an urn contains 5 blue balls and 6 orange balls. in how many ways can we select 1 blue balls and 2 orange balls from the urn? a) 17 b) 75 c) 35 d) 149 e) 30 f) none of the above.

subtracting a positive number

4 - 2 = 2

Adding a negative number

4+ (-2) = 4 - 2 = 2

So they are not completely different operations.

Answer : FALSE

Answer:

The radius of the cone is approximately 1.4 feet

Step-by-step explanation:

The given parameters of the cone are;

The height of the cone, h = 4 ft.

The volume of the cone, V = 7.77 ft.³

The volume, 'V', of a cone is given by the following formula;

V = 1/3 × π·r²·h

Where;

V = The volume of the cone = 7.77 ft.³

r = The radius of the cone

h = The height of the cone = 4 ft.

By substituting the vales of 'h' and 'V' in the above equation, we have;

7.77 ft.³ = 1/3 × π × r² × 4 ft.

∴ r = √(3 × 7.77 ft.³/(π × 4 ft.)) = 1.36196580784 ft.

∴ The radius of the cone, r ≈ 1.4 ft. (rounding the answer to the nearest 10th)

Answer:

1. Yes

2. Yes

3. No

4. Yes

Step-by-step explanation:

Complementary angles are angles that add up to 90 degrees.

For 1, 76+14 = 90.

Etc., you can do the math, I believe you are smarter than addition.

Answer:

\(C,Y_{envelope}(x,t), Y_{carrier}(x,t)=2A, \cos ((k_1-k_2)x/2-(\omega_1 -\omega_2)t / 2 ) , \sin ((k_1+k_2)x / 2 - (\omega_1 +\omega_2)t / 2 )\)

Step-by-step explanation:

Given

\(Y_1(x,t)=A \sin(K_1x- \omega _1 t)\\\\Y_2(x,t)=A \sin(K_2x- \omega _2 t)\)

using a trigonometrical identity

sin p + sin q = 2 sin ( p+q/2) cos ( p-q/2)

and here the condition is

the choice is in between sinax and cosax

where a > b

so we get using above equation

\(C,Y_{envelope}(x,t), Y_{carrier}(x,t)=2A, \cos ((k_1-k_2)x/2-(\omega_1 -\omega_2)t / 2 ) , \sin ((k_1+k_2)x / 2 - (\omega_1 +\omega_2)t / 2 )\)

The value of x in the diagram is 11°

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).

From the diagram, (6x -13) is corresponding to the exterior angle to 127°

The exterior angle at 127  (180 - 127) = 53°

So, (6x - 13) = 53

making x the Subject of the equation

6x = 53 + 13

6x = 66

x = 66/6

x = 11°

In conclusion the value of x is 11°

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The solution of the inequality, x-2 > -1 is x > 1

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Given is an inequality, x-2 > -1

Solving for x,

x-2 > -1

Add 2 to both the sides,

x-2+2 > -1+2

x > 1

The graph of the same is attached,

Hence, the solution of the inequality, x-2 > -1 is x > 1

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The variance of aggregate claims is 6.

What is Poisson distribution?

The Poisson distribution is a discrete probability distribution that describes the number of events that occur in a fixed interval of time or space, given the average rate of occurrence of those events. It is often used to model rare events that occur randomly and independently of each other.

To calculate the variance of aggregate claims, we need to use the properties of the probability distribution and the fact that the number of claims and claim amounts are mutually independent.

Let's denote the number of claims as N and the claim amount for each claim as X. We are given that N follows a probability distribution:

n | P(n)

0 | 0.1

1 | 0.4

2 | 0.3

3 | 0.2

We are also given that the claim amount X follows a Poisson distribution with a mean of 3.

To calculate the variance of aggregate claims, we can use the formula:

Var(Aggregate claims) =\(E(N) * Var(X) + Var(N) * E(X)^2\)

First, let's calculate E(N) and Var(N):

\(E(N) = \sum (n * P(n)) \\= 0 * 0.1 + 1 * 0.4 + 2 * 0.3 + 3 * 0.2 \\= 0 + 0.4 + 0.6 + 0.6\\ = 2\)

\(E(N)^2 =(\sum n * P(n))^2\\ = (0 * 0.1 + 1 * 0.4 + 2 * 0.3 + 3 * 0.2)^2\\ = (0 + 0.4 + 0.6 + 0.6)^2\\ = 2^2\\ = 4\)

\(Var(N) = E(N^2) - E(N)^2\\ = (\sum n^2 * P(n)) - E(N)^2 \\= (0^2 * 0.1 + 1^2 * 0.4 + 2^2 * 0.3 + 3^2 * 0.2) - 4\\ = (0 + 0.4 + 1.2 + 1.8) - 4 \\= 3.4 - 4 \\= -0.6\)

(since variance cannot be negative, we take the maximum of 0 and -0.6) = 0

Next, let's calculate E(X) and Var(X):

E(X) = Var(X) = mean of the Poisson distribution = 3

Finally, we can substitute these values into the formula for the variance of aggregate claims:

Var(Aggregate claims) =\(E(N)*Var(X) + Var(N)* E(X)^2\)

\(= 2 * 3 + 0 * 3^2 \\= 6\)

Therefore, the variance of aggregate claims is 6.

The correct option is B) 6.4

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Answer:

19

Step-by-step explanation:

A' represents everything out A

B' represents everything out B

C' represents everything out C

So only the outside is left hope this helps

Answer:

8

Step-by-step explanation:

45 divided by 5 is 9 and what you do on the to you do on the bottom which means you would do 40 divided by 5 which you would get 8 as your answer.

Answer:

x = 30°

Step-by-step explanation:

l₁ // l₂ and t is transversal. So, corresponding angles are congruent.

         3x - 10 = 2x + 20

Add 10 to both sides,

              3x  = 2x + 20 + 10

             3x  = 2x + 30

Subtract 2x from both sides,

       3x - 2x = 30

               x = 30°

Answer:

1

Step-by-step explanation:

Answer: R = 3/5

Step-by-step explanation:

i think

Answer:

coordinate plane

Step-by-step explanation:

1.true or false :The vertical axis is called the y-axis-

Part 1: The null and alternative hypotheses for the hypothesis test are A. H0: p1 ≥ p2, H1: p1 < p2. Part 2: The test statistic for comparing two proportions is calculated as -1.04. Part 3: The P-value needs to be calculated.

Part 4: The conclusion is to fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the rate of left-handedness among males is less than that among females.

Part 5: The 98% confidence interval needs to be calculated using the formula above and the appropriate critical value.

Part 1: The null and alternative hypotheses for the hypothesis test are:

Null hypothesis (H₀): The rate of left-handedness among males is equal to or greater than the rate of left-handedness among females. (p₁ ≥ p₂)

Alternative hypothesis (H₁): The rate of left-handedness among males is less than the rate of left-handedness among females. (p₁ < p₂)

Answer: A. H₀: p₁ ≥ p₂, H₁: p₁ < p₂

Part 2: The test statistic for comparing two proportions is calculated as:

z = (p₁ - p₂) / √(p × (1 - p) × ((1/n₁) + (1/n₂)))

Where:

p₁ = Proportion of left-handed males

p₂ = Proportion of left-handed females

n₁ = Sample size of males

n₂ = Sample size of females

p = Pooled proportion = (x₁ + x₂) / (n₁ + n₂)

In this case, p₁ = 24 / (24 + 221), p₂ = 63 / (63 + 446), n₁ = 24 + 221, n₂ = 63 + 446.

Calculating the test statistic:

z = (p₁ - p₂) / √(p × (1 - p) × ((1/n₁) + (1/n₂)))

Answer: z = -1.04

Part 3: The P-value is the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. To find the P-value, we would compare the test statistic to the standard normal distribution (Z-distribution) and calculate the corresponding probability.

However, the P-value is not provided in the question. It needs to be calculated using the test statistic and the standard normal distribution.

Answer: The P-value needs to be calculated.

Part 4: The conclusion based on the hypothesis test is determined by comparing the P-value to the significance level (α). If the P-value is less than the significance level, we reject the null hypothesis. If the P-value is greater than or equal to the significance level, we fail to reject the null hypothesis.

In this case, the P-value is greater than the significance level of α = 0.01.

Answer: The conclusion is to fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the rate of left-handedness among males is less than that among females.

Part 5: To test the claim by constructing a confidence interval, we can use the difference in sample proportions to estimate the difference in population proportions.

The formula for calculating the confidence interval for the difference in proportions is:

Confidence interval = (p₁ - p₂) ± z × √((p₁ × (1 - p₁) / n1) + (p₂ × (1 - p₂) / n))

Where:

p₁ = Proportion of left-handed males

p₂ = Proportion of left-handed females

n₁ = Sample size of males

n₂ = Sample size of females

z = Critical value from the standard normal distribution based on the desired confidence level

To construct a 98% confidence interval, we need to find the critical value associated with a 2% significance level (α = 0.02).

Answer: The 98% confidence interval needs to be calculated using the formula above and the appropriate critical value.

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The height of the triangular face of the box is 6 cm when the Volume of the box is 3,240 cubic cm.

Given Parameters,

The length of the box (l) = 30 cm

The breadth of the box (b) = 18 cm

The height of the box  = h

The Volume of the prism = l * b * h

It is given that the volume of the prism is 3,240 cubic cm.

Thus,

l * b * h = 3,240

Putting the values of length and breadth, we have

30 * 18 * h = 3,240

540 * h = 3,240

h = 3,240/540

h = 6

Thus, the height of the triangular face of the box is 6 cm.

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Answer:

14

Step-by-step explanation:

4 + 3 = 7 (as you do brackets first)

7 X 2 = 14

this is BIDMAS or BODMAS

Answer:

14

Step-by-step explanation:

2 ( 4+3) = 2x7=14

To make the expression x * equivalent to the C expression (x << 3) + (x << 1), the blank should be filled with 10.

In the given C expression, (x << 3) represents left-shifting the value of x by 3 bits, and (x << 1) represents left-shifting the value of x by 1 bit. To achieve an equivalent expression using multiplication, we need to determine the multiplication factor that corresponds to the left shifts.

The left shift by 3 bits is equivalent to multiplying by 2 raised to the power of 3, which is 8. Similarly, the left shift by 1 bit is equivalent to multiplying by 2 raised to the power of 1, which is 2.

Therefore, to make the expression x * equivalent to (x << 3) + (x << 1), the blank should be filled with 10, as x multiplied by 10 gives the same result as the given C expression.

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As A line goes through the point (5, 7) and has a gradient of 23, and when y = 13, the x-coordinate is 14.

A line is an incredibly long entity which lacks width, depth, as well as curvature. A line is therefore a one-dimensional object, even though it can also appear in two-, three-, and far more spaces. In everyday language, a line is described as a reference line with two locations acting as its ends. A line is a mono, straight object that has no breadth and can extend in both dimensions indefinitely. It is common for people to employ the terms "straight line" or "ancient precise line" to characterize a line that has no "wobble" anything along its length. (Casey 1893)

given

(i) Gradient of the line =6/x−5

18=2(x−5)

9=x−5

x=14

As A line goes through the point (5, 7) and has a gradient of 23, and when y = 13, the x-coordinate is 14.

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Answer: 700 tons of coal consumed in 10 weeks.

Step-by-step explanation:

first you find how much coal is consumed in 1 week which is 70 tons, then you multiply the 70 tons by 10 weeks because you are trying to find how much tons of coal can be consumed in to weeks and when you do that you should get 700 tons of coal for 10 weeks.

Answer:

144°

Step-by-step explanation:

m<1 =3x

m< 2= 12x

1&2 are supplementary angles, so

3x+12x= 180

15x=180

x= 12°

measure of angle 4 equals the measure of angle 2

because they're head opposite angles

m<4= 144°

Answer:

a)54 b)48 c)49 d)91

Step-by-step explanation:

here is your answer

MARK ME AS BRILLIANT

The volume of the solid generated by revolving the region enclosed by the triangle about the y-axis is 9π cubic units.

To find the volume of the solid generated by revolving the region enclosed by the given triangle about the y-axis, we can use the washer method.

The first step is to determine the limits of integration.

The triangle is bounded by the vertical lines x = 4, x = 5, and the line connecting the points (4, 1) and (5, 2).

We need to find the y-values that correspond to these x-values on the triangle.

At x = 4, the corresponding y-value on the triangle is 1.

At x = 5, the corresponding y-value on the triangle is 2.

So, the limits of integration for y will be from y = 1 to y = 2.

Now, let's consider an arbitrary y-value between 1 and 2. We need to find the corresponding x-values on the triangle.

The left side of the triangle is a vertical line segment, so for any y-value between 1 and 2, the corresponding x-value is x = 4.

The right side of the triangle is a line connecting the points (4, 2) and (5, 2).

This line has a constant y-value of 2, so for any y-value between 1 and 2, the corresponding x-value is given by the equation of the line: x = 5.

Now, we can set up the integral using the washer method. The volume can be calculated as follows:

V = ∫[1,2] π(\(R^2 - r^2\)) dy,

where R is the outer radius and r is the inner radius.

Since we are revolving the region about the y-axis, the outer radius R is the distance from the y-axis to the right side of the triangle, which is x = 5.

Thus, R = 5.

The inner radius r is the distance from the y-axis to the left side of the triangle, which is x = 4.

Thus, r = 4.

Substituting these values into the integral, we have:

V = ∫[1,2] π(5^2 - 4^2) dy.

Simplifying the integral:

V = ∫[1,2] π(25 - 16) dy

= ∫[1,2] π(9) dy

= 9π ∫[1,2] dy

= 9π [y] [1,2]

= 9π (2 - 1)

= 9π.

Therefore, the volume of the solid generated by revolving the region enclosed by the triangle about the y-axis is 9π cubic units.

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The p-value accurate to 4 decimal places is 0.0027.

In a right-tailed test, the null hypothesis is rejected if the test statistic is larger than the critical value or if the p-value is less than alpha (the level of significance). In this question, we are conducting a study to determine if the probability of a true negative on a test for a certain cancer is significantly greater than 0.3. Therefore, this is a right-tailed test.

The sample data produce the test statistic z = 2.983.

Since this is a right-tailed test, the p-value is the probability that the test statistic is greater than or equal to 2.983.

To find the p-value, we will use a standard normal table or calculator.

Using a standard normal table, the p-value for z = 2.98 is 0.0029, and the p-value for z = 2.99 is 0.0021. Since the test statistic is between 2.98 and 2.99, we can use linear interpolation to estimate the p-value as follows:

p-value = 0.0029 + [(2.983 - 2.98)/(2.99 - 2.98)] x (0.0021 - 0.0029) = 0.0029 + [0.003/0.01] x (-0.0008)= 0.0029 - 0.00024= 0.00266

Therefore, the p-value accurate to 4 decimal places is 0.0027.

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The linear function that relates y to x is given as y = 2x

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

From the table, using the points (0, 0) and (1, 2):

y - 0 = [(2 - 0)/(1 - 0)](x - 0)

y = 2x

The linear function that relates y to x is given as y = 2x

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Answer: 180-181?

Step-by-step explanation:

Step-by-step explanation:

1 parameter = 6x - 2y +19

2. x²-x-12

3. (9)

Area Principle. In a statistical display, each data value should be represented by the same amount of area. Bar chart (Relative Frequency Bar Chart)

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

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