On Tuesday Bob, Larry, and Joe studied for their Algebra test. Bob
studied for 12 minutes less than Larry, and Joe studied twice as long
as Bob. How many minutes did each student study if they studied a
total of 96 minutes?

Note that:

An origin-centered circle in 2D has a VC dimension of 3. This means that the circle can shatter any set of 3 points, but not any set of 4 points. In other words, there exists a set of 3 points that can be shattered by the circle, but for any set of 4 points, there exists at least one labeling of the points that the circle cannot produce.

An origin-centered sphere in 3D has a VC dimension of 4. This means that the sphere can shatter any set of 4 points, but not any set of 5 points. In other words, there exists a set of 4 points that can be shattered by the sphere, but for any set of 5 points, there exists at least one labeling of the points that the sphere cannot produce.

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Answer:

\( - \frac{1}{10} \times (25z + 52)\)

Step-by-step explanation:

-1/2 (7z + 4) + 1/5 (5z - 16)

-1/10 × (5(7z + 4) - 2 (5z - 16))

-1/10 × (35z + 20 - 10z + 32)

= -1/10 × (25z + 52)

Answer:

A =1017.9 cm^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

A = pi * (18)^2

Using the pi button

A =1017.87602 cm^2

Rounding to 1 decimal place

A =1017.9 cm^2

The probability for success is not the same for each trial, then the option D cannot be modelled using a geometric distribution.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

One of the assumptions to consider before the use of a geometric distribution can be valid is that, the probability of success must be the same for each outcome.

In the option D, selection is done without replacement, meaning that, the number total possible outcome will decrease as we make each selection and will also depend on how the colours are being chosen.

Hence, the probability of success will differ for each outcome, thus the option D is correct.

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Step-by-step explanation:

a probability is always desired cases over total possible cases.

so, we have actually 8 systems (5 + 3) we can pick from.

therefore, the total possible cases are 8.

the desired case is in this question to pick one of the 3 Wii consoles.

the probability to pick a Wii is therefore

3/8 = 0.375

Answer:

3/8, or 37.5%

Step-by-step explanation:

There are 8 different playing devices there.

There are only 3 Nintendo Wii consoles.

So, the probability is 3/8

Answer:18

Step-by-step explanation:

Answer:

3x

Step-by-step explanation:

x/2*6

6x/2

=3x

.

.

.

.

.

.

Answer:

513.45

Step-by-step explanation:

use intelligence

The simplification of the expressions in the question using the rules of indices are as follows;

1.) 6·e⁰ + (11·f)⁰ - 5/g⁰ = 2

2. (3⁻⁴ + 5⁻³)⁻¹ = \(49\frac{31}{206}\)

3. (3⁻⁴ + 5⁻³)⁻² = \(2415\frac{32685}{42436}\)

4.) \(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{10\cdot c^{-5} \cdot d^6 \cdot e^{-8}}\) = \(\dfrac{c^5\cdot e^8}{2\cdot d^5}\)

5.)  \(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5}\right)^{-3 }}{7\cdot \left(p^{-6} \cdot q^8\right)^{-4}} =\dfrac{-5\cdot m^{12}\cdot n^{15}\cdot q^{32}}{7\cdot p^{24}}\)

An index or indices is the power by which a number or variable or expression raised.

1.) 6·e⁰ + (11·f)⁰ - 5/g⁰

6·e⁰ + (11·f)⁰ - 5/g⁰ = 6 × 1 + 1 - 5/1

6 × 1 + 1 - 5/1 = 6 + 1 - 5 = 2

Therefore;

6·e⁰ + (11·f)⁰ - 5/g⁰ = 2

2.) (3⁻⁴ + 5⁻³)⁻¹

(3⁻⁴ + 5⁻³)⁻¹ = (1/(3⁴) + 1/(5³))⁻¹ = 1/(1/(3⁴) + 1/(5³))

1/(1/(3⁴) + 1/(5³)) = 1/(1/81 + 1/125) = 1/((125 + 81)/(81×125))

1/((125 + 81)/(81×125)) = (81 × 125)/(125+81) = 10125/209

10125/206 = 49 + 31/206

(3⁻⁴ + 5⁻³)⁻¹ = \(49 \frac{31}{206}\)

3.) (3⁻⁴ + 5⁻³)⁻²

(3⁻⁴ + 5⁻³)⁻² = 1/((1/3⁴ + 1/5³)²)

1/((1/3⁴ + 1/5³)²) = 1/((1/81 + 1/125)²)

1/((1/81 + 1/125)²) = 1/(((125 + 81)/(81 × 125))²)

1/(((125 + 81)/(81 × 125))²) = 1/((206/10125)²)

1/((206/10125)²) = (10125)²/(206)² = 102515625/42436

102515625/42436 = 2415 32685/42436

(3⁻⁴ + 5⁻³)⁻² = \(2415\frac{32685}{42436}\)

4.)  \(\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}\)

\(\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}} = \dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) }\)

\(\dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) } = \dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) }\)

\(\dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) }\)

\(\dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{c^5\times e^8}{2\cdot d^6}\)

\(\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}= \dfrac{c^5\times e^8}{2\cdot d^6}\)

5.) \(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\rright)^{-4}}\)

\(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} =\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} }\)

\(\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} }\)

\(\dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 }\)

\(\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) }\)

\(\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) } = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}\)

\(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}\)

6.) (3·x⁻⁴·y⁻⁵·z⁻²)⁻²

(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = \(3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right)\)

\(3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right) = 3\cdot \left(x^4\cdot y^5\cdot x^2\right)^2\)

3·(x⁴·y⁵·x²)² = 3·x⁸·y¹⁰·x⁴

Therefore;

(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = 3·x⁸·y¹⁰·x⁴

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Answer:

It's equal to itself. Here are the two ways to do this problem. ↓

Sheena receives change of $7.55 after paying $20 bill.

Information is graphically represented in a bar graph. To represent value, it makes use of bars that stretch to various heights. Vertical bars, horizontal bars, grouped bars (multiple bars that compare values in a category), and stacked bars can all be used to create bar graphs.

Therefore,

Sheena buys three items, one sandwich and two pretzels.

Given the rate of sandwich = $6.95

Rate of pretzels = $2.75 each

So rate of two pretzels = $2.75 x 2 = $5.5

Total amount paid = $20

To find the change she receives ,

Total payment paid - total amount of items

Total amount for items = $6.95 + $5.5

                                     = $12.45

Change receives = $20 - $12.45

                            = $7.55

Therefore the change Sheena receives is : $7.55.

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The difference in overall loss or gain between sell at the current day's high price or low price is found tp be the difference in overall gain as $280.10

The third option is correct.

High price value: 115 shares * $105.19 per share = $12,084.85

Low price value: 115 shares * $103.25 per share = $11,858.75

High price value: 30 shares * $145.18 per share = $4,355.40

Low price value: 30 shares * $143.28 per share = $4,298.40

The overall value at high price:

$12,084.85 + $4,355.40

= $16,440.25

The overall value at low price:

$11,858.75 + $4,298.40

= $16,157.15

In conclusion, the difference in overall gain or loss:

$16,440.25 - $16,157.15 = $280.10

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Answer:

(17/12)π radians

Step-by-step explanation:

π radians = 180º

255 * (π/180) = (17/12)π

12x²y² - 17xy - 40

xy (12xy - 17) - 40

As the x and y are shown in both variables but there is no other common factors. I didn't include the 40 as it didn't share any common factors with all of them.

Tom sold 27 raffle tickets and Steve sold 98 raffle tickets.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

Together, Steve and Tom sold 125 raffle tickets for their school.

Steve sold 17 more than three times as many raffle tickets as Tom.

Let s be the number of raffle tickets sold by Steve and t be the raffle tickets sold by Tom.

So,

3t + 17 + t = 125

4t = 108

t = 27

And s = 98

Therefore, Steve sold 98 and Tom sold 27 tickets.

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Answer:

7.65

Step-by-step explanation:

The total cost for 8 is 20.40, so you want to find what the cost for one panel is by dividing the total cost by the amount, which would be 20.40/8=2.55 then you want to know how much 3 of them cost, to find that you just multiply the cost of one of them by three, which would be 7.65

Answer:

Option 1

Step-by-step explanation:

\(40+20=60 \\ \\

5(8+20)=5(28)=140 \\ \\ 2(20+10)=2(30)=60 \\ \\ 5(8+4)=5(12)=60 \\ \\ 10(4+2)=10(6)=60\)

Answer:

Step-by-step explanation:

The value of x is 1.75 and y is 5. The solution is obtained using properties of congruent triangles.

What is a congruent triangle?

Two triangles that are congruent will have precisely the same three sides and three angles.

The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions.

The triangles are congruent by SAS congruency because

AC = CD (Given)

∠ACB = ∠DCE ( Vertically opposite angles)

BC = CE  (Given)

Thus, Triangle ABC ≅ Triangle DEC

Since, the triangles are congruent, therefore

⇒AC = CD

⇒4y-6 = 2x+6   ...(1)

Also, BC = CE

⇒3y+1 = 4x

⇒(3y+1)/4 = x    ...(2)

Now, substituting the value of x in (1), we get,

⇒4y-6 = 2(3y+1)/4+(6)

⇒4y-6 = (6y+2 +24)/4

⇒16y-24 = 6y+2 +24

⇒10y = 50

⇒y = 5

Now putting the value of y in (2), we get

⇒(3(2)+1)/4 = x

⇒7/4 = x

⇒ x = 1.75

Hence, the value of x is 1.75 and y is 5.

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Answer:

D. Completely randomized design

Step-by-step explanation:

Based on the description given about the experiment above and the manner in which the subjects were assigned to each of the treatment groups available, we can deduce that the study was conducted using a completely randomized design. The subjects weren't matched or blocked for any variable such as sex, height, age or any other variable. They were just evenly split randomly into the two available treatment levels ( those who receive the treatment and the placebo) group. With this design, all subjects have an equal chance of being in any of the two groups and the selection bias is almost totally eliminated using this sort of design as errors are being considered as arising from experimental faults.

The domain of the function R(x) is (-∞, -4) U (-4, 3) U (3, ∞).

The vertical asymptote is x = -4 and x = 3

The horizontal asymptote is y = 1.

In Mathematics, a domain refers to the set of all real numbers (x-values) for which a particular function is defined.

In Mathematics, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached below, we can logically deduce the following domain:

Domain = {0, ∞}.

In conclusion, an asymptote is a line which the graph of any given function approaches but would never cross or touch;

Vertical asymptote is x = -4 and x = 3

Horizontal asymptote is y = 1.

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Complete Question:

Analyze the graph of the function.

\(R(x)=\frac{x^2}{x^2+x-12}\)

a. What is the domain of R(x)?

b. What is the vertical and horizontal asymptote?

Answer:

Step-by-step explanation:

∠4 and 158° are supplementary as same side interior angles

Answer:

\(<4+<158=180\)[co- interior angle]

<4=180-158=22°

<4=22°

Answer:

k = - 10

Step-by-step explanation:

k - 3(k + 5) - 0.5 = 3(0.25k + 4) ← distribute parenthesis on both sides

k - 3k - 15 - 0.5 = 0.75k + 12

- 2k - 15.5 = 0.75k + 12 ( subtract 0.75k from both sides )

- 2.75k - 15.5 = 12 ( add 15.5 to both sides )

- 2.75k = 27.5 ( divide both sides by - 2.75 )

k = - 10

The intervals of each behavior of the function are given as follows:

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Given the equation:

Let's find the number of solutions.

Apply the following conditions:

x = x.....................Infinitely many solutions

x ≠ y ......................No solution

x = 2........................One solution

Let's simplify the equation

Apply distributive property:

Multiply all terms by 4:

Subtract x from both sides:

Since the right hand side does not equal the left hand side of the equation, we can say there is no solution.

ANSWER:

There is no solution

Given:

\(sinh(f(x))=1+x^2\)

To find:

The value of f'(x).

Solution:

Formulae used:

\(\dfrac{d}{dx}sinh(x)=cosh(x)\)

\(\dfrac{d}{dx}x^n=nx^{n-1}\)

\(\dfrac{d}{dx}C=0\)

Chain rule:

\(\dfrac{d}{dx}[f(g(x))]=f'(g(x))g'(x)\)

Where C is an arbitrary constant.

We have,

\(sinh(f(x))=1+x^2\)

Differentiate with respect to x.

\(cosh(f(x))f'(x)=0+2x\)

\(f'(x)=\dfrac{2x}{cosh(f(x))}\)

Therefore, the required values is \(f'(x)=\dfrac{2x}{cosh(f(x))}\).

Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs

Answer:

1

Step-by-step explanation:

10*4=40

so 1

Answer:

See below ~

Step-by-step explanation:

Sample Space : {HHH, HHT, HTH, HTT, TTT, TTH, THT, THH}

Event (first toss = heads)

Answer:

Sample Space is 3, {HTH, THH, TTT, THT, HTT, HHH}

Step-by-step explanation: