Solve.

3/4 + (1/3 divided by 1/6) - (-1/2) =

Thus, the value of the variable x for the given one variable linear equation is found as: x = 8.5.

A linear equation is a one-variable equation of such a straight line. The variable only has one power, which is 1. Simple algebraic operations are used to solve linear equations in one variable, which can have the form ax+b=0.

All values which it make this equation true are included in the solution set. All real numbers make up the solution set for this equation because, when a real number is used in place of x, the equation is proved to be true.

Given one variable linear equation :

3x + 8 = 5x - 9

Isolate the variable and the constants on the different sides;

5x - 3x = 8 + 9

2x = 17

x = 17/2

x = 8.5

Thus, the value of the variable x for the given one variable linear equation is found as: x = 8.5.

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Complete question:

What is the value of x? The given equation is: 3x + 8 = 5x - 9.

[tex]log_2(100)[/tex] is apprοximately 6.64 when evaluated using the change οf base fοrmula with base 10.

The change οf base fοrmula is used in lοgarithmic functiοns tο change the base οf the lοgarithm frοm οne value tο anοther.

The fοrmula states that fοr any base b, and any pοsitive numbers x and y, the fοllοwing equatiοn hοlds true:

[tex]log_b(x) = log_y(x) / log_y(b)[/tex]

Here,[tex]log_b(x)[/tex] represents the logarithm of x with base b, and [tex]log_y(x)[/tex]represents the logarithm of x with base y.

Tο evaluate the change οf base fοrmula, we need tο substitute the given values οf x, y, and b in the fοrmula and simplify the expressiοn. Fοr example, let's say we want tο find [tex]log_2(100)[/tex] using the change οf base fοrmula with base 10. We can write:

[tex]log_2(100)[/tex] [tex]= log_{10}(100) / log_{10}(2)[/tex]

Here, we know that log_10(100) = 2, as 10^2 = 100, and log_10(2) is approximately 0.301. Therefore, we can simplify the expression as:

[tex]log_2(100)[/tex]  = 2 / 0.301

This gives us:

[tex]log_2(100)[/tex]  ≈ 6.64

Therefore, [tex]log_2(100)[/tex] is approximately 6.64 when evaluated using the change of base formula with base 10.

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Complete Question:

How do you use the Change of Base Formula and a calculator to evaluate the logarithm log₂1 ?

Exponential growth function that relates the number n of plants found to the number x of volunteers Seth has,  

[tex]n = p\left(1+\frac{r}{100}\right)^x[/tex]

How to find an exponential function?

Exponential function is the function of growth or decay with the power of the independent variable.

As, n is the number of plants increased.

r is the percent increase

p is the initial plants

and x is the volunteers

Compound Interest/ Exponential equation is,

[tex]n = p\left(1+\frac{r}{100}\right)^x[/tex]

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The exponential growth function  [tex]n = p(1 + r)^X[/tex]

The exponential growth function that relates the number n of plants found to the number X of volunteers Seth has can be expressed as:

[tex]n = p(1 + r)^X[/tex]

where:

n is the number of plants found

p is the initial number of plants found before adding any volunteers

X is the number of volunteers added to the search

r is the percentage increase in the number of plants found per volunteer

he growth factor is represented by the term (1 + r), which is multiplied by the initial number of plants discovered to determine the new number of plants discovered when each volunteer is added. The value of (1 + r)X increases exponentially as X increases, resulting in an exponential increase in the number of plants found.

It is essential to keep in mind that the growth rate r in the formula must be expressed as a decimal rather than a percentage. For instance, r = 0.05 if the number of plants discovered increases by 5% for each volunteer added.

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Answers and explanation:

[tex]3x^{2} +12x+9=(3x+3)(x+3)[/tex]

Factored form:

[tex](3x+3)(x+3)=0[/tex]

First zero:

[tex]3x+3=0[/tex]

[tex]3x=-3[/tex]

[tex]x=\frac{-3}{3} =-1[/tex]

Second zero:

[tex]x+3=0[/tex]

[tex]x=-3[/tex]

Ordered pair:

[tex]x=-1, x= -3[/tex]

Hope this helps.

The relation between the area (a) and the side length (s) in the table is:

A. a = s²

What is an area?

To see this relationship, we can observe that the areas of the poster boards are the square of their respective side lengths. For example, when the side length is 2 feet, the area is 4 square feet (2²).

Similarly, when the side length is 4 feet, the area is 16 square feet (4²). This pattern holds true for all the side lengths listed in the table. Therefore, we can conclude that the area of each poster board is equal to the square of its side length.

Calculation:

Side Length (s)    |       Area (a)

  1                         |        1

  2                        |        4

  3                        |        9

  4                        |        16

As we can see, the area of each poster board is equal to the square of its side length. Thus, the relation between the area (a) and the side length (s) in the table is a = s².

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Answer:

A

Step-by-step explanation:

[tex]a = s {}^{2} \\ 1. \: + - \sqrt{a = s} \\ 2. \: s = + - \sqrt{a} [/tex]

Answer:

Angle A = Angle L

Angle D = Angle M

Angle C = Angle N

Segment AB = Segment LB

Segment CD = Segment NM

Segment DA = Segment ML

2nd part

Quadrilateral URST has moved by a translation of (x-5,y+2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The length of the side is 67.8 which gives us the perimeter as 67.8 x 10 = 678units

We are given a decagon, which is a 10-sided polygon with center O, and a radius of 11 units.

We are required to find the perimeter of the decagon and round the answer to the nearest tenth.

We begin by calculating the interior angle of e decagon.

We use the formula;

S = (n-2) 180, where,

S = sum of interior angles,

n = number of sides

therefore, S = (10 - 2) 180

S = 8 x 180

S = 1440

For a 10-sided polygon, each interior angle will now measure;

Interior angle = 1440/10 = 144

take note that the radius of the polygon divides the angle at the vertex (that is, the interior angle) into two equal halves.

With that in mind we can now construct the following triangle:

Take note that the line from the center to the side is the apothem, while the side labeled 11 is the radius (which was given). We can now extract one of the right angled triangles and use that calculate the apothem as follows:

The side labeled a; the apothem can be calculated using the angle 72 degrees as the reference angle:

reference angle = 72

opposite = a

hypotenuse = 11

therefore when we use the formula of sin, we get a = 10.46

Also, for the side labeled s (half the length of one side of the decagon); s = 3.39

For the length of one side of the decagon, we have the side s times 2. Hence, the length of the side is 67.8

67.8 x 10 = 678units

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Answer:

A)

Step-by-step explanation:

just look at the picture.

what must have happened to figure A to turn into figure B ?

is B more to the right or to the left of A ?

well, right. isn't it obvious ?

and when you look at the coordinates of a vertex, it is 3 units to the right of A.

and if the shift to the right had not happened - the 2 figures would be a mirrored image of each other with the x-axis being the mirror.

that is why A) is the right answer.

For instance: Let f(x) = 2x + 1 and g(x) = x^2. Find (f ∘ g)(3). First, we need to find g(3) which is 3^2 = 9. Then we plug this value into f: f(g(3)) = f(9) = 2(9) + 1 = 19. Therefore, (f ∘ g)(3) = 19.

Function composition is a mathematical concept that is used to combine two or more functions into a single function. This concept is widely used in real life situations, such as in computer programming, engineering, and physics.

For example, in computer programming, function composition is used to break down complex programs into smaller, more manageable parts. By using function composition, programmers can create complex programs that are easier to read and maintain. Therefore, function composition is a powerful tool that is used in various fields to simplify complex problems and create more accurate models of the world around us.

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To find the probability that the average of 25 randomly selected claims exceeds 20,000, we need to first determine the mean and standard deviation of the sample distribution.

Given:
- Mean of the population (μ) = 19,400
- Standard deviation of the population (σ) = 5,000
- Sample size (n) = 25

Step 1: Calculate the mean of the sample distribution (μ_sample)
Since the sample mean is an unbiased estimator of the population mean, μ_sample = μ = 19,400.

Step 2: Calculate the standard deviation of the sample distribution (σ_sample)
σ_sample = σ / √n = 5,000 / √25 = 5,000 / 5 = 1,000

Now, we need to find the probability that the sample mean exceeds 20,000. We can do this using the Z-score formula:

Z = (X - μ_sample) / σ_sample

where X is the sample mean we want to find the probability for (20,000 in this case).

Step 3: Calculate the Z-score
Z = (20,000 - 19,400) / 1,000 = 600 / 1,000 = 0.6

Step 4: Find the probability
Now, we need to find the area to the right of the Z-score in the standard normal distribution table or use a calculator/software that provides the probability.

The area to the right of Z = 0.6 is approximately 0.2743. So, the probability that the average of 25 randomly selected claims exceeds 20,000 is approximately 0.2743 or 27.43%.

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D

I graphed each one and then compared the graphs to the one in the question

Answer: -64

Step-by-step explanation:

To solve this problem, we use the rule of conditional probability which states that the probability of the joint event A and B happening is equal to the probability of A happening multiplied by the probability of B happening given that A has already happened.

So, the probability of drawing a green marble on the first draw is 4/15, since there are 4 green marbles out of a total of 15 marbles.

If the first marble drawn is green and not replaced, there are now 14 marbles remaining in the bag, out of which 3 are green.

Thus, the probability of drawing another green marble given that the first one was green is 3/14.

Therefore, the probability of drawing two green marbles without replacement is:

(4/15) * (3/14) = 2/35

So the answer is 2/35.

The answer is C) +18 ÷ +3 = +6. Micheal's 50-meter freestyle time was 24.73 meters faster than his 100-meter freestyle time.

Measure of how far an object travels in a certain amount of time. Speed is calculated by dividing the distance traveled by the time it took to travel that distance.

The answer is C) +18 ÷ +3 = +6.

This is because Alvin decreased his training by 18 miles over a period of 3 weeks.

Dividing the decrease by the number of weeks gives us 6 miles, which is the average weekly change in his training.

That is 18/3= 6.

To answer the second question, Micheal's 50-meter freestyle was 24.73 meters faster than his 100-meter freestyle.

To calculate this, we subtract the time of the 50-meter freestyle (23.04 seconds) from the time of the 100-meter freestyle (47.77 seconds) to get 24.73 seconds.

We then multiply this time by the speed of a meter per second (1 meter/second) to get 24.73 meters.

Therefore, Micheal's 50-meter freestyle time was 24.73 meters faster than his 100-meter freestyle time.

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Answer:

7 hours and 2 hours longer

The proportion of the rise to the run for each of the similar slope triangles is given by:

h / b = mh' / mb' = mh / b

What is proportion?

A proportion is a statement that two ratios or fractions are equal. It is commonly written in the form of two fractions separated by an equal sign, such as a/b = c/d.

To write a proportion comparing the rise to the run for each of the similar slope triangles, we can use the fact that the ratio of corresponding sides of similar triangles is the same.

Let's say we have two similar triangles with corresponding sides of length a, b, and c, and a', b', and c', respectively. Then we can write the following proportion:

a / a' = b / b' = c / c'

Now, let's apply this to finding the proportion of the rise to the run for each of the similar slope triangles.

In a right triangle, the slope is defined as the ratio of the rise (vertical change) to the run (horizontal change). Let's say we have two similar right triangles with slopes m and m', respectively, and the rise and run of the first triangle are h and b, respectively. The rise and run of the second triangle are then mh and mb', respectively.

We can write the proportion of the rise to the run for each triangle as:

h / b = mh' / mb'

Simplifying this proportion, we can cancel out the common factor of b:

h / b = mh' / mb'

h / 1 = mh' / m'

h = bmh'

Therefore, the proportion of the rise to the run for each of the similar slope triangles is given by:

h / b = mh' / mb' = mh / b

The numeric value of this proportion will depend on the specific values of the rise and run for each triangle and the slope of the triangles.

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Answer:

0.4 meters.

Step-by-step explanation:

The ratio of centimeters to meters is 100:1.

That means if there are 100 centimeters, there is 1 meter.

So:

centimeters divided by 100 is a meter.

In this case, we have 40 centimeters.

Since there are less than 100 centimeters, we can't divide by 100, so we go into the decimals.

40 divided by 100 is

40/100

simplified to:

4/10

turned into decimal:

0.4 meters.

Hope this helps :)

The answer is 0.4 meters

The given ratio of centimeters to meters is 100:1. The rope Laura has is 40 cm long. To determine how long the rope is in meters, we need to divide 40 cm by 100 to convert it to meters.

Therefore, the length of the rope in meters is 0.4 meters (40/100 = 0.4).Answer: 0.4 meters

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Answer:

Ok

Step-by-step explanation:

Y = mx + c

Slope is for the gradient =m therefore we have +3 as our gradient

Now we are going to substitute pont - 8mac- 8 on the above equation

Y = mx +c

-8=3(-8) +c

-8=-24 +c

-8+24 =c

16=c

This means that the y intecept of this straight line is 0 mac 16

Meaning that when the line touches the y axis at 16 x will be equal to zero

Therefore our equation is

Y =3x +16

The conclusion that can be drawn from the excerpt is: "If they are well planned, they can protect the shore from erosion while minimizing damage to important habitats for plants and animals." Therefore, the option "If they are well planned, they can replace sand that has been washed away" is not accurate, and the options "If they are well planned, they will most likely be too expensive," and "If they are not well planned, they can damage other structures" are not supported by the information provided in the excerpt. The correct answer is: "If they are not well planned, they can damage places with sea life."

Answer:

The answer to your problem is, B. mAngleA + 60° + 55° = 180°

Step-by-step explanation:

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

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

Let the triangle be represented as ABC:

Now , the first measure of angle = 55

The second measure of angle = 60

The angle of the first ∠A = 180

Thus the answer to your problem is, B. mAngleA + 60° + 55° = 180°

Answer:

let the height of second container be x

Then volume=6912

we know that volume of cuboid= lbh

so ，

24.x.16=6912

384.x=6912

x =6912divide 384

therefore x =18 that is the height of the container

The length of the altitude is

The similarity statement about the triangles is

The value of x in the pentagon is 21

The value of x is solved by applying the the proportions of the pentagon

20 / 15 = 18 / 13.5 = 4/3

therefore, 12 * 4/3 = x - 5

16 = x - 5

16 + 5 = x

x = 21

The altitude of the right triangle

h / 14 = 4 / h

h^2 = 14 * 4

h^2 = 56

h = sqrt (56)

h = 7.5

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[tex] \bf Question[/tex]

Write 8,360,000 in scientific notation

8,360,000

After one digit you should mark decimal then count after decimal how many digits are remaining after you get Ans then put your Ans always on 10.

Like this,

8.36× 100,000 = as 8.36 × 10⁶

Am mark decimal after one digit and count how many digits are remaining then am put my ans on 10

So, 8,360,000 written as 8.36 × 10⁶ in scientific notation

See this, there are two pairs one is 8.36 and one is 100,000 in first one we can't write zeros. We write numbers like 1,2,3,4,5,6,7,8,9 but not 0. Like this question is 8,360,000 , our first work is to mark decimal after one digit 8. then we have to notice that after decimal how many number are remaining like 360,000 As, we know we can't write zeros in first pair so we can write only 8.36× now our first pair is done , Second pair is so easy only you have to count digits after decimal 8360,000 So digits are 6 so our final answer is 8.36×10⁶

Always remember in second pair we write remaining no. of digits only on 10 like this 10⁶

8.36 × 10⁶

The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.

Now, can you express 40,000,000,000 in the similar way ?

Count the number of zeros in it. It is 10.

So, 40,000,000,000 = 4.0×10¹⁰

Do you agree with the fact, that the number when written in scientific notation is much easier to read and understand.

The scientific notation of the given number is 8.36×10⁶.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

The given number is 8,360,000.

In scientific notation

8,360,000 = 8.36×10⁶

Therefore, the scientific notation of the given number is 8.36×10⁶.

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The price of Groupon for revenue of $300 is $4 if the expected revenue is at least $390 per day.

Probability is assigned as

x =30, 60, 120, 180

P(x) = 0.10,0.40, 0.40, 0.10

Expected sales volume:

Number of tubes x =30, 60, 120, 180

Probability P(x)= 0.10,0.40, 0.40, 0.10

Expected values are 3, 24,48,18

Total = 93 tubes

Groupon price = $390/$93 = $4.19

Jane's price for each Groupon is the daily rental income divided by the expected number of tubes rented per day. The expected number of tubes is derived by multiplying the expected number of each tube by its probability and then summing the results. 

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Answer: We can use the fact that the sum and product of the roots of a quadratic equation are related to its coefficients, and use this relationship to find the values of p and q.

Given the equation ²-13x - 30 = (x+p)(x+q), we can see that the coefficient of the x^2 term is 1, the coefficient of the x term is -13, and the constant term is -30.

By comparing the coefficients with the formula for the sum and product of the roots of a quadratic equation, we have:

p + q = -(-13)/1 = 13

p*q = -30/1 = -30

Since the absolute value of p is greater than the absolute value of q, we know that either p is positive and q is negative, or p and q are both negative. We can eliminate the possibility of p being positive and q being negative, since their product would be negative, and we know that p*q = -30. Therefore, both p and q must be negative integers.

We also know that the sum of p and q is 13, which means that the absolute value of q is less than the absolute value of p. Since p and q are both negative, this means that q has a larger absolute value (i.e., is farther from zero) than p. Therefore, q is the negative integer in this case.

Step-by-step explanation:

The value of the indicated sides of the shape given above are as follows:

Scale factor = 1.67

X = 15

Y = 9

Z = 9

To call the scale factor of a given shape the formula used is given below;

Scale factor = Dimension of new shape(bigger)/dimension of the old shape(smaller).

Dimension of new shape = BC = 30

Dimension of old shape = FE = 18

scale factor = 30/18 = 1.67

X = AD/1.67

X = 25/1.67

X = 15 (approximately)

Y = DC/1.67

Y = 15/1.67

Y = 9 (approximately)

Z = AB/1.67

Z = 15/1.67

Z = 9(approximately)

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Answer:

29

Step-by-step explanation:

Given:

P = 88

Let's assume, that the length is x and the width is y

x = (2y - 1)

Let's write an equation for the perimeter:

2x + 2y = 88

2 × (2y - 1) + 2y = 88

4y - 2 + 2y = 88

6y = 88 + 2

6y = 90 / : 6

y = 15

We found the width, now we can find the length:

x = 2 × 15 - 1 = 30 - 1 = 29

The absolute value equation | x - (-5) | = 3 has a solution set corresponding to a straight horizontal line with marked points -8, -2, and x in left to right manner.

How to write an absolute value equation that has the following solution set?

The solution set given as a straight horizontal line passing through the points -1/2 and 3/2 can be represented as:

| x - 1 | = 1/2

Explanation:

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The required confidence interval for the given sample size and sample mean is,

95% confident interval which is true average porosity of the seam lies between 4.49 and 5.20 percent.

98% confident interval which is true average porosity of the other seam lies between 4.10 and 5.02 percent.

Sample size with 95% confidence interval with a width of 0.37 is 16 .

Sample size with 99% confidence interval with a width of 0.21 is 11 .

Sample size 'n' = 19

Confidence interval = 95%

Sample mean = 4.85

True average porosity of a certain seam is , we use the formula,

CI = sample mean ± t(α/2, n-1) ×(standard deviation / √(n))

where t(α/2, n-1) is the critical t-value.

α level (0.05 for a 95% confidence interval)

Degrees of freedom (n-1 = 18).

Plugging in the values, we get,

CI

= 4.85 ± t(0.025, 18) × (0.74 / √(19))

Using a t-table ,

t(0.025, 18) = 2.101.

So the confidence interval is,

CI

= 4.85 ± 2.101 × (0.74 / √(19))

= (4.49, 5.20)

95% confident that the true average porosity of the seam lies between 4.49 and 5.20 percent.

Compute a 98% confidence interval for the true average porosity of another seam .

Sample size = 18

Sample mean = 4.56,

Use the same formula as above but with a different t-value,

CI = 4.56 ± t(0.01, 17) ×(0.74 / √(18))

Using a t-table

t(0.01, 17) = 2.898.

So the confidence interval is,

CI

= 4.56 ± 2.898 × (0.74 / sqrt(18))

= (4.10, 5.02)

98% confident that the true average porosity of the other seam lies between 4.10 and 5.02 percent.

Sample size to obtain a 95% confidence interval with a width of 0.37,

Use the formula,

n = (t(α/2, n-1) × standard deviation / (width / 2))^2

Solving for n, we get,

n = [(t(α/2, n-1) × standard deviation) / (width / 2)]^2

Substituting the given values, we get,

n = [(t(0.025, n-1) × 0.74) / 0.37]^2

Using trial and error or a t-table,

t(0.025, n-1) is approximately 2 for large sample sizes.

So we have,

n = [(2 × 0.74) / 0.37]^2

  = 16

A sample size of at least 16 specimens is necessary to obtain a 95% confidence interval with a width of 0.37.

Sample size to estimate the true average porosity to within 0.21 with 99% confidence,

Use the same formula as above but solve for n with the given width and confidence level,

n = [(t(α/2, n-1) ×standard deviation) / (width / 2)]^2

Substituting the given values, we get,

n = [(t(0.005, n-1) × 0.74) / 0.21]^2

Using trial and error or a t-table,

t(0.005, n-1) is approximately 3 for large sample sizes.

So we have

n = [3 × 0.74) / 0.21]^2

  = 11.17

  ≈ 11

Sample size to estimate the true average porosity to within 0.21 with 99% confidence is 11.

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