3 consecutive terms of an arithmetic series are (7a-1), (5a + 3) and (4a+1) respectively. Find the value of a. Show all your working ​

Answer:

Step-by-step explanation:

3

two fingers plus one finger is three

Answer: 3

Step-by-step explanation:

If I had 2 apples, and then put 1 more apple along with those 2 apples, then I would count 3 apples. 2+1=3

Answer:

\(y=\frac{1}{2}x\)

Step-by-step explanation:

Slope-intercept form: y = mx + b

Slope formula: \(\frac{y2-y1}{x2-x1}\)

Given points: (2, 1), (-4, -2)

(2, 1) = (x1, y1)

(-4, -2) = (x2, y2)

To write the equation in slope-intercept form we need to find the slope(m) and the y-intercept(b) of the equation.

First, let's find the slope. To do this, input the given points into the formula used to find slope:

\(\frac{-2-1}{-4-2}\)

Simplify:

-2 - 1 = -3

-4 - 2 = -6

\(\frac{-3}{-6} =\frac{1}{2}\)

The slope is \(\frac{1}{2}\). We can input the slope and one of the given points (in this example I'll use point (2, 1)) into the equation to find b:

\(1= \frac{1}{2}(2)+b\)

1 = 1 + b

0 = b

The y-intercept is 0. Now that we know the slope and the y-intercept, we can write the equation:

\(y = \frac{1}{2}x+0\)

\(y=\frac{1}{2}x\)

9514 1404 393

Answer:

  A  7/25

Step-by-step explanation:

The cosine of an angle is equal to the sine of its complement. In a right triangle, angle A is the complement of angle B. So, ...

  cos(A) = sin(B)

  cos(A) = 7/25

Answer:

x = every time he goes to target.

y = the amount he has left.

25 - 5x = y

After 3 trips, he will have 10 dollars left.

Step-by-step explanation:

25 - 5(3) = y

25 - 15 = 10

Answer:

10

Step-by-step explanation:

25 - 5, 20 - 5, 15 - 5 = 10

Answer:

Step-by-step explanation:

V=(1/3)hπr^2

<=> 4487 = 1/3x21πxr^2

<=> r^2 = 641/π

<=> r = squrt( 641/π)

A minimum sample size of 62 is needed to be 95% confident that the sample mean is within 2 words of the true population mean, assuming a normal distribution of the number of words per sentence in the book and a population standard deviation of 4 words.

To determine the minimum sample size needed to be 95% confident that the sample mean is within 2 words of the true population mean, we can use the formula for the margin of error:

Margin of error = z * (standard deviation / sqrt(n))

Where z is the z-score for the desired confidence level, standard deviation is the population standard deviation (given as 4 words), and n is the sample size.

We want the margin of error to be no more than 2 words, so we can set up the inequality:

z * (4 / √n) ≤ 2

To find the value of z for 95% confidence level, we can use a z-table or calculator and find that z = 1.96.

Substituting this value into the inequality and solving for n, we get:

1.96 * (4 / √n) ≤ 2

Simplifying and solving for n, we get:

n >= 61.05

Since we can't have a fractional sample size, we can round up to the nearest whole number and conclude that a minimum sample size of 62 is needed to be 95% confident that the sample mean is within 2 words of the true population mean.

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Answer:

Step-by-step explanation:

22 +2.50x = 11 +3.75x

11+ 2.50x = 3.75x

11+2.5x=3.75x

2.5x+11=3.75x

2.5x+11−3.75x=3.75x−3.75x

−1.25x+11=0

−1.25x+11−11=0−11

−1.25x=−11

−1.25x/1.25 = 11/1.25

x=8.8

i solved in the picture..

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It takes approximately 19.26 hours for the size of the sample to double.

N(t) = N0 * \(e^(rt)\)

2N0 = N0 * \(e^(rt)\)

Dividing both sides by N0, we get:

2 = \(e^(rt)\)

Taking the natural logarithm of both sides, we get:

ln(2) = rt

Solving for t, we get:

t = ln(2) / r

Substituting r = 0.036 (since the growth rate parameter is 3.6% per hour), we get:

t =  \(\frac{ln(2)}{0.036}\)

t ≈ 19.26 hours

A logarithm is a mathematical function that represents the relationship between two quantities that are related by a constant ratio. In other words, it is the inverse operation of exponentiation. The logarithm of a number is the power to which another fixed number (called the base) must be raised to produce that number. For example, if the base is 10, the logarithm of 100 is 2 because 10 raised to the power of 2 equals 100.

Logarithms are useful in many areas of mathematics, science, and engineering because they allow for the simplification of complex mathematical expressions and the comparison of quantities that vary over a wide range of magnitudes. They are also used in the study of growth and decay processes, such as population growth and radioactive decay.

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Let x be the number of cans of food, since we need more than or equal to 2000 cans, we can write

where 668 is the number of cans that they have been collected.

Now, we must find x. If we move 668 to the right hand side as -668, we get

which gives

this means that they must collect more than or equalt to 1332 cans of food.

Answer:

Step-by-step explanation:

SAS side angle side

SSS side side side

AAA angle angle angle

Answer:

69.03 is 18% of 383.50

Answer:

you paid $350

Step-by-step explanation:

Okay so if we know that 383.50 is 18% more, we can say that:

118%=383.50,

then divide 383.50, it's not the most efficient way, but it works.

So, 383.50/118= 3.25

So, if 3.25 is one percent, just multiply by hundred, mode the decimal places and get $325  

You should survey at least 97 families in order to estimate the mean family income in the rural area of Florida with a margin of error of $1,000 and an expected standard deviation of $5,000, assuming a 95% confidence level.

To determine the sample size required for the survey, we need to consider the desired margin of error, the expected standard deviation, and the desired level of confidence. In this case, you mentioned that the margin of error should be within $1,000 and the expected standard deviation is $5,000. However, you didn't mention the desired level of confidence.

Typically, a 95% confidence level is used, which means we want to be 95% confident that the true mean family income falls within the margin of error. Based on this assumption, we can calculate the required sample size using the following formula:

n = (Z^2 * σ^2) / E^2

n = required sample size

Z = Z-score corresponding to the desired confidence level

σ = standard deviation

E = margin of error

For a 95% confidence level, the Z-score is approximately 1.96 (assuming a normal distribution).

Substituting the values into the formula, we get:

n = (1.96^2 * 5000^2) / 1000^2

n ≈ (3.8416 * 25,000,000) / 1,000,000

n ≈ 96,040,000 / 1,000,000

n ≈ 96.04

Since you cannot have a fraction of a family, you would need to round up the sample size to the nearest whole number. Therefore, you should survey at least 97 families and an expected standard deviation of $5,000, assuming a 95% confidence level.

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Answer:

Point-slope form:

y-5= -1/3 times (x+9)

This is only for the first part

Answer:

Step-by-step explanation:

the last choice .. about 3 hours spent on math

The values of the sides are;

41. x = 18√3. Option D

42. x = 6√3. Option A

Using the different trigonometric identities, we have;

41. Using the tangent identity, we have;

tan 60 = 9√2/y

cross multiply the values

y =9√2 ×√3

y = 9√6

Using the sine identity;

sin 45 = y/x

1/√2 = 9√6/x

cross multiply the values, we have;

x = 9√2 ×√3 ×√2

x = 18√3

42. Using the cosine identity

cos 60 = 3√3 /x

cross multiply, we have;

x = 6√3

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Answer:

Each crust is 1.2 inches

Step-by-step explanation:

12/10 is 1.2

Answer:

Each crust is 1.2 inches.

Step-by-step explanation:

12 ÷ 10 = 1.2

Hope this Helped! HAVE A GOOD DAY!!!!!!!!!!

See attachment for math work and answer.

Answer:

x = -2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = 3x - 1

f(x) = -7

Step 2: Solve for x

One pathology associated with special cell types is multiple sclerosis (MS), a chronic neurological disorder affecting the central nervous system. MS involves damage to the protective covering of nerve fibers, known as myelin, which disrupts the communication between the brain and the rest of the body.

This can lead to a wide range of symptoms, including fatigue, muscle weakness, coordination problems, and cognitive impairment. I have had personal experience with a family member who was diagnosed with MS. Witnessing their journey with this disease has highlighted the challenges they face on a daily basis. The unpredictable nature of MS, with periods of relapse and remission, has made it difficult for them to plan their activities and maintain a consistent quality of life.

They have undergone various treatments, including medication and physical therapy, to manage symptoms and slow down the progression of the disease. Seeing their resilience and determination in adapting to the limitations imposed by MS has inspired me and reinforced the importance of ongoing research and support for individuals affected by this condition.

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Answer:

180

Step-by-step explanation:

A 3-digit number cannot start with 0, so the leftmost digit is a choice of 6 digits out of the 7. The middle digit can be chosen from all 7 digits minus the one already used, so there are 6 choices. The right digit can be chosen from 5.

6 × 6 × 5 = .180

The number of three-digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 is 180.

This can be calculated by finding the number of element availabe at first place which is 6 excluding 0 than for second position 6 as first number is excluded and 0 is added and for the last positon the number of possibe combination is 5 as 2 digits are already used.

The final answer is 6*6*5 = 180

so count of 3 digit numbers that can be formed by the given set of digit without repetetion allowed is  180

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Answer:

A= 10x^2 + 7/ 2 xy − 3y^2

Step-by-step explanation:

( 1/ 2) (5x−2y))(4x+3y)

= ( 1/ 2(5x−2y)) (4x+3y)

= ( 1/ 2 (5x−2y)) (4x) + ( 1/ 2 (5x−2y)) (3y)

= 10x^2 − 4xy +  15/ 2 xy − 3y^2

= 10x^2 + 7/ 2 xy − 3y^2

Answer:

1 + 1 = 2

Step-by-step explanation:

:)

Answer:

1 + 1 = 2

Hope it Helps

Answer:

261 ft²

Step-by-step explanation:

We have a rectangle, a square and a triangle.

We already know the area of the square is 6²=36ft²

The rectangle would be (16-6)×19=190ft²

Now finding the area of the triangle is quite tricky as we don't have a height, but we do know its sides

We know that one leg has to be 10, and the other is 26-19=7. Using the pythagorean theorem we get the hypothenuse=12.21

Now we can use Heron's Formula.

Using s=a+b+c/2 we get s=14.605

Now we can use the formula:

\(area = \sqrt{s(s - a)(s - b)(s - c)} \)

Using this formula we get that the area of the triangle=35.

Add all three areas together: 35+36+190=261ft²

Answer: 261^2

Step-by-step explanation:

We have a rectangle, a square and a triangle.

We already know the area of the square is 6²=36ft²

The rectangle would be (16-6)×19=190ft²

Now finding the area of the triangle is quite tricky as we don't have a height, but we do know its sides

We know that one leg has to be 10, and the other is 26-19=7. Using the pythagorean theorem we get the hypothenuse=12.21

Now we can use Heron's Formula.

Using s=a+b+c/2 we get s=14.605

The correct equation is (a) because π/1 = C2/r2, \(C_2= 2\pi r\)

The complete question is added as an attachment

The given parameters are:

d1 = 1

d2 = 2r

The circumferences of the circles are calculated as:

C = πd

This gives

C1 = π * 1 = π

C2 = π * 2r = 2πr

So, we have:

C1 = π

C2 = 2πr

and

d1 = 1

d2 = 2r

Divide both equations

\(\frac{C_2}{d_1} = \frac{C_2}{d_2}\)

\(\frac{\pi}{1} = \frac{2\pi r}{2r}\)

This gives

\(\frac{\pi}{1} = \frac{C_2}{2r}\)

Hence, the correct equation is (a) because π/1 = C2/r2, \(C_2= 2\pi r\)

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Answer:

Its A

Step-by-step explanation:

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

\(4\frac{6}{12}\) hours play speed, what is the total running time of the video.

What does "speed" mean in mathematics?

Running time of cassettes

at standard speed = 1 hr

at standard speed = 4 hr

at standard speed = 4 hr

given the 1/4 part of tape is recorded at standard speed, 1/3 at long-play speed , 5/12 at super long-play speed,

so the running time of standard speed = 1/4 * 1 = 1/4

at long play speed

1/3 * 4 = 4/3 hours

and at super long-play speed,

5/12 * 7 = 35/12 hours

so, the total running time of the video

1/4 + 4/3 + 35/12 = 54/12 = \(4\frac{6}{12}\) hours

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