The Idol's Eye diamond weighs 79.2 carats.The Blue Hope diamond weighs 33.68 carats less than the Idol's Eye.What is the weight of the Blue Hope diamond?

We need to use mathematical logic to prove that the cardinality of the cross product of two sets is the cardinality of each individual set multiplied by each other.

     Let's take an example of two sets A and B.

      Let's say, A={a, b} and B={1, 2, 3}

      To find the cardinality of the cross-product of A and B, we need to make all possible ordered pairs with A and B.

             {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)}

 Counting the number of ordered pairs, we get six.

  So, the cardinality of the cross-product of two sets A and B equals the cardinality of each set multiplied by the other. Here,

           |A| = 2 and |B| = 3,

          so |A x B| = 2 x 3

                           = 6.

          Therefore, it is proved that the cardinality of the cross product of two sets is the cardinality of each individual set multiplied by each other.

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Answer:

7

Step-by-step explanation:

AB = 3x-2

Let x=3

AB = 3*3 -2

    = 9-2

    =7

Answer:

relation only

Step-by-step explanation:

The vertical line will be relation only.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable.

In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Noted that Linear function is a function whose graph is a straight line

We can conclude that  vertical line would be relation only.

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The volume of the cylindrical tin can is approximately 4288.65 cubic centimeters.

To find the volume of a cylindrical tin can, we can use the formula V = π\(r^2\)h, where V represents the volume, r is the radius, and h is the height of the cylinder. In this case, the given radius is 8 cm and the height is 21.2 cm.

Calculate the base area

The base area of the cylinder can be found using the formula A = π\(r^2\). Plugging in the given radius, we have A = π\((8 cm)^2\). Simplifying this, we get A = 64π \(cm^2\).

Multiply the base area by the height

Next, we multiply the base area by the height of the cylinder. Multiplying 64π \(cm^2\) by 21.2 cm gives us the volume V = 1356.8π \(cm^3\).

Approximate the value of π and calculate the volume

To find the approximate value of the volume, we substitute the value of π as 3.14. Multiplying 1356.8π \(cm^3\) by 3.14, we get V ≈ 4269.632\(cm^3\).

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The probability of flipping a heads on the coin and rolling a 5 on the die is 1/12 if a coin is flipped and die is rolled once.

The sample space for the coin toss is  {H,T}, so there are two possible outcomes. The favorable one is  H.

The probability of flipping a heads on the coin is equal to 1/2.

Die has six faces, meaning six possible outcomes, but we’re only interested in one of those outcomes: that roll of a 5. That means that only 1 in 6 outcomes is desirable and we can write it as  1/6

The probability of rolling a 5 on the die is equal to 1/6.

Since a coin is flipped and die is rolled independently, the joint probability is a product of above probabilities.

Therefore, the probability of flipping a heads on the coin and rolling a 5 on the die equals

\(\frac{1}{2} \times \frac{1}{6}\\= \frac{1}{12}\)

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Answer:

20 flapjacks is the answer.

Multiply using the distributive property.

14 x − 14

Hope this helps you!

Answer:

14x-14

Step-by-step explanation:

2(7x-7)=14x-14

The Simplification of 2x +26

simplify:

4(× + 5) - 2(x - 3)

4x + 20 - 2x +6

2x +26

Making something simpler is making it less intricate or crowded. When you describe a complex mathematical idea to a youngster in words they can easily comprehend, you are simplifying. When you eliminate many of the tasks that were keeping you occupied and stressed out, you have simplified.

Making something simpler refers to making it simpler to accomplish or comprehend. Therefore, when we reduce or simplify a fraction, we aim for maximum simplicity. In order to do this, we divide both the numerator and the denominator by the biggest integer that can be divided precisely into both numbers.

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The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Answer:

665.5

Step-by-step explanation:

840.50 - 175 =

Answer:

238

Step-by-step explanation:

the quotient simply means the result of the division. when you divide 952 by 4, you get 238

The value of 0.0062 is less that our significance level of 0.1, we reject the null hypothesis at the 0.1 level of significance and conclude with sufficient evidence that the manufacturer's MPG rating is incorrect.

To answer the question, we will conduct a hypothesis test to at the 0.1 level to ascertain whether or not the manufacturer's MPG rating is incorrect.

We start by stating the null and alternative hypotheses:

\($H_0$\): The mean miles/gallon for the vans is 53.8

\($H_A$\): The mean miles/gallon for the vans is not 53.8

We choose a significance level $\alpha = 0.1$ and calculate the following test statistic:

\($z = \frac{\bar{x}-\mu}{\sigma/\sqrt{n}} = \frac{53.4-53.8}{1/\sqrt{16}} = -2.5$\)

With a standard normal table, we look for the area to the left of -2.5, which is 0.0062. Because this value of 0.0062 is less that our significance level of 0.1, we reject the null hypothesis at the 0.1 level of significance and conclude with sufficient evidence that the manufacturer's MPG rating is incorrect.

Therefore, the value of 0.0062 is less that our significance level of 0.1, we reject the null hypothesis at the 0.1 level of significance and conclude with sufficient evidence that the manufacturer's MPG rating is incorrect.

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The intercepts of the line are (-3, 0) and (0, -6/5).

What is intercepts ?

In mathematics, intercepts refer to the points at which a line or curve intersects the x-axis or the y-axis of a coordinate plane.

To find the x-intercept, we need to set y = 0 and solve for x:

2x + 5(0) = -6

2x = -6

x = -3

Therefore, the x-intercept is (-3, 0).

To find the y-intercept, we need to set x = 0 and solve for y:

2(0) + 5y = -6

5y = -6

y = -6/5

Therefore, the y-intercept is (0, -6/5).

Thus, the intercepts of the line are (-3, 0) and (0, -6/5).

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Answer:

Sphere

Step-by-step explanation:

its a sphere with a radius of 5

The solid three dimensional image that is produced from the rotation of the semicircle is called a sphere.

This is used to define the movement of an object in a three dimensional plane around a fixed point.

This transformation os known to occur in a given point of the figure. The roataion is done at a certain degree.

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The derivative of the given function using product rule is 6x+1 .

What is Product Rule?

This rule is used when we want to differentiate a function that may be regarded as the product of one or more functions.

Let u(x) and v(x) be differentiable functions.Then the product of the functions u(x)v(x) is also differentiable and: (uv)′=u′v+uv′

Main Body:

We add the derivative of the first times the second to the first times the

derivative of the second.

Power Rule:

If f(x)=xn

where n is any real number, then:

(xⁿ)′=nxⁿ⁻¹

. We have,

f(x) = (x-1) (3x+4)

Differentiate with respect to z by using product rule

(uv)′=u′v+uv′

h' (x) = (x-1)' (3x+4) +(x-1)(3x+4)'

h'(X) = 1(3x+4) + (x-1) (3)

On simplifying:

h'(x) = 3x+4 +3x-3

h'(x) = 6x +1

Hence the derivative of function is 6x+1.

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tThe population in this scenario refers to the entire group of policyholders of the large automobile insurance company.

Set up the hypotheses ; Null hypothesis (H0): The mean age in the population of policyholders is 50.  Alternative hypothesis (Ha): The mean age in the population of policyholders is different from 50. Determine the significance level: The significance level is given as 5%.  Calculate the test statistic: The test statistic for a two-sample t-test is given by:
    t = (sample mean - hypothesized mean) / (standard error)

 In this case, the sample mean is 47.2, and the hypothesized mean is 50. The standard error can be calculated using the formula: standard error = sqrt(variance / sample size).  In this case, the variance is 121 and the sample size is 361. Calculate the degrees of freedom:  For a two-sample t-test, the degrees of freedom is calculated as the sum of the sample sizes minus 2.  In this case, the sample size is 361.  Determine the critical value:  Since the alternative hypothesis is two-tailed (different from 50), we divide the significance level by 2 (5% / 2) to get the critical value for each tail.

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Answer: 45°

Step-by-step explanation: Triangle ABC is similar to EDC, so their corresponding angles are going to be the same. Angle ACB corresponds to angle ECD, so their angles are going to be the same. Since angle ACB is 45°, that means angle ECD is also 45°.

Answer:

52 ounces

Step-by-step explanation:

6 1/2 * 8 = 52 ounces

Answer: the height of the pole is 16.782 meters

Step-by-step explanation: Let us take the height of the pole as "h".

i) Finding the height of the pole:

distance from the pole is 20m.

The angle of elevation is 40°

\(tan(40°) = h/20\)

Multiply both sides by 20:

\(20 * tan(40°) = h\)

\(h ≈ 20 * 0.8391 ≈ 16.782 meters\)

Therefore, the height of the pole is 16.782 meters.

ii) Finding the angle of depression

The angle of depression is the angle formed between the horizontal ground and the line of sight from the point of observation to the foot of the pole.

angle of depression = angle of elevation = 40°

Therefore, the angle of depression of the foot of the pole from the point of observation is 40°.

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Using trigonometric methods, it is determined that the height of the pole is found by using the formula for tangent, and adding the height of the observer. The angle of depression equals the angle of elevation, so both are 40 degrees.

To solve the problem, we use the properties of a right triangle and trigonometric functions. Since we know the angle of elevation and the length of one side, we can find the length of the other side using the tangent function.

For the height of the pole: we know that tan(θ) = opposite/adjacent, so,
tan(40) = height/20
height = tan(40) * 20

Let's denote the observer's height as h=1.54m, so the total height of the pole is height + h.

For the angle of depression: In a right triangle, the angle of depression and the angle of elevation are equal. Therefore, the angle of depression is also 40 degrees.

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Answer:

The answer is D

fifijfjgjgfghj

Step-by-step explanation:

Answer:

We need to see the graph to help you

Step-by-step explanation:

Answer:

the answer is 2, a randomly chosen study hall

Step-by-step explanation:

The gym after a game adds bias towards a sports event

The auditorium after a play is biased toward IMAX

The Nature Club is also possibly biased toward Imax

A normal distribution is a type of continuous probability distribution for a real-valued random variable in statistics.

Yes, the large-sample confidence interval will be valid.

A normal distribution is a type of continuous probability distribution for a real-valued random variable in statistics.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far from the mean.

The confidence interval will be valid regardless of the shape of the population distribution as long as the sample is large enough to satisfy the central limit theorem.

A sample is considered large when n ≥ 30.

By 'valid', it means that the confidence interval procedure has a 95% chance of producing an interval that contains the population parameter.

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Given:

Time taken by Amanda to fill the tank is 50 minutes.

The capacit of tank is 5 kiloliters.

Explanation:

The rate of pumping is determine by divide the capacity by time taken to fill it.

Determine the pumping rate to fill Amanda's milk tank.

Answer: 0.1 kL/min

The scale factor when AABC is a dilation of ADEF with center (0, 0) is 1/3.

A scale factor is a number that scales, or multiplies, some quantity. In the context of geometry, a scale factor is a ratio that describes how the dimensions of one geometric figure are related to the dimensions of another similar figure. Similarly, if a two-dimensional shape is scaled up or down by a factor of k, then all of its linear dimensions (such as length, width, and height) are multiplied by k, and its area is multiplied by k².

Here,

In triangle ABC,

AB=6 units

In triangle DEF,

DE=2 units

Scale factor=DE/AB

=2/6

=1/3

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Answer:  15/64 = 23.43%

Step-by-step explanation:

During each roll, there could be 2 possible outcomes either odd or even which gives us a probability of 50%-50%.

Since the die is rolled 6 times and the possible outcome for each roll is 2

so total possible outcomes are equal to 2x2x2x2x2x2=64 outcomes.

Since we want exactly 2 even outcomes out of 64,

so if assume E= Even & O=Odd.

The possible outcomes for which we get exact to even outcomes are:

1)EEOOOO

2)EOEOOO

3)EOOEOO

4)EOOOEO

5)EOOOOE

6)OEEOOO

7)OEOEOO

8)OEOOEO

9)OEOOOE

10)OOEEOO

11)OOEOEO

12)OOEOOE

13)OOOEEO

14)OOOEOE

15)OOOOEE

Hence total possible outcomes are 15/64

=23.4375%

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Answer:

An electric company calculates a person's monthly bill from the number of kilowatt-hours (kWh), x, used, x 200 The function b(ar) = { 0.102, 0.15(x - 200) +20, 200 determines the bill How much is the bill for a person who uses 800 kWh in a month?

Based on the information given, the vertex of the parabola can be found using the coordinates of the turning point (also known as the vertex).

The vertex is located at (4,-4), which means that the value of x is 4 and the value of y is -4. Therefore, the coordinates of the vertex are (4,-4).

The fact that the curve is on the upper and lower quadrants of the right side of the cartesian coordinate system suggests that the parabola opens upwards.

Also, since the curve meets the x-axis at two points, this indicates that the parabola intersects the x-axis at those two points, which are (2,0) and (6,0).

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Answer:

The probability of the baseball player getting exactly 10 hits in 50 at-bats is 0.136 or 13.6% (rounded to the nearest integer percent).

Step-by-step explanation:

Here are the steps to find the probability of getting exactly 10 hits:

Step 1: Find the probability of getting a hit of any kind using a batting average of .190, which is given as follows: Probability of getting a hit (p) = batting average = 0.190

Step 2: Find the probability of not getting a hit, which can be calculated by subtracting the probability of getting a hit from 1. Probability of not getting a hit (q) = 1 - p = 1 - 0.190 = 0.810

Step 3: Use the binomial distribution formula to find the probability of getting exactly 10 hits in 50 at-bats: P(X = 10) = (50C10) × (0.190)10 × (0.810)40 where n = 50, x = 10, p = 0.190 and q = 0.810

Step 4: Solve the above equation using a calculator or software and round the answer to 3 decimal places. P(X = 10) = 0.136

Therefore, the probability of the baseball player getting exactly 10 hits in 50 at-bats is 0.136 or 13.6% (rounded to the nearest integer percent).

The conclusion can be stated as follows: The baseball player has a 13.6% chance of getting exactly 10 hits in 50 at-bats given a batting average of .190.

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