(L5) Given: ΔABC with AC>AB;BD¯ is drawn so that AD¯≅AB¯Prove: m∠ABC>m∠C

To find the value of P(X≤4), you need to sum the probabilities of X=x for x≤4, which includes the probabilities for x=3 and x=4.
The probabilities for x≤4
P(X=3) = 0.2
P(X=4) = 0.2
The probabilities together
P(X≤4) = P(X=3) + P(X=4) = 0.2 + 0.2

Step 3: Calculate the result
P(X≤4) = 0.4
Answer: The value of P(X≤4) is 0.4 when rounded to one decimal place.

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The 98% confidence interval for the population mean (μ) is approximately (2.711, 3.009).

1: Identify the given data

Sample size (n) = 150 students

Sample mean (x) = 2.86

Population standard deviation (σ) = 0.78

Confidence level = 98%

2: Find the critical z-value (z*) for a 98% confidence level

Using a z-table or calculator, you'll find that the critical z-value for a 98% confidence level is 2.33 (approximately).

3: Calculate the standard error (SE)

SE = σ / √n

SE = 0.78 / √150 ≈ 0.064

4: Calculate the margin of error (ME)

ME = z* × SE

ME = 2.33 × 0.064 ≈ 0.149

5: Construct the confidence interval

Lower limit = x - ME = 2.86 - 0.149 ≈ 2.711

Upper limit = x + ME = 2.86 + 0.149 ≈ 3.009

The 98% confidence interval is approximately (2.711, 3.009).

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Hannah's debt-to-equity ratio when her liabilities was $30,000 (excluding her mortgage of $100,000 ) and her net worth is $45,000 is 0.75.

Debt-to-equity ratio is a financial ratio that measures the proportion of total liabilities to shareholders' equity. To calculate the debt-to-equity ratio for Hannah, we need to first calculate her total liabilities and shareholders' equity.

We are given that Hannah has liabilities of $30,000 excluding her mortgage of $100,000. Therefore, her total liabilities are $30,000 + $100,000 = $130,000.

We are also given that her net worth is $45,000. The net worth is calculated by subtracting the total liabilities from the total assets. Therefore, the shareholders' equity is $45,000 + $130,000 = $175,000.

Now we can calculate the debt-to-equity ratio by dividing the total liabilities by the shareholders' equity.

Debt-to-equity ratio = Total liabilities / Shareholders' equity = $130,000 / $175,000 = 0.74 (rounded to two decimal places)

Therefore, Hannah's debt-to-equity ratio is 0.74, which is closest to option 0.75.

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The rate at which the radius of the spherical balloon is increasing when the diameter is 40 cm is 0.005 cm/min. The rate at which the distance between Brad and Angelina is changing is 8 m/sec.

1. To determine the rate at which the radius of a spherical balloon is increasing, we can relate the radius and volume of the balloon. The formula for the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius.

We have that air is being pumped into the balloon at a rate of 10 cm³/min, we need to find the rate at which the radius is changing when the diameter (which is twice the radius) is 40 cm.

Since the diameter is 40 cm, the radius is 40/2 = 20 cm.

To determine the rate at which the radius is changing, we can differentiate the volume formula with respect to time:

dV/dt = (4/3)π(3r²)(dr/dt)

We have that dV/dt = 10 cm³/min, and r = 20 cm, we can solve for dr/dt:

10 = (4/3)π(3(20)²)(dr/dt)

10 = (4/3)π(1200)(dr/dt)

10 = (1600/3)π(dr/dt)

dr/dt = 10(3/1600π)

dr/dt = 0.005 cm/min

Therefore, the rate at which the radius of the balloon is increasing when the diameter is 40 cm is 0.005 cm/min.

2. To determine the rate at which the distance between Brad and Angelina is changing, we need to determine the rate at which the distance is changing with respect to time. Let's denote the distance between them as D.

Brad starts riding north at a rate of 4 m/sec, so his distance from the starting point can be represented as D_Brad = 4t, where t is the time in seconds.

Angelina starts riding south 6 minutes (or 6 * 60 = 360 seconds) later at a rate of 4 m/sec. Her distance from the starting point can be represented as D_Angelina = 4(t - 360).

The distance between them is given by D = D_Brad + D_Angelina.

D = 4t + 4(t - 360)

D = 4t + 4t - 1440

D = 8t - 1440

To determine the rate at which the distance is changing, we differentiate D with respect to time:

dD/dt = d(8t - 1440)/dt

dD/dt = 8

Therefore, the rate at which the distance between Brad and Angelina is changing is 8 m/sec.

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Answer:

Patriots

3.14159

Among us

Step-by-step explanation:

Answer:

The Steelers, 3.14159, Animal crossing.

Step-by-step explanation:

The vertex of the parabola is (2, 3), the focus is (2, 3.25), and the directrix is y = 2.75.

To rewrite the equation y - k = a(x - h)^2 in the form y - k = a(x - h)^2, we need to expand the given equation y - 3 = (2 - x)^2.

Expanding the equation, we have:

y - 3 = (2 - x)(2 - x)

y - 3 = 4 - 2x - 2x + x^2

y - 3 = x^2 - 4x + 4

Now, let's compare it with the standard form y - k = a(x - h)^2:

y - 3 = x^2 - 4x + 4

Comparing the terms, we have:

a = 1 (coefficient of x^2)

h = 2 (opposite of the coefficient of x)

k = 3 (constant term)

So, the equation y - 3 = (2 - x)^2 is already in the form y - k = a(x - h)^2.

Now, let's find the vertex, focus, and directrix of the parabola:

Vertex (h, k):

The vertex of a parabola in the form y - k = a(x - h)^2 is given by the coordinates (h, k). In this case, the vertex is (2, 3).

Focus (h, k + 1/(4a)):

The focus of the parabola is located at the point (h, k + 1/(4a)). Substituting the values, we get:

Focus = (2, 3 + 1/(4*1)) = (2, 3 + 1/4) = (2, 3.25)

Directrix (y = k - 1/(4a)):

The directrix of the parabola is a horizontal line given by the equation y = k - 1/(4a). Substituting the values, we have:

Directrix = y = 3 - 1/(4*1) = 3 - 1/4 = 3 - 0.25 = 2.75

Therefore, the vertex of the parabola is (2, 3), the focus is (2, 3.25), and the directrix is y = 2.75.

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Answer:

Step-by-step explanation: Here is your answer 97



Answer:

x = 1

Step-by-step explanation:

f(x) = (x - 1)²

f(x) = (x -1)(x - 1)

*Note: to find zeros set your equation equal to zero

x - 1 = 0

x = 1

*Since both quantities are the same x = 1 is your only zero.

Answer:

f(4) is 1/2

f(x)= 4 when x is 8

The line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1, 1), and the line segment from (1,1) to (0,1) is equal to 2/5.

What is integral?

The value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.

To evaluate the line integral using Green's theorem, we need to find a vector field F = (P, Q) such that ∇ × F = Qₓ - Pᵧ, where Qₓ represents the partial derivative of Q with respect to x, and Pᵧ represents the partial derivative of P with respect to y.

Let's consider F = (P, Q) = (x²y², xy).

Now, let's calculate the partial derivatives:

Qₓ = ∂Q/∂x = ∂(xy)/∂x = y

Pᵧ = ∂P/∂y = ∂(x²y²)/∂y = 2x²y

The curl of F is given by ∇ × F = Qₓ - Pᵧ = y - 2x²y = (1 - 2x²)y.

Now, let's find the line integral using Green's theorem:

∫[C] (Pdx + Qdy) = ∫∫[R] (1 - 2x²)y dA,

where [R] represents the region enclosed by the curve C.

To evaluate the line integral, we need to parameterize the curve C.

The arc of the parabola y = x² from (0, 0) to (1, 1) can be parameterized as r(t) = (t, t²) for t ∈ [0, 1].

The line segment from (1, 1) to (0, 1) can be parameterized as r(t) = (1 - t, 1) for t ∈ [0, 1].

Using these parameterizations, the region R is bounded by the curves r(t) = (t, t²) and r(t) = (1 - t, 1).

Now, let's calculate the line integral:

∫∫[R] (1 - 2x²)y dA = ∫[0,1] ∫[t²,1] (1 - 2t²)y dy dx + ∫[0,1] ∫[0,t²] (1 - 2t²)y dy dx.

Integrating with respect to y first:

∫[0,1] [(1 - 2t²)(1 - t²) - (1 - 2t²)t²] dt.

Simplifying:

∫[0,1] [1 - 3t² + 2t⁴] dt.

Integrating with respect to t:

[t - t³ + (2/5)t⁵]_[0,1] = 1 - 1 + (2/5) = 2/5.

Therefore, the line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1,1), and the line segment from (1,1) to (0,1) is equal to 2/5.

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Hello There!

1.8C+32=37.3

1.8C=37.3-32

1.8C=5.3

Now divide both sides by 1.8 to isolate C:

C=2.9

Hope this helps!

#HaveAnAmazingDay

\(GraceRosalia :)\)

Answer:

x = -1/3 - 3/2y

Step-by-step explanation:

Step 1: Write out equation

3y + 2x = -1

Step 2: Subtract 3y on both sides

3y - 3y + 2x = -1 - 3y

2x = -1 - 3y

Step 3: Divide both sides by 2

2x/2 (-1 - 3y)/2

x = -1/3 - 3/2y

Answer:

Hey there!

3y+2x=-1

2x=-3y-1

x=-3/2y-1/2

Let me know if this helps :)

Answer:

-10+4=-x

-x_=-6_

x=6

if you don't understand

negative x over negative x and negative x over 6 the negative will cancle the negative you will get x to be 6

The acceptable conclusions to a hypothesis test are option a, c, d, f.

What is hypothesis test?

Hypothesis Testing is a way of statistical analysis in which a person can  put his assumptions about a population parameter to the test. It usually  used to estimate the relationship between two statistical variables.

By the property of hypothesis test the following can be stated.

⇒The value of the test statistic lies in the non rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true.

⇒ The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the null hypothesis is not true.

⇒The value of the test statistic does not lie in the rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true.

⇒ The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the alternative hypothesis is true.

Hence the correct options are a, c, d, f.

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Answer:

-59/12

Step-by-step explanation:

finish whats inSide brackets first

so -12+3 =-9

-9*1/4 will be next and = -9/4

9/4+8/3 =. 59 /12

100th digit of the pi is 7

Pi (represented by the Greek letter π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159,

The decimal representation of pi (π) is an infinite non-repeating sequence of digits, so there is no simple formula or algorithm to determine the value of its digits. However, you can use a computer program or online tool to calculate the digits of pi to a certain number of decimal places.

Assuming you are looking for the 100th decimal digit of pi, it is 7. This means that if you write out the first 100 digits of pi, the 100th digit is 7.

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Answer:

$888

Step-by-step explanation:

I=P×T×R/100

=600×8.25×0.5/100 [8 year 3 months=99 months = 8.25 year ]

=1237.5/100

I =12.375

A= I +P

=600+12.375

A =612.375

hence the total amount will be $ 612.375

Percent cost of the total spent on

each equipment = 14.23%,fees=62.45% and transportation = 23.32%.

As given in the question,

Money spent on

Each equipment = $36

Fees = $158

Transportation = $59

Total money spent = $( 36 + 158 + 59)

                             = $253

Percent cost of the total spent on

Each equipment = (36/253) × 100

                          = 14.23%

Fees = (36/253) × 100

        = 62.45%

Transportation =(36/253) × 100

                       = 23.32%

Therefore, percent cost of the total spent on

each equipment = 14.23%,fees=62.45% and transportation = 23.32%.

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The estimated proportion of college students who drive stick shift cars is calculated with 90% confidence using sample data.

To estimate the proportion of college students who drive stick shift cars, we can use the sample data of 121 cars, out of which 22 have stick shifts. We will construct a confidence interval to estimate the true proportion. Using a graphing calculator, we can perform a proportion confidence interval calculation.

The calculator will take into account the sample size, the number of successes (cars with stick shifts), and the desired confidence level (90% in this case).

The resulting confidence interval will provide an estimate of the proportion of college students who drive stick shift cars. The answer should be rounded to at least three decimal places for accuracy.

This interval will represent a range within which we can be 90% confident that the true proportion of college students who drive stick shift cars lies.

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Answer:

the correct answer is 2/7

The maximum number of vectors in set S can be determined by the dimension of the vector space R3, which is three.

If S is a set of vectors in R3 that are linearly independent, but do not span R3, it implies that S is a proper subset of R3. Since the dimension of R3 is three, S cannot contain more than three vectors.

To understand this, we need to consider the definition of spanning. A set of vectors spans a vector space if every vector in that space can be written as a linear combination of the vectors in the set. Since S does not span R3, there must be at least one vector in R3 that cannot be expressed as a linear combination of the vectors in S.

If we add another vector to S, it would increase the span of S and potentially allow it to span R3. Therefore, the maximum number of vectors in S is three, as adding a fourth vector would exceed the dimension of R3 and allow S to span R3.

To understand why, let's break down the options and their implications:

(A) If S contains only one vector, it cannot span R3 since a single vector can only represent a line in R3, not the entire three-dimensional space.

(B) If S contains two vectors, it still cannot span R3. Two vectors can at most span a plane within R3, but they will not cover the entire space.

(C) If S contains three vectors, it is possible for them to be linearly independent and span R3. Three linearly independent vectors can form a basis for R3, meaning any vector in R3 can be expressed as a linear combination of these three vectors.

(D) This option is incorrect because S cannot contain any number of vectors. It must be limited to a maximum of three vectors in order to meet the given conditions.

Thus, the correct answer is (C) three.

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Answer:

225.08, which would just be 225.

Step-by-step explanation:

First, you multiply the percent, 17, times the total number of points, 1,324, which you should get 22,508. Then, divide that by 100, and you will get your answer 225.08. The reason you put it into the whole number, is because you can't score part of a point, so you always round down even if the number is in favor to round up. I hope this helps :)

The derivative of the given expression, cos(x³) * sin(x²) * x⁵, with respect to x is: d/dx [cos(x³) * sin(x²) * x⁵].

To differentiate this expression, we can apply the product rule and the chain rule. The product rule states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function. Let's break down the expression and differentiate each part separately:

Differentiate cos(x³): The derivative of cos(x³) with respect to x is -sin(x³). Applying the chain rule, we multiply by the derivative of the inner function, which is 3x².

Differentiate sin(x²): The derivative of sin(x²) with respect to x is cos(x²). Applying the chain rule, we multiply by the derivative of the inner function, which is 2x.

Differentiate x⁵: The derivative of x⁵ with respect to x is 5x⁴.

Now, we can put it all together using the product rule:

d/dx [cos(x³) * sin(x²) * x⁵] = (-sin(x³) * 3x² * sin(x²) * x⁵) + (cos(x³) * cos(x²) * x⁵ * 2x) + (cos(x³) * sin(x²) * 5x⁴).

Simplifying the expression further, we obtain the derivative of the given expression.

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Answer: A. Always study with a group of friends

Step-by-step explanation:

just had that same question and im 100% right ; )

The resultant of the expression (((-3/5)+(5/3))-(2-4/3)) will be 2/5.

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations that can be evaluated to produce a value. Expressions can be as simple as a single number or variable, or they can be more complex, involving multiple numbers, variables, and operations.

For example, 3 + 5 is an expression that represents the sum of two numbers, which evaluates to 8. Another example is 2x - 5, which involves a variable (x) and two operations (multiplication and subtraction).

Now,

Let's start by simplifying (-3/5 + 5/3):

First, we need to find a common denominator between 5 and 3, which is 15

then,

-3/5 + 5/3 = -9/15 + 25/15

Next, we can add the two fractions:

-9/15 + 25/15 = 16/15

So, (-3/5 + 5/3) simplifies to 16/15.

Now, let's simplify (2 - 4/3):

We can rewrite 2 as 6/3, then subtract 4/3:

6/3 - 4/3 = 2/3

So, (2 - 4/3) simplifies to 2/3.

Finally, we can subtract 2/3 from 16/15:

16/15 - 2/3

To subtract fractions, we need a common denominator between 15 and 3, which is 15. then

16/15 - 10/15 = 6/15

So, the resulting constant is 6/15, which can be simplified by dividing both the numerator and denominator by their greatest common factor (which is 3):

6/15 = 2/5

Therefore,

                the resulting constant is 2/5.

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Answer:

The answer is 0.8

Perimeter of a square is p= 4*s

Answer:

the measure of angle Z is 104

Step-by-step explanation:

the angle z and 76 form a suplementary angle, which they add up to 180.

To find angle z, just subtract 76 from 180.

Answer:

RS = 18 units

Step-by-step explanation:

the 2 red strokes through RM and MS indicate they are congruent, that is

RM = MS = 9 , then

RS = RM + MS = 9 + 9 = 18 units