About 5​% of the population of a large country is hopelessly romantic. If two people are randomly​ selected, what is the probability both are hopelessly romantic​? What is the probability at least one is hopelessly romantic​? Assume the events are independent.

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"

This is because the question is asking for a numerical response that can be measured and counted. The other options are not statistical questions that can result in numerical data.

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Answer:

A.  h'(2) = 5

B.  m'(2) = -24

C.  y = 8x - 31

D.  j'(2) = 3/25 = 0.12

Step-by-step explanation:

When differentiating composite functions, use the chain rule.

[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\$\left[f\left(g(x)\right)\right]'=f'\left(g(x)\right) \cdot g'(x)$\\\end{minipage}}[/tex]

Chain Rule: The derivative of a composite function is the product of the derivative of the outer function evaluated at the inner function and the derivative of the inner function.

Using the chain rule, if h(x) = g(f(x)) then h'(x) = g'(f(x)) ⋅ f'(x).

To find h'(2), substitute x = 2 into the differentiated equation:

[tex]\begin{aligned}h'(x)& = g'(f(x)) \cdot f'(x)\\\\\implies h'(2)& = g'(f(2)) \cdot f'(2)\\& = g'(5) \cdot 1\\& = 5 \cdot 1\\&=5\end{aligned}[/tex]

Therefore, h'(2) = 5.

Using the chain rule, if m(x) = f(x²) then m'(x) = f'(x²) ⋅ 2x.

To find m'(2), substitute x = 2 into the differentiated equation:

[tex]\begin{aligned}m'(x) &= f'(x^2) \cdot 2x\\\\\implies m'(2) &= f'(2^2) \cdot 2(2)\\&=f'(4) \cdot 4\\&=-6 \cdot 4\\&=-24\end{aligned}[/tex]

Therefore, m'(2) = -24.

To find the slope of the tangent line to the graph of k at x = 4, substitute x = 4 into the derivative of k(x).

If k(x) = f(g(x)) then k'(x) = f'(g(x)) ⋅ g'(x).

Therefore, the slope of the tangent line is:

[tex]\begin{aligned}k'(x) &= f'(g(x)) \cdot g'(x)\\\\\implies k'(4) &= f'(g(4)) \cdot g'(4)\\&= f'(5) \cdot 4\\&= 2 \cdot 4\\&= 8\end{aligned}[/tex]

Now calculate k(x) when x = 4:

[tex]\begin{aligned}k(x)&=f(g(x))\\\\\implies k(4) &= f(g(4))\\&=f(5)\\&=1\end{aligned}[/tex]

To write the equation of the tangent line, substitute the found slope m = 8 and point (4, 1) into the point-slope equation:

[tex]\begin{aligned}y-y_1&=m(x-x_1)\\y-1&=8(x-4)\\y-1&=8x-32\\y&=8x-31\end{aligned}[/tex]

Therefore, an equation for the line tangent to the graph of k at x = 4 is:

To find the derivative of j(x) use the quotient rule.

[tex]\textsf{If\;\;$j(x)=\dfrac{g(x)}{f(x)}$\;\;then:}\\\\\\j'(x)=\dfrac{f(x)g'(x)-g(x)f'(x)}{(f(x))^2}[/tex]

To calculate j'(2), substitute x = 2 into the equation:

[tex]\begin{aligned} \implies j'(2)&=\dfrac{f(2)g'(2)-g(2)f'(2)}{(f(2))^2}\\\\&=\dfrac{5 \cdot 1-2 \cdot 1}{(5)^2}\\\\&=\dfrac{5-2}{25}\\\\&=\dfrac{3}{25}\\\\&=0.12\end{aligned}[/tex]

Therefore, j'(2) = 3/25 = 0.12.

The equation a² + b² = c² represents the Pythagorean theorem.

This is a theorem that  states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

The Pythagorean theorem is used to find the length of one of the sides of a right-angled triangle when the lengths of the other two sides are known.

To solve the problem, you need to have at least two side lengths given. Then, you can use the equation to find the length of the third side. For example:

If you know the lengths of sides a and b and need to find the length of the hypotenuse (c):

Plug in the known values for a and b into the equation and solve for c.

Example: If a = 3 and b = 4, then 3² + 4² = c², which gives 9 + 16 = c², so c² = 25, and c = sqrt(25) = 5.

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We find that P(Z > 2.46) is roughly 0.007 using a calculator or a basic normal distribution table. The probability that a bag will contain more than 20% blue jellybeans is therefore approximately 0.007 or 0.7%.

The probability of an event is the ratio of good outcomes to all other potential outcomes. The number of successful outcomes for an experiment with 'n' outcomes can be expressed using the symbol x.

Here in the question,

We can utilise the binomial distribution formula to resolve this issue. In a bag of 200 jelly beans, let X represent the proportion of blue jelly beans. Following that, X exhibits a binomial distribution with parameters of n = 200 and p = 0.15, where p is the likelihood of drawing a blue jellybean.

The formula for determining the likelihood of finding more than 20% blue jellybeans in a bag is:

P (X > 0.2 × 200) = P (X > 40)

Since n is large (200) and p is not too near to 0 or 1, we can utilise the usual approximation to the binomial distribution. We may determine the equivalent mean and standard deviation of the normal distribution by using the mean and variance of the binomial distribution:

μ = np = 200 × 0.15 = 30

σ = √ (np(1-p)) = √ (200 × 0.15 × (1-0.15)) = 4.07

Then, we can standardize the random variable X as:

Z = (X - μ) / σ

So, we have:

P(X > 40) = P((X - μ) / σ > (40 - μ) / σ)

= P(Z > (40 - 30) / 4.07)

= P(Z > 2.46)

We find that P(Z > 2.46) is roughly 0.007 using a calculator or a basic normal distribution table. The likelihood that a bag will contain more than 20% blue jellybeans is therefore approximately 0.007 or 0.7%.

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Answer:

x=90°

Step-by-step explanation:

As in the angle, there is a box giving us info that x has to be 90°.

But to be sure that there is no mistake we have to do the following:

So we are looking at the surroundings of angle x (which is on a straight line) we see that it is a right angle and look at the angle on the same line is a right angle too.

The equation right angle=90° helps us see that because there are two right angles on a 180° line (90°+90°+180°).

Therefore the answer is:

x=90°

x is 25 and the congruent angles in the kite are 25 and 155 degrees.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x.

In a kite, the two pairs of adjacent angles are congruent. Let's call the congruent angles x and y:

   x       y

 +---+   +---+

/     \ /     \

+-------+-------+

\     / \     /

 +---+   +---+

   y       x

We know that the measurements of the angles in the kite are 3x, 75, 90, and 120, so we can set up an equation based on the sum of the angles in a quadrilateral:

3x + 75 + 90 + 120 = 360

Simplifying this equation, we get:

3x + 285 = 360

Subtracting 285 from both sides, we get:

3x = 75

Dividing both sides by 3, we get:

x = 25

So x is 25. To find y, we know that the sum of x and y must be 180 (because they are congruent angles that add up to a straight line). So we can set up another equation:

x + y = 180

Substituting x = 25, we get:

25 + y = 180

Subtracting 25 from both sides, we get:

y = 155

Therefore, x is 25 and the congruent angles in the kite are 25 and 155 degrees.

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Answer:

[tex]81\pi[/tex] [tex]mm^2[/tex]

Step-by-step explanation:

Let's recall the formula for the area of a circle:

[tex]A = \pi r^2[/tex]

We are given the diameter, but the formula uses the radius. Since the radius is equal to one-half of the diameter, we can find the radius by doing this:

[tex]r = \frac{1}{2}d=\\\\r=\frac{1}{2}(18)= \\\\r=9[/tex]

Now that we've found the radius is 9 mm, let's substitute the values into the formula for the area of a circle. We have:

[tex]A = \pi r^2=\\A=\pi (9^2)=\\A=\pi (81)=\\A=81\pi[/tex]

So, we've found that the exact area, in terms of pi, of either face of the coin is [tex]81\pi[/tex] [tex]mm^2[/tex].

To find the area of the coin/a circle use this equation:

(a = area, r = radius, d = diameter)

[tex]\text{a = r}^2[/tex]

So we need to do for the radius.

[tex]\text{r} = \dfrac{\text{d}}{2}[/tex]

[tex]\text{r} = \dfrac{18}{2}[/tex]

[tex]\text{r} = 9[/tex]

Then solve

[tex]\text{a = 9}^2[/tex]

[tex]\boxed{\bold{a = 81}}[/tex]

Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data. It is used in a wide range of fields such as science, engineering, social sciences, business, economics, and more.

In statistics, data is collected through various methods such as surveys, experiments, and observations. This data is then analyzed using statistical methods to extract meaningful insights, identify patterns and relationships, and make informed decisions.

Some common statistical techniques include descriptive statistics, inferential statistics, hypothesis testing, regression analysis, and probability theory. These techniques are used to help researchers and analysts to understand and draw conclusions about data, and to test whether their conclusions are statistically significant.

Statistics has many practical applications, such as market research, medical research, quality control, risk assessment, and many others. It plays a critical role in modern society, helping individuals and organizations make informed decisions based on data-driven insights.

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Answer: 3:7

Step-by-step explanation: since the simplest form of the fraction 36/84 is 3/7 that means 36:84 in simplest form is 3:7.

The correct answer is Jared has absolute advantage in washing the dishes.

This expression [tex]s_{i-j}[/tex] describes the distance between two points i and j in a geometric object

In the context of symmetry and rotations, [tex]s_{i-j}[/tex] typically refers to the distance between two points i and j in a geometric object, such as a crystal lattice or a molecule.

It is a vector that points from point i to point j, and its magnitude is the distance between the two points.

The distance vector [tex]s_{i-j}[/tex] is also used to describe the position of a point in the crystal lattice relative to the rotation axis.

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Answer: The best interpretation of the number -24 in the equation p = 2.75c-24 is option D: What her profit is.

The equation is in slope-intercept form, where the coefficient of c (2.75) represents the profit per cupcake and the constant term (-24) represents the fixed costs or expenses that Violet incurs regardless of how many cupcakes she sells.

In this case, the constant term of -24 represents the fixed costs such as the cost of ingredients, supplies, and other expenses that Violet incurs to make the cupcakes. This cost is subtracted from the total revenue generated by selling cupcakes to determine the profit. Therefore, the number -24 represents the fixed costs or expenses and its inclusion in the equation allows us to determine Violet's profit as a function of the number of cupcakes sold.

Step-by-step explanation:

Answer:

2004

Step-by-step explanation:

The original cost of a pair of gloves is 3.9

The percentage of females with brown eyes as follows is 25%.

Percentage is a way of expressing a number as a fraction of 100. It is represented by the symbol "%". The word "percent" means "per hundred".

Let's assume that the total population of Math town is 100 people for the sake of simplicity. Then, we can use the following information to create a table:

Population Males Females

Total         60         40

Brown eyes 18         ?

From the table, we can see that 60% of the population are males, so there are 60 x 0.3 = 18 males with brown eyes.

We also know that the total population with brown eyes is 28%, so there are 100 x 0.28 = 28 people with brown eyes. Therefore, there must be 28 - 18 = 10 females with brown eyes.

Finally, we can calculate the percentage of females with brown eyes as follows:

% of females with brown eyes = (10 / 40) x 100% = 25%

Therefore, the answer is (C) 25%.

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Answer: Spheres aren’t three-dimensional—they are two-dimensional. This is evident from the fact that in order to specify a point on a sphere, you only need two pieces of information, such as latitude and longitude.

If you include the interior of the sphere, this is instead called a closed ball, and that is three-dimensional. You can specify a point in the closed ball in all sorts of different ways; one of the most convenient would be latitude, longitude, and distance from the center. However, other than convenience, there is no reason to prefer one coordinate system over any other.

(This fact has nothing to do with spheres or closed balls—that is just a statement that is generally true. People who insist that “the three dimensions” are length, width, and height don’t know what they are talking about.)

Step-by-step explanation:

Therefore, we can predict that approximately 5,845,200 people left on cruises from this state in the year 2010.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

This linear equation depicts the number of passengers embarking on cruises from a certain state between 2005 and 2009.

It goes like this:

y = 117,000x + 4,919,200

For example, if x = 0, which represents the year 2005, then y = 4,919,200. If x = 1, which represents the year 2006, then y = 4,919,200 + 117,000 = 5,036,200. Similarly, if x = 2, which represents the year 2007, then y = 4,919,200 + 2(117,000) = 5,153,200.

y = 117,000(5) + 4,919,200

y = 5,845,200

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Question:

The number of people, y, leaving on cruises from a certain state from 2005 to 2009 can be approximated by y=117,000x+4,919,200, where x is the number of years after 2005.

The probability that a randomly selected score will be between 63 and 66 is approximately 0.0718, or 7.18%.

What is mean?

In statistics, the mean is a measure of central tendency, which is a way of describing the typical or central value of a set of data. The mean is also known as the average, and it is calculated by adding up all the values in a set of data and then dividing by the number of values in the set.

To find the probability that a randomly selected score will be between 63 and 66, we need to calculate the z-scores for these values and then find the area under the normal curve between these z-scores.

The z-score for a score of 63 is:

z = (63 - 74.4) / 8.3

z = -1.37

The z-score for a score of 66 is:

z = (66 - 74.4) / 8.3

z = -1.01

We can use a standard normal distribution table or calculator to find the area under the normal curve between these z-scores.

Using a standard normal distribution table, we find that the area to the left of a z-score of -1.01 is 0.1562, and the area to the left of a z-score of -1.37 is 0.0844. To find the area between these z-scores, we subtract the area to the left of -1.37 from the area to the left of -1.01:

P(-1.37 < z < -1.01) = 0.1562 - 0.0844 = 0.0718

So the probability that a randomly selected score will be between 63 and 66 is approximately 0.0718, or 7.18%.

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In linear equation, Her profit is rupees 4000.

No. of purses she must sell to have neither profit nor loss is 600 nos.

She made loss of rupees 2135.

What is a linear equation in mathematics?

A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables. 

The housewife earns,

Profit on 1 purse = 25 rupees

Loss on 1 vanity bag = 20 rupees

So,

Profit on 1000 purses = 25*1000 rupees

                                   = 25000 rupees

Loss on 1050 purses = 20*1050 rupees

                                  = 21000 rupees

Here, Profit > Loss

So,

Total profit = 25000-21000 rupees

                 = 4000 rupees

i) Her profit is 4000 rupees.

If no. of vanity bags sold = 750 nos.

She made loss of = 750*20 rupees

                            = 15000 rupees

ii) No. of purses she must sell to have neither profit nor loss

= 15000/25 nos.

= 600 nos.

Profit on selling 325 purses = 325*25 rupees

                                              = 8125 rupees

Loss on selling 513 vanity bags = 513*20 rupees

                                              =10260 rupees

Here, Profit < Loss

So,

iii) She made loss of = 10260-8125 rupees

                            = 2135 rupees

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The complete question is -

A housewife along with a group of ladies sold bags of different sizes. She earns a profit of 25 on a purse and a loss of 20 on a vanity bag sold. i. She received an order of 1050 vanity bags and 1000 purses. What is her profit or loss? ii. How many purses must she sell to have neither profit nor loss, if the number of vanity bags sold is 750? iii. How much profit/loss did she make in selling 325 purses and 513 vanity bags?

The skydiver is in the air for 23 seconds.

A diagram or pictorial representation that organises the depiction of facts or values is known as a graph.  

The relationships between two or more items are frequently represented by the points on a graph.

The skydiver is in the air as long as their height is greater than zero. From the graph, we can see that the skydiver reaches a height of zero at t = 23 seconds. Therefore, the skydiver is in the air for:

t = 23 seconds - 0 seconds = 23 seconds

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Answer:

32 I hope this helps please make me a brianlist that would help :)

We can estimate that there are approximately 134 glass beads in the bin.

What is probability?

Probability is a measure of the likelihood of an event occurring.

To estimate the number of glass beads in the bin, we can use the proportion of glass beads in the handful that Jasper selected.

There are 15 beads in the handful, and 4 of them are glass. So, the proportion of glass beads in the handful is:

4/15 ≈ 0.267

We can assume that the proportion of glass beads in the bin is similar to the proportion in the handful. Therefore, we can estimate the number of glass beads in the bin as

0.267 x 500 ≈ 134

Therefore, we can estimate that there are approximately 134 glass beads in the bin.

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Answer:

39.96

Step-by-step explanation:

the shape is a parallelogram ao the formula is base x height

A=10.8 x 3.7

A=39.97

The shaded area covers around 0.8664 square feet of space.

The mean and standard deviation of the standard normal distribution are 0 and 1, respectively. The standard deviation shows how much a particular measurement deviates from the mean, and the standard normal distribution is centred at zero.

Using a conventional normal distribution table, we must first determine the areas to the left of z= -1.5 and z=1.5, and then subtract those two areas to determine the area of the shaded zone.

Using a standard normal distribution table, we find that the area to the left of z= -1.5 is 0.0668, and the area to the left of z=1.5 is 0.9332. As a result, the darkened region's area is:

0.9332 - 0.0668 = 0.8664

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a. i. The function f(x)/g(x) = (2x - 1)/√(3x - 5)

ii.  The domain is x > 5/3

b. i. The function f(x) - g(x) = (2x - 1) - √(3x - 5)

ii.  The domain is x > 5/3

A function is a mathematical relation ship between two variables.

Since we have the functions f and g defined as follows

f(x) = 2x-1

g(x) = √3x-5

a. i To find f/g we note that

(f/g)(x) = f(x)/g(x)

So, substituting the values of the variables into the equation, we have that

f(x)/g(x) = (2x - 1)/√(3x - 5)

ii. The domain of f(x)/g(x) = (2x - 1)/√(3x - 5) is the value for which the denominator g(x) > 0.

So,g(x) > 0

⇒ √(3x - 5) > 0

⇒ 3x - 5 > 0²

⇒ 3x > 5

⇒ x > 5/3

So, the domain is x > 5/3

b. i. to find f - g, we note that

f - g = f(x) - g(x)

So, substituting the values of the variables into the equation, we have that

f(x) - g(x) = (2x - 1) - √(3x - 5)

ii. The domain of f(x) - g(x) is the value of x at which g(x) > 0

So. g(x) > 0

⇒  √(3x - 5) > 0

⇒ [√(3x - 5)]² > 0

⇒  3x - 5 > 0

⇒ 3x > 5

⇒ x > 5/3

So, the domain is x > 5/3

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The fraction that has been given illustrates that the person who ran further is Lisa and Jane.

Your information isn't complete. Therefore, an overview of the fraction will given.

Let's assume that Lisa ran 1/2 of a mile and Jane ran 3/6 of a mile. In order to know who ran more, you can convert the fraction to percentage.

This will be

[tex]\text{Lisa} = \dfrac{1}{2} \times 100 = \bold{50\%}[/tex]

[tex]\text{Jane} = \dfrac{3}{6} \times 100 = \bold{50\%}[/tex]

Therefore, both Lisa and Jane ran more.

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The truth table is given above for (A ⋀ B) → C.

What is the logical statement?

A logical statement, also known as a proposition or a statement of fact, is a declarative sentence that is either true or false, but not both. It is a statement that can be evaluated based on the available information or evidence to determine its truth value. In other words, a logical statement is a statement that can be either true or false, but not both.

To create a truth table for the logical statement (A ⋀ B) → C, we need to consider all possible combinations of truth values for propositions A, B, and C.

There are 2 possible truth values (true or false) for each proposition, so there are 2³ = 8 possible combinations.

We can organize these combinations into a table as follows:

| A | B | C | (A ⋀ B) | (A ⋀ B) → C |

|---|---|---|---------|-------------|

| T | T | T |    T    |      T      |

| T | T | F |    T    |      F      |

| T | F | T |    F    |      T      |

| T | F | F |    F    |      T      |

| F | T | T |    F    |      T      |

| F | T | F |    F    |      T      |

| F | F | T |    F    |      T      |

| F | F | F |    F    |      T      |

In this table, the column labeled (A ⋀ B) represents the truth value of the conjunction of A and B (i.e., A AND B), and the column labeled (A ⋀ B) → C represents the truth value of the conditional statement (A ⋀ B) → C.

The symbol "T" represents "true" and the symbol "F" represents "false".

Hence, The truth table is given above for (A ⋀ B) → C.

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[tex]\cfrac{5^7}{5^{-13}}\times\left( \cfrac{4^3}{7^{-2}} \right)^{-2}\implies 5^7\cdot 5^{13}\times \left( \cfrac{7^{-2}}{4^3} \right)^{+2}\implies 5^7\cdot 5^{13}\times\left( \cfrac{7^{-4}}{4^6} \right) \\\\\\ 5^{7+13}\times\left( \cfrac{1}{4^6\cdot 7^4} \right)\implies \cfrac{5^{20}}{4^6\cdot 7^4}\implies \cfrac{95367431640625}{9834496}[/tex]

Answer:

x < 11    &   x < 12

Step-by-step explanation:

x - 3 < 8 and 6x < 72

x < 11    &   x < 12

Answer: An even function is a function that satisfies the condition:

f(-x) = f(x)

Let's check which of the given functions satisfies this condition:

f(x) = (x - 1)^2

f(-x) = (-x - 1)^2 = x^2 + 2x + 1

f(x) = (x - 1)^2

The two expressions are not equal, so f(x) is not an even function.

f(x) = 8x

f(-x) = -8x = -f(x)

f(x) = 8x

The two expressions are equal with opposite signs, so f(x) is an odd function.

f(x) = x^2 - x

f(-x) = (-x)^2 - (-x) = x^2 + x

f(x) = x^2 - x

The two expressions are not equal, so f(x) is not an even function.

f(x) = 7

f(-x) = 7 = f(x)

f(x) = 7

The two expressions are equal, so f(x) is an even function.

Therefore, the only even function among the given functions is:

f(x) = 7.

Step-by-step explanation: