Question 5 of 10
Which expressions are equivalent to the one below? Check all that apply.
64^x

A. 8^x •8^x
B. 8^2x
C. 8•8^2x
D.8^2•8^x
E. (8•8)^x
F. 8•8^x

Answer:

I don't get the question very well

Answer:

Greater than

Step-by-step explanation:

In the given condition, as your family is having pizza for dinner, the number of servings of size 13 out of the 2 pizzas, depends on the size of the pizzas you take.

Pizza is an Italian meal prepared of flat, typically circular, baked bread that is frequently topped with mozzarella cheese, tomatoes, or sauce made with tomatoes. Depending on the location, culture, or personal choice, additional toppings may be added. The dish, which is a staple of Italian cuisine, has gained popularity around the globe, especially in the United States, where a variety of variations have been created.

Pizza has a variety of vitamins and minerals, including calcium, carbs, and lipids. Grain is one of the main elements in the crust, albeit it is not always whole grain.

To find out how many servings of size 13 you can make out of the 2 pizzas, you first need to determine the total size of the pizzas. If each pizza is 13 inches in diameter, then the combined size of the two pizzas is 26 inches. You can then divide this total size by the size of each serving to find out how many servings you can make.

For example, if you want to make servings that are each 13 inches in size, you can make 2 servings out of the 2 pizzas, because 26 inches / 13 inches/serving = 2 servings.

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The Cartesian equation of the plane is: -4x + 3y + 3z + 21 = 0

The equation holds true, the point D(6, -9, 10) lies on the plane.

To find the Cartesian equation of the plane, we need to determine the coefficients of the variables x, y, and z in the equation of the plane.

The plane is defined by the point (-1, 2, 1) and the direction vectors (3, 4, 0) and (0, 1, -1).

To find the normal vector of the plane, we can take the cross product of the two direction vectors:

N = (3, 4, 0) × (0, 1, -1)

N = (4 * (-1) - 0 * 1, -(3 * (-1) - 0 * 0), 3 * 1 - 4 * 0)

N = (-4, 3, 3)

The Cartesian equation of the plane can be written as:

-4x + 3y + 3z + D = 0

To determine the value of D, we substitute the coordinates of the given point D(6, -9, 10) into the equation:

-4 * 6 + 3 * (-9) + 3 * 10 + D = 0

-24 - 27 + 30 + D = 0

-21 + D = 0

D = 21

Therefore, the Cartesian equation of the plane is:

-4x + 3y + 3z + 21 = 0

To check if the point D(6, -9, 10) is on the plane, we substitute its coordinates into the equation:

-4 * 6 + 3 * (-9) + 3 * 10 + 21 = 0

-24 - 27 + 30 + 21 = 0

0 = 0

Since the equation holds true, the point D(6, -9, 10) lies on the plane.

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The Cartesian equation of the plane is: -4x + 3y + 3z + 21 = 0

The equation holds true, the point D(6, -9, 10) lies on the plane.

In order to get the Cartesian equation of the plane, we need to find the coefficients of the variables x, y, and z that are in the equation of the plane.

We are told that the plane is the plane r = (-1,2,1) + s(3,4,0) + t(0,1,-1)

Thus, the point of the plane is (-1, 2, 1) and its' direction vectors (3, 4, 0) and (0, 1, -1).

We will get the normal vector of the plane, by finding the product of the two direction vectors as:

N = (3, 4, 0) × (0, 1, -1)

N = (4 * (-1) - 0 * 1, -(3 * (-1) - 0 * 0), 3 * 1 - 4 * 0)

N = (-4, 3, 3)

The Cartesian equation of the plane is expressed as:

-4x + 3y + 3z + D = 0

To find the value of D, we will substitute the coordinates of the given point D(6, -9, 10) into the equation to get:

(-4 * 6) + (3 * (-9)) + (3 * 10) + D = 0

-24 - 27 + 30 + D = 0

-21 + D = 0

D = 21

Therefore, the Cartesian equation of the plane is expressed as:

-4x + 3y + 3z + 21 = 0

To check if the point D(6, -9, 10) is on the plane, we substitute its coordinates into the equation:

(-4 * 6) + (3 * (-9)) + (3 * 10) + 21 = 0

-24 - 27 + 30 + 21 = 0

0 = 0

Due to the fact that the equation holds true, the point D(6, -9, 10) is said to lye on the plane.

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The square root of the decimal number is √0.0016 = 0.04

Here we can find the square root of the decimal number:

N = 0.0016

Notice that we can write this number as:

0.0016 = 16*10⁻⁴

Now we can take the square root of that, so we will get:

√(16*10⁻⁴)

We can distribute the square root to get:

√16*√10⁻⁴

These two are easy, we will get:

√16*√10⁻⁴ = 4*10⁻² = 0.04

That is the square root.

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Hours satellite will take  to reach a star that is three light years away is 1.039 * \(10^{9}\) hours.

Given :

satellite can move at 17,000 miles per hour.

let t be the number of hours

Convert the disance to miles

3 light years = 3 * 9.5 * \(10^{12}\) kilometers

= 3 * 9.5 * \(10^{12}\) * 0.62 miles

= 1.767 *  \(10^{13}\) miles

divide by the speed to get the time in hours

t = 1.767 *  \(10^{13}\) miles /17000 miles /hour

t = 1.039 * \(10^{9}\) hours

Hence hours satellite will take  to reach a star that is three light years away is 1.039 * \(10^{9}\) hours.

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Answer:

\(\boxed{\mathtt{Area \approx 227ft^{2}}}\)

Step-by-step explanation:

\(\textsf{We are asked to find the area of a circle.}\)

\(\textsf{First, we should identify the formula for the area of a circle.}\)

\(\large\underline{\textsf{Formula:}}\)

\(\mathtt{Area = \pi (radius)^{2}}\)

\(\textsf{The radius is \underline{half} of the diameter.}\)

\(\mathtt{\frac{17}{2} = 8.5ft.}\)

\(\textsf{Let's begin solving for the area.}\)

\(\large\underline{\textsf{Substitute:}}\)

\(\mathtt{Area = \pi (8.5)^{2}}\)

\(\mathtt{Area = 72.25 \pi}\)

\(\boxed{\mathtt{Area \approx 227ft^{2}}}\)

Answer:

Step-by-step explanation:

Increasing

Domain: (-∞,∞)

Domain: -∞<x<∞

Range: (-∞,∞)

Range: -∞<y<∞

For the given quadratic function f(x) = 2x² - 13x - 24 its Vertex = (13/4, -25/8), Largest z-intercept = -24,  Y-intercept = -24.

The standard form of a quadratic function is:

f(x) = ax² + bx + c   where a, b, and c are constants.

To calculate the vertex, we need to use the formula:

h = -b/2a  where a = 2 and b = -13

therefore  

h = -b/2a

= -(-13)/2(2)

= 13/4

To calculate the value of f(h), we need to substitute

h = 13/4 in f(x).f(x) = 2x² - 13x - 24

f(h) = 2(h)² - 13(h) - 24

= 2(13/4)² - 13(13/4) - 24

= -25/8

The vertex is at (h, k) = (13/4, -25/8).

To calculate the largest z-intercept, we need to set

x = 0 in f(x)

z = 2x² - 13x - 24z

= 2(0)² - 13(0) - 24z

= -24

The largest z-intercept is z = -24.

To calculate the y-intercept, we need to set

x = 0 in f(x).y = 2x² - 13x - 24y

= 2(0)² - 13(0) - 24y

= -24

The y-intercept is y = -24.

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\(\huge \frak{ \: \: ༆ \: Answer \: ༄ \: \: }\)

According to given graph we can infer that ~

Domain of function is :

Range of function is :

Note : Use intervals carefully ~

That's all ~

\(\mathrm{✌TeeNForeveR✌}\)

The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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T test is used to compute the confidence interval, when the mean and standard deviation is given.

What is Standard Deviation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be very close to the set mean. The lower case Greek letter (sigma), again for population standard deviation, or even the Latin letter s, again for sample standard deviation, are most frequently used in mathematical texts and equations to represent standard deviation. Standard deviation may be abbreviated as SD. A random variable, specimen, statistical population, data set, as well as probability distribution's standard deviation is equal to the square root of its variance. When the number in a sample, sample mean and sample standard deviation is given, the test statistic that should be used when computing a confidence interval is t test

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Answer:

see explanation

Step-by-step explanation:

Expressing ratios in fractional form, then

\(\frac{a}{c}\) = \(\frac{a}{b}\) × \(\frac{b}{c}\) = \(\frac{2}{3}\) × \(\frac{5}{6}\) = \(\frac{1}{3}\) × \(\frac{5}{3}\) = \(\frac{5}{9}\)

That is a : c = 5 : 9

Answer:

6 ways

Step-by-step explanation:

The number of ways he can display the stamps as follows:

Here we find the factors of 32

i.e.

= 1 × 32 represent 1 row, 32 stamps each

= 2 × 16 represent 2 rows, 16 stamps each.

= 4 × 8 represent 4 rows, 8 stamps each.

= 8 × 4 represent 8 rows with 4 stamps each

= 16 × 2 represent 16 rows with 2 stamps each

= 32 × 1 represent 32 rows with 1 stamp each

So in 6 ways he can displayed  

(a) The probability that the series will last exactly m games is:(1 - (pA + pB))^m(pA (1 - pB) + pB (1 - pA))where pA and pB are the probabilities of teams A and B, respectively. Therefore, the probability that the series will last less than 5 games is the probability that the series will last exactly 3 games or exactly 4 games:1 - (1 - 0.6 * 0.4)^3 - (1 - 0.6 * 0.4)^4 ≈ 0.684.

The probability that the series will last 5 games is the probability that the first four games have two wins for each team, and the last game is won by Team A:0.6^3 * 0.4^3 * 4 ≈ 0.055.The probability that the series will last 6 games is the probability that the first five games have two wins for each team, and the last game is won by Team A:0.6^3 * 0.4^3 * 5 ≈ 0.077The probability that the series will last 7 games is the probability that the first six games have two wins for each team, and the last game is won by Team A:0.6^3 * 0.4^3 * 6 ≈ 0.091.

The expected number of games played is thus approximately:0.684 * 4 + 0.055 * 5 + 0.077 * 6 + 0.091 * 7 + ∑m=8^∞ (1 - (pA + pB))^m(m + 1)(pA (1 - pB) + pB (1 - pA))The sum above can be computed by expressing it as the product of three factors:1 - (pA + pB) is a common factor for all terms, (pA (1 - pB) + pB (1 - pA)) is a sum of two terms that can be replaced by 1 - (1 - pA)(1 - pB), and m + 1 is a sum of m and 1. After replacing the sum of two terms, we obtain:0.684 * 4 + 0.055 * 5 + 0.077 * 6 + 0.091 * 7 + (1 - (0.6 + 0.4))^8(8 + 1)(1 - (1 - 0.6 * 0.4)^2) / (0.6 + 0.4 - 0.6 * 0.4) ≈ 0.684 * 4 + 0.055 * 5 + 0.077 * 6 + 0.091 * 7 + 0.02525 / 0.34 ≈ 5.43.

Therefore, the expected number of games played is approximately 5.43.(b) Given that Team B wins the first game, the series can last 7 or 8 games. The probability that the series will last 8 games is the probability that the first seven games have three wins for each team, and the last game is won by Team A:0.6^3 * 0.4^3 ≈ 0.013824.The probability that the series will last at least 8 games is therefore approximately 0.091 + 0.013824 = 0.104824, or 10.48%.Answer: (a) The expected number of games played is approximately 5.43. (b) The probability that the series will last at least 8 games is approximately 0.104824 or 10.48%.

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This behavior demonstrates the theory of social contagion, where individuals are influenced by the actions and emotions of others in a social setting.

The theory of social contagion suggests that individuals in a social setting can be influenced by the emotions, behaviors, and actions of those around them. When people laugh, clap, or cheer in a crowded arena, it creates a contagious atmosphere where the emotions and behaviors spread rapidly among the individuals present. This phenomenon can be attributed to various psychological mechanisms, such as conformity, social facilitation, and emotional contagion.

Conformity plays a role in this scenario, as individuals have a natural tendency to conform to the norms and expectations of the group. When others laugh, clap, or cheer, it signals social approval and acceptance of the speaker's performance. Consequently, individuals may feel inclined to join in, even if they do not genuinely find the speaker entertaining or compelling.

Social facilitation also contributes to this behavior. The presence of a large crowd can heighten arousal and increase individuals' performance on simple or well-practiced tasks. In this case, clapping, laughing, or cheering are relatively easy actions that require minimal cognitive effort, making it more likely for individuals to engage in these behaviors.

Emotional contagion is another factor at play. Humans are wired to empathize and connect with others emotionally. When people around us display positive emotions, such as laughter or excitement, we tend to "catch" those emotions and experience them ourselves. This emotional contagion further reinforces the tendency to follow along with the crowd's actions.

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There is a 99% chance that the backpack will not fall because at least one of the spools will not have a taped joint. To find the probability that the backpack falls because both spools have a taped joint, we can use the multiplication rule of probability.

Let's define the following events:

A: The first spool has a taped joint

B: The second spool has a taped joint

We are given that the probability of each spool having a taped joint is 0.1, and we are told that the events A and B are independent.

Using the multiplication rule of probability, we can find the probability of both events A and B happening:

P(A and B) = P(A) * P(B)

P(A and B) = 0.1 * 0.1

P(A and B) = 0.01

Therefore, the probability that the backpack falls because both spools have a taped joint is 0.01 or 1%.

Therefore, there is a 99% chance that the backpack will not fall because at least one of the spools will not have a taped joint. It is important to note that this assumes that the rest of the equipment is in good condition and the webbing itself is strong enough to hold the weight of the backpack.

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Answer:

The person must kick the ball around 31.62 feet high (They really want an apple!)

Step-by-step explanation:

If you think about it, the diagram will look like a triangle, so using the Pythagorean theorem, (a² + b² = c²), you will get around 31.62.

Have a good ay :)

Answer: 31.62

Step-by-step explanation:

To answer this question we will use the following formula to compute the surface area of a sphere:

Therefore the surface area of a sphere with a diameter of 20cm is:

Simplifying the above result we get:

Answer:

Answer:

Mr.Samson is 58 years old. Mr.Rogers is 35.

Step-by-step explanation

Samson's age            Roger's age

      2x - 12                          x          ( 12 years less than twice Mr.Rogers(x))

Equation:   2x - 12 + x = 93            Sum of ages is 93

3x - 12 = 93           Simplified

x = 35               Solve

Rogers = x, so Rogersis 35

But Sampson is 2x - 12 ( 2 * 35 - 12 ), so Sampson is 58

The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."

A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.

B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.

C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.

D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.

Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.

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Answer:

the perimeter is 960

Step-by-step explanation:

The computation of the perimeter is shown below;

If we assume

= (24 × 2) + (6 × 2)

= 48 + 12

= 60

And, the area is 16 times to that of original So

= 60 × 16

Hence, the perimeter is 960

All second derivatives are negative, all critical values are maxima. Therefore, the firm should produce 12 units in market 1, 9 units in market 2, and 3 units in market 3 to maximize its profit.

The optimization problem that the firm wants to solve is to maximize its profit, given by:

π = P₁Q₁ + P₂Q₂ + P₃Q₃ - (20+15Q₁+15Q₂+15Q₃)

subject to the constraints:

Q = Q₁ + Q₂ + Q₃

where π is the total profit, Pᵢ is the price in market i, and Q is the total quantity produced.

To find the first-order conditions, we need to take the partial derivative of the profit function with respect to each of the three variables Q₁, Q₂, and Q₃, and set them equal to zero:

∂π/∂Q₁ = P₁ - 15 = 0

∂π/∂Q₂ = P₂ - 15 = 0

∂π/∂Q₃ = P₃ - 15 = 0

These are the first-order conditions.

From the first-order conditions, we can see that the optimal quantities in each market are given by:

Q₁ = (63-15)/4 = 12

Q₂ = (105-15)/10 = 9

Q₃ = (75-15)/18 = 3

These are the critical values.

To check the second-order condition, we need to compute the second derivatives of the profit function with respect to the variables Q₁, Q₂, and Q₃, and evaluate them at the critical values. If the second derivatives are negative, then the critical values are maxima, and if they are positive, then the critical values are minima.

The second derivatives are:

∂²π/∂Q₁² = -4, ∂²π/∂Q₁∂Q₂ = 0, ∂²π/∂Q₁∂Q₃ = 0

∂²π/∂Q₂∂Q₁ = 0, ∂²π/∂Q₂² = -10, ∂²π/∂Q₂∂Q₃ = 0

∂²π/∂Q₃∂Q₁ = 0, ∂²π/∂Q₃∂Q₂ = 0, ∂²π/∂Q₃² = -18

Evaluating these at the critical values gives:

∂²π/∂Q₁² = -4 < 0

∂²π/∂Q₂² = -10 < 0

∂²π/∂Q₃² = -18 < 0

Since all second derivatives are negative, all critical values are maxima. Therefore, the firm should produce 12 units in market 1, 9 units in market 2, and 3 units in market 3 to maximize its profit.

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Answer:

\(\frac{4}{9}\)

Step-by-step explanation:

The equation would be

\(\frac{1}{3} +\frac{1}{9} =total\)

First, change the denominator to a common multiple.

The LCM (least common multiple) of 3 and 9 is 9.

\(\frac{3}{9} +\frac{1}{9} =total\)

Add to solve.

\(\frac{4}{9}\)

I hope this helps!

Answer:

4/9

Step-by-step explanation:

We need to add the amounts together

1/3 + 1/9

Getting a common denominator

1/3 *3/3   + 1/9

3/9 + 1/9

4/9

Solution:-

Let's find roots of x² - 3x + 2

=> x² - 3x + 2 = 0.

=> x² - x - 2x + 2 = 0.

=> x ( x - 1 ) -2 ( x - 1) = 0.

=> ( x - 1 ) ( x - 2 ) = 0.

=> x = 2, 1.

Now

So , equⁿ would be ,

=> x² - ( 9 + 1)x + 9×1=0.

=> x² - 10x + 9=0.

Answer:

No the point (20,15) is not on line j.

Answer:

B i believe x -y

Step-by-step explanation:

sorry if its no help <3

Answer:

c. (-x, y)

Step-by-step explanation:

Answer:

86.5

We add them together, which is 173, and since there are two terms, divide by 2

173/2=86.5

Answer:

86.5

127 + 46 / 2 = 86.5

I could be wrong but I believe this is correct.