Researchers wanted to determine if there was an association between the level of happiness of an individual and their risk of breast cancer. The researchers studied 1813 people over the course of 5 years. During this 5-year period, they interviewed the individuals and asked questions about their daily lives and the hassles they face. In addition, hypothetical scenarios were presented to determine how each individual would handle the situation. These interviews were videotaped and studied to assess the emotions of the individuals. The researchers also determined which individuals in the study experienced any type of breast cancer over the 9-year period. After their analysis, the researchers concluded that the happy individuals were less likely to experience breast cancer. (a) What type of observational study was this? Explain. (b) What is the response variable? What is the explanatory variable?

The vector i + j + k is not a unit vector.

A unit vector is a vector with a magnitude (length) of 1. To determine if a vector is a unit vector, we calculate its magnitude and check if it equals 1.

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields and weight.

For the vector i + j + k, the magnitude can be calculated as:

|i + j + k| = √(1^2 + 1^2 + 1^2) = √3

Since the magnitude of i + j + k is √3 and not 1, it is not a unit vector.

In summary, the vector i + j + k is not a unit vector because its magnitude is √3, which is different from 1.

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For lines to be parallel, the slope has to be the same.

For lines to be perpendicular, the slope has to be the negative reciprocal.

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Answer:I think its 2x-5/3

Step-by-step explanation:

please let me know if I'm wrong.

Given:

Line FG and line GH lie in plane P.

To find:

The postulates that can be used to show that line FH lies in plane P.

Solution:

Ling FG and line GH lie in plane P. It means, all the points on the lines FG and GH lie on the plane P.

So, points F, G and H are the three points lie in the plane P.

We know that, if two points lie in a plane, then the entire line containing those points lies in that plane.

Since, F and H are in plane P, therefore, the line FH containing the points F and H, lies in plane P.

Hence, the correct option is D.

Value of mean is, 40.2

Value of median is, 45

Value of mode is, 28

Value of range is, 25

Given that;

Data set is,

⇒ 28, 45, 53, 28, 47

Now, We can arrange into ascending order as;

⇒ 28, 28, 45, 47, 53

Hence, Value of mean is,

⇒ (28 + 28 + 45 + 47 + 53) / 5

⇒ 40.2

And, The value of median is,

⇒ (5 + 1) / 2

⇒ 6/2

⇒ 3rd term

⇒ 45

The value of mode =28

And, The value of range is,

⇒ 53 - 28

⇒ 25

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Answer:

Both gyms charge the same after 2 months and LA fitness has a greater initial fee.

An estimated 50118 peοple will be infected after 60 days

The given fοrmula fοr mοdeling the number οf peοple infected with the virus is:

\(P(t) = e^{0.22t\)

Tο estimate the number οf peοple infected after 30 days, substitute t = 30 intο the fοrmula:

\(P(30) = e^{(0.22*30)} = e^{6.6 = 787.9\)

Therefοre, an estimated 788 peοple will be infected after 30 days.

Tο estimate the number οf peοple infected after 60 days, substitute t = 60 intο the fοrmula:

\(P(60) = e^{(0.22*60)} = e^{13.2 = 50117.9\)

Therefοre, an estimated 50118 peοple will be infected after 60 days.

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Answer:

a) 18x+9x+4x+16

b) 41x+16

Answer:

What-?

\(\(\purple{\rule{45pt}{1000000pt}}\tex\)

Part A:  yes, p = 7/2 g;

Part B: no, p = g+3.

Fractions play a major role in the explanation of ratio and proportion. At the point when a division is addressed as a: b, in which case it is a ratio, whereas a proportion asserts that two ratios are equal. A and b are any two integers in this case. The ratio and proportion are two crucial concepts that serve as the foundation for comprehending a variety of scientific and mathematical concepts.

Given tables for different beads for picture frame,

Mia's picture frame

Green beads     2   4   6    8   10  

purple beads     7  14  21  28  35

Part A:  since   2/7  = 4/ 14 =  6/21  =  8/28  =  10/35 =  2/7

so the beads are in proportion,

since 2/7  = g/p, where p = purple beads and g = green beads

p = 7/2 g.

Part B Riley's picture frame

Green beads     5   10   15    20   25  

purple beads     8   13    18   23   28

now  5/8  ≠  10/13   ≠  15/18  ≠  20/23  ≠ 25/28

the ratio of green beads are not equal so they are not in proportion,

but they are linear (10 - 5)/(13 - 8)  = (15 - 10)/(18 - 13)  = (20 - 15)/(23 - 18)  =1

let the equation be (g + a= p), where  p = purple beads and g = green beads and a, is constant, as we find that purple beads are 3 more than green the equation is  p =  g + 3

Hence beads in Mia's picture frames are in proportion and not in proportion for Riley's picture frames, and equation for Mia's picture frames is p = 7/2 g, and for Riley's picture frames is   p =  g + 3.

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It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

Here, we have,

given that,

min t_i

x₁ = x₂-u

x₂ = u

-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.

and origin  (0,0) be the begging of the coordinate.

also given that, (x₁, x₂)→ (0,0)

so, min t_i at origin (0,0) = t

Therefore, the generality condition of the situation does not met.

so, we get,

The given system can be represented by the following equations:

x₁' = x₂ - u

x₂' = u

To analyze the behavior of the system, we can examine the dynamics of each variable separately.

For x₁:

x₁' = x₂ - u

The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.

For x₂:

x₂' = u

The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.

Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).

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Answer:

8

Step-by-step explanation:

Answer:

18 and 1 Over 6 meters squared

Step-by-step explanation:

Hello There!

We can find the area of a square by multiplying its side by itself ( more specifically squaring it)

So the area of the square is equal to

\(4.25^2\\4.25*4.25=18.06\)

so the area of the square is 18.06

The volume of the solid generated when the right triangle below is rotated about side is 564.2.

The volume will be calculated by using the formula:

= 1/3πr²h

where, r = 7

h = 11

Therefore, the volume will be:

= 1/3πr²h

= 1/3 × 3.14 × 7² × 11

= 564.2

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Answer:

12m

Step-by-step explanation:

Answer:

9<✓88<10

Step-by-step explanation:

✓88 = 9.38083

Answer:

Yes, Chen earned a bonus for the journey.

Step-by-step explanation:

1 hour = 61 km

4.5 hrs = 61 * 4.5 = 274.5 km

Now,

96 litres = 274.5 km

1 litre = 274.5/96 km

1 litre = 2.859 = 2.9 km (approximately)

So, he drived more than 2.8 kilometers per litre of fuel.

Answer:

Yes

Step-by-step explanation:

Calculating distance travelled by Chen

Calculating distance covered per litre of fuel

To determine if a differential form is exact, we need to check if its partial derivatives satisfy the condition of equality. If the differential form is not exact, we can multiply it by an integrating factor to make it exact.

Given a differential form of the form M(x, y)dx + N(x, y)dy, we can determine if it is exact by checking if ∂M/∂y = ∂N/∂x. If this condition is not satisfied, the differential form is not exact. However, we can multiply the differential form by an integrating factor to make it exact.

By multiplying the original differential form by an integrating factor, which is usually a function of either x or y, the resulting form will have equal partial derivatives, satisfying the condition for exactness. The integrating factor effectively "corrects" the form and makes it exact.

By finding the appropriate integrating factor and multiplying it with the given differential form, we can transform it into an exact form. This process is a fundamental technique in solving certain types of differential equations and allows us to find solutions that would otherwise be challenging to obtain.

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Answer:

(2x+7)(x-1)

Step-by-step explanation:

2x²+5x-7

2x²+7x-2x-7

x(2x+7)-1(2x+7)

(2x+7)(x-1)

Based on the given confidence interval, there is evidence to support the claim that the true average echo duration of lightning flashes is 0.8 seconds.

To determine if the evidence supports the claim that the true average echo duration of lightning flashes is 0.8 seconds, we need to check if the value 0.8 falls within the confidence interval.

The 95% two-sided confidence interval for the true average echo duration is (0.743, 0.877). Since the value 0.8 falls within this interval, it means that the true average echo duration of lightning flashes of 0.8 seconds is within the range of values that is supported by the data.

Therefore, based on the given confidence interval, there is evidence to support the claim that the true average echo duration of lightning flashes is 0.8 seconds.

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To test whether the production volume is significantly related to the total cost using the estimated regression equation, we need to perform an analysis of variance (ANOVA).

The ANOVA table will provide us with the necessary information to determine the significance of the relationship. The ANOVA table consists of several components: the sum of squares (SS), the degrees of freedom (df), the mean squares (MS), the F-test statistic, and the p-value.  The total sum of squares (SST) is also computed by summing the squares of the differences between the observed values and the mean of the dependent variable.  dfR is equal to the number of independent variables (excluding the intercept term), while dfE is calculated as the total number of observations minus the number of independent variables.

The mean squares for the regression (MSR) and the error (MSE) are then calculated by dividing the respective sum of squares by their corresponding degrees of freedom. To obtain the F-test statistic, we divide MSR by MSE. The p-value is determined by comparing the F-test statistic to the critical value corresponding to the chosen significance level.  we can determine whether the production volume has a significant relationship with the total cost. If the p-value is below the chosen significance level, typically 0.05, we reject the null hypothesis and conclude that there is a significant relationship between the variables.

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Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the required figure is not attached to the question.

From the question, we can deduce that the telescope is a composite figure made from a cone and a cylinder.

To get the volume of the materials used, you have to calculate the volume of the cone and that of the cylinder.

The sum of these volumes, is your answer.

Assume the following dimensions:

Cone

\(r = 5\\\) --- radius

\(h = 7\) --- height

Cylinder

\(r = 5\\\) --- radius

\(h = 20\) --- height

The volume of the cone is:

\(Volume = \frac{1}{3} \pi r^2h\)

\(V_1= \frac{1}{3} \pi *5^2*7\)

\(V_1= \frac{1}{3} \pi *25*7\)

\(V_1= \frac{175}{3} \pi\)

The volume of the cylinder is:

\(Volume = \pi r^2h\)

\(V_2 = \pi * 5^2 * 20\)

\(V_2 = \pi * 25* 20\)

\(V_2 = 500\pi\)

The total is:

\(Volume = V_1 + V_2\)

\(Volume = \frac{175\pi}{3} + 500\pi\)

Take LCM

\(Volume = \frac{175\pi+1500\pi}{3}\)

\(Volume = \frac{1675\pi}{3}\)

Answer:

The surface area is the area that describes the material that will be used to cover a geometric solid. When we determine the surface areas of a geometric solid we take the sum of the area for each geometric form within the solid.

Answer:

The volume of a pyramid

V=1/3⋅B⋅h

The area of the rectangle:

A=C⋅h

A=12.6⋅6

A≈75.6

To find the volume of a cylinder we multiply the base area (which is a circle) and the height h.

V=πr2⋅h

The value of y from the given figure is 6√3

From the given figure, according to the theorem;

H² = 6² - 3²

H² = 36 - 9

H²  = 27

H = 3√3

Determine the value of y using the same theorem;

y² = 9² + ( 3√3)²

y² = 81. + 27

y = √108

y = 6√3

Hence the value of y from the given figure is 6√3

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To solve a problem, we often Translate the given information into algebraic expressions and equations.

Step-by-step explanation:

Consider the provided statement.

In order to solve a mathematical problem, we often translate the given information into algebraic expressions and equations.

For example: “6 less than twice a number"

We first need to translate it.

This can be translated as: 2n-6

Where n represents the number.

Hence, the complete statement is To solve a problem, we often Translate the given information into algebraic expressions and equations.

Answer:

$6.96

Step-by-step explanation:

5.25% of 5.79

5.79 × 5.25/100 = $0.303975 or $0.30

15% of 5.79

5.79 × 15/100 = $0.8685 or $0.87

total

$5.79 + $0.30 + $0.87 = $6.96

Answer:

Step-by-step explanation:

6) 3750

7) 244

1. P(X + Y ≤ 2) = -e⁻² - 2e⁻², 2. Marginal PDF for X: fₓ(x) = -2e⁻ˣ and marginal PDF for Y: fᵧ(y) = 2e⁻ʸ - 2e⁻ˣ⁻ʸ.

1. To find P(X + Y ≤ 2), we need to integrate the joint PDF over the region where X + Y is less than or equal to 2. Since X and Y are non-negative random variables, the region of interest is the triangle bounded by the lines X = 0, Y = 0, and X + Y = 2. Integrating the joint PDF over this region gives:

P(X + Y ≤ 2) = ∫∫ fₓᵧ(x, y) dx dy

The integral bounds can be determined by considering the constraints 0 ≤ X ≤ Y ≤ ∞:

0 ≤ x ≤ y

0 ≤ y ≤ ∞

Setting up the integral,

P(X + Y ≤ 2) = ∫[0,∞] ∫[x,2-x] 2e⁻ˣ⁻ʸ dy dx

Solving the integral,

P(X + Y ≤ 2) = ∫[0,∞] -2e⁻ˣ⁻ʸ ∣ x to 2-x dx

Simplifying the integral bounds,

P(X + Y ≤ 2) = ∫[0,∞] -2e⁻ˣ⁻²⁻ˣ + 2e⁻²⁻ˣ dx

Evaluating the integral,

P(X + Y ≤ 2) = -e⁻²⁻ˣ - 2e⁻²⁻ˣ ∣ 0 to ∞

As x approaches infinity, e⁻²⁻ˣ approaches 0, so the second term in the integral becomes zero.

P(X + Y ≤ 2) = -e⁻²⁻⁰ - 2e⁻²⁻⁰

P(X + Y ≤ 2) = -e⁻² - 2e⁻²

Therefore, P(X + Y ≤ 2) = -e⁻² - 2e⁻².

2. To find the marginal PDFs for X and Y, we integrate the joint PDF over the respective variable while treating the other variable as a constant. The marginal PDF for X, denoted as fₓ(x), is obtained by integrating the joint PDF fₓᵧ(x, y) over the range of Y:

fₓ(x) = ∫[x,∞] fₓᵧ(x, y) dy

Substituting the given joint PDF,

fₓ(x) = ∫[x,∞] 2e⁻ˣ⁻ʸ dy

Simplifying the integral,

fₓ(x) = -2e⁻ˣ⁻ʸ ∣ x to ∞

As y approaches infinity, e⁻ˣ⁻ʸ approaches 0, so the integral becomes,

fₓ(x) = -2e⁻ˣ⁻ˣ

Simplifying further,

fₓ(x) = -2e⁻ˣ

Therefore, the marginal PDF for X is fₓ(x) = -2e⁻ˣ.

Similarly, the marginal PDF for Y, denoted as fᵧ(y), is obtained by integrating the joint PDF fₓᵧ(x, y) over the range of X,

fᵧ(y) = ∫[0,y] fₓᵧ(x, y) dx

Substituting the given joint PDF,

fᵧ(y) = ∫[0,y] 2e⁻ˣ⁻ʸ dx

Simplifying the integral,

fᵧ(y) = 2e⁻ˣ⁻ʸ ∣ 0 to y

fᵧ(y) = 2e⁻ʸ - 2e⁻ˣ⁻ʸ

Therefore, the marginal PDF for Y is fᵧ(y) = 2e⁻ʸ - 2e⁻ˣ⁻ʸ.

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Complete question - Let the random variables X and Y have the joint PDF given below:

fₓᵧ(x, y) = 2e⁻ˣ⁻ʸ when 0 ≤ X ≤ Y ≤ ∞

fₓᵧ(x, y) = 0 otherwise.

1. Find P(X + Y ≤ 2)

2. Find the marginal PDF for X and Y.

x = 12.

Perpendicular lines are lines that intersect at a 90-degree angle. So, for example, line ST is perpendicular to line CD. So line ST is perpendicular to line CD.

Perpendicular lines always intersect each other, however, all intersecting lines are not always perpendicular to each other. The two main properties of perpendicular lines are: Perpendicular lines always meet or intersect each other. The angle between any two perpendicular lines is always equal to 90.

Given that

line m and n are perpendiculars

then angle ∠a = ∠b

then

5x + 20 = 7x -4

7x -5x = 20 + 4

2x = 24

x = 24/ 2

x = 12.

Hence the value of x = 12

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Answer:

3x-y=15 should be the answer

7(x+2)

Let's find the common term in this expression to factor it out. it is 7.

Factoring is the opposite of distributing.

If we distribute, we will get the original expression.

Next:

45-27k

Here, the common term is 9:

9(5-3k)

12ab+7b - the common term is b:

b(12a+7)

y^2-9y.

Here the common term is y:

y(y-9)

8r-32r² the common term here is 8r:

8r(1-4r)

16gh+28gh: the Common Term is 4gh:

4gh(4+7)

21w²-77wx The common term is 7w:

7w(3w-11x)

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