Identify the type of conic that follwoing equation represents and write the standard form of each equation.

25x² + 100y² - 450x - 400y - 75 = 0

The standardized test statistic is -2.68  and the critical value is 1.44.

Given that, Claim: h = 30 Sample statistics: x = 28.9, n = 65 α = 0.08 σ = 3.31

We need to calculate the standardized test statistic and critical value.

Test statistic: The standardized test statistic can be calculated as follows:

Z = (x - μ) / (σ / √n)

Substitute the given values in the above formula to get

Z = (28.9 - 30) / (3.31 / √65) = -2.68

Critical value: Since the level of significance α is given, we can calculate the critical value using the z-score table for standard normal distribution.

Since α is given,  the right-tailed test is conducted.

The critical value is obtained by subtracting the α-level from 1 and then find the z-score value.

Let's find the z-score value corresponding to the area 0.92 in the z-score table.

We get the corresponding z-score as 1.44, which is the critical value.

Hence, the standardized test statistic is -2.68 (Round to two decimal places as needed.) and the critical value is 1.44.

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Answer:

2000.2 cm³

Step-by-step explanation:

Finding the volume of a cylinder is quite simple if you under what pi (3.14) is. You can watch khan academy. It has some useful videos on solving for volume. It also explains very well. Hope this helps!

Answer:

The number 1/3 is a rational number. A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero.

1/3 is not a natural number, whole number, or integer. Natural numbers are the set of positive integers (1, 2, 3, …). Whole numbers are the set of non-negative integers (0, 1, 2, 3, …). Integers are the set of whole numbers and their additive inverses (-3, -2, -1, 0, 1, 2, 3, …).

Step-by-step explanation:

Answer:

864

Step-by-step explanation:

To find the area of a shape, you have to multiply length times width.

Answer:

72 ft. sq.

Step-by-step explanation:

The way to look at it it to multiply length times width ( l x w )

there are 2 obvious  numbers to get the answer, which is 8 and 9 so 8 x 9 = 72

Answer: [tex]202.5\ in.^3[/tex]

Step-by-step explanation:

Given

The area of the base is [tex]A=40.5\ in.^2[/tex]

height of the triangular prism is [tex]h=15\ in.[/tex]

The volume of a triangular prism is  [tex]V=\dfrac{1}{3}Ah[/tex]

The volume of given Prism is

[tex]V=\dfrac{1}{3}\times 40.5\times 15=202.5\ in.^3[/tex]

The volume of the triangular prism is [tex]202.5\ in.^3[/tex]

In a case whereby sheri’s cab fare was $32, with a 20% gratuity and no taxes. sheri's write a check to the cab driver for $40, this can be considered as being reasonable amount because it is  $1.60 more to the cab driver.

A gratuity is a sum of money that customers typically give to specific service sector employees, including those in the hotel industry, in addition to the service's base charge for the work they have completed.

Given ; Sheri’s cab fare was $32 and the percentage of gratuity is 20%

amount of gratuity = 20% 0f 32 = 6.40

The fare of the cab  + gratuity = 32 + 6.40 = 38.40

Check to the cab driver for $40 ,  implies ($40 - $38.40)= $1.60 more to the cab driver.

Hence, it is reasonable.

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Answer:

yes your answer is correct

Step-by-step explanation:

Answer:

1/67

Step-by-step explanation:

Complete question

If X+2/3x is equal to 45. find the value of x​

Given the equation

x+2/3x = 45

Cross multiply

x+2 = 3x(45)

x+2 = 135x

x - 135x = -2

-134x = -2

x = 2/134

x = 1/67

Hence the value of x is 1/67

Answer:

Step-by-step explanation:

Find the log of both the equation and the expression:

b log a = log x              this can be solved for log a in terms of log x:

              log x

log a = ------------

                  b

"Name" the second expression "y."  Then y = a^26 and log y = 26 log a.

                             log x

Then log y = 26--------------

                                 b

and the expression a^26 is found by taking the antilog of both sides of log y:

   log y                             log x

10           =   y   =    10^(26----------)

                                            b

Please double check to ensure that you have copied this problem down correctly.  

Answer:

x = 6

Step-by-step explanation:

Using the rules of logarithms

logx - logy = log ([tex]\frac{x}{y}[/tex] )

logx = logy , then x = y

Given

log(x) - log(x + 6)

= log([tex]\frac{x}{x+6}[/tex] )

Then

log )[tex]\frac{x}{x+6}[/tex] ) = log([tex]\frac{1}{2}[/tex] ) , thus

[tex]\frac{x}{x+6}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = x + 6 ( subtract x from both sides )

x = 6

Answer:

18.2 miles

Step-by-step explanation:

simple multiplication:

We know that 1 inch of distance on the map is equal to 5.2 miles.

Using this knowledge we can multiply the amount of inches by the miles per inch.

5.2*3.5=18.2 miles apart

Hope this helps!!

Answer:

9526/87

Step-by-step explanation:

87·x=9,526

x=9526/87

Answer:

The equations are

X + Y = 48 ----Eq (1)

Y = 2 X -----Eq (2)

Solution of the equations and the two number are

X = 16, Y = 32

Step-by-step explanation:

Let the two numbers be X and Y

Given -

The sum of two numbers is 48.

Thus, X + Y = 48 ----Eq (1)

The second number is twice the first

Thus, Y = 2 X -----Eq (2)

Substituting the value of Y in equation (1), we get -

X + 2X = 48

3 X = 48

X = 16

Y = 2 X = 32

Answer:

You basically grow rep

Step-by-step explanation:

Brainly points you need for asking questions and people are more likely to trust you with their questions if you have alot!

Answer:

i actually dont know

Step-by-step explanation:

Answer:

Step-by-step explanation:

15,13,11,9,1,3,5,7

Answer:

13

Step-by-step explanation:

Supplementary angles add up to 180 and angles on a straight line add up to 180 so 13

Answer: 6

Step-by-step explanation:

Step 1: Set up equation:

90=40.62+8.23p

^ the 'p' represents pounds.

Step 2: Subtract 40.62 from both sides

49.38 = 8.23p

Step 3: Divide both sides by 8.23 (We do this to get the variable "p" by itself)

6=p

Trust Milky. Milky Smart

The required results are:

(i) E(S) = -m₁

(ii) [tex]Var(S) = k(1 − p)(m₂ - m₁²)/p + [k(1-p)/p]² (m₁² + m₂ - m₁²)[/tex]

(iii) Skew = 3(1 − 2p)/sqrt{k(1 − p)}.

The aggregate claim amount is defined as S X₁, where Xį are independent and i=1 identically distributed claim amounts and N is the number of claims.

And also suppose N follows a negative-binomial distribution with

E(N) = k(1 − p)/p

and variance

Var(N) = k(1 − p)/p².

Now we have to show that:

k(1 − p)

(i) [tex]E(S) = -m₁ and р k(1 − p) k(1-P)² m²,[/tex]

(ii) Var (S) = -M2 + p² -

(iii) [tex]Skew k(1 − p)m² 3k(1 − p)²m₁m2 p² + + 2k(1 − p)³m³ p³ P(i) E(S) = -m₁[/tex]

Where S = X1 + X2 + ...... + XN.

Also, N and Xi's are independent.

So, E(S) = E(E(S|N))

From the law of total expectation,

E(S|N) = E(X1 + X2 +......+XN|N)

Using linearity of expectation

,E(X1 + X2 +......+XN|N) = E(X1|N) + E(X2|N) +......+ E(XN|N) = NE(X1)Now, E(S) = E(E(S|N)) = E(NE(X1))= NE(X1) = m₁

Therefore,

E(S) = -m₁.(ii) Var (S) = -M2 + p² -Where Var(S|N) = Var(X1 + X2 +......+XN|N) = Var(X1|N) + Var(X2|N) +......+ Var(XN|N)Also, E(S|N) = NE(X1)Thus, E(S) = E(E(S|N)) = E(NE(X1)) = NE(X1) = m₁ And Var(S) = E(Var(S|N)) + Var(E(S|N))

Using independence,

[tex]Var(S|N) = Var(X1 + X2 +......+XN|N) = Var(X1|N) + Var(X2|N) +......+ Var(XN|N)Var(S|N) = N Var(X1)Using independence, E(S|N) = NE(X1)Var(E(S|N)) = Var(NE(X1)) = N²Var(X1)Hence, Var(S) = E(Var(S|N)) + Var(E(S|N))= E(N Var(X1)) + Var(NE(X1))= (k(1 − p)/p) Var(X1) + N²Var(X1)= k(1 − p)Var(X1)/p + N²Var(X1)[/tex]

Also, [tex]Var(X1) = E(X1²) - (E(X1))² = m₂ - m₁²[/tex]

Therefore,

Var(S) = k(1 − p)(m₂ - m₁²)/p + N²(m₂ - m₁²)

And N follows a negative-binomial distribution with

E(N) = k(1 − p)/p and variance

[tex]Var(N) = k(1 − p)/p². Thus, E(N²) = Var(N) + (E(N))²E(N²) = k(1-p)/p² + [k(1-p)/p]²[/tex]

Therefore,

[tex]Var(S) = k(1 − p)(m₂ - m₁²)/p + [k(1-p)/p]² (m₁² + m₂ - m₁²)(iii) Skew = 3(1 − 2p)/sqrt{k(1 − p)}[/tex]

Therefore,

[tex]k(1 − p)m² 3k(1 − p)²m₁m2 p² + + 2k(1 − p)³m³ p³ P = 3(1 − 2p)/sqrt{k(1 − p)}.[/tex]To know more about binomial distribution, visit:

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Answer:

9/30

Step-by-step explanation:

Answer:

The recipe will make 7.2 quarts of punch.

Step-by-step explanation:

A punch recipe calls for 3 liters of ginger ale and 1.5 liters of tropical fruit juice.

Then the recipe will make 4.5 liters of punch, obtained by the sum of ginger ale and tropical fruit juice.

The ration is the comparison of two quantities and is measured from the division of two values, then: [tex]\frac{a}{b}[/tex].

The proportion is the equality between two or more ratios. That is, [tex]\frac{a}{b}=\frac{c}{d}[/tex] equals a proportion.

In this case, being 1 L= 1.6 quarts, you have:

[tex]\frac{1.6 quarts}{1 L}=\frac{x}{4.5 L}[/tex]

Solving:

[tex]x=4.5 L*\frac{1.6 quarts}{1 L}[/tex]

x= 7.2 quarts

So, the recipe will make 7.2 quarts of punch.

Answer:

x = 9

Step-by-step explanation:

5x + 7 = 52

5x = 52-7

5x = 45

x= 9

Vectors along the lines:
To find vectors along the lines, we need two points on each line. Let's denote the points on Line A as A₁ and A₂, and the points on Line B as B₁ and B₂.
Vector along Line A: v₁ = A₂ - A₁
Vector along Line B: v₂ = B₂ - B₁.

Define the vectors along the lines:
Let's say we have two lines represented by the following equations:
Line 1: r₁(t) = a₁ + t * u₁
Line 2: r₂(t) = a₂ + t * u₂
Here, a₁ and a₂ are points on the lines, and u₁ and u₂ are the direction vectors of the lines.

Find the cross product:
To find the unit vector n, we can take the cross product of the direction vectors:
n = u₁ × u₂
Note: × represents the cross product operator.

Define a vector spanning two points on each line:
Let's choose two points on each line, which we'll call b₁ and b₂. The vector spanning these points on Line 1 is given by:
v₁ = b₁ - a₁

Similarly, the vector spanning the points on Line 2 is given by:
v₂ = b₂ - a₂

Determine the minimum distance:
The minimum distance (d) between the lines can be found using the formula:
d = |(v₁ × u₂) · n| / |n|
In this formula, · represents the dot product operator, and | | represents the magnitude or length of the vector.

Alternatively, if you prefer using symmetric equations, you can substitute the equations of the lines directly into the formula to find the minimum distance.

Remember to substitute the appropriate values for a₁, a₂, u₁, u₂, b₁, and b₂ based on the specific problem you are solving.

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Answer:

r= 9

Step-by-step explanation:

radius (r) = diameter (D)/2

= 18/2

= 9

a) Language L = {u#v: u, v ∈ {0,1}* and u is a substring of v}

b) Language L = {0^2^k : for k ≥ 0}

Time Analysis: The time complexity of this program is O(n), where n is the length of the input. This is because we only need to scan through the input string once, counting the consecutive '0' symbols, and check if the count is a power of 2.

a) Language L = {u#v: u, v ∈ {0,1}* and u is a substring of v}

To sketch a 1-tape Turing machine program for this language, we can follow these steps:

1. Start at the leftmost symbol of the input.

2. Scan to the right until we encounter the '#' symbol, marking all the scanned symbols.

3. Once we encounter the '#' symbol, start scanning to the right again, comparing each scanned symbol with the marked symbols.

4. If a match is found, continue scanning until the end of the input, ensuring that the remaining symbols match the unmarked symbols.

5. If a mismatch is found at any point, reject the input.

6. If the end of the input is reached and all symbols match, accept the input.

Time Analysis: The time complexity of this program is O(n^2), where n is the length of the input. This is because, in the worst case, we need to compare each symbol in the input string with the marked symbols, and we may need to scan through the input string twice.

b) Language L = {0^2^k : for k ≥ 0}

To sketch a 1-tape Turing machine program for this language, we can follow these steps:

1. Start at the leftmost symbol of the input.

2. Scan to the right, counting the number of consecutive '0' symbols until a different symbol is encountered.

3. If the count of '0' symbols is not a power of 2, reject the input.

4. If a different symbol is encountered, check if it is the end of the input. If it is, accept the input.

5. If a different symbol is encountered and it is not the end of the input, reject the input.

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Rounding this to two decimal places, the equivalent nominal interest rate compounded monthly is approximately 2.53%.

To determine the equivalent nominal interest rate compounded monthly for a given nominal interest rate compounded quarterly, we can use the formula for nominal interest rate conversion.

The formula is:

r = (1 + i/n)^n - 1

Where:

r is the nominal interest rate compounded annually (we're looking for this),

i is the nominal interest rate compounded quarterly (2.50% in this case),

n is the number of compounding periods per year (4 for quarterly compounding).

Plugging in the values, we have:

r = (1 + 0.025/4)^4 - 1

Calculating this expression, we find:

r ≈ 0.025335

Rounding this to two decimal places, the equivalent nominal interest rate compounded monthly is approximately 2.53%.

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Answer:

1) D

2) B

Step-by-step explanation:

Hope this Helps!

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The y-values are changing at a rate of 24 units per second at the point Q(1, 8).

To find how fast the y-values are changing at the point Q(1, 8), we need to calculate the derivative of the given equation with respect to x. The derivative of y = x^3 + x^2 + 6 is dy/dx = 3x^2 + 2x.

At the point Q(1, 8), we substitute x = 1 into the derivative to find the rate of change.

dy/dx = 3(1)^2 + 2(1) = 3 + 2 = 5.

Therefore, the y-values are changing at a rate of 5 units per second at the point Q(1, 8). However, the rate at which the x-values are changing is given as 2 units per second.

Thus, to determine how fast the y-values are changing with respect to time, we multiply the rate of change in y by the rate of change in x: 5 units/second * 2 units/second = 10 units/second. Hence, the y-values are changing at a rate of 10 units per second at the point Q(1, 8).

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Answer:

B. and D.

Step-by-step explanation:

If you folded that shape along the lines o and m, it would match up.

There are two lines of symmetry m and o. Options B and D are correct.

From the given figure we have to determine the axes of symmetries.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

Here,
As of the given figure,
There are 2 axes of symmetry first line m and the other is line o.
Line l and line n are not symmetrical lines because the reflection of one portion will not be superimposed with the other.

Thus, there are two lines of symmetry m and o. Options B and D are correct.

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(a) If f is uniformly continuous, then fn converges to f uniformly.

(b) Uniform continuity of f is necessary for the uniform convergence of fn to f; a counterexample is provided with a continuous f but non-uniform convergence of fn.

(a)If f is uniformly continuous, then we want to show that fn converges to f uniformly.

Given ε > 0, since f is uniformly continuous, there exists δ > 0 such that for any x, y in R, if |x - y| < δ, then |f(x) - f(y)| < ε.

Now, consider fn(x) = f(x + 1/n) for each n. We need to show that for any ε > 0, there exists N such that for all n ≥ N, |fn(x) - f(x)| < ε for all x in R.

Fix ε > 0. By the uniform continuity of f, there exists δ > 0 such that for any x, y in R, if |x - y| < δ, then |f(x) - f(y)| < ε.

Now, for any x in R, let N > 1/δ. Then for all n ≥ N and for any y = x + 1/n, we have |x - y| = |x - (x + 1/n)| = 1/n < δ.

By choosing y = x + 1/n, we have |fn(x) - f(x)| = |f(x + 1/n) - f(x)| < ε.

Since ε was chosen arbitrarily, this shows that fn converges to f uniformly.

(b) Counterexample: To show that  uniform continuity  of f is necessary for the uniform convergence of fn to f, we need to find an example where f is continuous but fn does not converge to f uniformly.

Consider the function f(x) = x on R. This function is continuous.

Now, let's examine the sequence fn(x) = f(x + 1/n). For any x in R, we have:

|fn(x) - f(x)| = |(x + 1/n) - x| = 1/n.

Notice that for any fixed x, as n approaches infinity, 1/n approaches 0. However, the convergence is not uniform since the choice of x affects the convergence rate.

For any ε > 0, no matter how large N is chosen, there will always exist x such that |fn(x) - f(x)| = 1/n ≥ ε, for n > 1/ε.

Therefore, fn does not converge uniformly to f(x) = x, despite f(x) being continuous.

This counterexample demonstrates that the assumption of uniform continuity of f is necessary for the uniform convergence of fn to f.

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