Order each expression from least to greatest when x = 20.
Drag and drop the expressions to order them from least to greatest.

The angle between vectors u and v is approximately 43.7 degrees to the nearest tenth of a degree.

To find the angle between two vectors, we can use the dot product formula and the magnitude of the vectors. The dot product of two vectors u and v is given by:

u · v = |u| |v| cos(theta)

where |u| and |v| are the magnitudes of vectors u and v, respectively, and theta is the angle between the vectors.

Given vectors u = <6, 4> and v = <7, 5>, we can calculate their magnitudes as follows:

|u| = sqrt(6^2 + 4^2) = sqrt(36 + 16) = sqrt(52) ≈ 7.21

|v| = sqrt(7^2 + 5^2) = sqrt(49 + 25) = sqrt(74) ≈ 8.60

Next, we calculate the dot product of u and v:

u · v = (6)(7) + (4)(5) = 42 + 20 = 62

Now, we can substitute the values into the dot product formula:

62 = (7.21)(8.60) cos(theta)

Solving for cos(theta), we have:

cos(theta) = 62 / (7.21)(8.60) ≈ 1.061

To find theta, we take the inverse cosine (arccos) of 1.061:

theta ≈ arccos(1.061) ≈ 43.7 degrees

Therefore, the angle between vectors u and v is approximately 43.7 degrees to the nearest tenth of a degree.

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The required answer is he equilibrium price will be $8, and the equilibrium quantity will be 320 units.

After the introduction of the new desalination technology, the market supply curve will shift to the right, since firms will be able to produce more water at a lower cost. The new supply curve will be given by:

! = 5P + (8 * quantity) - 5

This is because the cost of producing each unit of water has now increased by $8, but the supply function remains the same.  specifically general equilibrium theory, a perfect market, also known as an atomistic market, is defined by several idealizing conditions, collectively called perfect competition, or atomistic competition. In theoretical models where conditions of perfect competition hold, it has been demonstrated that a market will reach an equilibrium in which the quantity supplied for every product or service, including labor, equals the quantity demanded at the current price

To find the equilibrium price and quantity, we need to set the new supply curve equal to the demand curve:

400 - 10P = 5P + (8 * quantity) - 5

Simplifying and solving for P:

15P = 405 + 8Q

P = 27 + (8/15)Q

Next, we substitute this expression for P into either the demand or supply curve and solve for Q. Let's use the demand curve:

400 - 10(27 + (8/15)Q) = Q + 5

Simplifying:

Q = 60

Therefore, the equilibrium quantity is 60 units of water, and the equilibrium price can be found by plugging this quantity into the expression for P:

P = 27 + (8/15)(60) = $43.20
So the equilibrium price is $43.20 per unit of water.

To find the market supply curve after the introduction of the new desalination technology and the equilibrium price and quantity, follow these steps:

Step 1: Determine the new supply curve.
Since the desalination technology allows for unlimited water production at a cost of $8, the new supply curve will be a horizontal line at P = $8. This is because suppliers will be willing to supply any quantity of water at that price.
Step 2: Find the new equilibrium price and quantity.

To find the new equilibrium, we need to determine where the new supply curve intersects the demand curve. The demand curve is given by Qd = 400 - 10P. To find the intersection, set the price P equal to $8 in the demand equation:

Qd = 400 - 10(8)
Qd = 400 - 80
Qd = 320

So, at the equilibrium price of $8, the quantity demanded is 320 units.

In conclusion, the market supply curve after the introduction of the new desalination technology will be a horizontal line at P = $8. The equilibrium price will be $8, and the equilibrium quantity will be 320 units.

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Answer:

B.

Step-by-step explanation:

Therefore, the probability that X is less than 11.5 is approximately 0.0186. So the correct option is (d) 0.0186.

To find the probability that X is less than 11.5, we can standardize the value using the z-score formula and then use the standard normal distribution table.

The z-score formula is given by:

z = (x - μ) / σ

Where:

x = the value we want to find the probability for (11.5 in this case)

μ = the mean of the distribution (24 in this case)

σ = the standard deviation of the distribution (6 in this case)

Substituting the values:

z = (11.5 - 24) / 6

z ≈ -2.0833

Now, we look up the corresponding area/probability in the standard normal distribution table for z = -2.0833. From the table, we find that the area to the left of z = -2.0833 is approximately 0.0186.

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In a family with five girls and the probability of a boy being born is 1/2, the probability of the next child being a boy is still 1/2.

The previous births do not affect the probability of the next birth since each birth is an independent event.

The probability of an event occurring is determined by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the event of interest is the birth of a boy.

Since each birth is an independent event, the probability of having a boy on any given birth is always 1/2, regardless of the previous children born.

In the given scenario, the family already has five girls. This information is not relevant to the probability of the next child being a boy. The gender of the previous children does not affect the probability of the next child being a boy or a girl.

Therefore, the probability of the next child being a boy remains 1/2, as it is for any independent birth event.

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The length of the major arc ACB is given as follows:

65π/3 feet.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The radius for this problem is given as follows:

r = 12 ft.

The angle measure of the major arc ACB is given as follows:

360 - 35 = 325º.

Hence the length of the arc is given as follows:

325/360 x 2π x 12 = 65π/3 feet.

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Part A

f(0)

that means the value of f(x) for x=0

looking at the table

For x=0 ----> f(x)=4

therefore

f(0)=4

Part B

f(x)=0

looking at the table

f(x)=0 when the value of x=1

therefore

f(1)=0

Part C

f^-1(0)

For f(x)=0 -----> the value of x=1

therefore

f^-1(0)=1

Part D

f^-1(x)=0

looking at the table

For x=0 -----> f(x)=4

therefore

f^-1(4)=0

Answer:

I believe it is d

Step-by-step explanation:

it is the only option where every combination of two sides is larger than the third

Answer:

d

Step-by-step explanation:

if you add up 2 sides it is larger than the third, which is what we are looking for :))

y = -1/3x + 1

y = -2x - 3

We can compare the equations to the graphs and see which graph represents the intersection point of the two equations.

The first equation, y = -1/3x + 1, has a negative slope (-1/3) and a y-intercept of 1.

The second equation, y = -2x - 3, also has a negative slope (-2) and a y-intercept of -3.

Based on the slopes and y-intercepts, we can identify the correct graph by finding the point where the two lines intersect.

Unfortunately, since the graphs are not provided, I am unable to determine which specific graph shows the solution to the system of linear equations. I recommend referring to the graph representation of the equations and identifying the intersection point to determine the correct graph.

76 yd

This is very simple

Perimeter is the sum of all the outer sides

22yd + 22yd + 16yd +16yd

This will give you

76yd

Answer: 76

Step-by-step explanation: Perimeter is 2(length +breadth)

2(22+16)

The scale factor is 2 and center dilation is reduced.

The scale factor is a ratio that describes how much a figure has been enlarged or reduced. It is calculated by dividing the length of the corresponding sides of the original and dilated figures. If the scale factor is greater than 1, then the figure is enlarged, and if it is less than 1, then the figure is reduced.

To find the scale factor in an IXL dilations problem, you need to compare the corresponding sides of the original and dilated figures.

If the original figure has a side length of 4 units, and the dilated figure has a corresponding side length of 8 units, then the scale factor is 8/4=2. This means that the dilated figure is twice as large as the original figure.

The center of dilation is the point about which the figure is enlarged or reduced. It is the fixed point that remains unchanged during the dilation process.

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The solution to the given initial-value problem is:

x(t) = (3/7) sin(t) - (12/7) sin(2t).

First, Taking the Laplace transform of the differential equation:

Applying the Laplace transform to the given differential equation

x" + 4x = f(t),

s²X(s) - sx(0) - x'(0) + 4X(s) = F(s),

Since x(0) = 0 and x'(0) = 0,

s²X(s) + 4X(s) = F(s).

Now, applying the Laplace transform to the initial conditions x(0) = 0 and x'(0) = 0, we get:

X(s) - 0 + s(0) - 0 = 0,

X(s) = 0.

Then, For t < 5, f(t) = 3sin(t-5). Taking the Laplace transform of f(t), we have:

F(s) = 3L[sin(t-5)],

Using the Laplace transform property L[sin(at)] = a / (s² + a²), we have:

F(s) = 3  [1 / (s² + 1²)].

Substituting the expressions for F(s) and X(s) into the differential equation equation, we get:

s²X(s) + 4X(s) = 3 / (s² + 1²).

(s² + 4)X(s) = 3 / (s² + 1²).

X(s) = 3 / [(s² + 1²)(s² + 4)].

Using partial fraction decomposition, we can express X(s) as:

X(s) = A / (s² + 1) + B / (s² + 4),

To find A and B, we multiply both sides by (s² + 1)(s² + 4) and equate the numerators:

3 = A(s² + 4) + B(s² + 1).

0s⁴ + (4A + B) s² + (4A + B) = 0s⁴ + 0s³ + 0s² + 3s⁰.

Equating coefficients, we have:

4A + B = 0, and

4A + B = 3.

Solving these equations, we find A = 3/7 and B = -12/7.

Then, X(s) = (3/7) / (s² + 1) - (12/7) / (s² + 4).

Taking the inverse Laplace transform of X(s),

x(t) = (3/7) sin(t) - (12/7) sin(2t).

Hence, the solution to the given initial-value problem is:

x(t) = (3/7) sin(t) - (12/7) sin(2t).

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Answer: f(x)=15m+100

Step-by-step explanation:

Because the flat fee is 100 so that should be your y intercept as they won't change it no matter what.

the 15 is the x (or slope) as it may vary depending on how many mils you walk

Hope this helps :)

Answer:

A 2,3,6 :)

Step-by-step explanation:

thats answer corect me if im wrong hope it help

The statement "as the confidence level increases, the width of the confidence interval increases" is true. When constructing a confidence interval, the confidence level represents the level of certainty or reliability we have in our estimate. A higher confidence level requires a wider interval to capture a larger range of possible values.

To understand this, imagine constructing a 90% confidence interval and a 95% confidence interval for the same population parameter. The 95% confidence interval needs to provide a higher level of confidence, so it will be wider than the 90% interval to accommodate a larger range of values. However, the other statements are not true. Increasing the sample size actually leads to a narrower confidence interval. As the sample size increases, the estimate becomes more precise, resulting in a smaller margin of error and a narrower interval. Therefore, the statement "as the sample size increases, the width of the confidence interval increases" is false.

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It takes 9.6 minutes for Thoriso to get to school if she walks to school.

Given:

Thoriso can walk at a speed of 5 km/h.

Thoriso can ride her bicycle at a speed of 5 km/h.

The time taken by Thoriso to get to school by Bicycle = 10 minutes

To Find:

The time taken by Thoriso to get to school by walking.

Solution:

→ Thoriso can ride her bicycle at a speed of 5 km/h.

The time taken by Thoriso to get to school by Bicycle = 10 min = 1/6 hour

                               ∵ Distance = Speed × Time

∴ The distance that Thoriso need to cover to reach school = 5 × 1/6

∴ The distance that Thoriso need to cover to reach school = 0.8 km

→ Thoriso can walk at a speed of 5 km/h.

∴ The time taken by Thoriso to get to school by Walking = 0.8/5 = 0.16 Hr

∴ The time taken by Thoriso to get to school by Walking  = 0.16 Hr = 9.6 min

Therefore the time taken by Thoriso to get to school by Walking comes out to be equal to 9.6 minutes.

Answer:

True:

it is a nonagon

angle GFE is 140 degrees

angle AJB is 40 degrees

all triangles are isosceles*

*as it appears in the illustration

Step-by-step explanation:

On solving the provided question, we can say that from equation \(diagonal ^2 = 8^2 + 8^2\), the answer is \(DIAGONAL = 8\sqrt(2) \\\)

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

\(diagonal ^2 = 8^2 + 8^2\\diagonal ^2 = 64 + 64\\diagonal ^2 = 128\\diagonal ^2 = 64 * 2\\\)

\(diagonal ^2 = 8 * sq root (2)\\Diagonal of a square = SqrRoot (2 * side^2)\\Diagonal = \sqrt{2 * 8^2} \\Diagonal = \sqrt(128)\\\)

\(\sqrt(128) = \sqrt(2 * 64) = \sqrt(2) * 8\\DIAGONAL = 8\sqrt(2) \\\)

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To find two linearly independent solutions of the given differential equation, let's substitute the given forms of the solutions and determine the coefficients.

Let's start with the form Y₁ = 2⁽ⁱ⁺ᵃ⁺α₂x²⁺³ˣ⁺⁾ (1 + a + α₂x² + 3x³ + ...).

Taking derivatives:

Y₁' = 2⁽ⁱ⁺ᵃ⁺α₂x²⁺³ˣ⁺⁾ (0 + a + 2α₂x + 9x² + ...)

Y₁" = 2⁽ⁱ⁺ᵃ⁺α₂x²⁺³ˣ⁺⁾ (0 + 2α₂ + 18x + ...)

Substituting these into the differential equation:

2x²(2α₂ + 18x + ...) - x(1 + a + α₂x² + 3x³ + ...) + (-x + 1)(1 + a + α₂x² + 3x³ + ...) = 0

Expanding and grouping terms according to powers of x:

(2α₂ + 18x + ...) - (1 + a + α₂x² + 3x³ + ...) + (-x + x(a + α₂x² + 3x³ + ...)) + (x(-1 + a + α₂x² + 3x³ + ...)) = 0

Simplifying:

2α₂ + 18x + ... - 1 - a - α₂x² - 3x³ - ... - x + ax + α₂x³ + 3x⁴ + ... - x - ax - α₂x³ - 3x⁴ - ... = 0

Combining like terms:

1 + (2α₂ - a - 1)x + (-α₂ - a)x² + (-3 - a)x³ + ... = 0

For this equation to hold for all values of x, each term must be equal to zero. Therefore, we have the following equations:

2α₂ - a - 1 = 0 -- (1)

-α₂ - a = 0 -- (2)

-3 - a = 0 -- (3)

From equation (2), we can solve for α₂:

α₂ = -a -- (4)

Substituting equation (4) into equation (1):

2(-a) - a - 1 = 0

-2a - a - 1 = 0

-3a - 1 = 0

-3a = 1

a = -1/3

From equation (3), we can solve for a:

-3 - a = 0

a = -3

Now let's consider the form Y₂ = x(1 + b₁x + b₂x² + b³x³ + ...).

Taking derivatives:

Y₂' = 1 + 2b₁x + 3b₂x² + 4b³x³ + ...

Y₂" = 2b₁ + 6b₂x + 12b³x² + ...

Substituting into the differential equation:

2x²(2b₁ + 6b₂x + 12b³x² + ...) - x(1 + b₁x + b₂x² + b³x³ + ...) + (-x + 1)(1 + b₁x + b₂x² + b³x³ + ...) = 0

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The value of the expression is 1/(9x)^2

From the question, we have the following parameters that can be used in our computation:

(-9x)^-2

We can write the expression without negative exponents by using a fraction with a positive exponent:

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

And without parentheses, this expression becomes:

1/(9x)^2

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Answer: w = 2x + 4

Step-by-step explanation: The rabbit started at 4 ounces, and gained two each week.

Week 0 = 2(0) + 4 = 4

Week 1 = 2(1) + 4 = 6

Week 2 = 2(2) + 4 = 8

Week 3 = 2(3) + 4 = 10

Answer:

80

Step-by-step explanation:

This is a combination question that contains multiple clothing items and to solve such question we multiply the given numbers :

5 × 4 × 4 = 80

Answer: c

Step-by-step explanation:

Write the Equation

= 5.5x + 6.2y + 4.3x + 8.3z + 1.6z - 5.1y

Re-arrange them

= 5.5x + 4.3x + 6.2y - 5.1y + 8.3z + 1.6z

Add them

= 9.8x + 0.1y + 9.9z

Recall the Central Limit Theorem.

The Central Limit Theorem says that no matter what the distribution of the population is, as long as the sample is “large,” meaning of size 30 or more, the sample mean is approximately normally distributed.

If the population is already normal, then any sample size will produce a normal sampling distribution.

The owner cannot conclude that attendance has decreased at the 0.10 level of significance.

To determine if the attendance has decreased, we can perform a hypothesis test. The null hypothesis (H₀) assumes that the average attendance has not changed, while the alternative hypothesis (H₁) assumes that the average attendance has decreased.

Define the hypotheses

H₀: μ = 112 (the average attendance has not changed)

H₁: μ < 112 (the average attendance has decreased)

Set the significance level

The significance level (α) is given as 0.10, which represents a 10% chance of making a Type I error (rejecting the null hypothesis when it is true).

Calculate the test statistic

Since we have the sample mean (x= 102), the population mean (μ = 112), the standard deviation (σ = 15.2), and the sample size (n = 35), we can calculate the test statistic using the formula:

t = (x- μ) / (σ / √n)

Plugging in the values:

t = (102 - 112) / (15.2 / √35)

t ≈ -3.425

Determine the critical value

Since the alternative hypothesis is one-tailed (μ < 112), we need to find the critical value for a one-tailed t-distribution with degrees of freedom (df) equal to n - 1. In this case, df = 34. Using a t-table or a t-distribution calculator, we find the critical value to be approximately -1.310.

Make a decision

If the test statistic falls in the rejection region (i.e., t < critical value), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

In this case, -3.425 < -1.310, so the test statistic falls in the rejection region. Therefore, we reject the null hypothesis and conclude that attendance has decreased at the 0.10 level of significance.

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Answer: Yes, the two triangles are similar.

Step-by-step explanation:

The triangle on the right needs to be turned. But you don't necessarily have to do that for this problem, just match up the two highest numbers, the two middle, and the two lowest.

Put them over each other:

32/48, 30/45, 24/36

Divide.

Each ratio equals 2/3

Answer:

No it is not

Step-by-step explanation:

Answer:

Step-by-step explanation:

bc²-2a/b=6(3)²-2×12/6=54-4=50

\( \sf{15}^{0} = 1\)