The data set is: 6, 2, 6, 3, 5, 6, 7, 9, 1 For this question, find the IQR

2. The side AC corresponds to side AE of the other triangle.

3. The length of side BC is 15.

Two or more triangles are said to be similar if on comparing their properties, there exist some common relations. Some of the common relations are; measure of internal angles, scale factor etc.

From the diagram given, we have;

2. Given that the triangles are similar, thus:

The side AC corresponds to side AE of the other triangle.

3. On comparing the corresponding length of the triangles, we have;

15/ 25 = 9/ BC

15BC = 9 x 25

         = 225

BC = 225/ 15

     = 15

The length of side BC is 15.

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The value of the term a5 is 39

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

{3, 12, 21, 30, 39, 48, 57}

The expression a5 means the 5th term of the sequence

In {3, 12, 21, 30, 39, 48, 57} , the fifth eterm is 39

Hence, a5 = 39

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The measure of  each interior angle of a regular 16-sided polygon is 157.5 degrees

To determine the value of the interior angle, we need to note that;

The formula for calculating the sum of the interior angles of a polygon is expressed with the expression;

(n -2)180

Such that the variable n in the expression represents the number of sides of the polygon

From the information given, we have that;

(16- 2)180

expand the bracket

14(180)

multiply the values

2520 degrees

Then, we have;

16x = 2520

Make 'x' the subject

x= 157. 5 degrees

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Answer:

B always because a rectangle has two sets of parallel sides

Hope this helps

↬ x² - 6x -5

Substituting x = 3:-

⟶ x² - 6x -5

⟶ (3)² - 6(3) -5

⟶ 9 - 6 × 3 - 5

⟶ 9 - 18 - 5

⟶ 9 - 23

⟶ -14

Answer:

[tex] \gg{ \underline{ \large \: \boxed { \bf {- 14}}}}[/tex]

Step-by-step explanation:

[tex] \large \: \sf { \underline{Given}}[/tex]

[tex] \large \sf \underline{Solution }[/tex]

[tex] \large \: \displaystyle \sf {x}^{2} - 6x - 5[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \large \bf \blue{ \underline{putting \: the \: value \: of \: x}}[/tex]

[tex]\large \: \displaystyle \sf \: {3}^{2} - 6(3) - 5 [/tex]

[tex]\large \: \displaystyle \sf \: = \: 9 - 18 - 5[/tex]

[tex]\large \: \displaystyle \sf \: = \: - 9 - 5[/tex]

[tex]\large \: \displaystyle \bf \red{= - 14}[/tex]

The completed calculation with regards to the area of the congruent triangles can be presented as follows;

The distance formula indicates;

AM = √((x₂ - x₁)² + (y₂ - y₁)²)

Therefore, we get;

AM = √((4 - 0)² + (0 - 0)²) = √(4²)

AM = √(4²) = 4

BM = √((x₂ - x₁)² + (y₂ - y₁)²)

BM = √((4 - 4)² + (6 - 0)²) = √(6²)

BM = √(6²) = 6

AM ≅ CM Definition of the midpoint of AC

AM = CM Definition of congruent segments

CM = 4 Substitution property

Area ΔABM

A = (1/2)·b·h

= (1/2) × 4 × 6

= 12

Area ΔCBM

A = (1/2)·b·h

= (1/2) × 4 × 6

= 12

Therefore Area ΔABM = area ΔCBM by congruence

Triangles are congruent if they have the same size and shape.

The details of the reasons for the calculation steps and values are presented as follows;

Definition of midpoint of a segment

The midpoint of a line segment is the point that divides the segment into two parts of the same length

Definition of congruence?

Congruence refers to the existence of compatibility or harmony between objects, which in geometry indicates that the two geometric figures have the same measurement

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The given images shows us that we have a total of two lines

In mathematics, a point is referred to as the particular location on a plane. A point is identified by a dot.  It has no length, shape or size.

A line is straight, without any type of thickness and it is the shortest distance that exists between 2 points. It has only length. It is without width.

A line segment has two end points. The difference that a line segment has with a line is that a line is extensive while the line segment has two end points.

Ray is defined as a line that has only one endpoint. The other end of the line just goes on. It has one start point and one end point.

From the attached image, it is vert clear that we have two lines which are the horizontal line and the line that divides it.

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To convert 5.4 square meters to square centimeters is 54,000 cm²

To convert 5.4 square meters (m²) to square centimeters (cm²),

We need to multiply it by 10,000 (since 1 meter = 100 centimeters).

5.4 m² = 5.4 x 10,000 cm² = 54,000 cm²

Therefore, 5.4 square meters is equal to 54,000 square centimeters.

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Answer:

V = (1/2)(4/3)π(6.5^3) = 575.17 cubic inches

V = (1/2)(4/3)(3.14)(6.5^3) =

574.88 cubic inches

The correct answer is 574.9 cubic inches.

[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log_3(N)=x\implies 3^x=N[/tex]

Answer:

5/36

Step-by-step explanation:

hope this helps

Answer:

2.38888

Step-by-step explanation:

That's what is says hope this helps

The probability that the total team time in the 400-meter freestyle relay is less than 215 seconds is: 0.8345

From the table given the mean and standard deviation, we can say that:

Total time spent = 54.2 + 57 + 55.3 + 53.7

Total time spent = 220.2 secs

The total standard deviation is:

2.8 + 3 + 2.4 + 2.5 = 10.7 secs

Formula for z-score here is:

z = (x' - μ)/(σ/√n)

where:

x' is sample mean

μ is population mean

σ is standard deviation

n is sample size

Thus:

z = (220.2 - 215)/(10.7/√4)

z = 0.972

From online p-value from z-score calculator, we have:

p(x < 0.972) = 0.8345

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Answer: b

Step-by-step explanation: cause i just did it

Answer:

19.5625

Step-by-step explanation:

[tex]\frac{2(12) + 4(15) + 16 +18 + 2(20) + 22 +3(25) +2(29)}{16}[/tex] = [tex]\frac{313}{16}[/tex] = 19.5625

We add up all the numbers that are represented on the graph and then divide that by 16 because there are 16 numbers.

Helping in the name of Jesus.

The test score for Jason will be 55% for answering 11 questions right.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Jason is taking a multiple-choice test with a total of 20 points available. Each question is worth exactly 1 point.

The test score will be calculated as,

[tex]\text{Test score} =\dfrac{\text{Total questions - wrong answers}}{\text{Total questions}} \times100[/tex]

[tex]\text{Test Score}=\huge \text[\dfrac{(20-9)}{20}\huge \text] \times100[/tex]

[tex]\text{Test Score}=0.55\times100[/tex]

[tex]\text{Test Score}=0.55\%[/tex]

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The rate of each bus which leave a station at the same time are 76 mi/h and 68 mi/h respectively.

Given that,

Two buses leave a station at the same time and travel in opposite directions.

Let x be the distance travelled by the the first bus in 3 hours.

Then the distance travelled by the other bus in 3 hours = 432 - x

Rate of first bus = x/3 miles per hour

Rate of second bus = (432 - x) / 3 miles per hour

One bus travels 8 mi/h slower than the other bus.

x/3 - (432 - x) / 3 = 8

(x - 432 + x) / 3 = 8

2x - 432 = 24

2x = 456

x = 228

Rate of one bus = 228/3 = 76 mi/h

Rate of second bus = (432 - 228)/3 = 68 mi/h

Hence the rate of each bus are 76 mi/h and 68 mi/h respectively.

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Answer:

19cm

Step-by-step explanation:

I think it's 19cm as sides BC on the green triangle measure 15cm, and EF is 25cm on the blue triangle. It also mentions that they are similar, meaning that ∆ DEF is just a translated and enlarged version of ∆ ABC

25 - 15 = 10cm

9 + 10 = 19cm

Hope this helped :)

The likelihood that Mia and Lia place in 1st or 2nd is unlikely

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

People = 50

Positions = 1st, 2nd, and 3rd place

The probabilities are

P(1st) = 1/50

P(2nd) = 1/49

Using the above as a guide, we have the following:

P = 1/50 * 1/49

Evaluate

P = 0.00040816326

This value is less than 50%

So, the likelihood is unlikely or less likely

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The number shown is not written in scientific notation because the 10 do not raise to power of any number, and exponential on the second value do not represent a particular power.

Scientific notation  can be described as the way of writing very large  as well as very small numbers.

It should be noted that the  number is written in scientific notation which is been done as a result of the number falling between 1 and 10 and then this number is been multiplied by a power of 10 instance of this is 6.5 ✕ 10^8, then we can see that none of the given values have the sa,me expresion with this example.

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The term that refers to the basic characteristics of a population segment such as gender, age, and income is demographics.

We have,

Demographics refers to statistical data that describes a population and its characteristics, such as age, gender, income, education level, marital status, and other relevant factors.

Demographic information is commonly used by businesses and organizations to analyze consumer behavior, market trends, and patterns in the population.

By understanding the demographics of a particular population segment, businesses can tailor their products and services to better meet the needs and preferences of their target audience.

Demographic information is also used by government agencies and policymakers to allocate resources, plan for future development, and assess the needs of the population.

Thus,

The term that refers to the basic characteristics of a population segment such as gender, age, and income is demographics.

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Answer:

True, a cone has an apex which is the point where the sides of the cone meet to form a tip.

The true statement about the graphs:

Their slopes will be different from the slope of f(x), and their x-intercepts will be the same as the x-intercept of f(x).

The correct answer is an option (C)

First we draw a graph of function f(x) = -x + 3.

Find the graph in attached figure.

the x-intercept of f(x) is:

0 = -x + 3

i.e., x-intercept = (3, 0)

Then, three graphs of k(-x + 3) are drawn, for k = -1, -2, -3.

Let g(x) = -1(-x + 3)

The x-intercept of g(x) would be,

0 = -1(-x + 3)

i.e., x-intercept = (3, 0)

Let h(x) = -2(-x + 3)

The x-intercept of h(x) would be,

0 = -2(-x + 3)

2x = 6

i.e., x-intercept = (3, 0)

Let t(x) = -3(-x + 3)

The x-intercept of t(x) would be,

0 = -3(-x + 3)

3x = 9

i.e., x-intercept = (3, 0)

the graph of functions g(x), h(x) and t(x) is shown below.

We can observe that the x-intercept is same for all graphs but the slopes are different.

Therefore, the correct answer is an option (C)

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Answer:

$814 she kept for 5 years if she don't spend it

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

4x - 2y = 8

x - int y = 0

4x = 8

x = 2

(2, 0)

y-int, x = 0

-2y = 8

y = -4

The rate of interest with the given amount and compound interest is 5 percent.

Given that,

After 1 year: compound interest = $30 and total amount=$630.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].

Here, principal = 630-30=600

630=600(1+r/100)¹

630/600 = 1+r/100

1.05=1+r/100

1.05-1=r/100

0.05=r/100

r=5%

Therefore, the rate of interest with the given amount and compound interest is 5 percent.

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Step-by-step explanation:

The hypotenuse of each of these right triangles can be found using Pythagorean theorem....the hypotenuse is also the DIAMETER of the circle

   diamter * pi = circumference

First one:

  Hypot^2 = 13^2 + 13^2

    hypot ^2 = 338

     hypot = diameter = sqrt (338)

   circumference = diamter * pi  =  sqrt 338 pi   ft   ( or 13 sqrt(2) pi   ft )  

The second one is the same with slightly different numbers...you try it ...

Answer:[tex]\sqrt{338}\pi[/tex], [tex]25\pi[/tex]

Step-by-step explanation:

I will start with the second one, since it will be easier. Because this is a right triangle, you can use the given side lengths of the triangle to find the hypotenuse, which is also equal to the diameter of the triangle. Since the pythagorean theorem states that a^2(the shorter leg, squared) + b^2 (the longer leg, squared) = c^2 (the hypotenuse, squared) we can turn it into an equation like this:

[tex]7^{2\ }+\ 24^{2}\ =\ c^{2}[/tex]

(lets use x in place of c in the next few equations, for algebraic simplicity)

Simplify

[tex]49+\ 576\ =x^{2}[/tex]

[tex]625=x^{2}[/tex]

Get the square roots

[tex]\sqrt{625}=\sqrt{x^{2}}[/tex]

[tex]x=25[/tex]

Since x is equal to the hypotenuse, we know that the hypotenuse is also 25. This means the diameter of the second circle is 25, and we can now find the circumference. The EXACT circumference of the second circle is 25π, but a simplified version can be created by calculating it as if it were an equation. This comes out to around 78.5398163397, which would trail for infinity. which is why to get an exact measurement of the diameter, the most simplified exact version is displayed by multiplying the diameter by the pi symbol, because it is impossible to fit an infinite number in a finite space.

Now for the first circle, which I am now realising is no more difficult than the last one. We can do the same thing in this case, using pythagorean theorem, because there are two dash lines marking two of the lines on the circle to be equal to one another, we know that the two marked lines are equal to 13, despite not appearing to be.

We can use the same equation as we did before, but slightly modified.

[tex]13^{2}+13^{2}=x^{2}[/tex]

Simplify:

[tex]169+169=x^{2}[/tex]

[tex]338=x^{2}[/tex]

Now we can take the square roots of both sides of the equation.

[tex]\sqrt{338}=\sqrt{x^{2}}[/tex]

This is where we come to a bit of a pause. Because the square root of 338 is an irrational constant number, we have to use the unsimplified square root in our answer for the circumference, otherwise, our answer would not be exact.

The diameter of our circle is [tex]\sqrt{338}[/tex], which means that we can use an equation like this to find the circumference:

[tex]\sqrt{338}\pi[/tex]

But since we cannot simplify this any further without it not being exact, we must leave it as is.

The values of the trigonometric ratios for the given triangle are sinθ = 8/17, cosθ = 15/17 and tanθ = 8/15.

From the given right triangle hypotenuse= 17 units and legs of triangle are 15 units and 8 units.

We know that, sinθ = Opposite/Hypotenuse

sinθ = 8/17

We know that, cosθ = Adjacent/Hypotenuse

cosθ = 15/17

We know that, tanθ = Opposite/Adjacent

tanθ = 8/15

Therefore, the values of the trigonometric ratios for the given triangle are sinθ = 8/17, cosθ = 15/17 and tanθ = 8/15.

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1. Using the formula for Pearson correlation coefficient, we have:

x y xy x^2 y^2

1 3 3 1 9

1 1 1 1 1

2 3 6 4 9

3 7 21 9 49

3 9 27 9 81

4 5 20 16 25

6 8 48 36 64

6 7 42 36 49

7 10 70 49 100

7 7 49 49 49

n = 10

sum(x) = 40, sum(y) = 53, sum(xy) = 286, sum(x^2) = 214, sum(y^2) = 506

r = [n(sum(xy)) - sum(x)sum(y)] / sqrt{ [n(sum(x^2)) - sum(x)^2][n(sum(y^2)) - sum(y)^2] }

r = [10(286) - (40)(53)] / sqrt{ [10(214) - (40)^2][10(506) - (53)^2] }

r = 0.832 (rounded to 3 decimal places)

2. The critical value (rcrit) for a 2-tailed test with a 0.05 alpha level and 8 degrees of freedom is 0.632 (using a t-distribution table or calculator).

3. The calculated correlation coefficient (r = 0.832) is greater than the critical value (rcrit = 0.632), which means that the correlation is statistically significant. We would reject the null hypothesis and conclude that there is a significant positive correlation between client expectations and satisfaction with therapy sessions.

The statements that defines the term resources is A. materials that help you achieve your goals.

Resource  can be described as all the materials available  that is available in individual environment  and can be seen as one that is  technologically accessible.

It should be noted that resources do help us to achieve most of our goals and can be seen as one that is economically feasible  as welll as culturally sustainable and they serves as things that can help us and thjat can  satisfy our needs and wants which is needed on daily basis.

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