Which expression is equivalent to 12/5x -2 A. 12x-2/5 B. 2(2/5x -1) C. 2/5(6x-10) D. 1/5(12x-10)​

Answer:

Step-by-step explanation:

5 and 15

5^2=25

15^2=225

225+25=250

Step-by-step explanation:

Use the Ratio Test since Ratio Test guarantee absolutely convergence.

[tex] \frac{ ( - 1) {}^{k + 1}(k + 1) {}^{a} }{5 {}^{k + 1}(3(k + 1) } \times \frac{5 {}^{k}(3k) }{(k) {}^{a} ( - 1) {}^{k} } [/tex]

This simplifes to

[tex] \frac{( - 1) {}^{k} ( - 1) ((k + 1)!) {}^{a} }{5 {}^{k}(5)(3k +1) ! } \times \frac{5 {}^{k} (3k)!}{( - 1) {}^{k} (k!) {}^{a} } [/tex]

[tex] \frac{ - (k + 1) {}^{a} }{5(3k + 3)(3k + 2)(3k + 1)} [/tex]

Take the absolute value

[tex] \frac{(k + 1) {}^{a} }{5(3k + 3)(3k + 2)(3k + 1)} [/tex]

In order for this series to be convergent,

the limit as k approaches infinity must be less than 1.

In order for this series to have a limit less than 1, our numerator and denominator degree must be equal or the denominator must have the larger degree.

Why

If the numerator has a larger degree, our test would make this divergent, so the limit would be infinity

Since the denominator have 3 binomials, our power for the denominator will be 3, this the numerator having a degree of 3 or less as well.

So one of the answer is 3.

The values of AB and BC are equal and equal to

Information given in the problem includes

DE bisects AC at point B

AC = a + 23

AB = 3a + 4

From  the definition of a bisector, point B divides AC into two equal sides, this means that

AB = BC = (1/2) * AC

Substituting the value of AC and AB

AB = 3a + 4 = (1/2) * (a + 23)

3a + 4 = (1/2) * (a + 23)

solving for a

2 * (3a + 4) = a + 23

6a + 8 = a + 23

6a - a  = 23 - 8

5a = 15

a = 3

Then we have that:

AB = 3a + 4 = 3(3) + 4 = 9 + 4 = 13

and, AB = BC

so BC = 13

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The t-statistic value of the hypothesis is 2.236

The population mean is equal to 6,500 (H0: μ = 6500)

Alternative hypothesis:

The population mean is greater than 6,500 (Ha: μ > 6500)

We are given the sample mean (x) = 6,600, sample size (n) = 500, population standard deviation (σ) = 1,000, and level of significance (α) = 0.05.

First, we need to calculate the t-statistic using the formula:

t = (X - μ) / (σ / √n)

where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (6,600 - 6,500) / (1,000 / √500)

= 2.236

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In the above triangle,

1) the sum of side 1 and 2 is: 4x² + 3x + 4
2) the length of side 3 is: 5x³-6x²-12

1) To find the sum of side 1 and side 2, we simply need to add them together.

Side 1 = 3x² - x - 1

Side 2 = x² + 4x +  5

Side  1 + Side 2 = (3x²  - x - 1) + (x²  + 4x +  5)

= 3x² + x² - x + 4x - 1 + 5

= 4x² + 3x + 4

Therefore, the sum of side 1 and side 2 is = 4x² + 3x + 4

2)  We can derive the expression of the thried side by removing the expression in  (1) above form the perimeter.

That is;

(5x³-2x² + 3x - 8) - (4x² + 3x + 4)

First we distribute the negative sign

= 5x³-2x² + 3x - 8 + -1 (4x² + 3x + 4)

= 5x³-2x² + 3x - 8 + -1 (4x²) -1( 3x) -1( 4)

= 5x³-2x² + 3x - 8 + -4x² - 3x - 4

Combining like terms we have

= (5x³) (-2x²+-4x²) + (3x +- 3x) + (-8 +   - 4)

= 5x³-6x²-12

Hence the missing side (thrid side is) 5x³-6x²-12

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Answer:

$3.58

Step-by-step explanation:

Because we know that the 2 lbs of bananas will be purchased at the same rate, the price per pound for 5 lbs of bananas is proportional to the price per pound for 2 lbs of bananas.

Thus, we can solve for price, p of 2 lbs of bananas by setting up a proportion:

[tex]\frac{8.95}{5}=\frac{p}{2}\\ \\ 17.90=5p\\\\3.58=p[/tex]

Answer:60 degrees

Step-by-step explanation: The three angles of a triangle add to 180, a right angle is 90 so 180-90-30= 60.

Answer:

The answer to your problem is, 6.1 inches

Step-by-step explanation:

So we know that 1 inch of there model in real life is 50 feet.

Divide:

305 / 50

= 6.1 but we are going to use 6

Since it is 6 there model is 6 inches.

But remember we still have that 0.1 which we need to full fill for that:

Note that 6.1 will be in inches.

So it is done.

Thus the answer to your problem is, 6.1 inches

The value of the expression is $-56x² + 266x + 261

Algebraic expressions are simply described as mathematical expressions that consists of coefficients, certain variables, terms, constants and factors.

Algebraic expressions are also identified with arithmetic operations, such as;

From the information given, we have;

$49x^2+14x(19-7x)+(19-7x)^2

expand the bracket, we get;

49x² + 266x - 98x² + 361 - 7x²

Now, collect the like terms, we get;

49x² - 98x² - 7x² + 266x + 361

Add or subtract the values

$-56x² + 266x + 261

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Answer: To solve a two-step inequality, undo the addition or subtraction first, using inverse operations, and then undo the multiplication or division. The inverse operation of addition is subtraction and vice versa. Similarly, the inverse operation of multiplication is division and vice versa.

Step-by-step explanation:

Answer:

  42 units³

Step-by-step explanation:

You want the volume of a rectangular prism that has a base area of 5 1/4 units² and a height of 8 units.

The formula for the volume of a prism is ...

  V = Bh

where B is the base area and h is the height perpendicular to the base.

Here, we have B = 5 1/4 u² and h = 8 u. The volume is ...

  V = (5 1/4 u²)(8 u) = 42 u³

The volume of the prism is 42 cubic units.

C. No, because a difference in proportions of 0.4 or more occurred 7 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.

====================================================

Explanation:

If the new additive was more effective than the old one, then the difference in proportions (new - old) should be fairly large.

Count the dots over the x axis labels of "0.4" through "0.6"

That makes 5+1+1 = 7 dots total.

There are 7 instances where the difference of proportions is 0.4 or larger.

This is out of 200 observations, so 7/200 = 0.035 = 3.5% of the differences have 0.4 or larger.

This is not very significant. The general rule of thumb is to use 5% as the threshold. Some stats textbooks will use 10%. Other times your teacher will specify the significance level. The Greek letter alpha is often used.

Because 3.5% < 5%, we consider the new additive to not be that effective compared to the original additive.

Answer:

x=3/2

x=-2

Step-by-step explanation:

Answer:

r 0.6 kWh to run for 30 minutes.

Answer:

ok so it takes 1200 watts for a hair dryer to run for a full hour, that means it takes 600 watts, or 600 Wh, or 0.6 kWh to run for 30 minutes

Step-by-step explanation:

The two compositions give:

Here we have two functions:

f(x) = 3x + 5

g(x) = -7x + 6

And we want to fin the two compositions:

f(g(2))

g(f(2))

First, let's find g(2) = -7*2+  6 = -14 + 8 = -8

Then:

f(g(2)) = f(-8) =  3*-8 + 5 = -19

Now the other one:

f(2) = 3*2 + 5 = 11

Evaluating g in that:

g(11) = -7*11 + 6 = -77 + 6 = -71

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The measure of angle ABC is 30 degrees. Option B

It is important to note the properties of a circle, they include;

Also note that the measure of the angle at the circumference is half to twice the measure of the angle at the center.

From the information given, we have that;

<ADC = 60 degrees

This is the angle at the circle

Then,

<ABC is the angle at the circumference

<ABC = <ADC/2 = 60/2 = 30 degrees

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8% will be the value of sales tax that has been charged on a tie will be.

The tie cost is $22.50

The cost after the tax is $24.30.

The change in the cost will be:

= cost after-tax - cost before tax

=24.30-22.50

=1.8

The percentage change will be

Next, assemble a ratio of the sales tax to the pre-tax cost of the tie.

=Sales tax/Pre-tax value

= (1.8/22.50)*100

=8%

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Answer: The correct answer would be n/255 = 115/360 (N= 81.46)

Step-by-step explanation:

n/255 = 115/360

155/360 = (255)

n = 81.46 ft squared

If the graphs of the linear equations in a system are parallel: A. There is no solution.

The general form for the equation of a line is:

y = mx + c

where:

m is slope

c is y-intercept

Usually, for two equations to have a solution, they must intersect each other.

However, If the graphs of the two equations are parallel lines, then there will be no solution, and the system is called an inconsistent system because the two lines will never intersect each other.

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The linear function that describes the distance (in miles) is therefore y = 65x + 80

We have to find the slope and the intercept in other to get the linear function

The data points are:

(1, 145) and (3, 275).

m = (y2 - y1) / (x2 - x1)

fixing the data points we have

m = (275 - 145) / (3 - 1)

= 130 / 2

= 65

y = mx + b

(1, 145):

145 = 65(1) + b

b = 145 - 65

= 80

y intercept is 80

The linear function is therefore y = 65x + 80

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Answer:

Step-by-step explanation:

The mean of data is 5.5

Given that

The number of data is = n = 4

The given Numbers are 5, 6, 8, 13

We know

Mean x bar = (sum of data)/(number of data)

                   = (5 + 6 + 8 + 3)/4

                   = 22/4

                   = 5.5

Thus,  x bar = 5.5

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Answer:

Step-by-step explanation:

tax

We know that the mode of the integers is 9, which means that 9 occurs more frequently than any other number in the set of integers.

We also know that the median of the integers is 8, which means that when the integers are arranged in order from smallest to largest, the middle number is 8.

Finally, we know that the range of the integers is 4, which means that the difference between the largest and smallest integers in the set is 4.

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The height of the triangle is h = 18.18 inches

Given data ,

In an equilateral triangle, all three sides are equal in length.

Let the length of each side be s

Now , the perimeter of the equilateral triangle is given as 63 inches, so we have:

Perimeter of the triangle = 3s = 63 inches

Dividing both sides by 3, we get:

s = 63/3 = 21 inches

Let's now plot an altitude from one of the equilateral triangle's vertex to the side's midway. As a result, two right-angled triangles will be formed, each with the hypotenuse "s" and sides "s/2" and "h"

From the Pythagoras theorem , we get

(h²) + ((s/2)^2) = s²

Substituting the values we found earlier for "s", we get:

(h²) + ((21/2)²) = 21²

Simplifying further, we have:

(h²) + (10.5²) = 21²

(h²) + 110.25 = 441

Subtracting 110.25 from both sides, we get:

h² = 330.75

On taking square roots on both sides , we get

h = √(330.75)

h ≈ 18.18 inches

Hence , the height of the equilateral triangle is 18.18 inches

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Answer:

It's linear

Step-by-step explanation:

Answer:

Linear

Step-by-step explanation:

The missing values from ratio table are 17 and 28.

We have table as

3      1

48    16

51      x

78    26

84     y

So, the ratio are in proportion then

48 / 16 = 51 /x

3 = 51/x

x= 51/3

x = 17

and, 3/1 = 84/y

y= 84/3

y= 28

Thus, the values are 17 and 28.

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The weekly benefit of the employees is A = £ 11.40

Given data ,

Let's calculate the weekly benefit for an employee who spends an average of £14 each weekday and £22 on each day of the weekend, considering the 10% discount they receive at Tesco stores.

First, we'll calculate the total amount spent on weekdays and weekends separately:

Amount spent on weekdays = £14/day x 5 days/week = £70/week

Amount spent on weekends = £22/day x 2 days/week = £44/week

Next, we'll calculate the total amount spent in a week by adding the amounts spent on weekdays and weekends:

On simplifying the equation , we get

Total amount spent in a week = £70 + £44 = £114

Now, we'll calculate the 10% discount on the total amount spent:

10% of £114 = £11.40

Hence , the weekly benefit to the employee who receives a 10% discount on their shopping at Tesco stores would be £11.40

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The volume of water in the aquarium up to the 15 inch mark is 3465 cubic inches.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length

The volume of water in the aquarium up to the 15 inch mark will be equal to the volume of a rectangular prism with a length of 21 inches, a width of 11 inches, and a height of 15 inches.

This is because the water level is 15 inches from the bottom of the aquarium.

Hence, the volume of water in the aquarium up to the 15 inch mark is:

V = l × w × h

V = 21 × 11 × 15

V = 3465 cubic inches

Therefore, the volume of water in the aquarium is 3465 cubic inches.

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Answer:

45

Step-by-step explanation: