Which of the following equations can be solved for x in one step by multiplying both sides of the equation by 2?

A researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. this is a prospective study.

Individuals are tracked over time in prospective studies, and information is gathered about them as their characteristics or circumstances change. Prospective studies include things like birth cohort studies. In retrospective research, people are sampled, and details about their past are gathered. Always after a predetermined number of incidents, the analysis takes place. The fact that individuals were enrolled and baseline data was obtained before any subjects experienced an outcome of interest identifies a study as prospective.

Given,

A researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. this is a ...

Prospective study

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Answer:

Find the slope between the points (1,2) and (9,12).

Step-by-step explanation:

If I was going to draw the line of best fit without a calculator, I would draw it including these two points.  Once I had these two points, I would find the slope using these points.

The graph of equation y=4|x-1|+3 is as shown below.

In this question, we need to graph the equation y=4|x-1|+3

We know that the parent function of given equation is z = |x|

A parent function is translated right by 1 unit then it is dilated vertically by 4 units and the resulting image is translated up by 3 units.

The graph of equation y=4|x-1|+3 is as shown below.

The vertex of equation y=4|x-1|+3 is at (1, 3)

Therefore, the graph of equation y=4|x-1|+3 is as shown below.

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The probability that Laura does not win the prize is 119 / 175.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

Given that,

Total number of raffle rickets to be sold is 350.

The number of tickets bought by Laura is 12.

Since, the probability of an event is defined as the ratio of favorable outcome to the total outcomes, the probability of winning the prize is,

P = 12 / 350

Thus, the probability of not winning the prize is,

1 - 12 / 350

= 338 / 350

= 119 / 175

Hence, the probability of not winning a prize is 119 / 175.

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Answer:

( y + 3 ) = - ( x + 6 )

Step-by-step explanation:

The Equation of Line in Point-Slope Form is

[tex](y-y_1)=m(x-x_1)\\where\ m \is \ the \ slope\ and \ (x_1 , y_1) \ is \ any \ point \ on \ the \ line[/tex]

So by Substitution by the Givens

( y - (-3) ) = -1( x - (-6) )

( y + 3 ) = - ( x + 6 )

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The time taken, to the nearest minute, by the element to decay until only 30 grams of it are left is 14 minutes.

An element with an initial mass of 200 gram, decays by 12.6% per minute. We need to find out, to the nearest minute, how long it took for the element to decay until only 30 grams were left.

In exponential decay, a quantity diminishes slowly at first and then rapidly. The exponential decay formula is used to calculate population decay (depreciation), and it may also be used to calculate half-life (the amount of time for the population to become half its size).

Let the initial mass, remaining mass, decay rate, and time taken be represented by the variables M, m, d, and t, respectively. We can form the equation given below.

m = M(1 - d)^t

30 = 200(1 - 0.126)^t

3/20 = (0.874)^t

Take the logarithm on both sides of the equation.

log(3/20) = t × log(0.874)

t = log(3/20)/log(0.874)

t = 14.087

t ≈ 14

Hence, the time taken, to the nearest minute, by the element to decay until only 30 grams of it are left is 14 minutes.

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The graph of the linear equation:

y - 4 = (2/3)*(x + 2)

Can be seen on the image at the end.

Here we have the following linear equation:

y - 4 = (2/3)*(x + 2)

Isolating y, we get:

y = (2/3)*(x + 2) + 4

To graph the line, we just need to evaluate it in two different values of x so we get two points, once we get the points, we can graph them on a coordinate axis and then connect them with a line.

If we use x = 1 we get:

y = (2/3)*(1 + 2) + 4

y = (2/3)*3 + 4

y = 2 + 4 = 6

y = 6

Then we have the point (1, 6)

if x = 4 then:

y = (2/3)*(4 + 2) + 4

y = (2/3)*6 + 4

y = 4 + 4 = 8

So we have the point (4, 8)

Then the graph of the linear equation is the one you can see below:

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The number of groups formed is 10 if we consider 5 cars in groups of 3.

Given, 5 cars in groups of 3, we can use the formula,

(5 3) = 5! / 3! × 2!

= 10

Permutation and combination are the various ways in which one can form a set that may be selected without any replacement. When the selection of a subset is where we use the permutation and when the ordering of the subset is there we use a combination.

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The inequality expression given as -x/3 < 5 has a solution of x > -15

From the question, the inequality is given as

-x/3 < 5

The above inequality can be re-written as follows

-x/3 < 5

There is no constant to add or subtract in the expression

So, we start by multiplying both sides of the expression by a constant

Multiply both sides by 3

expression

-x < 15

Divide both sides by -1

So, we have the following representation

x > -15

Hence, the solution to the expression is x > -15

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The value of x is 15

If two angles sum to 90 degrees, they are said to be complimentary angles. In other terms, a right angle is created when two complementary angles are combined (90 degrees). If the sum of angles 1 and 2 equals 90 degrees (i.e., angle 1 plus angle 2 = 90°), then the angles are complementary and are referred to as one another's complements.

∠1 and ∠2 are complementary angles i.e the sum of ∠1 and ∠2 is 90° .

Thus

∠1 + ∠2 = 90°

x° + (3x+30)° = 90°

x + 3x + 30 = 90

4x = 90-30

4x = 60

x = 15

Therefore the value of x is 15.

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The selling price of the the purse in a department store is cents.

For the given question-

A purse in such a department store costs $12.50 at wholesale.

The purse will be 140% more expensive at the store.

Then,

140% of 12.50 = 140 x 12.50 / 100

140% of 12.50 = 17.5

Selling price  = percent increase + cost price

Selling price  = 17.5 + 12.5

Selling price  = $30.0

Selling price  = 3000 cents

Thus, the selling price of the the purse in a department store is cents.

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Javieratta worked for a total of 32 hours in the week of June to earn an amount of 304 dollar.

Javieretta earns $9.50 each hours she works at camp clap happy.

She earned $304 in week of june and $247 during a week in july.

Let us assume that she works X hours.

So, using unitary method, we can write,

X times the amount she earns in one hour = Earning in the week of june.

X(9.50) = 304

X = 304/9.50

X = 32 hours.

So, she worked for a total of 32 hours in the camp clap happy summer vacation.

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The salary of Kayden after 4 years will be $ 221,952.00

The annual salary is $48000

Salary rise is $4500

The rate of the this salary can be found out by [tex]\frac{48,000- 4500}{48000}[/tex]

= [tex]\frac{43,500}{48,000}[/tex] × 100

= 90.6 %

The time interval is 4 years

thus the prinicipal amount is given as $48000.

thus simple interest is P × R × T/ 100

which when calculated will give us

simple interest = $221,952.00

$221,952.00 is the total amount accrued from simple interest on a principal of $48,000.00 at a rate of 90.6% per year for 4 years. This includes both principal and interest.

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From the logistic population differential equation for approximate the growth of the world population , which is given here as [tex]P = L/1+ e^{-k(x-x_{0} )[/tex]

The general form of the logistic population equation is given as [tex]dP/dt = kP(1- P/L)[/tex]. While k is the relative growth rate, L is the carrying capacity.An ordinary differential equation with a logistic function as the solution is known as a logistic differential equation. Standard exponential functions do not account for the limitations that prevent infinite growth, but logistic functions correct this oversight. This is how bounded growth is represented by logistic functions. These contexts include machine learning, chess ratings, medical therapy (e.g., modelling tumour growth), economics, and even language adoption research.

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The probability that a computer will not crash in a period of 4 months is 0.632.There is a 75% chance that the computer will not crash in a period of 4 months.

To solve this problem stepwise, first calculate the probability that the computer will crash in a given month. This can be done by using the Poisson distribution. The probability that the computer will crash in a given month is 0.0333.

Next, calculate the probability that the computer will not crash in a given month. This is simply 1 - 0.0333, or 0.9667.

Now, to calculate the probability that the computer will not crash in a period of 4 months, simply take the probability of not crashing in a given month and raise it to the 4th power. This gives us a probability of 0.632.

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Answer:

64/125 > 150/512

Step-by-step explanation:

4/5 *4/5 *4/5 = 64/125 (also equals 0.512)

5/8 * 6/8 * 5/8 = 150/512 (also equals 0.293)

Therefore: 0.512 > 0.293

Answer:

(f ￮ g)(0) = 3

Step-by-step explanation:

evaluate g(0) then substitute the value obtained into f(x)

g(0) means what is the value of g(x) when x = 0

from the graph g(0) = 2 , then

f(2) , that is what is the value of f(x) when x = 2

from the graph  f(2) = 3

then

(f ￮ g)(0) = 3

The equation would represents the graph is y = 20000 + 1750x and the graph has been plotted

From the table

The investment in 1 year = $20000

The investment in 2 year = $21750

The investment in 3 year = $23500

The investment in 4 year = $25250

The investment in 5 year = $27000

Then the equation will be

y = 20000 + 1750x

Where y is the investment in dollars

x is the number of years

Draw the graph as number of years in x axis and the amount of investment in y axis

Hence, the equation would represents the graph is y = 20000 + 1750x and the graph has been plotted

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Answer: [tex]y=-\frac{1}{2}x+6[/tex]

Step-by-step explanation:

The slope of the line segment is [tex]\frac{-1-7}{4-8}=2[/tex].

The midpoint of the line segment is [tex]\left(\frac{4+8}{2}, \frac{-1+7}{2} \right)=(6, 3)[/tex].

Thus, the equation is:

[tex]y-3=-\frac{1}{2}(x-6)\\\\y-3=-\frac{1}{2}x+3\\\\y=-\frac{1}{2}x+6[/tex]

Answer: 31

Step-by-step explanation:

the prime factorization of 961 is 31×31  the value of the square root of 961 is 31.

Hope this helps! Have a good day! :)

The height of the trees in the year 2010, given their average rate of growth will be 21 foot

The trees are said to grow at a rate of 3/4 foot per year. In decimals this is:

= 3 / 4

= 0.75

The number of years between 1990 and 2010 is:

= 2010 - 1990

= 20 years

The height of the trees in 2010 would be:

= Current height x ( Rate of growth x number of years)

= 6 x (0.75 x 20)

= 21 foot

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The amount that Charlotte earn per hour on the weekends than she earns during the week is: C. $2.30.

Number of dollars earn per hour during the week = x

Number of dollars earn per hour on the weekend =y

Formulate an equation

13x + 14y = 250.90  Equation 1

15x + 8y = 204.70 Equation 2

Solving  for x and y by multiply equation 1  by -8 and equation 2 by 14 -104x - 112y = -2007.20

210x +112y = 2865.80

106x             = 858.60

Divide both sides by 106x

x = 858.60/106

x =  $8.10

Substitute x into eq 1 so as to solve for y

13(8.10) + 14y = 250.90

105.30 + 14y = 250.90

Subtract 105.30 from both sides

14y = 145.60

Divide both side by 14y

y = 145.60 /14

y  = 10.40

Hence,

Additional earning per hour = y-x

Additional earning per hour = $10.40 - $8.10

Additional earning per hour=$2.30 per hours

Therefore the correct option is C.

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Answer:

 3x + y - 4z = -222x + 3y + 4z = 32x - y + 2z = 16 Write and number each equation. Eq 1 3x+y-4z = 16. Eq 2 -222x+3y+4z = 16. Eq 3 32x-y+2z = 16 

Step-by-step explanation:

Hope it helps you buddy(:

Answer: 16

You already got the answer- But whatever.

The values of [x], [y] and [z] are 2, 0 and 7.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written to express proportional relationship as -

y = kx  {k is constant}

We have the following system of equation -

3x+y-4z=-22

2x+3y+4z=32

x-y+2z=16

We can write -

x - y + 2z = 16

x = 16 + y - 2z

So, we can write 3x + y - 4z = -22 as -

3(16 + y - 2z) + y - 4z = -22      ...eq[1]

and we can write 2x + 3y + 4z = 32 as -

2(16 + y - 2z) + 3y + 4z = 32      ...eq[2]

Plot eq[1] and eq[2], and find [y] and [z]. Refer to graph.

We get y = 0 and z = 7

So -

x = 16 + 0 - 14

x = 2

Therefore, the values of [x], [y] and [z] are 2, 0 and 7.

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Step-by-step explanation:

the flight path of a rocket or a thrown object is a parabola as described by the function.

h(t) = -16t² + 40t + 7

the negative sign of the prime coefficient (-16) tells us that the parabola opens downwards, and that the vertex as the extreme point of the parabola is a maximum.

we get the extreme point of a curve by finding the zero solution of the first derivative of the function.

and the extreme value itself by using that value in the original equation and calculate the result.

h'(t) = -32t + 40

0 = -32t + 40

32t = 40

t = 40/32 = 5/4 = 1.25 seconds

h(5/4) = -16×(5/4)² + 40×5/4 + 7 =

= -16×25/16 + 10×5 + 7 =

= -25 + 50 + 7 = 32 ft

the rocket will reach its maximum height of 32 ft after 1.25 seconds.

Answer:

Step-by-step explanation:

Answer 10.5

The number of Male voters =14700, The number of female voters =14100 and the number of voters to "Others" category=1200

How do you calculate a percentage?

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. It's frequently represented by the sign "%" or just "percent" or "pct." For instance, the decimal 0.35, or the fraction, represents 35%.

Given : Total  votes = 300000

males = 49%
females = 47%
Others = 4%

Number of votes for males =   [tex]\frac{49}{100} *300000[/tex] = 14700
Number of votes for females = [tex]\frac{47}{100} *300000[/tex] = 14100

Number of votes for others = [tex]\frac{4}{100} *300000\\[/tex] = 1200

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Step-by-step explanation:

remember, the circumference of a circle is

2×pi×r

and that is for the full 360° of a circle.

how long will the arc length of 1° be ?

well,

2×pi×r / 360

and how long will the arc length of 78° be ?

well,

78 × 1° = 2×pi×r × 78/360

you see ? that is the whole trick ...

now we only need to enter the value for r (radius).

and that is GH = 9 units.

so, the length of the arc GJ is

2×pi×9 × 78/360 = 2×pi × 78/40 = pi × 78/20 =

= 12.25221135... ≈ 12.25 units

The estimate for the number of cars that are red will be 9450000.

From the information, when Ben sat outside his school in Cambridge and made a note of the colour of the first 100 cars that passed, he found out that 27 of them were red.

Based on the above, the ratio of red cars to total cars is 27:100.

Therefore, if thee are 35 million cars, the red cars will be:

= Ratio of red cars × Total cars

= 27/100 × 3500000

= 9450000

The number of red cards is 9450000.

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Using the concept of percentage we get 16-inch pizza is 43.75% larger than a 12-inch pizza.

Percentage means out of hundred. A number that is expressed as a fraction of a hundred is called a percentage. Percentage change = Change in the value / Initial value.

Area of circle = π R²,

Where R is the radius of circle.

Given that size of a pizza is measured by its diameter and surface area.

Diameter of the first pizza = 16 inch

So its radius = 8 inch

Hence area = π×8²

= 64π

And the diameter of the other pizza = 12 inch

So, its radius = 6 inch

Hence its area = π×6²

= 36π

Now the difference in areas of Both the pizza = 64π - 36π

= 28π

Now percentage difference in areas of both pizzas = 28π×100)/64π%

= 2800/64

=43.75%

Hence, 16-inch pizza is 43.75% larger than a 12-inch pizza.

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