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Solve the inequality and graph it’s solution.

Length of the line AB is 1.414 units and midpoint of AB is (3.5,5.5).

Given in the graph,

A(4,6)  and B(3,5)

Distance formula = [tex]\sqrt{(x1-x2)^{2} +(y1-y2)^{2} }[/tex]

                      AB =  [tex]\sqrt{(4-3)^{2} +(6-5)^{2} }[/tex]

                            = [tex]\sqrt{1^{2} +1^{2} }[/tex]

                            = [tex]\sqrt{2}[/tex]

                            = 1.414 units

Midpoint = [tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

Let midpoint of AB be C(x,y)

C = (x,y) = [tex](\frac{4+3}{2},\frac{6+5}{2})[/tex]

             = [tex](\frac{7}{2},\frac{11}{2})[/tex]

             = (3.5,5.5)

Hence, length is 1.414 units and midpoint is (3.5,5.5).

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Step-by-step explanation:

Angle BAC = angle BCA

as sum of angles in triangle = 180

49 + 49 + ABC = 180

180 - 49 - 49 = ABC

ABC = 82°

The value of x in the angle illustrated as (5x + 2)° and (4x + 6)° is 4

It is important to note that line m and line n are parallel. In the diagram, they also intersect each other.

Therefore, it should be noted that according to angle rule, (5x + 2) and (4x + 6) are alternate angles. In this case, they're equal.

These will be illustrated as:

5x + 2 = 4x + 6

Collect like terms

5x - 4x = 6 - 2

x = 4

Therefore, x is 4°.

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The chief of police use sample statistical study  to estimate the number of people above the age of 18 who are using illegal substances in town.

In the given question,

The chief of police in statville wanted to estimate the number of people above the age of 18 who are using illegal substances in town.

He obtained 200 random names of statville residents from a computer database and sent his officers to survey these people about substance abuse.

Once the results came in, he calculated the margin of error and got an estimate of the percentage of residents who use illegal substances.

We have to explain what type of statistical study the chief of police use.

In the given question chief of police wants to check number of people who using illegal substances in town above the age of 18. So he take  200 random names from a computer database. That means he take the sample of 200 random people.

As we know that a sample is a selection from a larger population of individuals, things, or things that are used for measurement. To enable us to extrapolate the research sample's findings to the entire population, the sample must be representative of the population.

So we can say that the chief of police use sample statistical study  to estimate the number of people above the age of 18 who are using illegal substances in town.

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Answer: Sample Study

No because there’s a great risk of obtaining biased answers.

Answer:

No , x = -2

Step-by-step explanation:

When Dividing the Equation by a Constant , all terms in both sides must be divided by this Constant.

So here we divided both sides by 2 , but -6 is not divided , so this step is incorrect

The correct Answer is

[tex]\frac{-6}{2}+\frac{2x}{2} =\frac{-10}{2} \\-3+x=-5\\x=-5+3=-2[/tex]

The angle C = 103.85° using the sine rule and rounded to the nearest hundredth.

In trigonometry, the sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

Considering the ∆ABC, the sine rule states that;

(a/sinA) = (b/sinB) = (c/sinC)

so

25/sin120° = 20/sinB

sinB = (20 × sin120°)/25 {cross multiplication}

sinB = 0.6928

B = sin^(-1)[0.6928)] {sine inverse}

B = 43. 85°

Sum of interior angles in ∆ABC is 180° so;

C = 180° - (120° + 43.85°)

C = 180° - 76.15°

C = 103.85°

With the application of the sine rule, we can conclude that the value of the angle C is 103.85° rounded to the nearest hundredth.

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Answer:

a = 3, b = 12

Step-by-step explanation:

x^2-6x-3=(x-a)^2-b

Lets expand the right side:

(x-a)^2-b = (x-a)(x-a)-b

(x-a)(x-a)-b = x^2 -2ax + a^2 - b

The left side is equal to the right, as per the original equation:

x^2-6x-3 = x^2 -2ax + (a^2 - b)

Compare each term:

1)  x^2 = x^2 OK

2) -6x = -2ax;  a = 3 so that -6x = -2(3)x

3)  -3 = (a^2-b);  a^2 = (b-3)

    a = [tex]\sqrt{b-3}[/tex]

   a is 3, from above

    3 =  [tex]\sqrt{b-3}[/tex]

9 = b-3

b = 12

Considering the dimensions of the rectangular prism and it's volume, it is found that:

The volume of a rectangular prism is given by the multiplication of the dimensions of the prism, which are the width symbolized by w, the height symbolized by h and the length symbolized by l, that is:

V = l x w x h.

In the context of this problem, from the image, the dimensions are given as follows:

Then the polynomial expression regarding the volume of the prism is obtained as follows:

V(x) = 2x(x - 3)(2x - 5)

V(x)= 2x(2x² - 11x + 15)

V(x) = 4x³ - 22x² + 30x.

The features of the polynomial expression V(x) = 4x³ - 22x² + 30x is obtained as follows:

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For 0 < a < b <  1,  a^x < b^x, for x < 0.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given,  0 < a < b < 1.

Assuming a = 0.25 and b = 0.5.

∴ (0.25)^x < (0.5)^x for x > 0, again assuming x to be 2.

∴ (0.25)^2 = 0.625 and (0.5)^2 = 0.25.

Now, 0.625 > 0.25 which is not satisfying a^x < b^x, for x > 0.

Therefore, if 0 < a < b <  1, then a^x < b^x, for x < 0.

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Answer:

111%

Step-by-step explanation:

£3 × 60 = £180

(35 × £8) + ( 25 × £4) = £380

£380 ‐ £180 = £200

200/180 × 100% = 111% (nearest whole number)

The least sample size needed to assure with 90% confidence that the sample mean will not differ from the population mean by more than 5 minutes will be 416.16.

A normal distribution is a data set design in which the majority of values cluster around the middle of the range and the remainder taper off symmetrically toward either end. Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central location, with values decreasing as one moves out from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same. The normal distribution, like any other probability distribution, defines how the values of a variable are distributed. Because it properly captures the distribution of values for many natural occurrences, it is the most important probability distribution in statistics.

Here,

The z value at the 90 percent confidence interval is 1.645.

t ≥ z*s/√n

5≥1.645*62/√n

√n≥20.398

√n≥20.4

n≥416.16

The smallest sample size required to ensure that the sample mean does not deviate from the population mean by more than 5 minutes with 90% confidence is 416.16.

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Answer:

1/2

Step-by-step explanation:

if you take the (2,2) and make it (6,10), you add 4 to the x and 8 to the y. putting this as rise over run (x/y) it comes out to four eighths (4/8). reducing that comes out to one half (4/8).

2x + 6 = x - 4

x ≈ -0,67

or

x = -2^3

By using a trigonometric relation we will see that the height of the kite is 8.82 feet above the point where you hold the line.

We can view this as a right triangle, where the hypotenuse has a measure of 15 feet, we know one angle that measures 36°, and the opposite cathetus to that angle is x, the height we want to find.

We want to get the value of x, which is the opposite cathetus to the given angle, then we can use the trigonometric relation:

sin(a) = (opposite cathetus)/(hypotenuse)

Replacing what we know we will get:

sin(36°) = x/15ft

Solving this for x we get:

x = sin(36°)*15ft = 8.82ft

The height of the kite is 8.82 feet.

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The equation of the line, in slope-intercept form, that passes through

(4, 2) and (-2, -3) is y = 5/6 x - 4/3.

What is slope-intercept form?

The meaning of slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

Using two points and slope-intercept form we can find the equation of the line.

According to the given question:

The formula to find the slope of two points (x₁, y₁) and (x₂, y₂) is

m = (y₂ - y₁) / (x₂ - x₁)

The points given are (4, 2) and (-2, -3)

m = (-3 - 2) / (-2 - 4)

m = -5/ -6

m = 5/6

Now using the slope and the point (4, 2) the y intercept is

y = mx + b

2 = 5/6 (4) + b

2 = 10/3 + b

By further calculation,

b = 2 - 10/3

Taking LCM

b = (6 - 10)/3 = -4/3

By writing the equation in slope intercept form

y = mx + b

y = 5/6x - 4/3

Therefore, the equation of the line in slope intercept form is

y = 5/6 x - 4/3.

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Answer: 6.2

Step-by-step explanation:

Geometric Mean = √( 2 x 19 ) = 2√38 = 6.1644

Answer:

-0.86

Step-by-step explanation:

What is the slope of the line created by this equation? Round your answer out to two decimal places. 6x + 7y = 5

_____________________________________________

Slope intercept form solves for y:

y = mx + b when m = slope and b = y-intercept

First, solve for y:

6x + 7y = 5

subtract 6x from both sides:

6x + 7y - 6x = 5 - 6x

7y = 5 - 6x

divide both sides by 7:

7y/7 = (5 - 6x)/7

y = 5/7 - 6/7x

rearrange right side:

y =  - 6/7x + 5/7

Back to the equation: y = mx + b when m = slope and b = y-intercept

your slope is -6/7

in decimal form, rounded to two digits: -0.86

Step-by-step explanation:

I don't see the options and how they are written, but I can tell you the right answer in numbers :

sin(F) = 3/5 = 0.6

cos(F) = 4/5 = 0.8

sin(G) = 4/5 = 0.8

cos(G) = 3/5 = 0.6

why ?

remember the norm circle (radius 1) with ask the trigonometric functions.

the sine of an angle is the vertical height from that point in the circle arc down to x-axis.

the cosine of an angle is the length on the x-axis from the center of the circle to the point, where the sine touches the x-axis.

in any case, sine and cosine enclose the right angle (90°).

each function is now defined for the norm circle with radius = 1.

for angles in larger circles we need to divide the find lengths by the actual radius (we formality do this in the norm circle too, but a division by 1 does not change anything).

for the angles at F and G the radius is the side with the length 5.

Step-by-step explanation:

8x + 24 is a simplified expression.

It is not an equation, so it can't be solved.

There are two terms in 8x + 24, 8x and 24.

The two terms are unlike terms, so they cannot be combined together.

The parent function is y = x ; shift 2 units downwards.

Given,

In the question:

The function is :

g(x) = x - 2

Now, According to the question ;

Let's know

What is the Parent function and transformation?

The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit. Reflection. A reflection on the x-axis is made on a function by multiplying the parent function by a negative. Multiplying by a negative “flips” the graph of the function over the x-axis.

According to the above statement is;

g(x) = x -2

Hence, The parent function is y = x ; shift 2 units downwards.

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Answer:

Use the formula to find distance

The probability is 8/9.

From the question, we have

probability = (1/3)*(1/3)*(1/3) = 1/27 chance (all of them lie)

probability = (2/3)*(2/3)*(2/3) = 8/27 chance (all of them true).

Since, they all say it's heads.

Thus, the probability of it being heads = (8/27)/ ((8/27)+(1/27)) = 8/9.

Probability:

Chance is referred to as probability. This branch of mathematics studies the probability of a random event. The value is between 0 and 1. Probability is a concept that mathematics has adopted to predict the likelihood of particular events. Probability is just the measure of how likely something is to occur. With the help of this fundamental theory of probability, which is also used to describe the probability distribution, you will be able to comprehend the possible results for a random experiment. How likely something is to occur can be determined using probability. It might be challenging to predict many things with complete certainty. We can only predict whether an event will occur or how likely it is using it, not if it will actually occur.

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The answer of this question can be given by using congruence
Answer is 20°

What is an example of congruence?

Congruent relates to anything that is "exactly equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.

Given That:

∡DBC = 20°

DC = AD

DB is common on both triangle

As we have hypotenuse common in both triangle and 1 side equal then we can sa it is a congruent triangle by RHS

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Answer: 14

Step-by-step explanation: 10 + (6-2) = 14

The quantity of sugar Isabelle would need to make 4 1/5 batches of cookies is 21 cups of sugar

From the question, we are to determine the quantity of sugar that Isabelle would need to make the given number of batches. The number of batches Isabelle wants to make is 4 1/5 batches.

From the given information, Isabelle's lemon cookie recipe calls for 5 cups of sugar. If 1 batch of the lemon cookie calls for 5 cups of sugar

Then, 4 1/5 batches of the lemon cookie will call for 5 × 4 1/5 cups of sugar 5 × 4 1/5

= 5 × 21/5= 21

Hence, Isabelle will need 21 cups of sugar

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Answer:yes

Step-by-step explanation:

for every week he gets 3 cars so it can only incre ment by 3. (1,3) (2,6) (3,9) and so on.

Answer:

7+2/8+5

Step-by-step explanation:

The value of expression -23 +-15+|-17| + -35 is -56

In this question, we have been given a numerical expression.

-23 +-15+|-17| + -35

We need to find the value of given numerical expression.

Consider given numerical expression,

-23 +-15+|-17| + -35

= -23 + (-15) + |-17| + (-35)

= -23 - 15 + |-17| - 35

We know that for any real number a, |±a| = a

So, |-17| = 17

= -38 + 17 - 35

= -56

Therefore, the value of expression -23 +-15+|-17| + -35 is -56

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"We are 95% confident that the mean sodium content for all beef hot dogs is between 353.2 and 449.1 mg." is the correct statement.

The true parameter must be properly and contextually stated.

We are researching confidence intervals for population means rather than for particular observations. The parameter is, to put it in plain English, the average sodium content of all beef hot dogs. The phrase "We are 95% confident" would be a better translation.

Thus the correct statement is as mentioned above.

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Answer:

200

Step-by-step explanation:

20*10=200