According to a study published in the journal Social Psychological and Personality Science, people with
religious affiliations live longer, on average, than those without religious affiliations. The study analyzed
more than 1,000 obituaries and accounted for other variables like sex and marital status.
What type of study is this, and what is the explanatory variable?

Considering the expression of a line, the correct answer is option a.) the relationship between the line that passes through (-1, -8) and (4,-4) and the line that passes through (2, -9) and (7,-5) is parallel.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

Parallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

In this case, you can calculated in this case:

Being (x₁, y₁)= (-1; -8) and (x₂, y₂)= (4; -4), the slope m can be calculated as:

m= (-4 - (-8))÷ (4 - (-1))

m= (-4 + 8)÷ (4 + 1)

m= 4÷ 5= 4/5

Considering point 1 and the slope m, you obtain:

-8= 4/5× (-1) + b

-8= -4/5 +b

-8 + 4/5= b

-36/5=b

The equation of the line that passes through the pair of points (-1, -8) and (4,-4) is y=4/5x - 36/5.

Being (x₁, y₁)= (2; -9) and (x₂, y₂)= (7; -5), the slope m can be calculated as:

m= (-5 - (-9))÷ (7 - 2)

m= (-5 + 9)÷ (5)

m= 4÷ 5= 4/5

Considering point 1 and the slope m, you obtain:

-9= 4/5× (-2) + b

-9= -8/5 +b

-9 + 8/5= b

-37/5=b

The equation of the line that passes through the pair of points (-1, -8) and (4,-4) is y=4/5x - 37/5.

You can see that the lines y=4/5x - 36/5 and y=4/5x - 37/5 have the same slope of 4/5 and different ordinates to the origin. So, this lines are parallel.

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By solving the given equation (y = 0.43x + 5) we know that the cost of renting the car is $215 when we plan to drive 489 miles.

So, y = 0.43x + 5 where 'x' is car driven and 'y' is the cost of renting.

Now, solve for y when the value of x is 489.

Rounding off: y = $215

Therefore, by solving the given equation we know that the cost of renting the car is $215 when we plan to drive 489 miles.

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Answer:

y = 5, 3

x = 155, 171

(y = 5, x = 155)

(y = 3, x = 171)

Step-by-step explanation:

(8y - 15) = (y²)

-8y + 15          -8y + 15

--------------------------------

y² - 8y + 15 = 0

(y - 5) (y - 3) = 0

--------------

y = 5, 3

----------------------------------------------------------------------------------------------------------

y² + x = 180

(5)² + x = 180

25 + x = 180

-25         -25

--------------------

x = 155

(3)² + x = 180

9 + x = 180

-9            -9

------------------

x = 171

----------------------------------------------------------------------------------------------------------

I really hope this helps!

Answer: 13

Step-by-step explanation:

As the sum of the angles of a triangle is 180, we have that 39 + 90 + 3x+12 = 180.

3x = 180 - 39 - 90 - 12

3x = 39

x = 13

Answer:

When A = 0 and y = 1 and C = 2

0x + 1y = 2

y = 2 No matter what x is, y will always be 2 and this will create a horizontal line.

Step-by-step explanation:

Assume to contrary that the sum of the squares of two odd integers can be the square of an integer. Since, [tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex] is odd it shows that sum of the squares of two odd integers cannot be the square of an integer.

A quadrilateral with four equal sides is called a square. There are the numerous items in our environment that have a square shape. Equal sides and internal angles that are both 90 degrees distinguish each square shape. Let's find out more about square's characteristics, mathematics, and design.

A square has four corners and is closed, two-dimensional (2D) object.

Assume to contrary that the sum of the squares of two odd integers can be the square of an integer.

Suppose that x,y,z∈Z such that [tex]x^{2} +y^{2} =z^{2}[/tex], and x and y are odd.

Let, x=2m+1 and y=2n+1.

Hence,

[tex]x^{2} +y^{2} =(2m+1)^{2} + (2n+1)^{2}[/tex]

           =[tex]4m^{2}+4m+1+4n^{2}+4n+1[/tex]

           =[tex]4(m^{2}+n^{2}) + 4(m+n)+2[/tex]

           =[tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex]

Since, [tex]2[2(m^{2}+n^{2})+2(m+n)+1][/tex] is odd it shows that sum of the squares of two odd integers cannot be the square of an integer.

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Answer:

13 units

Step-by-step explanation:

[tex]d=√((x_2-x_1)²+(y_2-y_1)²) [/tex]

[tex] \sqrt{( - 2 - ( -14)^{2} } + ( - 4 - 1) {}^{2} [/tex]

[tex] \sqrt{12 {}^{2} } + ( - 5) {}^{2} [/tex]

[tex] \sqrt{169} [/tex]

They could buy 8 small notebooks or 3 large notebooks and 3 small notebooks.

Answer: just one way to do it. You can buy 3, large books and 3 small books

Step-by-step explanation:

10x3=30

48-30=18

18 divided by 3 = 6

Answer:

f(4) = 11

Step-by-step explanation:

f(x) = 3 x -1

Let x = 4

f(4) = 3*4 -1

     = 12-1

     = 11

f (x) = 3x - 1

f (4) = 3 × 4 - 1

f (4) = 12 - 1

f (4) = 11

Hope Helpful :-;

Answer:

26000:48000

26000/48000

26/48(cancel the zeros)

13/24

fractional form=13/24

Answer:

9

Step-by-step explanation:

[tex]p(x)=4x^6+x^2+4 \\ \\ p(1)=4+1+4=9[/tex]

Answer: 1/4

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that A'D'=2 and AD=8, so the scale factor is 2/8 = 1/4.

Check the picture below.

Answer:

$3337.92

Step-by-step explanation:

$3.66 x 912 = $3337.92

Using simple interest, the amounts invested into each account are given as follows:

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

A(t) = P(1 + rt)

In which:

The amount of interest after t years is given by:

I(t) = Prt

You invest $8,000 in 3 investment accounts, hence:

[tex]P_1 + P_2 + P_3 = 8000[/tex]

From the rates of the account, we have that:

The amount invested in the glass account was double the amount invested in the metal account, hence:

[tex]P_3 = 2P_2[/tex]

The yield was a total of $280 at the end of one year, hence:

[tex]I_1 + I_2 + I_3 = 280[/tex]

[tex]0.02P_1 + 0.04P_2 + 0.05P_3 = 280[/tex]

From the first and the third equations, we have that:

[tex]P_1 + P_2 + P_3 = 8000[/tex]

[tex]P_1 + 3P_2 = 8000[/tex]

[tex]P_1 = 8000 - 3P_2[/tex]

Hence the amount of the metal investment can be found as follows:

[tex]0.02P_1 + 0.04P_2 + 0.05P_3 = 280[/tex]

[tex]0.02(8000 - 3P_2) + 0.04P_2 + 0.05(2P_2) = 280[/tex]

[tex]0.08P_2 = 120[/tex]

[tex]P_2 = \frac{120}{0.08}[/tex]

[tex]P_2 = 1500[/tex]

Hence the other investments are given as follows:

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The most appropriate choice for Independent event and multiplicative counting rule will be given by

This is known as multiplicative counting rule.

What is Independent event and multiplicative counting rule?

Event that is not dependent on any other event is called independent event.

Let A and B be two independent events.

P(A∩B) = P(A) [tex]\times[/tex] P(B)

If two independent events occur m ways and n ways respectively then both the event together will happen in mn ways.

Here,

Let first event occur [tex]n_1[/tex] ways, second event occur [tex]n_2[/tex] ways, third event occurs [tex]n_3[/tex] ways and so on

Also assuming that the events are independent

The event together can happen [tex]n_1 \times n_2 \times n_3\times...[/tex] ways

This is known as multiplicative counting rule.

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Answer:

u= 30

Step-by-step explanation:

the sum of all angles on a triangle is 180* so u add the others (120+30)

that brings it to 150 then 180-150=30*

Answer:

20

Step-by-step explanation:

The sum of the exterior angles of a polygon add to 360.  360 divided by 18 is 20.

Answer: The answer I came up with is:  $237,737

the answer is this

4 4/8.

Answer:

c because if the number next to the underlined is above 5 u round up under 4 u round down

Step-by-step explanation:

Answer: c. 76

Step-by-step explanation: 0.758 to the hundredth place is 0.76 because numbers5 and above round up.

Answer: 5/3

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.

The equation for the hourly rate is 55x = 1578.5

For double hourly rate for overtime, it is 55 x 2x= 1578.5

Given

Antonia makes X dollars for regular hours

And 2x dollars for over time

Since he works 55 hours this week he works 8 hours a day

Hence the equation is as follows

55x = 1578.5

x= $28.7

In case of double payment during overtime

He gets double amount as following equation

55 x 2x

55 x 2(28.7) =  $3157

Hence the equation to find his hourly rate is 55x = 157.85

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Answer:

Length = 15

Step-by-step explanation:

The problem can be solved by dividing the total length of the rope (90-feet) by the total pieces you want from the rope (6 pieces). This information can be used to make this equation

90 feet / 6 pieces

Which equals

90 feet / 6 pieces = 15 feet/piece        (15 feet per peice)

Hope this helps :)

The term "if and only if" makes the sentence bi-conditional. A triangle is equilateral if and only if it has three congruent sides.

A conditional statement with its opposite expressed in the form of "if and only if," collectively known as a bi-conditional statement. Bi-conditional logic is the theory behind bi-conditional assertions.

This can be compared to the conditional sentence, "if this, then that." Due to the lack of a "if and only if," it is not bi-conditional. The reversal of a conditional statement's ability to produce a bi-conditional depends on whether it is also true.

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The rate of interest is 10% and the sum is Rs 10,1000.

The interest calculated on the principal and the interest accrued over the prior period is known as compound interest. Compound interest is commonly abbreviated C.I. in mathematics.

The compound interest formula is given by

Compound Interest = Amount – Principal

Here, the amount is

[tex]A=P(1+\frac{r}{100} )^{n}[/tex]  where,

A = amount

P = principal

r = rate of interest

n = time (in years)

Given:

C.I. of a sum of money in 3 years = Rs 13310

C.I. of a sum of money in 4 years = Rs 14641

Let the principal be P and the rate of interest be r%

Then, according to the question,

For 3 years:

[tex]13310=P(1+\frac{r}{100} )^{3}[/tex]       ..... (1)

For 4 years:

[tex]14641=P(1+\frac{r}{100} )^{4}[/tex]       ..... (2)

Dividing equation (2) by (1), we obtain

[tex]\frac{14641}{13310} =(1+\frac{r}{100} )[/tex]

⇒[tex]\frac{14641-13310}{13310} =\frac{r}{100}[/tex]

⇒[tex]\frac{1331}{13310} =\frac{r}{100}[/tex]

⇒[tex]r=\frac{100}{10}[/tex]

⇒ r = 10%

Now, substituting r in equation (1),

[tex]13310=P(1+\frac{10}{100} )^{3}[/tex]

⇒[tex]13310=P(\frac{1331}{1000} )[/tex]

⇒P = Rs 10,000

Therefore, the rate of interest is 10% and the sum is Rs 10,1000.

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The number of rectangular containers will be necessary to package 6,400 candles is 143

The number of cylindrical containers will be necessary to package 6,400 candles is 157.

The container that would minimise cost is the rectangular container because it would $67 less to use the rectangular container.

The first step is to determine the total cost of packing 6400 candles using the rectangular container.

Total cost = number of containers needed x cost of one rectangular container

Number of containers needed = total number of candles to be packages / number of candles the container can hold

6400 / 45 = 142.22 = 143 rectangular containers

Total cost = $16 x 143 = $2,288

The next step is to determine the total cost of packing 6400 candles using the cylindrical container.

Total cost = number of containers needed x cost of one cylindrical container

Number of containers needed = total number of candles to be packages / number of candles the container can hold

6400 / 41 = 156.1  = 157 cylindrical containers

Total cost = $15 x 157 = $2,355

Difference in costs = $2,355 - $2,288 = $67

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