Which of the following correctly uses exponents to write "6 factors of 2"?
26
6.2
12
62

The expression (p⁶ +q) + 8 is equivalent to the given expression. which is the correct answer would be an option (C).

The commutative property is associated with mathematical operations such as addition and multiplication. It indicates that switching the order or location of two integers while adding or multiplying them has no effect on the outcome. For example, 4 + 5 gives 9, and 5 + 4 also gives 9.

The expression is given in the question below as

p⁶ + (q + 8)

We have to determine the expression equivalent to the given expression.

As per the given question, we have

⇒ p⁶ + (q + 8)

Using the commutative property of addition, we get

⇒ (p⁶ +q) + 8

Thus, the expression (p⁶ +q) + 8 is equivalent to the given expression.

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Answer:

x = 1/9

Step-by-step explanation:

(a) The probability that the top card is an ace or a king is \($\frac{2}{13}\)

(b) The probability that the top card is spades and the second card is clubs is \($\frac{1}{2652}\)

(c) The probability that the top card is spades and the second card is an ace is \($ \frac{1}{663}\)

(d) The probability that the top 3 cards are all spades is \($\frac{1}{132600}\)

(e) The probability that the top 4 cards include 3 different ranks, with one rank appears twice is \($\frac{2}{925}\)

As per the data given:

A standard deck of 52 cards has 13 ranks (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king) and 4 suits (spades, hearts, diamonds, and clubs), such that there is exactly one card for any given rank and suit.

a) The probability that the top card is an ace or a king:

The probability that the top card is an ace \($\frac{4}{52} = \frac{1}{13}\)

The probability that the top card is an king \($\frac{4}{52}=\frac{1}{13}\)

The probability that the top card is an ace or a king is \($\frac{1}{13} +\frac{1}{13} =\frac{2}{13}\).

b) The probability that the top card is spades is \($\frac{1}{52}\)

Already a card is drawn then the probability that the second card is clubs is \($\frac{1}{51}\)

The probability that the top card is spades and the second card is clubs is \($\frac{1}{52}\times\frac{1}{51} = \frac{1}{2652}\)

c) The probability that the top card is spades is \($\frac{1}{52}\)

Already a card s drawn then the probability that the second card is an ace is \($\frac{4}{51}\)

The probability that the top card is spades and the second card is an ace  is \($\frac{1}{52}\times\frac{4}{51} = \frac{4}{2652} = \frac{1}{663}\)

d) The probability that the top 3 cards are all spades is \($\frac{1}{52}\times\frac{1}{51}\times\frac{1}{50} = \frac{1}{132600}\)

e) There are C(52, 4) ways to choose 4 cards from the deck, and the 4 ways to choose the rank that appears twice.

So, the total number of ways to choose 4 cards with 3 different ranks and one rank appearing twice is 4 C(52, 4) = 4 × 270725.

The number of ways to choose the 4 cards such that they include 3 different ranks, with one rank appearing twice is 4  C(13, 2)  C(4, 2) = 672.

Hence, the probability is \($\frac{672}{270725} =\frac{2}{925}\)

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A standard deck of 52 cards has 13 ranks (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king) and 4 suits (spades, hearts, diamonds, and clubs), such that there is exactly one card for any given rank and suit. The deck is randomly arranged. What is the probability that

(a) the top card is an ace or a king.

(b) the top card is spades and the second card is clubs.

(c) the top card is spades and the second card is an ace.

(d) the top 3 cards are all spades.

(e) the top 4 cards include 3 different ranks, with one rank appears twice (for example, an ace of hearts, a 3 of clubs, a 3 of hearts, and a 7 of spades).

Answer:

x = 3

Step-by-step explanation:

x+(2)=5

This is the same as x+2=5

To find x,

x + 2 = 5

   -2     -2

This is to bring the 2 to the right hand side, leaving x

x = 3

if the level of significance is 0.01, we would expect to commit a Type I error 15 times out of 1,500 tests. if the level of significance is 0.05, we would expect to commit a Type I error 75 times out of 1,500 tests.

Assuming that the null hypothesis is true in all 1,500 tests, the probability of committing a Type I error (rejecting the null hypothesis when it is actually true) is equal to the level of significance (alpha) of the test.

(a) If the level of significance is 0.01, then the probability of committing a Type I error in one test is 0.01. Therefore, the expected number of Type I errors in 1,500 tests is:

Expected number of Type I errors = (number of tests) x (probability of Type I error per test)

= 1,500 x 0.01

= 15

So, if the level of significance is 0.01, we would expect to commit a Type I error 15 times out of 1,500 tests.

(b) If the level of significance is 0.05, then the probability of committing a Type I error in one test is 0.05. Therefore, the expected number of Type I errors in 1,500 tests is:

Expected number of Type I errors = (number of tests) x (probability of Type I error per test)

= 1,500 x 0.05

= 75

So, if the level of significance is 0.05, we would expect to commit a Type I error 75 times out of 1,500 tests.

(c) If the level of significance is 0.001, then the probability of committing a Type I error in one test is 0.001. Therefore, the expected number of Type I errors in 1,500 tests is:

Expected number of Type I errors = (number of tests) x (probability of Type I error per test)

= 1,500 x 0.001

= 1.5

So, if the level of significance is 0.001, we would expect to commit a Type I error 1.5 times out of 1,500 tests, which we round to 1 decimal place as 1.5 rounds to 2.

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Answer:

Step-by-step explanation:

243.28-17.29=225.99 after the diet

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

Function

Step-by-step explanation:

This is a function

Each input goes to only one output

Answer: He paid 13$ for the hat

Step-by-step explanation:

If you minus the ammount  on the right then you will get 13  

Answer:

$14

Step-by-step explanation:

there´s 20 dollars on the left and after he spends $6 is left so you do $20-$6=$14

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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The total number of yards the friends who paddle the Adventure Mid travel is 8,580 yards

Number of friends who paddle Adventure Mid Trip = 40% of 15

= 0.4 × 15

= 6 friends

Total yards the friends who paddle the Adventure Mid Trip travel = Total length of travel

= 4 7/8 miles

Recall,

1 mile = 1760 yards

Total yards the friends who paddle the Adventure = 4 7/8 × 1,760

= 39/8 × 1,760

= (39 × 1,760) / 8

= 68,640 / 8

= 8,580 yards

Consequently, the task content is solved by converting number of miles to yards.

Complete question:

Great Adventures Canoe and Kayak company offers 3 different options as shown in the table. This afternoon a group of 15 friends paddle the different options in individual kayaks and 40% of the group paddle the Adventure Mid Trip. How many total yards will the friends who paddle the Adventure Mid Trip travel? (Hint: 1 mile = 1760 yards)

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Answer:

Scale factor = 3

Step-by-step explanation:

Scale factor used for the dilation = the ratio of the corresponding side length of the new figure to the side length of the original figure

Scale factor = B'C'/BC

B'C' = 9 units

BC = 3 units

Scale factor = 9/3 = 3

The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

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Answer:

b = 5

Step-by-step explanation:

All quadratic equations are formed in the format of \(a^{2}\) + bx + c = 0

Using this formula, we can re-arrange the equation to fit the given format.

\(3x^{2}\) - 2 = -5x
\(3x^{2}\) + 5x - 2 = 0

5 is plugged in for "b" in this equation, therefore b = 5.

Answer:

Substitute the value of the variable into the expression and simplify.

121

Step-by-step explanation:

Step-by-step explanation:

(y + z)^2

substitute in the given

y = -8, z = 19

(-8 + 19)^2

(11)^2

121

Hope this helps :)

complete analysis (carrying out steps A-H in section 4.4 from the Stewart textbook)

results as The graph of f(2) = et te is a straight line with a y-intercept of 1.

A) f(2) = et te

Step A) Identify the domain and range of the function:

Domain: All real numbers

Range: All real numbers

Step B) Find any x-intercepts:

x-intercepts: None

Step C) Find any y-intercepts:

y-intercept: f(0) = e0te = 1

Step D) Find any vertical asymptotes:

Vertical asymptotes: None

Step E) Find any horizontal asymptotes:

Horizontal asymptote: None

Step F) Find any points of inflection:

Points of inflection: None

Step G) Find any symmetry:

Symmetry: None

Step H) Sketch the graph:

The graph of f(2) = et te is a straight line with a y-intercept of 1.

B) f(x) = tan-(+)

Step A) Identify the domain and range of the function:

Domain: All real numbers

Range: All real numbers except -π/2, π/

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If the workers' union at a particular university is quite strong.  the probability that exactly 4 of the workers interviewed are union members is 0.1699.

You must count all conceivable outcomes as well as favourable outcomes in order to compute probability. The number of favourable outcomes divided by the total number of possible outcomes yields the chance that an event will occur.

Using this formula to the probability

P(X = k) = (n choose k) * \(p^{k}\) * \((1-p)^{n-k}\)

Where:

X = random variable

n = 5

p = 0.96

k = 4

Let plug in the formula

P(X = 4) = (5 choose 4) *\(0.96^{4}\) *\((1-0.96)^{5-4}\)

= 5 *\(0.96^{4}\) * 0.04

= 0.1699

Therefore the probability is 0.1699.

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Answer:

Step-by-step explanation:

V = 3.9V

I = 0.12A

Ohm's Law, V = IR

Rearranging Ohm's Law, R = V/I

R = 3.9/0.12 = 32.5Ω

Answer: 17 rolls

Step-by-step explanation:

First, we need to find the total length of crepe paper needed to go around the perimeter of the ceiling. To do this, we can multiply the length of each side by the number of sides:

length of crepe paper = length of each side x number of sides

The ceiling of Frank's living room is a square, so it has four sides. Plugging in the given values, we get:

length of crepe paper = 20 ft x 4

Performing the calculation gives us:

length of crepe paper = 80 ft

Next, we need to find the length of crepe paper needed to go from each corner of the ceiling to the opposite corner. To do this, we can use the Pythagorean theorem to find the length of the diagonal of the ceiling:

diagonal length = sqrt(length^2 + width^2)

Plugging in the given values, we get:

diagonal length = sqrt(20^2 + 20^2)

Performing the calculation gives us:

diagonal length = 28.28 ft

Since there are four corners in the ceiling, we will need 4 x 28.28 ft of crepe paper to go from each corner to the opposite corner. This is a total of 113.12 ft of crepe paper.

To find the total length of crepe paper needed, we can add the length needed for the perimeter and the length needed for the corners:

total length = perimeter length + corner length

Plugging in the values we calculated above, we get:

total length = 80 ft + 113.12 ft

Performing the calculation gives us:

total length = 193.12 ft

Finally, we can divide the total length of crepe paper needed by the length of each roll to find out how many rolls Frank needs to buy:

number of rolls = total length / length of each roll

Plugging in the given values, we get:

number of rolls = 193.12 ft / 12 ft

Performing the calculation gives us:

number of rolls = 16.09 rolls

Since Frank can only buy whole rolls of crepe paper, he will need to buy 17 rolls to decorate

So with sine cosine and tangent, try remembering the following:

Sin : Opposite / Hypotenuse

Cos: Adjacent / Hypotenuse

Tan: Opposite / Adjacent

Or just remember "Soh-cah-toa".

Anyways, with this, its asking for the sine ratio of angle Z. So we need the opposite side length and the hypotenuse side length

For the opposite side length, look to see where the angle is "opening" up towards, like a door that is opening. With this, Angle Z is opening up towards the Side XY, which has a length of 21.

To find the hypotenuse, it is always the largest side length of a right triangle. It is also where the right angle opens up it's "door" up to. This would be Side XZ, which has a length of 29.

With both of these, back to the ratio formula:

Sin : Opposite / Hypotenuse

To finish the question, simply plug in the values that were found above.

This will give you:

Sin Z : 21 / 29

This will be Choice A.

Answer:

djjdjdjdjdjdjdjdjdidi

$28.62 not including tax.

Answer:

y = 2 \((3)^{x}\)

Step-by-step explanation:

the standard form of an exponential function is

y = a \(b^{x}\)

to find a and b use ordered pairs from the table

using (1, 6 )

6 = a\(b^{1}\) , that is

6 = ab → (1)

using (3, 54 )

54 = ab³ → (2)

divide (2) by (1) on both sides

\(\frac{54}{6}\) = \(\frac{ab^3}{ab}\) , that is

b² = 9 ( take square root of both sides )

b = \(\sqrt{9}\) = 3

substitute b = 3 into (1) and solve for a

6 = 3a ( divide both sides b 3 )

2 = a

then the exponential function for the table is

y = 2 \((3)^{x}\)

The diameter of the circle is 396 units.

The length of the arc is 0.83π units.  

The length of an arc of a circle is given by the formula:

L = θ/360 * πd

where θ is the measure of the angle and is the diameter of the circle

Given: θ = 80° and L = 88π

L = θ/360 * πd

88π = 80/360 * π * d

88 = 80/360 * d

80 * d = 88 * 360

80d = 31680

80d = 31680/80

d = 396 units

PART 2

If  θ = 25°, r = 6 (from the image above). Thus, d = 2 * 6 = 12

L = θ/360 * πd

L = 25/360 * π * 12

L = 0.83π units

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Answer:

2/3 x - 5 < 11

2/3 x < 16 (add 5 to both sides)

x < 16 * 3/2 (multiply both sides by 3/2)

x < 24

Step-by-step explanation:

The mean and the standard deviation, from the frequency table, are given as follows:

The frequency table gives the number of times that each observation appears.

The mean of a data-set is given by the sum of all observations divided by the number of observations, hence it is given as follows:

Mean = (1 x 13 + 2 x 12 + 3 x 5)/(13 + 12 + 5) = 1.73.

The standard deviation is given by the square root of the sum of the difference squared between each observation and the mean, divided by the number of observations, hence it is given as follows:

Standard deviation = sqrt((13 x (1 - 1.73)² + 12 x (2 - 1.73)² + 5 x (3 - 1.72)²)/30) = 0.73.

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Answer:

Conditional statement:  p → q  (if p, then q)

⇒ If you give respect, you get respect

Converse:  q → p  (if q, then p)

⇒ If you get respect, you give respect

Inverse:  ~p → ~q  (if not p, then not q)

⇒ If you don't give respect, you don't get respect

Contrapositive:  ~q → ~p  (if not q, then not p)

⇒ If you don't get respect, you don't give respect

Part A

The equation

Part b

The parent function name; cube root parent function

Part c

Part D

Table

Part E

The domain of a function is the set of all possible inputs for the function.

Domain

The range of a function is the set of its possible output values

Range

Answer:

8.5

Step-by-step explanation:

Twice the difference of a number and 6 equals 5 is written algebraically as 2(x-6)=5, where x is the number. Solving for x:

2(x-6)=5

(x-6)=5/2

x=6+5/2

x=17/2

So the number is 17/2, or, expressed as a decimal number, 8.5