how to solve 156 x 6=
938 But how did you get 938

156
X 6
____________

(1 , -5) satisfy the inequality y ≤ 3x + 2  but not to y > –2x – 3

According to the question,

It is Given : y ≤ 3x + 2  

y > –2x – 3

We have to find the relationship between the point (1, –5) and the given system of inequalities.

Substituting the point (1,5) in our inequality y ≤ 3x + 2  

=> x = 1

=> y ≤ 3(1) + 2  

=> y ≤  5

=> - 5 ≤ 5

Which is true

Hence point (1, –5)  satisfy y ≤ 3x + 2  

Substituting the point (1,5) in our inequality  y > –2x – 3

x = 1

=> y > -2(1) - 3

=> y > - 5

but - 5 = -5

Hence  point (1, –5)   does not satisfy y > –2x – 3

I've answered the question in general as the given question is incomplete

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The 'b' value of the given expression is -8. The solution has been obtained by using quadratic equation.

What is a quadratic equation?

Any algebraic equation that can be expressed in standard form as where x represents an unknown value and where a, b, and c represent known values, where a 0 is a quadratic equation.

We are given an expression as 16\(x^{2}\) - 8x - 24.

Since, it is a quadratic equation, so it will form a parabola.

We know that the general form of a quadratic equation is

y = a\(x^{2}\) + bx + c.

Now, on comparing the given expression with the general form, we get

a = 16

b = -8

c = -24

Hence, the 'b' value of the given expression is -8.

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1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is: ∠A = 39.6°

3) The length of side x is: x = 39.5 mm

The six trigonometric ratios of a right angle triangle are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

cot x = 1/tan x

sec x = 1/cos x

cosec x = 1/sin x

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is gotten from:

∠A = cos⁻¹ (47/61)

∠A = 39.6°

3) The length of side x using trigonometric ratios is:

21/x = tan 28

x = 21/tan 28

x = 39.5 mm

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Answer:

-5 5/6

Step-by-step explanation:

1 2/3=5/3

-3 1/2=-7/2

5/3*-7/2=-35/6= -5 5/6

Answer:

- 5 5/6 or Decimal: -5.833333

Step-by-step explanation

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

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Answer:

We can simplify the expression as follows:

4^3 * 4^4 / 4^9

First, we can simplify the terms in the numerator by adding the exponents of 4:

4^3 * 4^4 = 4^(3+4) = 4^7

Now, we can substitute this value in the expression:

4^7 / 4^9

To divide powers with the same base, we can subtract their exponents:

4^(7-9) = 4^(-2)

Therefore, the simplified expression is:

4^3 * 4^4 / 4^9 = 4^(-2)

So, the final answer is 1/16 or 0.0625.

Answer:

9x - 6

Step-by-step explanation:

9 times a number, x, is written as 9x

“6 less than” means to subtract 6 from something else.

Answer:

Step-by-step explanation:

9x-6

Option(A) is the correct answer is A. 1,335 birds.

To calculate the number of birds that will be left after 20 years, we need to consider the annual decline rate of 2%.

We can use the formula for exponential decay:

N = N₀ * (1 - r/100)^t

Where:

N is the final number of birds after t years

N₀ is the initial number of birds (2,000 in this case)

r is the annual decline rate (2% or 0.02)

t is the number of years (20 in this case)

Plugging in the values, we get:

N = 2,000 * (1 - 0.02)^20

N = 2,000 * (0.98)^20

N ≈ 2,000 * 0.672749

N ≈ 1,345.498

Rounded to the nearest whole number, the number of birds that will be left after 20 years is 1,345.

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Answer:

A). Estimate of population 0.61

(b) Margin of error = 0.07 The real population interval estimation is ± 7%.

c). Margin of error = 0.15

d) The real population's interval estimation is ± 15%

e). Yes, the action argument of the group is based on a half-range estimation of the true population. The reason that 62% ± 15% = 47%, or 77%, while 47% is similar to 45%, as the Collective action group states.

Step-by-step explanation:

For the poll of 1000 residents, a newspaper article claims that 62% of the residents is in favor of development of a recreational park has,

The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.

Based on a poll of 1000 residents, a newspaper article claims that 62% of the residents in town favor the development of a recreational park on the west side of town.

This will be equal to the population, which is 0.62.

The margin of error of the population proportion is found using an estimate of the standard deviation.

The sample is 200 and population, is 0.62. Margin of error for z value 1.96 can be found using the following.

\(MOE=z\sqrt{\dfrac{p(1-p)}{n}}\\MOE=1.96\sqrt{\dfrac{0.62(1-0.62)}{200}}\\MOE=0.0672\)

This gives the interval estimate of the true population proportion is 6.72%.

The minimum sample proportion from the simulation is 0.46 and the maximum sample proportion is 0.76.

The margin of error of the population proportion using the half the range can be given as,

\(MOE=\dfrac{0.76-0.46}{2}\\MOE=0.15\)

The interval estimate of the true population proportion using half the range is 0.15.

A community action group interested in preserving the environment claims that 45% of the town's residents favor the development of a recreational park.

As, the value of confidence interval is greater than 0.45. Thus, the community action group's claim likely based on either interval estimate of the true population proportion.

Hence, for the poll of 1000 residents, a newspaper article claims that 62% of the residents is in favor of development of a recreational park has,

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Answer:

Explanation:

The given equation is

5x + 3y = 15

The points to be plotted of on the graph are

(3, 0)

(0, 5)

The graph is shown below

To rewrite as slope intercept equation, it becomes

3y = 15 - 5x

Dividing both sides by 3, we have

y = 3 - 5x/3

y = - 5x/3 + 3

The slope intercept equation is

y = - 5x/3 + 3

Answer:

3 pages per minute

75÷25

Answer:

3 pages in 1 minute

Step-by-step explanation:

75/25=3

Key features for the graph given in the problem will be-:Vertex (-1, -5), Axis of symmetry=> (x = -1), y-intercept (0,-3), Minimum=> (y=-5), Domain=> (All Real), Range=>( y >= -5)

Refering to the graph given in the problem(refer image attached).The key features of the graph can be given as:

The graph has an upward-opening form, an axis of symmetry at x = -1, a y-intercept at (0, -3), a minimum point at y = -5 (which is also the vertex), and it spans all real numbers on the x-axis (domain) while being larger than or equal to -5 on the y-axis (range).

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Answer:

A. If Frank is on the toll road for 8.00 miles and then leaves the lane, how much will he have to pay total for the trip?

B. Each day, Susan has to pay a toll of $10.00 when she uses the toll lane to get to school. How many miles does Susan travel on the toll lane to get to school?

C. John started a carpool with his coworkers to save money. He and his three passengers split the cost of the toll. If each person pays about $2.31 (which includes their contribution to the toll lane entry fee), how many miles do they travel on the toll lane?

Step-by-step explanation:

the toll lane charges $0.25 fixed plus $0.75 per mile driven: fee = $0.25 + $0.75miles

a) Frank ⇒ $0.25 + (8 x $0.75) = $6.25

b) Susan ⇒ $10 - $0.25 = $9.75 / 0.75 = 13 miles

c) John ⇒ $2.31 x 3 = $6.93 - $0.25 = $6.68 / 0.75 = 8.91 ≈ 9 miles. Each passenger should pay $2.33 because the total toll lane fee is $7.

Answer:

y=5/8x+4.5

Step-by-step explanation:

You have to do y-y divided by x-x so 7-2 which equals 5 and 4-(-4) which equals 8 so your slope is 5/8. For y-intercept, you have to do plug in one of your points into y and x in y=mx+b, so I used the point (4, 7) and I put 7 in the y spot and 4 in the x spot and I put the slope in the slope spot so now you have 7=5/8(4)+b. Next, you multiply 5/8 and 4 which gives you 5/2 or 2.5, so now you have 7=2.5+b. Then you subtract 7-2.5 which gives you 4.5 and there is your y-intercept and your whole equation is y=5/8x+4.5.

The total number of students who graduated from the Cincinnati universities and colleges are 15382.

We are given that 6.76 % of Cincinnati college and university graduates majored in Registered Nursing.

The number of the Cincinnati college and university graduates who majored in Registered Nursing = 1026.

We need to find the total number of students that graduated from the Cincinnati universities and colleges altogether in 2016.

Let the total number of students be x.

ATQ:

6.67 % x = 1026

6.67 x = 102600

667 x = 10260000

x = 10260000 / 667

x = 15382.309

Rounding off to the nearest whole number is:

x = 15382.

Therefore, we get that the total number of students who graduated from the Cincinnati universities and colleges are 15382.

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The values of a and b are a = -3 and b = 42. The solutions for x can be written as:

x = -3 - √42

x = -3 + √42

To solve the quadratic equation 2x² + 12x = 66 by completing the square, we need to follow these steps:

Step 1: Move the constant term to the right side:

2x² + 12x - 66 = 0

Step 2: Divide the equation by the leading coefficient (2):

x² + 6x - 33 = 0

Step 3: To complete the square, we take half of the coefficient of x, square it, and add it to both sides of the equation:

x² + 6x + (6/2)² = 33 + (6/2)²

x² + 6x + 9 = 33 + 9

x² + 6x + 9 = 42

Step 4: Rewrite the left side as a perfect square:

(x + 3)² = 42

Step 5: Take the square root of both sides:

√(x + 3)² = ±√42

x + 3 = ±√42

Step 6: Solve for x:

x = -3 ± √42.

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Answer:

Step-by-step explanation:

The number on the top line of the table is 14/7 = 2 times the number on the bottom line.

To find the bottom number, divide the top number by 2.

To find the top number, multiply the bottom number by 2.

The missing ratios are ...

  42 : 21

  6 : 3

  48 : 24

Answer:

Step-by-step explanation:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)\)

Lets look at the derivative part:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2]\)

\(=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)\)

Substituting in eq(1), we have:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)]\)

The simplified sum of the second and forth integers are; -1 + 5 = 4

An integer is defined as a whole number that can be positive, negative, or zero. Examples of integers are: -7, 2, 9, 18, 125, and 9803

Now, we are given the consecutive integer sequence as;

x, 1, 3, 5

Now, since the integers are consecutive, then the common difference is the same. Thus;

1 - x = 3 - 1

1 - x = 2

x = 1 - 2

x = -1

Sum of first and fourth term = -1 + 5 = 4

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The calculated measure of m∠PNM is 87 degrees

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

The circle

Where, we have

PM = 360 - 64 - 122

Evaluate

PM = 174

Next, we have

m∠PNM = 1/2 * 174

So, we have

m∠PNM = 87

Hence, the measure of m∠PNM is 87 degrees

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Answer:

Option A) The volume is multiplied by 1/8.

Step-by-step explanation:

For the first volume problem involving the rectangular pyramid, the normal volume formula is V = 1/3 (l)(w)(h).  Since all 3 dimensions are being multiplied by 1/2, this involves multiplying the original formula by (1/2)(1/2)(1/2) which, put together, is multiplying by 1/8, so the volume will be 1/8 of what it was with the original dimensions.

The volume of the rectangular pyramid is multiplied by ( 1/8 )

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

Let the length of the rectangle be L

Let the width of the rectangle be W

Let the height of the rectangle be H

Now , the volume of rectangle be V = L x W x H

And , when the length , width and height are multiplied by ( 1/2 ) , we get

L' = L/2

W' = W/2

H' = H/2

So , the volume V' = ( L' x W' x H' )

The volume of rectangular pyramid V' = ( 1/8 ) V

Hence , the volume is multiplied by ( 1/8 )

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Answer:

1) 7/8     8/7

2) 4.4

3) 3.7

4) 2.8

Step-by-step explanation:

Length of bottom side of Figure A: 8 cm

Length of bottom side of Figure B: 7 cm

From Figure A to Figure B, the scale factor is 7/8.

7/8

8/7

5 × 7/8 = 35/8 = 4.375

4.4

3.2 × 8/7 = 3.657...

3.7

3.2 × 7/8 = 2.8

2.8

Answer:

fghwjklpkjqkhb cghdbhn bwn x wxhw hwbmx

Step-by-step explanation:

The Scientific Notation is 3.583008 x \(10^5\) and quotient is 358300.8

Given,

In the question:

(26.4 x 10-3) (13.2 × 104)

Determine the quotient and write the answer in scientific notation.

Now, According to the question:

(26.4 x 10-3) (13.2 × 104)

Calculate the product or quotient.

(264 - 3) x (13.2 x 104)

(264 - 3) x 1372.8

calculate the sum or difference

261 x 1372.8

= 358300.8

Hence, The Scientific Notation is 3.583008 x \(10^5\) and quotient is 358300.8

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The value of x in the angles is 19.

When lines intersect, angle relationships are formed such as vertically opposite angles, adjacent angles etc.

Therefore, let's find the value of x in the intersecting lines.

Hence,

7x - 8 = 6x + 11 (vertically opposite angles)

Vertically opposite angles are congruent and they share the same vertex point.

Hence,

7x - 8 = 6x + 11

subtract 6x from both sides of the equation

7x - 8 = 6x + 11

7x - 6x - 8 = 6x - 6x + 11

x - 8 = 11

add 8 to both sides of the equation

x - 8 + 8 = 11 + 8

x = 19

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The patient needs 17.66 mg of medication A .

It is given that a patient has weight 157 lbs.

We apply division because we need to find the cost of one item given the  cost of many items. If you need to find the cost of many items from the cost of one item,  apply the multiplication operation.

We need to convert this weight in kilogram using unitary method , we get      1 pound have = 0.45 kilogram

           157 pound will have \(=157\times0.45\)

                                              \(=70.65\) kilogram

A patient receive 0.25 mg of Medication A per kg

Using unitary method , we get

  1 kg of body receives = 0.25 mg of medication A

  70.65 kg of body receives \(=0.25\times 70.65\)

                                                \(=17.66\) mg of medication A

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