Suppose that the mean systolic blood pressure for women over age seventy is 131 mmHg (millimeters of mercury), with a standard deviatiob of 9 mmHg. Supposed that the blood pressures are normally distributed. Complete the following statements. Choose the correct answer (68,75,95,99.7)

Answer:

When you multiply both sides by a negative value you make the side that is greater have a "bigger" negative number, which actually means it is now less than the other side! This is why you must flip the sign whenever you multiply by a negative number.

Step-by-step explanation:

Answer:

Step-by-step explanation:

I guess 6%?

Answer:

8:12 or 8 to 12

Step-by-step explanation:

You have to know that a ratio is a fraction so you say 8 over 12

Answer:

First, there are NO 5-digit pin codes that include the digits 7, 2, 4, 6, 9, and 3. But, there are 720 pin codes that include 5 out of the 6 digits.

Step-by-step explanation:

The question is incorrect, please see the correct question below;

Kevin is 2 times as old as Gabriela. 12 years ago, Kevin was 6 times as old as Gabriela.

How old is Gabriela now?

Gabriela age is 30 years

Let a represent Gabriela age

Let b represent Kelvin age

a= 2b

a-12= 6(b-12)

a-12= 6b-72

2b-12= 6b-72

2b-6b= -72+12

-4b= -60

b= 60/4

b= 15

a= 2(15)

a= 30

Hence Gabriela age now is 30 years

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Answer:

C. (5, -3)

Step-by-step explanation:

Ordered pair just means the coordinate or the point at which both of the graphs intersect. On the x-axis, this is at point 5, and on the y-axis, this is at point -3. Since an ordered pair is in the form (x, y), the answer is therefore C.

The solution to the set of graphical equations are P ( 5 , -3 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y = -x + 2

y = x - 8

On simplifying , we get

-x + 2 = x - 8

Adding x on both sides , we get

2x - 8 = 2

Adding 8 on both sides , we get

2x = 10

Divide by 2 on both sides , we get

x = 5

So , the value of x = 5 and y = -3

Hence , the solution is the point of intersection of lines on the graph which is P ( 5 , -3 )

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Answer:

Step-by-step explanation:

Well you already known 12 is the y-intercpet.

You go up 1 and go right 3 times and you start to repeat

which is called rise over run.

Which will look something like this:

Answer:

$348

Step-by-step explanation:

Unit rate:

Sales clerk: $12/h

Assistant manager: 1/2 x 12= $6/h

Manager: 2 1/2 x 12= $30/h

Now for how long they will work (7.25 hours long):

Sales clerk: 12 x 7.25= $87

Assistant manager: 6 x 7.25= $43.5

Manager: 30 x 7.25= $217.5

In total: 87 + 43.5 + 217.5= $348 is paid in one day for each of the employees when they work 7.25 hours.

I hope this will help qwq

The pros and cons of Kernel Density Estimation (KDE) over histogram has been compared and advantage and disadvantage to each has been given.

Kernel Density Estimation (KDE) and histograms are both methods used for visualizing and estimating probability density functions.

KDE offers advantages such as its ability to capture smooth and continuous distributions, while histograms have benefits like simplicity and ease of interpretation.

However, KDE can be computationally intensive, and histograms may suffer from binning bias.

Kernel Density Estimation (KDE) is a non-parametric method used to estimate the probability density function of a random variable. It offers several advantages over histograms.

Firstly, KDE is able to capture smooth and continuous distributions, providing a more accurate representation of the underlying data.

Additionally, KDE does not rely on binning, allowing for a more precise estimation of the density at any point.

Furthermore, KDE can handle missing or irregularly spaced data.

On the other hand, histograms have their own advantages. They are simple and intuitive, making them easy to understand and interpret.

Histograms also tend to be less computationally intensive compared to KDE, making them suitable for large datasets.

Moreover, histograms can reveal the presence of outliers or gaps in the data due to the discrete nature of the bins.

However, there are also drawbacks to consider. KDE can be computationally intensive, especially for large datasets, requiring more processing power and time compared to histograms.

This can be a limitation when dealing with real-time or interactive applications. In contrast, histograms suffer from binning bias, where the choice of bin size can affect the visual representation and interpretation of the data.

Selecting an inappropriate bin size can lead to either over-smoothing or over-detailing the data distribution.

In summary, KDE offers advantages in capturing smooth distributions and avoiding binning bias, but it may be computationally intensive.

Histograms, on the other hand, are simple and computationally efficient but can suffer from binning bias.

The choice between KDE and histograms depends on the specific characteristics of the data and the objectives of the analysis.

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The estimate for the probability of drawing a red ball is m/n.

Sure! Based on the given information, we have a black box with red balls and white balls. We draw a ball from the box, write down the color, and put it back. We repeat this process for n times, and we end up with m red balls.
To estimate the probability of drawing a red ball from the box, we can use the ratio of the number of red balls obtained (m) to the total number of draws (n).
Therefore, the estimate for the probability of drawing a red ball is m/n.

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make a probability tree it will really help so much

Answer:

1584

Step-by-step explanation:

The take-home salary would be $1584 each month if Erin earns $2200 per month her deduction amount to 28% of her paycheck.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

Erin earns $2200 per month.

The deduction amount to 28% of her paycheck.

Let's assume the 28% is deducted from the monthly salary.

The total dedcution = 28% of 2200

The total dedcution = (28/100)x2200

The total dedcution = 0.28x2200

The total dedcution = $616

Total net amount = Take home = 2200 - 616

Take home = 2200 - 616

Take home = $1584

Thus, the take-home salary would be $1584 each month if Erin earns $2200 per month her deduction amount to 28% of her paycheck.

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Answer:

the answer is 3GB

Step-by-step explanation:

30-21=9 9/3 = 3

Given:

Nana has a water purifier that filters \(\dfrac{1}{3}\) of the contaminants each hour.

Water has contaminants = \(\dfrac{1}{2}\)

To find:

The function that gives the remaining amount of contaminants in kilograms, C(t), t hours after Nana started purifying the water.

Solution:

Let C(t) be the remaining amount of contaminants in kilograms after t hours.

Initial amount of contaminants = \(\dfrac{1}{2}\)

Decreasing rate is \(\dfrac{1}{3}\) .

Using the exponential decay model:

\(C(t)=C_0(1-r)^t\)

where, \(C_0\) is initial amount of contaminants, r is the decreasing rate and t is time in hours.

Substituting the values, we get

\(C(t)=\dfrac{1}{2}(1-\dfrac{1}{3})^t\)

\(C(t)=\dfrac{1}{2}(\dfrac{2}{3})^t\)

Therefore, the required function is \(C(t)=\dfrac{1}{2}(\dfrac{2}{3})^t\).

Answer:

\(\frac{1}{2} (\frac{2}{3} )^t\)

Step-by-step explanation:

It's correct on Khan.

The term for the value that occurs most often in a series of numbers is called the mode.

The mode is one of the three main measures of central tendency, along with the mean and the median. It is a useful descriptive statistic that can provide insights into the characteristics of a dataset.

To find the mode of a set of data, you first need to arrange the data in order, either in increasing or decreasing order. Then, you simply identify the most frequent data point, which is the mode. In some cases, there may be more than one mode if multiple data points occur with the same maximum frequency.

The mode is particularly useful when dealing with categorical or nominal data, where there are distinct categories or values that cannot be ordered in a meaningful way. For example, the mode can help identify the most popular color among a group of people or the most common type of car on a given street. It can also be used for continuous data, although it may be less useful in this case than the mean or median.

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For the utility function U(x, y) = \((x^4)/(y^4)\), we can derive the indifference curve equations by setting the utility function equal to the given values U = 1, U = 2, and U = 3.

1. When U = 1:

  \((x^4)/(y^4) = 1\)

 \(x^4 = y^4\)

  Taking the fourth root of both sides, we get:

  x = y

2. When U = 2:

  \((x^4)/(y^4) = 2\)

  \(x^4 = 2y^4\)

  \(x = (2^(1/4)) * y\)

3. When U = 3:

  \((x^4)/(y^4) = 3\)

  \(x^4 = 3y^4\)

  \(x = (3^(1/4)) * y\)

The indifference curves for this utility function are shaped like a rectangular hyperbola, where the ratio of x to y remains constant along each curve.

(b) For the utility function U(x, y) = y - 2x, the indifference curves can be derived by setting the utility function equal to the given values U = 1, U = 2, and U = 3.

1. When U = 1:

  y - 2x = 1

  y = 2x + 1

2. When U = 2:

  y - 2x = 2

  y = 2x + 2

3. When U = 3:

  y - 2x = 3

  y = 2x + 3

The indifference curves for this utility function are straight lines with a slope of 2. They have a positive slope, indicating a positive marginal rate of substitution between x and y.

(c) Both utility functions satisfy completeness, transitivity, and monotonicity.

1. Completeness: The preferences are complete if, for any two bundles of goods, the consumer can compare and rank them. Both utility functions provide a ranking of bundles based on their utility values, indicating completeness.

2. Transitivity: Transitivity implies that if bundle A is preferred to bundle B, and bundle B is preferred to bundle C, then bundle A must be preferred to bundle C. Both utility functions satisfy this assumption.

3. Monotonicity: Monotonicity assumes that more is better. If a bundle has higher quantities of both goods compared to another bundle, it should be preferred. Both utility functions satisfy this assumption as well.

The violations of these assumptions would affect the shape and properties of the indifference curves. For example, if completeness is violated, there may be some bundles that cannot be compared or ranked, resulting in incomplete indifference curves.

If transitivity is violated, there may be cycles of preferences, leading to inconsistent indifference curves. If monotonicity is violated, the indifference curves may not have a consistent upward slope. However, in the case of the given utility functions, all assumptions are satisfied, allowing for well-defined indifference curves.

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The group of numbers that includes all prime numbers is: (b) 13, 11, 23, 31.

Let's go through each group of numbers and determine which one includes all prime numbers:

a) 2, 5, 15, 19: In this group, 2 and 5 are prime numbers because they are divisible only by 1 and themselves. However, 15 is not a prime number as it is divisible by 3 and 5. Similarly, 19 is a prime number because it is divisible only by 1 and itself.

b) 13, 11, 23, 31: In this group, all the numbers are prime. They are divisible only by 1 and themselves, satisfying the definition of prime numbers.

c) 2, 3, 5, 9: In this group, 2, 3, and 5 are prime numbers because they are divisible only by 1 and themselves. However, 9 is not a prime number as it is divisible by 3.

d) 7, 17, 29, 49: In this group, 7, 17, and 29 are prime numbers as they are divisible only by 1 and themselves. However, 49 is not a prime number as it is divisible by 7.

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By applying the central angle property, the measure of angle HLK is equal to 29°.

The central angle property states that an inscribed angle is equal to half the measure of a central angle that is subtended by the same arc.

This ultimately implies that, a central angle is double (twice) the measure of an inscribed angle that is subtended by the same arc.

By applying the central angle property, we have:

HK = 2m∠HLK

58 = 2m∠HLK

m∠HLK = 58/2

m∠HLK = 29°.

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The expression which represents the given relatiοn is  x(1 + 0.13). Thus, option A is cοrrect.

Equatiοns are statements in mathematics that have twο algebraic expressiοns οn either side οf the equals (=) sign. It shοws that the expressiοns printed οn the left and right sides have an equal relatiοnship.

In any mathematical equatiοn, we have LHS = RHS (left hand side = right hand side). Equatiοns can be sοlved tο find the value οf an unknοwn variable that represents an unknοwn quantity.

If there is nο "equal tο" symbοl, a statement is nοt an equatiοn. When twο expressiοns have equal values, a mathematical statement knοwn as an equatiοn includes the symbοl "equal tο" between them.

Let the x represent the price οf  mοnster truck

Then He has tο pay extra 13% οf the tοy = 0.13

Tοtal price = x + x × 0.13

simplifying

x + x × 0.13

x + 0.13x

x(1 + 0.13)  ⇒ οptiοn A

x(1.13)

1.13x   ⇒ οptiοn D

Thus, The expressiοn which represents the given relatiοn is x(1 + 0.13). Thus, οptiοn A and D is cοrrect.

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Complete question:

Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a %13 monster truck tax. Which of the following expressions could represent how much Camacho pays in total for the truck?

Choose 2 answers:

(Choice A) (1+0.13)x

(Choice B) 13/100 x

(Choice C) 14x

(Choice D) 1.13x

(Choice E) 13x+x

The length of the legs of the right triangle are the ones in option D;

4.9 units, 14.2 units

Here we have a right triangle with one interior angle that measures 19°, and the hypotenuse measures 15 units.

To find the measures of the legs we can use trigonometric relations; we will get the measures of the two legs.

cos(19°) = x/15 ----> x = cos(19°)*15 = 14.2 units.

sin(19°) = y/15 ----> y = sin(19°)*15 =  4.9  units

Then the correct option will be D, these are the two lenghts of the legs of the right triangle.

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Given:

A soda and two slices of the pizza of the day cost $10.25.

A soda and four slices of the pizza day cost $18.75.

To find:

The cost of each item.

Solution:

Let x be the cost of a soda and y be the cost of each slice of the pizza.

A soda and two slices of the pizza of the day cost $10.25.

\(x+2y=10.25\)           ...(i)

A soda and four slices of the pizza day cost $18.75.

\(x+4y=18.75\)           ...(ii)

Subtracting (i) from (ii), we get

\(x+4y-x-2y=18.75-10.25\)

\(2y=8.50\)

\(y=\dfrac{8.50}{2}\)

\(y=4.25\)

Putting y=4.25 in (i), we get

\(x+2(4.25)=10.25\)

\(x+8.50=10.25\)

\(x=10.25-8.50\)

\(x=1.75\)

Therefore, the cost of each soda is $1.75 and the cost of each slice of pizza is $4.25.

If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5. Also, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7. Therefore, it is clear that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn

A Pythagorean triple is a set of three integers that satisfy the Pythagorean theorem, which states that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the longest side, or hypotenuse. For example, the triple (3, 4, 5) is a Pythagorean triple because 3^2 + 4^2 = 5^2.

Now let's talk about triangular numbers. A triangular number is the sum of the first n positive integers, and it can be represented by the formula Tn = 1 + 2 + 3 + ... + n = (n(n+1))/2. The first few triangular numbers are 1, 3, 6, and 10.

Interestingly, in the list of the first few Pythagorean triples, we can observe a pattern where the value of b is four times a triangular number. For example, in the Pythagorean triple (3, 4, 5), we have b = 4T1. In (5, 12, 13), b = 4T2. In (7, 24, 25), b = 4T3. And in (9, 40, 41), b = 4T4.

So the question is: is this pattern true for all triangular numbers? Let's investigate further.

a) To find a primitive Pythagorean triple (a, b, c) with b = 4T5, we need to find a value of a and c such that a^2 + b^2 = c^2 and b = 4T5. Using the formula for T5, we get T5 = (5(5+1))/2 = 15. Therefore, b = 4T5 = 60. We can use the Euclid's formula for generating Pythagorean triples, which states that for any two positive integers m and n with m > n, a Pythagorean triple (a, b, c) can be generated by a = m^2 - n^2, b = 2mn, and c = m^2 + n^2.

If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5.

Similarly, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7.

b) Now, the question is whether there is a primitive Pythagorean triple (a, b, c) with b = 4Tn for any triangular number Tn. Let's assume this is true and try to prove it.

Using the same Euclid's formula, we can generate a primitive Pythagorean triple (a, b, c) with b = 4Tn by setting m = 2Tn+1 and n = Tn. This gives us a = 4Tn^2 + 1 and c = 4Tn^2 + 2Tn + 1, and we can verify that b = 4Tn using the formula for Tn.

Therefore, we have proven that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn

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The value of x/y is 35/37. The correct answer is option B).

Let's start by the first right triangle and the inscribed square. We know that the square has side length x and is inscribed in the right triangle with sides 3, 4, and 5, where 5 is the hypotenuse. Since one vertex of the square coincides with the right-angle vertex of the triangle, we have that the side length x of the square is also the length of the altitude from the right angle to the hypotenuse of the triangle. Therefore, we can write:

x = \((3*4)/5 = 12/5\)

Now the second right triangle and the inscribed square:

We know that the square has side length y and is inscribed in the right triangle with sides 3, 4, and 5, where 5 is the hypotenuse. Since one side of the square lies on the hypotenuse of the triangle, we have that the sum of the areas of the two smaller squares is equal to the area of the larger square. Therefore, we can write:

\(x^{2} + y^{2} = 5^{2} = 25\)

Substituting\($x = {12}/{5}\) gives

\((12/5)^{2} + y^{2} = 25\)

Simplifying this equation gives

\(y^{2} = 25 - (144/25) = (25^{2} - 144)/25 = 481/25\)

Taking the square root of both sides gives

y = \(\sqrt{481}/5\)

Finally, we compute x/y:

x/y = \(12*\sqrt{481}/ \sqrt{481}*5\)

x/y = 35/37

The correct option is B)

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--The given question is incomplete, the complete question is

"A square with side length x is inscribed in a right triangle with sides of length 3, 4, and 5 so that one vertex of the square coincides with the right-angle vertex of the triangle. A square with side length y is inscribed in another right triangle with sides of length 3, 4, and 5 so that one side of the square lies on the hypotenuse of the triangle. What is x/y?

(A) 12/13

(B) 35/37

(C) 1

(D) 37/35

(E) 13/12"

4.47 mass of sodium chloride (NaCI) is contained in 30.0 mL of a 17.9% by mass solution of sodium chloride in water. c). 4.47. is the correct option.

Mass of the solution (m) = Volume of the solution (V) × Density of the solution (d)= 30.0 mL × 0.833 g/mL= 24.99 g

Now, let the mass of sodium chloride be x.

So, the percentage of sodium chloride in the solution is given by: (mass of NaCl / mass of solution) × 100%

Hence, we can write the given percentage as:(x/24.99)× 100= 17.9% ⇒x = (17.9/100) × 24.99= 4.47 g

Hence, the mass of sodium chloride (NaCl) is contained in 30.0 mL of a 17.9% by mass solution of sodium chloride in water is 4.47 g.

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Using Heron's formula, the area of the porch is 294 squared feet

To calculate the area of the porch, we need to use Heron's formula which is given as;

Heron's formula is a mathematical formula used to calculate the area of a triangle when the lengths of all three sides are known. It is named after the ancient Greek mathematician Heron of Alexandria. The formula is:

Area = sqrt(s(s-a)(s-b)(s-c)),

where s is the semi-perimeter of the triangle (s = (a+b+c)/2) and a, b, and c are the lengths of the three sides.

Substituting the values into the formula;

s = (21 + 28 + 35) / 2

s = 84 / 2

s = 42

Using the value of s

A = √42(42 - 21)(42 - 28)(42 - 35)

A= 294

The area is 294 ft²

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The equation of the circle of radius 4 and center at (-1, 1) is given as follows:

\((x + 1)^2 + (y - 1)^2 = 16\)

The equation of a circle of center \((x_0, y_0)\) and radius r is given by:

\((x - x_0)^2 + (y - y_0)^2 = r^2\)

In this problem:

Hence, the equation is given as follows:

\((x - (-1))^2 + (y - 1)^2 = 4^2\)

\((x + 1)^2 + (y - 1)^2 = 16\)

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a. μ is approximately 0.2679 when p = 20 pounds and θ = 15°.

b. θ is approximately 68.65° when p = 35 grams and μ = 2.6.

To find the coefficient of static friction μ in each scenario, we can rearrange the given equation and solve for μ.

a. Given p = 20 pounds and θ = 15°, we have:

p sin θ = μp cos θ

Substituting the given values, we get:

20 pounds * sin(15°) = μ * 20 pounds * cos(15°)

Simplifying the equation:

sin(15°) = μ * cos(15°)

Now we can solve for μ:

μ = sin(15°) / cos(15°)

Using a calculator, we find:

μ ≈ 0.2679

Therefore, μ is approximately 0.2679 when p = 20 pounds and θ = 15°.

b. Given p = 35 grams and μ = 2.6, we have:

p sin θ = μp cos θ

Substituting the given values, we get:

35 grams * sin(θ) = 2.6 * 35 grams * cos(θ)

Canceling out the units of grams, we have:

sin(θ) = 2.6 * cos(θ)

Dividing both sides by cos(θ), we get:

tan(θ) = 2.6

Using the inverse tangent function, we can find θ:

θ = tan⁽⁻¹⁾(2.6)

Using a calculator, we find:

θ ≈ 68.65°

Therefore, θ is approximately 68.65° when p = 35 grams and μ = 2.6.

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Answer:

40

Step-by-step explanation:

so it is just like a regular equation like 30+10=40 but your just finding what A means so 40 yea