Solve the compound Inequalities, graph the solutions and write the solutions in interval notation. Show all work.-5<2x+3 less then or equal to 11

The Solution.

Step 1:

We shall state the variation as direct ( positive).

Step 2:

We shall solve the equation in step1 above to get the value of n.

Step 3:

Presentation of the Answer.

The correct answer is n = 8.

The classification of triangle BDC is given by the following option:

d. Obtuse Isosceles.

The classification of the triangles relative to their side lengths are given as follows:

The classifications of a triangle according to it's greatest angle measure is given as follows:

For triangle BCD, we have that:

Thus option D is correct.

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Answer:

Step-by-step explanation:

Answer:

1) 1.33

2) 0

Step-by-step explanation:

1) 9-1/8-2 = 8/6= 4/3= 1.33

2)-3-(-3)/8-4 = 0/4=0

Answer:

The 7th term is 729

Step-by-step explanation:

Given

\(Sequence: 1, 3, 9...\)

Required: Determine the 7th term

The given sequence is a geometric function. So, we calculate the common ratio (r) first.

\(r = \frac{T_2}{T_1}\)

\(r = \frac{3}{1}\)

\(r = 3\)

The nth term of gp is:

\(T_n = ar^{n-1\)

Where

\(a = T_1\)

The 7th term is:

\(T_7 = ar^{7-1\)

\(T_7 = ar^6\)

\(T_7 = 1 * 3^6\)

\(T_7 = 729\)

Answer:

17.5

Step-by-step explanation:

Angle EDF added up equals to 37.5

12+8=20

37.5-20=17.5, so the answer is 17.5, hope this helps :)

Answer:

BC = 5

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion , that is

\(\frac{BC}{DF}\) = \(\frac{AC}{EF}\) ( substitute values )

\(\frac{BC}{7.5}\) = \(\frac{8}{12}\) ( cross- multiply )

12 BC = 60 ( divide both sides by 12 )

BC = 5

The inequalities that are represented by the given graph are expressed as;

y - x > 0 and y ≥ 1

Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

For the dashed line, shading is above the line, the y-intercept is 0.

Slope is 1. Thus, equation is;

y - x > 0

For the horizontal line, the inequality is expressed as;

y ≥ 1

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The median of the given data set is 26.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

Given the data set, we need to find the median.

So, let's arrange the numbers from smallest to largest in order to find the median.

\(\sf 15,20,22,26,28,35,36.\)

\(\text{Median}=\sf 26\)

Therefore, the median of the data set is 26.

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Based on the time it takes to patrol one neighborhood, the number of neighborhoods that the sheriff can patrol in 5/8 of an hour is 3.125 neighborhoods

The number of neighborhoods that the sheriff can patrol in 5/8 hours depends on the number of hours that it takes the sheriff to patrol one neighborhood.

The number of neighborhoods she can patrol can therefore be found by the formula:

= Number of hours sheriff has / Number of hours required to patrol one neighborhood

= 5/8 ÷ 3/15

= 5/8 x 15/ 3

= 75 / 24

= 3.125 neighborhoods

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Answer:

Domain = {0.-6}

Range = {-2, 4}  

Notes We find coordinates and radius and state

Then we show formula  (x -x1)^2 + (y +y1) = r ^2 and show

(x -3 )^2 + (y − 1)^2 = 9 = R^2  THE RADIUS^2

then ;

Domain formula = x - r   and x + r

Range formula = y - r  and  y + r

Step-by-step explanation:

The graph is a circle so all the points are enclosed in it

The domain is the values for x so you subtract the radius from the centre coordinate and you add the radius to it The range is the values for y so you do the same to the y coordinate If you use

(x- x1) ^2 + (y - y1) ^2

(x -3 )^2 + (y − 1)^2 = 9

However this changes if centre coordinate shows negatives

we change negative x or y to + positive in the formula in bold.

Centre coordinate = (3.,1) radius is 3  SO = MUST BE THE RADIUS ^2

= (x - 3)^2 + (y - 1)^2 = 3^2  = 9  

Domain formula = x - r   and x + r

Domain  = 3 - 3 = 0

and - 3 + 3 = -6

Domain = {0.-6}

Range formula = y - r  and  y + r

Range = 1 - 3 = -2

and  1 +3 = 4

Range = {-2, 4}  

NSQ can be turned into SQ through hypothesis testing and statistical analysis to determine significant relationships and patterns in the data.

To turn a non-statistical question (NSQ) into a statistical question (SQ), we need to rephrase it in a way that allows for statistical analysis. A statistical question is one that can be answered by collecting and analyzing data. Here is an example of how to turn an NSQ into an SQ:

This is a non-statistical question because it cannot be answered by collecting and analyzing data. It is purely a matter of personal preference and cannot be measured quantitatively. However, we can turn it into a statistical question by rephrasing it as:

To answer this question, we would need to collect data from a sample of the population and analyze it statistically. For example, we could conduct a survey of 1000 people and ask them which beverage they prefer. We would then calculate the percentage of respondents who prefer tea over coffee and use statistical methods to estimate the margin of error and confidence interval.

By turning the non-statistical question into a statistical question, we have made it possible to collect and analyze data to answer it. This approach is useful in many fields, including market research, social sciences, and healthcare, where data-driven decisions are increasingly important.

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The quantity of the hardener added to 18 containers of resin will be 990 ml.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the formula for glue says to add 55ml of hardener to each container of resin.

The quantity of hardener for 18 containers will be calculated as,

Q = 18 x 55

Q = 990 ml

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The statement which is not true about the circle M is ∆ABM is isosceles.

The correct answer choice is option 2.

Based on the circle M;

diameter AC,

chords AB and BC,

radius MB

Isosceles triangle: This is a type of triangle which has two equal sides and angles.

Equilateral triangle is a triangle which has three equal sides and angles.

Hence, ∆ABM is equilateral triangle.

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Answer:

\( \huge \boxed{ \boxed{ - \frac{6}{7} }} \\ \)

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\\)

From the question we have

\(m = \frac{ - 3 - - 9}{ - 5 - 2} = \frac{ - 3 + 9}{ - 5 - 2} = - \frac{6}{7} \\ \)

We have the final answer as

\( - \frac{6}{7} \\ \)

Hope this helps you

Answer:

the number has 2 resumable 6+5

Answer: 10,500 hits

Step-by-step explanation:

I WANT BIG BRAIN! I WANT BIG BRAIN AHAHHHHHHH!!!!!!!

ok there are a number of ways to go about this

it is unclear whether or not the YT content creator will get one pound for 500 hits

i honestly dont know but i am going to assume it will

1000 times 20 (we are plugging in a test variable, 20, here)

so lets say we have 20,000 hits

lets divide that by 1000 and we get 20. 20 times 2 is 40 pounds so obviously thats too much

lets try 1000 times 10

so we have 10 times 2 and thats 20 pounds. we are closer

10,500 hits

(i put in 500 because half of 1000 is 500 and that will give you one pound instead of two)

Answer:

9. FEG is 65 and HEG is 115

Step-by-step explanation:

For FEG you can get this by doing supplementary angle and simply subtracting 180-115. For HEG, you realize that it is a vertical angle and from there you know that it is the same angle as DEF

Answer:

19.2

Step-by-step explanation:

Let x be the missing number

2 1/2x =48

5/2x =48

x=48(2/5)

x=19.2

Answer:

1/12

Step-by-step explanation:

Probability of 4 = 1/6

Probability tail = 1/2

Multiply them

Answer:

1/12

Step-by-step explanation:

Probability of 4 = 1/6

Probability tail = 1/2

1/6 x 1/2 = 1/12

Step-by-step explanation:

The ratio of the number of baskets made by Tony to the number of baskets made by Colin is 2 to 3

let the ratio be 2x and 3x

Tony made 10 baskets

so , 2x=10

x=5

3x =3×5=15

so , Collin made 15 baskets

The statement that describes inverse function best is the amount of time she has walked (in hours) when she is kilometers from tomsville i.e. option A

According to the question,

The given function denotes the distance travelled by Kira in kilometers from tomsville after hours of walking

D(t) =  10.4 - 4t

The inverse of the function is D⁻¹(x)

=> D(t) =  10.4 - 4t

Converting equation in terms of t,

=>  D(t) + 4t = 10.4

=> 4t = 10.4 - D(t)

=> t = 10.4 - D(t) /4

Inverse function =  D⁻¹(x) = 10.4 - D(x) /4

It denotes the amount of time she has walked (in hours) when she is kilometers from tomsville.

From the following statements in the question

Option (a) is correct about inverse function

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Answer:

600

Step-by-step explanation:

Answer:

52500

Step-by-step explanation:

first do 5*105 to get 525 then mutiply by 100 to get 52500

The 95% confidence interval is {0.01962, 0.37438}

Given:

123 children of certain race are the sample size

The percentage who did not go to school: 23/23 + 31 = 42.6%

In this sample, the children who attend preschool are more likely to.

n2p2=  54(0.426) = 23.004 = 23

n2(1-p2) = 54(1-0.426) = 30.996 = 31

P(x1 + x2)/n1 + n2 = 43 + 23/69 + 54 = 0.54

SE = \(\sqrt{0.54(1-0.54)[\frac{1}{69} + \frac{1}{54} }\)

SE = 0.0905

z value for 95% confidence interval

z value = 1.96

(0.623 - 0.426) - 1.96 * 0.0905

= 0.01962

0.623 - 0.426 + 1.96  * 0.0905

= 0.37438

Hence, The 95% confidence interval is {0.01962, 0.37438}

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Keegan's error is assuming that the product of the slopes of any two sides of a triangle should be -1 for the triangle to be a right triangle.

To determine if the triangle LMN is a right triangle, Keegan should instead calculate the lengths of the three sides of the triangle and check if they satisfy the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

To correct his approach, Keegan should calculate the lengths of sides LM, MN, and NL using the coordinates of the vertices and then check if the Pythagorean theorem holds true.

If the squared length of one side is equal to the sum of the squares of the other two sides, then the triangle LMN is a right triangle.

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Answer:

5 mph

Step-by-sep explanation:

To find of out the difference between the speed of the two drivers in miles per hour (not in miles per minute), first, calculate the unit rate or speed of driver 1 using the graph, and driver 2 using the table given.

Unit rate/speed = distance travelled/time = y/x.

Speed of Driver 1/unit rate:

The graph shows 1.5 miles (y) is travelled in 2 minutes (x).

Convert the 2 minutes to hour, you will have:

\( \frac{2}{60} = \frac{1}{30} hr \)

Speed in mph = \( \frac{y}{x} = \frac{1.5}{\frac{1}{30}} = 1.5*\frac{30}{1} = 45 \)

Speed of Driver 1 in mph = 45 mph

Speed of Driver 2/unit rate:

The table shows 2.5 miles (y) is travelled in 3 minutes (x).

Convert the 3 minutes to hour, you will have:

\( \frac{3}{60} = \frac{1}{20} hr \)

Speed in mph = \( \frac{y}{x} = \frac{2.5}{\frac{1}{20}} = 2.5*\frac{20}{1} = 50 \)

Speed of Driver 2 in mph = 50 mph

Difference between the speed of the two drivers = 50 - 45 = 5 mph

Answer:

\(\Huge \boxed{x=-2}\)

Step-by-step explanation:

\(-136=8(6x-5)\)

Dividing both sides by 8.

\(-17=6x-5\)

Adding 5 to both sides.

\(-12=6x\)

Dividing both sides by 6.

\(-2=x\)

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{x = - 2}}}}}\)

Step-by-step explanation:

\( \sf{ - 136 = 8(6x - 5)}\)

Distribute 8 through the parentheses

⇒\( \sf{ - 136 = 48x - 40}\)

Swap the sides of the equation

⇒\( \sf{48x - 40 = - 136}\)

Move 40 to right hand side and change it's sign

⇒\( \sf{48x = - 136 + 40}\)

Calculate

⇒\( \sf{48x = - 96}\)

Divide both sides of the equation by 48

⇒\( \sf{ \frac{48x}{48} = \frac{ - 96}{48} }\)

⇒Calculate

\( \sf{x = - 2}\)

Hope I helped!

Best regards!!

The concept of type I and type II error was used to set hypothesis and to pick the correct option

What is Hypothesis?

In a scientific setting, a hypothesis (plural: hypotheses) is a tested claim regarding the relationship between two or more variables or a suggested explanation for a phenomenon that has been observed.

Given that,

Significance level: α = 0.05

Power of the test = 0.80

Making statistical claims about the characteristics of the population is made possible by hypothesis testing.

The type I error is also known as significance level.

Since, the given α = 0.05

Therefore, the type I error is 0.05

As a result, choice (a) is accurate.

Type I error is the probability of rejection \(H_{0}\) when \(H_{0}\) is true.

The type II error is denoted by β .

Now,

Power = 0.80

1 - β = 0.80

β = 1 - 0.80

β = 0.20

Therefore, the type II error is 0.20

Hence, option (b) is correct.

Type II error is fail to reject \(H_{0}\) when \(H_{0}\)  is false.

The concept of type I and type II error was used to set hypothesis and to pick the correct option

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Answer:

The exponential function is

\(y = {2}^{x} \)