Jason and Kaden took turns driving on a
585-mile trip. Both drove 65 mph. Kaden
drove 1 hour longer than Jason. How many
hours did Kaden drive?

By using Orbit-Stabilizer Theorem, we can prove that the number of G-subsets of X is 2n, where n is the number of distinct orbits in X

The Orbit-Stabilizer Theorem states that, for any element x in a G-set X, the number of elements in the orbit of x is equal to the number of elements in the stabilizer of x, multiplied by the number of orbits in X. In other words, if G is a group and X is a finite G-set, then the following equation holds:

|G| = |Orbit(x)| * |Stabilizer(x)|

where |G| is the number of elements in G, |Orbit(x)| is the number of elements in the orbit of x, and |Stabilizer(x)| is the number of elements in the stabilizer of x.

A subset is a set of objects or elements that are contained within another set.

we can use the Orbit-Stabilizer Theorem. This theorem states that, for any element x in a G-set X, the number of elements in the orbit of x is equal to the number of elements in the stabilizer of x. The orbit of x is the set of all elements that can be obtained from x by applying the action of G, and the stabilizer of x is the set of all elements of G that leave x unchanged.

Since each element of X belongs to exactly one orbit, there are a total of n orbits in X. For each orbit, we can either include all of the elements in the orbit in our G-subset or exclude all of the elements in the orbit. This gives us 2 options for each of the n orbits, so the total number of G-subsets of X is 2^n = 2n.

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It is not possible for a cross section of a cylinder to have a triangular shape

Cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces

A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes

A triangle is a shape formed when three straight lines meet

Cross section of the cylinder is depends on how we cut .The cross-section of a cylinder may be either circle, rectangle, or oval

Hence, the cross section of of a cylinder can not be a triangular shape

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Answer:

x>8

Step-by-step explanation:

2(x-9)>-2

(x-9)>-2/2 = (x-9)>-1

x>-1+9  =  x>8

Answer:

I did not understand

Step-by-step explanation:

Why is the question like that

Answer:

[B]. (1,-5)

Step-by-step explanation:

Given:

\(\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}\)

Solve:

\(\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}\)        Since 2y - 2y = 0 we take that away now we have;

\(4x=-6\\3x=13\)        Add 4x + 3x = 7x

\(\frac{7x}{7} =\frac{7}{7}\) Divide both sides by 7.

\(x=1\)

Now substitute x to find y.

\(4(1)+2y=-6\)

\(4 + 2y =-6\)  Add 6 to the other side.

\(10 = 2y\) Divide both sides by 2.

\(\frac{10}{2} =\frac{2y}{2}\)

\(y = 5\)

Hence, the answer is [B]. (1,-5)

RevyBreeze

Answer:

X=11 trust me on my mom

9514 1404 393

Answer:

  x = 36

Step-by-step explanation:

The parallel lines divide the transversals proportionally, so ...

  x/60 = 24/40

  x = 60(24/40) = 60(3/5)

  x = 36

\(g(x) > -6\)

Graphically, we can see from the graph that \(g(x)\) is will not go less than or equal to \(-6\).

Answer:

g(x)>-6

Step-by-step explanation:

This is a very small probability, approximately equal to 1.000000000009.

There are 10 bands, and each of them has an equal chance of being selected for each performance. Therefore, the probability that your band will not be selected for the last performance on Saturday is:

P(not last performance) = 1 - P(last performance)

To calculate the probability of your band being selected for the last performance, we need to consider the number of ways that the other bands can be selected for the first 9 performances. There are 9 performances, and for each performance, there are 10 bands to choose from.

Therefore, the number of ways to select the other bands for the first 9 performances is:

\(10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 = 10^9\)

To calculate the number of ways that your band can be selected for the last performance, we need to consider the number of ways that the other bands can be selected for the first 9 performances, and then your band can be selected for the last performance. There are 9 performances before the last one, and there are 9 bands that can be selected for those performances. Therefore, the number of ways that your band can be selected for the last performance is:

\(9 * 1 = 9\)

Therefore, the probability of your band being selected for the last performance is:

P(last performance) = \(9 / 10^9\)

And the probability that your band will not be selected for the last performance is:

P(not last performance) = 1 - P(last performance) = \(1 - 9 / 10^9\)

This is a very small probability, approximately equal to 1.000000000009.

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Answer:

37

Step-by-step explanation:

x=-4

=2(5-(-4)2+1

=2(5+4)2+1

=2(9)2+1

=18(2)+1

=36+1

=37

The rules that are functions on an appropriate domain are A and D, and other solutions are shown below

Given that

g(x) = 4x² + x + 7

For g(-2), we substitute -2 for x in g(x) = 4x² + x + 7

So, we have

g(-2) = 4(-2)² + (-2) + 7

Evaluate

g(-2) = 21

Here, we have

A(t) = 3- 2t² + 4^t.

To calculate A(2) - A(1), we calculate A(2) and A(1) and then subtract the values

So, we have

A(2) = 3 - 2(2)² + 4² = 11

A(1) = 3 - 2(1)² + 4¹ = 5

So, we have

A(2) - A(1) = 11 - 5

A(2) - A(1) = 6

Here, we have

g(x) = 3(x - 6)² + 1

The vertex above is

vertex = (6, 1)

Because the leading coefficient (a) is greater than 0

i.e. a = 3, then the vertex is a minimum

So, the range is y ≥ 1

Here, we have the following definition

a ♡ b = (a + b)/2.

This means that

(5 ♡ 7) ♡ 11 = (5 + 7)/2 ♡ 11

(5 ♡ 7) ♡ 11 = 6 ♡ 11

So, we have

(5 ♡ 7) ♡ 11 = (6 + 11)/2

(5 ♡ 7) ♡ 11 = 8.5

The rules that are functions on an appropriate domain are A and D.

Rules B, C, E, and F are not functions on an appropriate domain

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Complete question

Let g(x) = 4x^2 + x + 7. Find g(-2)

Let A(t) = 3- 2t^2 + 4^t. Find A(2) - A(1).

Let g(x) = 3(x - 6)^2 + 1. Find the range of g. Write your answer in interval notation.

Define the operation ♡ so that a ♡ b = (a + b)/2.

Find the value of (5 ♡ 7) ♡ 11

Which of these rules are functions on an appropriate domain?

Select all that apply.

A inputs a real number, subtracts 100, then outputs the square root of the result if it is real.

B inputs a date, then outputs the name of a person born on that date.

C inputs a real number x, then outputs a real number y that is less than 1/1000 larger than x

D inputs a real number x, then outputs the result of the calculation (x^2-1)/(x-1)(x+1)

E inputs a real number x, then a coin is flipped. If the coin flips heads, the output is x+2. If the coin flips tails, the output is x+3.

F inputs a person, then outputs their birth date.

Answer: 72

Step-by-step explanation:

Set it up as a ratio

\(\frac{12}{15} =\frac{x}{90} \\15x=1080\\x=72\)

The answer is 0.7%

Hope this helped!

Answer:

0.6%

Step-by-step explanation:

Percentage = 24/4000 *100

=0.6%

Answer:

Souta made his first error in Step 3, where he found the differences between each score and the mean. He did not find the absolute values of these differences, which means he did not calculate the mean absolute deviation correctly.

Answer:

This might help

Step-by-step explanation:

Answer:

(1) Pr(A > B + C) = 0

(2)   \(\mathbf{\dfrac{1}{27}}\)

Step-by-step explanation:

From the information given:

What is the probability A is the last customer to complete service when:

(1) the service time for each clerk is precisely ten minutes?

The probability (Pr)  that A is the last customer can be computed as:

P( A > B + C )

if we recall, we are being told that the service time for each clerk is 10 minutes. As such, there is no occurrence of any event.

Therefore, the probability A is the last customer to complete service when the other customers had left will be :

Pr(A > B + C) = 0

(2) when the service time are (i) with probability(pr) 1/3, i=1,2,3?

when service time i are (1,2,3) with probability \(\dfrac{1}{3}\)

Then the event that A will be the last customer to complete service when the other two customers had left will occur when A = 3, B= 1, C= 1

Thus, the probability that A  is the last customer to complete service when the other customers had left will be :

Pr ( A > B + C ) = Pr( A = 3, B = 1, C = 1)

Pr ( A > B + C ) = \(\begin {pmatrix} \dfrac{1}{3} \end {pmatrix}^3\)   given that the service times are independent

Pr ( A > B + C ) = \(\begin {pmatrix} \dfrac{1}{3} \times \dfrac{1}{3} \times \dfrac{1}{3} \end {pmatrix}\)

Pr ( A > B + C ) = \(\mathbf{\dfrac{1}{27}}\)

Answer:

The amount in Roxy's table listing of expenses gives the ratio of the items in the pie chart as follows;

Emergency fund; 3.89%

Cell phone; 6.93%

Internet; 4.28%

Rent payment; 76.79%

Transportation; 2.34%

Insurance; 1.17%

Gym membership; 1.97%

Entertainment; 2.73%

The pie chart can then be constructed using those percentage as a proportion of 100

Please see the attached pie chart of the expenses created with Sheets

A pie chart illustrates the numerical proportion of items in a dataset by using a circular graphic that is divided into sector slices

The given values in the question are;

Emergency fund = $50

Cell phone = $89

Internet = $55

Rent payment = $986

Transportation = $30

Insurance = $15

Gym membership = $24

Entertainment = $35

The total cost of the fixed expense is therefore;

$50+$89+$55+$986+$30+$15+$24+$35 = $1284

The proportion of each component in the pie chart is found as follows;

\( \displaystyle{Emergency \: fund = \frac{50}{1284} \times 100 \approx 3.89 \%}\)

\( \displaystyle{Cell \: phone = \frac{89}{1284} \times 100 \approx 6.93 \%}\)

\( \displaystyle{Internet = \frac{89}{1284} \times 100 \approx 4.28 \%}\)

\( \displaystyle{Rent \: payment = \frac{986}{1284} \times 100 \approx 76.79 \%}\)

\( \displaystyle{Transportation = \frac{30}{1284} \times 100 \approx 2.34 \%}\)

\( \displaystyle{Insurance = \frac{15}{1284} \times 100 \approx 1.17 \%}\)

\( \displaystyle{Gym \: membership = \frac{24}{1284} \times 100 \approx 1.87 \%}\)

\( \displaystyle{Entertainment = \frac{35}{1284} \times 100 \approx 2.73 \%}\)

Using the above percentages, the pie chart can be constructed

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Answer:

69

Step-by-step explanation:

69

Answer:

a) 0815

b) 22 minutes

Hope this helps!

Answer:

side xy = 9.41 cm

Step-by-step explanation:

Answer:

side xz is 78°

90+12=102

180-102

Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

Using the Central Limit Theorem, the sampling distribution of the sample mean wait time for random samples of size 84 has mean of 11.4 minutes and standard deviation of 0.28 minutes.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

In this problem, the population has:

Samples of 84 are taken, thus, by the Central Limit Theorem:

\(n = 84, s = \frac{2.6}{\sqrt{84}} = 0.28\)

The sampling distribution of the sample mean wait time for random samples of size 84 has mean of 11.4 minutes and standard deviation of 0.28 minutes.

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3xy²(x - 5)

The equation: 3x²y²-15xy²

x is common to both expression, we factorise it:

x(3xy² - 15y²)

y² is common to both expression, we factorise it:

xy²(3x - 15)

3 is common to both expression, we factorise it:

3xy²(x - 5)

The missing variables on item 2 are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

For the angle of 60º, we have that:

Hence the length o is given as follows:

tan(60º) = o/12.

\(\sqrt{3} = \frac{o}{12}\)

\(o = 12\sqrt{3}\)

Applying the Pythagorean Theorem, the length i is given as follows:

i² = 12² + \((12\sqrt{3})^2\)

i² = 576

i² = 24²

i = 24.

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Answer:

o = 12√3

i = 24

Step-by-step explanation:

From observation of the given right triangle, we can see that two of its interior angles measure 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, the triangle is a special 30-60-90 triangle.

The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.

In triangle #2, the shortest leg is 12 units.

As "a" is the shortest leg, the scale factor "a" is 12.

The side labelled "o" is the longest leg opposite the 60° angle. Therefore:

\(o = a\sqrt{3}=12\sqrt{3}\)

The side labelled "i" is the hypotenuse of the triangle. Therefore:

\(i= 2a = 2 \cdot 12=24\)

Therefore:

Answer:

organelle

Explanation: Mitochondria and the cell wall are both examples of organelles since they have their own specific functions (Mitochondria produces the energy and the cell wall protects the cell from things that might be a danger to the cell.

Each "organelle " in a cell has its own specific function.

Mitochondria and the cell wall are both examples of organelles since they have their own specific functions. Mitochondria produces the energy and the cell wall protects the cell from things that might be a danger to the cell.

A Cellular respiration is a component of a metabolic process which splits the glucose sugar molecule to produce energy in the form of ATP.

Since we know that Krebs' cycle, oxidative phosphorylation, and glycolysis are all components of cellular respiration.

The cellular respiration activities take place in the mitochondria of the cell, where the oxygen-rich environment which causes the sugar-like glucose to break down into an energy molecule.

A cell organelle having a membrane is a 'mitochondria'. It is a location for cellular respiration and metabolic activities which produce energy.

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Answer:

5470

Step-by-step explanation:

\(5000(1+\frac{.03}{12})^{12*3}=5470.257\)

The future value of the investment in the savings account with montly compounding is $5470.

When an investment is compouded monthly, it means that it increases in value every month.

The formula for calculating future value:

FV = P (1 + r)^nm

5000 x ( 1.0025)^36 = $5470

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Answer:

13 is a prime number, not divisible by any number greater than 1 or less than 13. So the prime factorisation of 78 is: 78 = 2 ⋅ 3 ⋅ 13 This can also be represented by a factor tree:

Step-by-step explanation:

Answer:

78 = 2 ⋅ 3 ⋅ 13

Step-by-step explanation:

78  ends with an even digit, so is divisible by  2 and we find:  78 = 2 ⋅ 39

39  ends with an odd digit, so is not divisible by  2 .

The digits of  39  add up to a multiple of  3 , namely  3 + 9 = 12 . So we can tell that  39  is divisible by  3 : 39 = 3 ⋅ 13

13  is a prime number, not divisible by any number greater than  1  or less than  13 .

So the prime factorization of  

78  is:

78= 2 ⋅ 3 ⋅ 13