Which of the following describes the graph of the
equation 3y = 6x +12?
a line with slope 2 and y-intercept (0,4)
a line with slope 2 and y-intercept (0, 12)
a line with slope 6 and y-intercept (0,4)
a line with slope 6 and y-intercept (0, 12)

1) Number of participants whose headache remained is: 62

2) The probability of randomly selecting an individual whose headache remained is: 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933

From the table, we have the parameters as:

Number of participants that took medicine and headache went away = 120

Number of participants that took placebo and headache went away = 68

Number of participants that took and headache remained = 18

Number of participants that took placebo and headache remained = 44

1) Number of participants whose headache remained = 18 + 44 = 62

2) The probability of randomly selecting an individual whose headache remained is:

62/(62 + 120 + 68)

= 62/150

= 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is:

44/150 = 0.2933

Read more about  probability of random selection at: https://brainly.com/question/251701

#SPJ1

Answer:

67766788786686

Step-by-step explanation:

86686868686867

Answer:

-95

Step-by-step explanation:

Answer:

x -intercept is 4

y -intercept is -2

Step-by-step explanation:

SOLUTION:

(x -intercept)

-4x+8y= -16

-4x+8×0= -16

-4x+0= -16

-4x/-4 = -16/-4 (divide both sides by -4)

x=4

______________________

(y -intercept)

-4x+8y= -16

-4×0+8y= -16

0+8y= -16

8y/8 = -16/8 (divide both sides by 8)

y= -2

•| HOPE IT HELPS |•

Answer:

I think it's a 90 degree rotation

Given the formula:

where F is the cost, in dollars, of the fine is a person caught driving at a speed of ( s )miles per hour

When F = $192, we will solve the formula to find s

so,

So, the answer will be:

The person's speed was 79 miles per hour.​

Ans4863

Step-by-step explanation:

The first three terms of the arithmetic sequence are -97, -63, and -29.

The value of x = -14.

To find the value of x and the first three terms of the arithmetic sequence, we can equate the differences between consecutive terms:

The common difference (d) is the same between all consecutive terms.

So, we have:

(5x + 7) - (7x + 1) = (2x - 1) - (5x + 7)

Simplifying the equation:

5x + 7 - 7x - 1 = 2x - 1 - 5x - 7

-2x + 6 = -3x - 8

Now, let's solve for X:

-2x + 3x = -8 - 6

x = -14

Substituting the value of X back into the expressions, we can find the first three terms:

First term: 7x + 1 = 7(-14) + 1 = -97

Second term: 5x + 7 = 5(-14) + 7 = -63

Third term: 2x - 1 = 2(-14) - 1 = -29

Learn more about Arithmetic Sequence on:

https://brainly.com/question/6561461

#SPJ1

The distance between the tops of the buildings is 28.5 meters.

To find the distance between the top of the buildings, we can use the concept of similar triangles.

Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).

We can set up a proportion based on the similar triangles formed by the buildings:

a/c = b/x

Substituting the known values:

12/18 = 19/x

To find "x," we can cross-multiply and solve for "x":

12x = 18 * 19

12x = 342

x = 342/12

x = 28.5 m

Therefore, the distance between the tops of the buildings is 28.5 meters.

for such more question on distance

https://brainly.com/question/12356021

#SPJ8

Answer:

Less likely

Step-by-step explanation:

The only prime numbers on the circle are 2 and 7, meaning they take up 3/8 spaces which is less than half.

Answer:

See Below.

Step-by-step explanation:

We can write a two-column proof.

Statements:                                                Reasons:

\(\displaystyle 1)\, \angle 4\cong \angle 2\)                                                   Given

\(\displaystyle 2)\, \angle 3 \cong \angle 4\)                                                   Vertical Angles are Congruent

\(\displaystyle 3) \, \angle 1 + \angle 2 = 180\)                                          Linear Pair

\(\displaystyle 4)\, \angle 1 + \angle 4 = 180\)                                          Substitution

\(\displaystyle 5) \, \angle 1 + \angle 3 = 180\)                                          Substitution

\(\displaystyle 6) \, \text{$\angle 3$ and $\angle 1$ are supplementary}\)                  Definition of Supplementary Angles

Answer:

40.2

Step-by-step explanation:

Side 1= x

Side 2= x+20

Side 3= x+40

Side 4= x+60

Side 5= x+80

Total perimeter= 401

x+x+20+x+40+x+60+x+80= 401

Simplify it...

5x=201

x= 40.2

This is the answer= 40.2

Please award me brainliest!

Thanks!

The length of the shortest side of the pentagon would be:

40.2

Given that,

Every side of a pentagon is longer by 20 inches.

No. of sides in pentagon = 5

So,

Ist side of the pentagon \(= x\)

IInd Side of the pentagon \(= x + 20\)

IIIrd Side of the pentagon \(= x + 40\)

IVth Side of the pentagon \(= x + 60\)

Vth Side of the pentagon \(= x + 80\)

We know that,

Perimeter = Sum of all the sides

Since the perimeter is 401 inches, the side can be determined through:

\(401 = x+x+20+x+40+x+60+x+80\)

⇒ \(401 = 5x + 200\)

⇒ \(401 - 200 = 5x\)

⇒ \(201/5 = x\)

∵ \(x = 40.2\)

Thus, 40.2 is the correct answer.

Learn more about "perimeter" here:

brainly.com/question/6465134

Answer:

(−∞,∞)

Step-by-step explanation:

Since |x−5| is always positive and −2 is negative, |x−5| is always greater than −2, so the inequality is always true.

All real numbers

So, the answer is (−∞,∞)

Given data:

The area of the single plywood is a= 32 sq-feet.

The given figure of the ramp.

The expression for the hypotenuse of the triangle is,

The area of the ramp is,

The numbers of plywood sheet require are,

Thus, the numbers of plywood sheet needs are 5, so option (H) is correct.

The ratio that is equivalent to Stefanie's rate is 1 : 2

The given parameters are

Distance = 4 miles

Trips = 2

The ratio that is equivalent to Stefanie's rate is represented as

Rate = Trips/Distance

So, we have

Rate = 2 trips /4 miles

Evaluate

Rate = 1/2 trip per mile

Express as raton

Ratio = 1 : 2

Hence, the ratio that is equivalent to Stefanie's rate is 1 : 2

Read more about rate at

https://brainly.com/question/2784798

#SPJ1

By b be bb nbbgnbbghggnynyyjyytyg

Step-by-step explanation:

By hhggtgtggpyphphpglyylylhlh,hly

I need to deposit $1558.41 to have $2000 in the account in 5 years.

What is compound interest?

The interest charged on a debt or deposit is known as compound interest. It is the idea that we use the most regularly. Compound interest is calculated for a sum based on both the principal and cumulative interest.

    ∴ Compound interest = P(1 + \(\frac{r}{100*12}\))ⁿ  (∵ for monthly interest)

        P = Principal

        r = rate of interest per month

        n = number of months

Given:

r = 5% per month

n = 5 years = 5*12 = 60 months

  CI = P (1+5/(12 * 100))⁶⁰

2000 = P(1.0041)⁶⁰

2000 = P(1.2834)

      P = 1558.41

Therefore, the amount required to deposit is 1558.41 dollars to get 2000 dollars after 5 years with 5 percent interest per month.

To know more about Compound interest visit:

brainly.com/question/14295570

#SPJ1

Answer:

it is option A bro

follow me if it is helpful

Answer: 5/6

Step-by-step explanation:

1/2 / 3/5 (you have to divide so you invert the 3/5 and multiply)

1/2 x 5/3 (then you multiply the upper numbers and write them up, and multiply the lower numbers and write them down

The normal range using a compound inequality is 1.5 < x < 4

From the question, we have the following parameters that can be used in our computation:

pH values less than 4

pH values greater than 1.5

Represent the pH values with x

Using the above as a guide, we have the following:

x is less than 4

x is greater than 1.5

When represented as inequality, we have

x < 4 and x > 1.5

Combine the inequalities

1.5 < x < 4

Hence, the normal range is 1.5 < x < 4

Read more about inequalities

https://brainly.com/question/25275758

#SPJ1

Answer:

the amount of Basil Yamey's capital is £16,480.

Step-by-step explanation:

To calculate Basil Yamey's capital, we need to add up the value of his assets and subtract his liabilities.

The value of his assets is:

Van: £9,000

Market stall: £1,800

Computer: £280

Inventory of goods: £11,200

Cash in hand: £900

Money in the bank: £6,300

Total value of assets = £9,000 + £1,800 + £280 + £11,200 + £900 + £6,300 = £29,480

His liabilities are:

Amount still owed for inventory of goods: £5,000

Amount borrowed from Luca Pacioli: £8,000

Total liabilities = £5,000 + £8,000 = £13,000

Therefore, Basil Yamey's capital is:

Capital = Total value of assets - Total liabilities

Capital = £29,480 - £13,000 = £16,480

So the amount of Basil Yamey's capital is £16,480.

Answer:

Basil Yamey's capital is the total amount of money that he has invested in his business. This can be calculated as the sum of the cost of the assets that he has purchased, minus any outstanding debts, plus any cash or cash equivalents he has on hand.

The cost of the assets that Basil has purchased is:

£9,000 (van) + £1,800 (market stall) + £280 (computer) + £11,200 (inventory) = £21,280

He still owes £5,000 for the inventory, so the total cost of the assets minus the outstanding debt is:

£21,280 - £5,000 = £16,280

He borrowed £8,000, so the total amount of his capital is:

£16,280 + £8,000 = £24,280

He also has cash on hand and in the bank:

£900 (cash) + £6,300 (bank balance) = £7,200

So, Basil Yamey's total capital is £24,280 + £7,200 = £31,480.

The largest angle of the triangle is ∠C = 66°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Now , the measure of ∠A = measure of ∠B = x

And , the measure of ∠C = measure of ∠A + 9°

Substituting the values in the equation , we get

x + x + ( x + 9 ) = 180

On simplifying the equation , we get

3x + 9 = 180

Subtracting 9 on both sides of the equation , we get

3x = 171

Divide by 3 on both sides of the equation , we get

x = 57°

So , the measure of ∠A = 57°

Now , the measure of ∠C = 57 + 9 = 66°

Hence , the measure of ∠C of triangle is 66°

To learn more about triangles click :

https://brainly.com/question/16739377

#SPJ1

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

2338.82

Step-by-step explanation:

3^8 × 27.9 ÷ 78 - 8

3^8 × 279/10 × 1/78 - 8

3^8 × 93/10 × 1/26 - 8

(93 × 3^8)/260 - 8

(93 × 6561)/260 - 8

610173/260 - 8

(610173 - 2080)/260

608093/260

2338.8192 ≈ 2338.82

If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.

Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.

First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:

Social Security tax = $102,000 x 0.062 = $6,324

Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:

Social Security tax = $1,100 x 0.062 = $68.20

Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

For more such answers on Tax

https://brainly.com/question/28414951

#SPJ8

Answer:

Step-by-step explanation:

Surface area is:

Substitute x:

Answer:

10

Step-by-step explanation:

f(o) is given when x= 0 in f(x)

f(0) = 5 ( 0 + 2 ) 2 - 10

= 20 - 10

= 10

Answer:

\( \boxed{ \bold{ \huge{ \sf{f{(0) = 10}}}}}\)

Step-by-step explanation:

Given, f ( x ) = 5 ( x + 2 )² - 10

Let's find f ( 0 ) :

\( \sf{f(0) = 5( {0 + 2)}^{2} - 10}\)

Add the numbers

⇒\( \sf{f(0) = 5( {2)}^{2} - 10}\)

Evaluate the power

⇒\( \sf{f(0) = 5 \times 4 - 10}\)

Multiply the numbers

⇒\( \sf{ 20 - 10}\)

Subtract 10 from 20

⇒\( \sf{10}\)

Hope I helped !

Best regards !!

Using the points A(1,5), B(1,-4), C(-3,5), D(-3,-4) the following are matched:

Distance between points B and C = √97.

Distance between points A and B = 9.

Midpoint between points  B and C = (-1, 1/2).

Midpoint between C and D = (-3, 1/2).

Slope of the line through B and D = 0.

The distance between two points of a line is given as:

Distance = \(\sqrt{c - a)^2 + (d - b)^2}\)

We have,

A(1,5), B(1,-4), C(-3,5) and D(-3,-4).

The distance between A and B.

= \(\sqrt{(1 - 1)^2 + (-4 - 5)^2}\)

= √81

= 9

The distance between B and C.

= \(\sqrt{(-3 - 1)^2 + (5 + 4)^2}\)

= √(16 + 81)

= √97

The midpoint (x, y) between B and C.

x = (1 - 3)/2 = -1

y = (-4 + 5) / 2 = 1/2

The midpoint (x, y) between C and D.

x = (-3 -3) / 2 = -6/2 = -3

y = (5 - 4) / 2 = 1/2

The slope of the line through points B and D.

= (-4 + 4) / (-3 - 1)

= 0/ -4

= 0

Thus,

The distance between A and B is 9.

The distance between B and C is √97.

The midpoint between B and C is (-1, 1/2).

The midpoint between C and D is (-3, 1/2).

The slope of the line through B and D is 0.

Learn more about the distance of a line here:

https://brainly.com/question/14645718

#SPJ1

Answer:

the last one

is/of = x/100

12/20 = x/100

20x = 1200

x = 60% students would rather ride a bike

Step-by-step explanation:

The last pie graph best represents the given scenario. The correct option is D.

A circular statistical visual with slices illustrating numerical proportion is called a pie chart. Each slice's arc length in a pie chart corresponds to the quantity it represents.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

It is given that twelve out of twenty students say they would rather ride a bike than walk to school. The correct fraction represented on a pie graph will be calculated as below:

12/20 = x/100

20x = 1200

x = 60%

Therefore, the last pie graph best represents the given scenario. The correct option is D.

To know more about pie graphs follow

https://brainly.com/question/24461724

#SPJ2