factorise the following by grouping pairs (1) a2_9a+3a_27​

Answer:

  a) rise 5, run 5, slope 1

  b) rise 10, run 5, slope 2

Step-by-step explanation:

The rise is the vertical difference between the points. It is the length of the vertical side of the triangle you have drawn. You can determine that length by counting grid squares or by finding the difference of the y-coordinates of the points.

The run is the horizontal difference between the points. It is the length of the horizontal side of the triangle you have drawn. You can determine that length by counting grid squares or by finding the difference of the x-coordinates of the points.

rise = 5; run = 5. (counting grid squares)

slope = rise/run = 5/5 = 1

__

rise = 10; run = 5. (taking coordinate differences: 5-(-5) = 10; 4-(-1) = 5)

slope = rise/run = 10/5 = 2

In the medical industry, new drugs undergo thorough tests before they can be approved for use. One aspect of drug testing is the assessment of possible side effects on patients.

The medical company that conducted the tests analyzed data and used tables to show the relative frequency that a study participant experienced side effects. This approach provided the company with insights on the occurrence of side effects.The table below shows the relative frequency of a side effect that a study participant experienced.

Side Effect Number of Participants who experienced the side effect
Nausea 45
Headache 33
Dizziness 21
Vomiting 12
Fever 8
Fatigue 5
Total 124
Relative Frequency = Number of participants who experienced a side effect / Total number of participants in the study
Using this formula, we can determine the relative frequency of each side effect.

For example, the relative frequency of nausea is 45/124, which equals 0.3637 or 36.37%. This shows that out of the 124 study participants, 45 experienced nausea, which was the most frequent side effect.

The relative frequency of each of the other side effects was 0.2661 (26.61%) for headaches, 0.1693 (16.93%) for dizziness, 0.0968 (9.68%) for vomiting, 0.0645 (6.45%) for fever, and 0.0403 (4.03%) for fatigue.
The company can use these findings to decide whether to continue with the development of the drug.

For instance, the high occurrence of nausea may mean that the drug needs further development or modification before it is approved for use.

On the other hand, a lower frequency of side effects may mean that the drug can proceed to the next stage of testing.

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O sin(0.0005) ≈ 0.0005. The line tangent to the graph of f(x) = sin x at (0,0) is y = x.

The line y = x touches the graph of f(x) = sin x at exactly one point, (0,0). This means that the point (0,0) is on the line y = x and the slope of the line y = x is equal to the derivative of the function f(x) = sin x evaluated at x = 0. The slope of the line y = x is 1, so the derivative of f(x) = sin x evaluated at x = 0 is 1.

The line y = x is the best straight line approximation to the graph of f(x) = sin x for x near 0. This is because the first derivative of sin x evaluated at x = 0 is 1, which is the same as the slope of the line y = x. Therefore, the tangent line to the graph of f(x) = sin x at (0,0) is y = x.

Finally, O sin(0.0005) ≈ 0.0005. This is because sin x is approximately equal to x for small values of x. When x = 0.0005, sin x is approximately equal to 0.0005. Therefore, O sin(0.0005) ≈ 0.0005.

In summary, the line tangent to the graph of f(x) = sin x at (0,0) is y = x. The line y = x touches the graph of f(x) = sin x at exactly one point, (0,0). The line y = x is the best straight line approximation to the graph of f(x) = sin x for x near 0. O sin(0.0005) ≈ 0.0005.

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\(\frac{1}{2} | 261-161|\)The area of the quadrilateral whose vertices are A(1,1)B(7,−3),C(12,2) and D(7,21) is 49 square units

To find the area of the quadrilateral with vertices A(1, 1), B(7, -3), C(12, 2), and D(7, 21), you can follow these steps:

1. Divide the quadrilateral into two triangles: Triangle 1 (A, B, C) and Triangle 2 (A, C, D).

2. Calculate the area of each triangle using the   determinant method for the coordinates.

For Triangle 1 (A, B, C):
Area =   \(\frac{1}{2} | (1(-3)+7(2)+12(1) )- (-3(2)+1(12)+7(1)|\)
Area =\(\frac{1}{2} | (-3+14+12) - (-6+112+7)|\)
Area = \(\frac{1}{2} | (23-13)|\)
Area =\(\frac{1}{2} (10)\)

Area = 5 square units

For Triangle 2 (A, C, D):
Area =  \(\frac{1}{2} | (1(2)+12(21)+7(1))- (2(1)+21(7)+1(12)|\)
Area = \(\frac{1}{2} | (2+252+7)- (2+147+12)|\)
Area = \(\frac{1}{2} | 261-161|\)
Area = \(\frac{1}{2} (100)\)

Area = 44 square units

3. Add the areas of the two triangles to get the area of the quadrilateral:

Area of quadrilateral = Area of Triangle 1 + Area of Triangle 2 = 5 + 44 = 49 square units.

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Answer:

32.24

Step-by-step explanation:

Answer:

2/5 is bigger

Step-by-step explanation:

if you have a pie with 8 slices and you eat 2, and have a pie containing 5 slices and eat 2 which empty space will be larger? think of it that way and i hope that helps

Step-by-step explanation:

the 1st shop=196-(17.5/100×196)

=196-34.3

=161.7+196

=357.7

the 2nd shop=196-(22.5/100×196)

=196-44.1

=151.9+196

=347.9

so the difference between two shop is

357.7-347.9=9.8

Answer:

the story of my life

Step-by-step explanation:

good luck <3

Lucia's piece of wood is 81/8 inches long, or 10 1/8 inches.

To determine the length of Lucia's piece of wood, add 1 5/8 to Carman's length.

We can begin by converting Carman's length to an incorrect fraction:

8 1/2 = (8 × 2 + 1) / 2 = 17/2

Then we multiply by 1 5/8:

1 5/8 = (1 × 8 + 5) / 8 = 13/8

Lucia's piece of wood is thus:

17/2 + 13/8

We must find a common denominator between the numbers 2 and 8, which is 8:

17/2 + 13/8 = 68/8 + 13/8 = 81/8

Lucia's piece of wood is thus 81/8 inches long, or 10 1/8 inches.

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equation of line

y=mx+b

If m=-3/2

we have

From points (2,3), we find b

Therefore

As you can see we have a trapezoid inside a rectangle. The blue section is equivalent to the area of the rectangle that it's not covered by the trapezoid. Then the area of this section is equal to the area of the rectangle less the area of the trapezoid. Then we just need to find the areas of both figures. Remember than the area of a rectangle is given by the product between its height and its base:

Trapezoids are figures with two parallel sides known as bases. The area of a trapezoid is given by product between the sum of its bases and its height divided by 2:

Then the area of the rectangle in the picture is given by:

So it's 80 cm².

The area of the trapezoid considering that its base has the same length as the rectangle is:

So its area is of 21 cm².

Finally the area of the blue section is given by:

Then the answer is 59cm².

Answer:

45

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

1. Subtract 2 from both sides.

5y=22 -2

This equals 5y=20

2.Divide by 5 on each side. That gets 4.

Hope it helped :)

Step-by-step explanation:

3x²+4=31

3x²=31-4

3x²=27

x²=27÷3

x²=9

x=±3

Answer:

I hope you got it. I tried my best to give answer

a. The sampling method that I would use for the given scenario is stratified random sampling.

b. The sampling method that I would use for the given scenario is systematic sampling.

Stratified random sampling is the most effective way to get accurate results in this situation. The university wants to conduct a mail survey of its alumni to collect information about their current employment status to justify charging a higher tuition rate than other universities. Stratified random sampling divides the population into strata based on certain characteristics.

In this case, strata would be the alumni that have different degrees from the university. The information collected through this method will be more representative of the population than simple random sampling. It ensures that each stratum is represented accurately in the sample. It also minimizes the variability within each stratum. It is an effective way of ensuring that each stratum is properly represented.  

Systematic sampling involves selecting every kth element from a list of the population. In this situation, the Environmental Protection Agency (EPA) wants to inspect a sample of 1000 containers from the 40,000 containers known to be in landfills to determine if leakage from the containers has occurred. As the exact location of the containers is no longer known, systematic sampling can be used.

EPA can select every 40th container from the list of the population, as 40,000/1000 = 40. In this way, they will have a random sample of 1000 containers from the 40,000 containers. This sampling method is less time-consuming and more cost-effective than other sampling methods. It also ensures the sample is representative of the entire population.

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i believe the answer is  B.

The correct answer is D. $2.75 / $3.24

To determine how much you should expect to pay for gas in Philadelphia versus Cleveland, we need to compare the transportation expenses in both cities. Based on the given data, the transportation expenses are as follows:

Philadelphia: $117

Cleveland: $106

To calculate the expected gas prices, we need to consider the transportation expenses relative to the national average. The formula to find the expected gas price is:

Expected Gas Price = National Average * (Transportation Expense / National Average)

National Average for gas = $2.59

For Philadelphia:

Expected Gas Price in Philadelphia = $2.59 * ($117 / 92) ≈ $3.30

For Cleveland:

Expected Gas Price in Cleveland = $2.59 * ($106 / 78) ≈ $3.51

Comparing the expected gas prices, we find that:

A. $3.03 / $2.75: This option does not match the expected gas prices in Philadelphia and Cleveland.

B. $1.95 / $2.59: This option does not match the expected gas prices in Philadelphia and Cleveland.

C. $2.34 / $2.75: This option does not match the expected gas prices in Philadelphia and Cleveland.

D. $2.75 / $3.24: This option matches the expected gas prices in Philadelphia and Cleveland.

Therefore, the correct answer is:

D. $2.75 / $3.24

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Answer:

1/6

Multiply 5/12 x 2/5 then cross cancel 12 and 2 and get 6 then cross cancel 5 and 5 to get 1.

Final answer:

1/6

The expressions given in option A and option C on solving will have same value 3/2 or 1.5.

Numeric values can be obtained through the evaluation of numeric expressions, which consist of a mixture of numeric components including variables, numbers or functions, and operators. A blend of arrays and mathematical operators can be present within an expression to derive a numeric solution.

Now solving numerical expressions in the problem (refer to image attached)

A. \(\frac{1}{6} +(\frac{5}{6}+\frac{3}{6} ) = \frac{1+5+3}{6} = \frac{9}{6} =\frac{3}{2} =1.5\)

B. \(\frac{1}{3}+ \frac{5}{3}+ \frac{2}{3} =\frac{1+5+2}{3} =\frac{9}{3} =3\)

C. \(\frac{3}{5} +(\frac{1}{2} +\frac{2}{5} )=\frac{15}{10} =\frac{3}{2} =1.5\)

D. \(2+\frac{1}{2} =\frac{4+1}{2} =\frac{5}{2} =2.5\)

Hence, expressions in option A and option C have same values

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Answer:

7.071

Step-by-step explanation:

Hope this helps (:

Answer:

C

Step-by-step explanation:

(-2x+9-3x-4)

-2x-3x+9-4

-5x+5

Answer:

Q1 = 61

Q3 = 63

Step-by-step explanation:

From the plot attached :

Data obtained is :

Temperature frequency

59 0

60 2

61 3

62 3

63 4

64 2

65 1

Frequency Total 15

Data in raw format :

60,60,61,61,61,62,62,62,63,63,63,63,64,64,65

The first quartile :

Q1 = 1/4(n+1)th term

n = 15

Q1 = 1/4(15+1)th term

Q1 = 1/4 * 16th

Q1 = 4th term

Q1 = 61

Third quartile (Q3):

Q3 = 3/4(n+1)th term

n = 15

Q3 = 3/4(15+1)th term

Q3 = 3/4 * 16th

Q3 = (48/4)th term

Q3 = 12th term

Q3 = 63

Answer:

Q1 is 61 and Q3=63

The approximate distance between Padma and the bear is 21.2 ft, which corresponds to option A.

The approximate distance between Padma and the bear, we can use trigonometry. Since James and Padma are on opposite sides of the 100-ft-wide canyon,

we can form two right triangles with the bear's position as one of the vertices.

Step 1: Determine the horizontal distance from James to the bear.

Since the angle of depression from James to the bear is 45 degrees, the horizontal distance (x) and vertical distance (y) are equal due to the properties of a 45-45-90 right triangle. Therefore, x = y. Since the canyon is 100 ft wide, x + y = 100 ft. We can solve for x:

x + x = 100

2x = 100

x = 50 ft

Step 2: Determine the vertical distance from James to the bear.
Since x = y in the 45-45-90 right triangle, the vertical distance from James to the bear is also 50 ft.

Step 3: Determine the horizontal distance from Padma to the bear.
We can now use Padma's angle of depression, 65 degrees, to find the horizontal distance (p) from Padma to the bear. Using the tangent function:

tan(65) = vertical distance / horizontal distance

tan(65) = 50 ft / p

Solving for p:

p = 50 ft / tan(65) ≈ 21.2 ft

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Answer:

Solve the equation for  x  by finding  a ,  b , and  c

of the quadratic then applying the quadratic formula.

x = − 2  Double roots

Answer:

The answer is 180.20

Have a great day!

Answer:

to make a number a percentage you have to multiply by 100%.Mmmh so you take the 6/4 and multiply it by 100%.Which will give you 150%. The percentage is higher than 100% because in the fraction 6/4 the numerator is higher than the denominator

Answer:

The answers are below.

Step-by-step explanation:

The answer to the first question....Second Option (-4<x<infinity sign)

The answer to your second question....is 7

Hope this helped.

Have a great day/week.

Answer:

f(n)= f(1)+d(n-1)

Step-by-step explanation:

the aerithmetric explict formula is the one above, but im  not sure what the question is asking, your difference is 4 btw    

3)  since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.

(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:

Total payment A = Monthly installment * Number of installments

              = $375 * 36

              = $13,500

Therefore, Adrian paid a total of $13,500 over the course of 36 months.

(2) In the simple interest formula I = Prt, the letters used represent the following variables:

I: Interest (the amount of interest paid)

P: Principal (the initial amount, or in this case, the car worth)

r: Rate of interest (expressed as a decimal)

t: Time (in years)

(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:

r = (I / Pt) * 100

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