two cards are drawn from a deck of 52 cards without replacement. (a) what is the probability that the second card is a heart, given that the first card is a heart? (b) what is the probability that both cards are hearts, given that at least one of them is a heart?

Answer:

Step-by-step explanation:

4/56\8

H does not satisfy all three properties required for a subspace, we can conclude that H is not a subspace of R2.

The set H is a subspace of R2, we need to check if it satisfies the three properties required for a subspace

1. The zero vector is in H.

2. H is closed under vector addition.

3. H is closed under scalar multiplication.

Now each property

1. The zero vector (0, 0) is in H since it lies on the unit circle.

2. To check closure under vector addition, suppose we have two vectors (x₁, y₁) and (x₂, y₂) in H. If we add them together, (x₁, y₁) + (x₂, y₂), the resulting vector will not necessarily lie on the unit circle. For example, if we add (1, 0) and (-1, 0), the result is (0, 0), which is not on the unit circle. Therefore, H is not closed under vector addition.

3. To check closure under scalar multiplication, suppose we have a scalar c and a vector (x, y) in H. If we multiply them, c × (x, y), the resulting vector will not necessarily lie on the unit circle. For example, if we multiply (1, 0) by 3, the result is (3, 0), which is not on the unit circle. Therefore, H is not closed under scalar multiplication.

Since H does not satisfy all three properties required for a subspace, we can conclude that H is not a subspace of R2.

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Answer:

\(10(n - 2p + 2) \\ = 10n - 20p + 20\)

I hope I helped you^_^

Answer:

hi

Step-by-step explanation:

hi

Answer: The slope m of the line through any two points (x 1, y 1) and (x 2, y 2) is given by: The y-intercept b of the line is the value of y at the point where the line crosses the y axis. Since for point (x 1 , y 1 ) we have y 1 = m x 1 + b , the y-intercept b can be calculated

Step-by-step explanation:

Chebyshev's Theorem can be applied to any data set

Chebyshev's Theorem: Chebyshev's Theorem estimates the minimum proportion of observations that fall within a specified number of standard deviations from the mean. This theorem applies to a broad range of probability distributions. Chebyshev's Theorem is also known as Chebyshev's Inequality.

it is asked that Chebyshev's theorem is applicable to,

Chebyshev's Theorem is a fact that applies to all possible data sets. It describes the minimum proportion of the measurements that lie must within one, two, or more standard deviations of the mean

So, we can say that it is applicable to any data set

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Answer:

(3 ÷ 8) + (-7 ÷ 8)

0.375 + -0.875  

        -0.5

Hope this helps !

Answer:

25480

Step-by-step explanation:

28000 x 0.91

Answer:

$16.85

Step-by-step explanation:

since Maria is only buying the shirts and shorts you would add how much this shirt is and how much the shorts are and then subtract that by 50

Answer

3*a*2*b equals 6ab

Answer:

7.

Step-by-step explanation:

-5 x -2 = 10 (2 negatives being multiplies = positive)

Then, 10 - 3 = 7.

The statement ''A frequency polygon is a very useful graphic technique when comparing two or more distributions'' is true because a frequency polygon is a very useful graphic technique for comparing two or more distributions.

A frequency polygon is a line graph that shows the distribution of a dataset.

It is created by plotting the frequency of each data value or interval on the y-axis and the corresponding values or intervals on the x-axis, and then connecting the points with line segments.

By using frequency polygons, it becomes easy to compare the shapes and spread of two or more distributions. We can overlay different frequency polygons on the same graph and compare them.

This helps to identify similarities and differences between the data sets.

For instance, frequency polygons can help identify which data set has a higher mean or median, and which distribution has a greater variance.

In summary, frequency polygons are a useful visual tool for comparing distributions and identifying patterns in data.

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To prove that a sequence is not a Cauchy sequence , we need to show the existence of an ε > 0 such that for any N in the natural numbers, there exist n, m > N such that |s(n) - s(m)| ≥ ε.

(a) s(n) = \(n^(1/3)\):

Let's consider ε = 1. We need to show that for any N, there exist n, m > N such that |s(n) - s(m)| ≥ 1.

Let's choose n = \((N + 1)^3\) and m = \(N^3\). Then, we have:

|s(n) - s(m)| = |\((n)^(1/3) - (m)^(1/3)\)| = |\(((N + 1)^3)^(1/3) - (N^3)^(1/3)\)| = |(N + 1) - N| = 1.

Therefore, for ε = 1, we can find n, m > N such that |s(n) - s(m)| ≥ ε for any N. This proves that the sequence s(n) = \(n^(1/3)\) is not a Cauchy sequence.

(b) s(n) = n ln(n):

Let's consider ε = 1. We need to show that for any N, there exist n, m > N such that |s(n) - s(m)| ≥ 1.

Let's choose n = \(e^(2N)\) and m = \(e^N\). Then, we have:

|s(n) - s(m)| = |n ln(n) - m ln(m)| = |\((e^(2N) ln(e^(2N))) - (e^N ln(e^N))\)| = |(2N) - N| = N.

Since N can be arbitrarily large, we can choose N such that N ≥ 1. In that case, we have N ≥ 1 > ε = 1. Therefore, we can find n, m > N such that |s(n) - s(m)| ≥ ε for any N, proving that the sequence s(n) = n ln(n) is not a Cauchy sequence.

-----------------------

To determine whether the limit limₙ→[infinity] s(n) exists for the given sequence:

s(n) = (-1)ⁿ (1 - 3/2ⁿ)

We can examine the subsequences separately for even and odd values of n:

For even values of n, s(n) = (-1)ⁿ (1 - 3/2ⁿ) = 1 - (3/2ⁿ).

As n approaches infinity, the term (3/2ⁿ) approaches 0, and therefore, s(n) approaches 1.

For odd values of n, s(n) = (-1)ⁿ (1 - 3/2ⁿ) = -(1 - 3/2ⁿ).

As n approaches infinity, the term (3/2ⁿ) approaches 0, and therefore, s(n) approaches -1.

Since the subsequences of s(n) approach different limits (1 and -1) as n goes to infinity, the limit limₙ→[infinity] s(n) does not exist.

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Carolyn made an error in her work because she did not correctly distribute the negative in Step 3.

A system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

The question gives:3x-2y=7 (1)y=x+2The question shows that Carolyn applies the substitution method because she replaces the variable y (equation 2) in equation 1. See the given step 2.

3x – 2y = 7

3x – 2(x + 2) = 7

3x – 2x - 4 = 7 - here it is the mistake. (Carolyn did not correctly distribute the negative).

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The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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Answer:

3

Step-by-step explanation:

Answer:

Step-by-step explanation:

12 x 3 = 36

answer is 36

Answer:

12 x 3 = 36

Step-by-step explanation:

A rational number is a number that can be represented by the division of 2 integers (no decimal parts)

So, the answer is yes.

-11/4 is a rational number.

The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in

An equation is an expression that shows the relationship between two or more variables and numbers.

Let w represent the width, hence:

length = w + 33, height = w - 13

Volume (V) = w(w + 33)(w - 13) = w³ + 20w² - 429w

V(w) = w³ + 20w² - 429w

Rate of change = dV/dw = 3w² + 40w - 429

When w = 38, dV/dw = 3(38)² + 40(38) - 429 = 5423

When w = 53, dV/dw = 3(53)² + 40(53) - 429 = 10118

Rate = 10118 - 5423 = 4695 in³/in

The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in

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Answer:

Step-by-step explanation:

kkkkk 55 67888000

To find the probability of accepting a lot with a defect rate of 4% using an acceptance sampling plan with n = 27 and c = 0, we need to calculate the binomial probability of having zero defects in a sample of 27 items.

The probability of accepting a lot is equal to the probability of having zero defects, which can be calculated using the binomial probability formula. The formula is P(X = k) = C(n, k) * p^k * (1 - p)^(n - k), where P(X = k) is the probability of getting k successes, n is the sample size, p is the probability of success (defect rate), and C(n, k) is the binomial coefficient.

In this case, we want to find P(X = 0) where n = 27 and p = 0.04 (4% defect rate). Substituting these values into the binomial probability formula and calculating it will give us the desired probability of accepting the lot with zero defects.

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The interest rate is 10.89%

1. Given,С = 200+ 0.69YI = 80 - 1,000rG = 20NX = 850.09ee = 90M = 115YL = 0.5Y - 200rY = 300Using the equation for National Saving, we get,National Saving = Investment + Government Saving + Net exports(S – I) + (T – G) + (X – M) = 0T = 0, hence (S – I) + (X – M) = 0(1 – t)Y – C – (I + G) + NX = 0Where t = 0, we get,0.5Y – 200r – 200 – 69/100Y + 80 – 850.09e = 0.5Y – 200r – 970.09e – 120 = 0.5Y – 200r – 970.09e – 120 = 0Therefore, Y = 325.0454 - 0.5r + 4.851eThis is the equation for the IS curve.On the other hand, the equation for the LM curve is given by,Ms / P = YL(i)115 / 1 = 0.5Y - 200rTherefore, Y = 400 + 400rThis is the equation for the LM curve.The interest rate is given by the point of intersection of the two curves. Equating Y from both equations, we get,325.0454 - 0.5r + 4.851e = 400 + 400rSolving the above equation for r, we get r = 0.1089 or 10.89%..

The size of the nominal money supply in the new short-run equilibrium is 121.07.

2. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate.Flexible Exchange Rates:In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output.Real exchange rate will fall.Increase in output will be higher compared to the fixed exchange rate case.Fixed Exchange Rates:In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.Real exchange rate will remain unchanged.Increase in output will be less compared to the flexible exchange rate case.The nominal money supply in the new short-run equilibrium will change in the case of Fixed Exchange Rates. In the fixed exchange rate case, the domestic interest rate will increase, leading to an inflow of capital. This will increase the money supply and the LM curve will shift downwards until it intersects the IS curve at the new equilibrium point.

Real exchange rate will remain unchanged.

3. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate. Flexible Exchange Rates :In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output .Real exchange rate will fall. Value of the real exchange rate in the new equilibrium is 0.891.Fixed Exchange Rates: In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.

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Answer:

175

Step-by-step explanation:

30% of 250 is 75 and 70% of 250 is 175

Answer:

175

Step-by-step explanation:

K = 30%

Y = ???

X = 250

Turn 30% into a decimal then mutiply from 250

Answer:

B. \( 11^2 \)

Step-by-step explanation:

\( \frac{ {11}^{6} }{ {11}^{4} } = {11}^{6 - 4} = {11}^{2} \\ \)

The simplified form of the given expression is \(\frac{11^{6} }{11^4}\) will be \(11^2\).

The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.

The given expression is

\(\frac{11^{6} }{11^4}\)

Therefore, the exponent will subtract,

= \(11 ^{6-4}\)

= \(11^2\)

Thus, the simplified form will be \(11^2\).

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The measurement of all four angles is 105°

What is an angle?

180° [Linear pair with angles] = m1 + 75°

The opposite angles of either a rectangle are equal: m1 = 180° - 75° = 105° m2 = m1.

[Vertically opposing angles] m2 = m1 = 105° m2 = m3 = 105°

m∠3 = m∠4 = 105° Coordinating angles

As a result, the measurement of all four angles is 105°.

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The derivative of the function y = x^2x using logarithmic differentiation is dy/dx = x^2x(2 + 2ln(x)).

To find the derivative of the function y = x^2x using logarithmic differentiation, we follow these steps:

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To find the derivative of the function y = x^(2x) using logarithmic differentiation, we take the natural logarithm of both sides, apply logarithmic properties, and then differentiate implicitly.

Start by taking the natural logarithm of both sides of the equation:

ln(y) = ln(x^(2x))

Apply the power rule of logarithms to simplify the expression:

ln(y) = 2x * ln(x)

Now, differentiate both sides of the equation implicitly with respect to x:

(1/y) * dy/dx = 2 * ln(x) + 2x * (1/x)

Simplify the expression:

(1/y) * dy/dx = 2 * ln(x) + 2

Multiply both sides by y to isolate dy/dx:

dy/dx = y * (2 * ln(x) + 2)

Substitute the original value of y = x^(2x) back into the equation:

dy/dx = x^(2x) * (2 * ln(x) + 2)

The derivative of the function y = x^(2x) using logarithmic differentiation is dy/dx = x^(2x) * (2 * ln(x) + 2). Logarithmic differentiation is a useful technique for differentiating functions that involve exponentials or complicated algebraic expressions, as it allows us to simplify the calculation by taking the logarithm of both sides and then differentiating implicitly.

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Answer:

55mph

Step-by-step explanation:

110/2=55

speed = distance/time

The two real number solutions to a quadratic equation are rational numbers, then the discriminant is a rational number.

The discriminant of a quadratic equation is a scalar value that describes the nature of the solutions to the equation. Specifically, if the discriminant of a quadratic equation of the form \(ax^{2} + bx + c = 0\) is a positive value, then the equation has two real solutions.

This is because the discriminant is given by the expression \(b^2 - 4ac\), and the coefficients of a quadratic equation can be either rational or irrational numbers. If the coefficients are rational, then the discriminant will also be rational, and vice versa.

Hence, if the two real number solutions to a quadratic equation are rational numbers, then the discriminant is a rational number.

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Hello!

What is the standard form of the parabola:

 \(\hookrightarrow y=(x-h)^2+k\)

          => h: x-coordinate of vertex

          => k: y-coordinate of vertex

Since our vertex is (1,-8)

 \(\hookrightarrow \text{Our equation is }y=(x-1)^2}-8\)  <== Answer

Hope that helps!