sold for the homecoming game was 600, with total receipts of $700. To find out how many tickets were sold at the gate, we can set up and solve a system of equations.

Let's assume that x tickets were sold before the day of the game and y tickets were sold at the gate. We can create two equations based on the given information:

To solve this system of equations, we can use the substitution method. From equation 1, we can express x in terms of y: x = 600 - y. Substituting this expression into equation 2, we get 1.00(600 - y) + 1.50y = 700. Simplifying the equation, we find 600 - y + 1.50y = 700. Combining like terms, we have 0.50y = 100. Dividing both sides by 0.50, we get y = 200.

Therefore, 200 tickets were sold at the gate.

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Answer:

[tex]-\frac{1}{32}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2^{-2}*x^{-3}*y^{5}   }[/tex]

Substitute x = 2 and y = -4 into [tex]\frac{1}{2^{-2}*x^{-3}*y^{5}   }[/tex]

2⁻² = [tex]\frac{1}{4}[/tex]

2⁻³ = [tex]\frac{1}{8}[/tex]

-4⁵ = -1024

[tex]\frac{1}{4}[/tex]  × [tex]\frac{1}{8}[/tex] × -1024 = -32

Answer:

130.5

Step-by-step explanation:

145% of 90 = 145% * 90

145% = 1.45

Substitute: 1.45 * 90

Multiply: 130.5