Find AB. Round to nearest tenth

Answer:

27.87

Step-by-step explanation:

In a right triangle, the length of the hypotenuse can be found using the Pythagorean theorem, which states that the sum of the squares of the two shorter sides is equal to the square of the length of the hypotenuse.

Using the given sides, we can write the equation:

AB^2 + BC^2 = AC^2

Substituting the given values, we have:

17^2 + 22^2 = AC^2

Simplifying the left side, we get:

289 + 484 = AC^2

773 = AC^2

Taking the square root of both sides, we find:

AC = √773 = 27.87

Rounding to two decimal places, the length of side AC is approximately 27.87.

The probability of buying 3 tires is 0.05 and the cumulative probability distribution table is created.

What is meant by probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given,

     Percentage of people who buys 4 tires = 50%

      Percentage of people who buys 2 tires = 32%

      Percentage of people who buys less than 2 tires = 13%

    Percentage of people who buys none = 6%

a) Prob(X=0) = 0.06

    Prob(X=2)  = 0.32

   Prob(X=4)  = 0.50

 Prob(X < 2) = Prob(X=0) + prob(X=1) = 0.06+ prob(X=1)

   prob(X=1) =   Prob(X < 2) - 0.06  = 0.13 - 0.06 = 0.07

Therefore prob(X = 3) = 1 - ( 0.5+0.32+0.07+0.06) = 1 - 0.95 = 0.05 = 5%

b) Cumulative probability distribution is as given in the figure.

Therefore the probability of buying 3 tires is 0.05 and the cumulative probability distribution table is created.

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Answer:

[tex]-6[/tex]

Step-by-step explanation:

[tex]-5.f(-2) - 3g(7)[/tex]

The values of [tex]f(-2)[/tex] and [tex]g(7)[/tex] have to be read and deduced from the respective [tex]f(x)[/tex] and [tex]g(x)[/tex] graphs

[tex]f(-2)[/tex]:

For x = [tex]-2[/tex], draw a straight vertical line connecting x = [tex]-2[/tex] and the blue [tex]f(x)[/tex] graph. It can be observed that the the blue [tex]f(x)[/tex] graph is touching the x-axis at x = [tex]-2[/tex]. Therefore, the corresponding y [or [tex]f(x)[/tex]] value is 0.

[tex]g(7)[/tex]:

For x = 7, draw a straight vertical line connecting x = 7 and the red dashed [tex]g(x)[/tex] graph. Then (from this meeting point) draw a straight horizontal line that touches the y-axis. It can be observed that the corresponding y [or [tex]g(x)[/tex]] value is 2

Now substitute the deduced values in the expression:

[tex]-5.[/tex](0) [tex]-3.[/tex](2) = [tex]0 - 6[/tex]

                     = [tex]-6[/tex]

Using trigonometry,  solving the provided question, we can say that here, [tex]2ab cos A = \frac{b^{2} + c^{2} - a^{2}}{2bc}[/tex] and [tex]\theta = 37[/tex]

The relationship between triangle side lengths and angles is examined in the branch of mathematics known as trigonometry. The application of geometry in astronomical study gave rise to the area's first appearance in the Hellenistic era, roughly in the third century BC. Exact approaches mathematics focuses on certain trigonometric functions and how they could be applied to calculations. In trigonometry, there are six well-known trigonometric functions. They are known by their various names and acronyms: sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of the properties of triangles, particularly of right triangles. The features of all geometric figures are studied in geometry.

where the sides b and c are forced together, trapping the angle A in (1). There are three options if you wish to rearrange the formula. You can get the answer for B, C, or A.

Reverse the cosine rule provided:

[tex]A^{2} = b^{2} + c^{2}- 2abcos A[/tex]

[tex]2ab cos A = \frac{b^{2} + c^{2} - a^{2}}{2bc}[/tex]

Replace A = θ with a = 17, b = 14, and c = 26,

then simplify:

[tex]Cos \theta = \frac{14^{20} + 26^{2} - 17^{2}}{2\times 14 \times 26}[/tex]

[tex]Cos \theta = \frac{583}{728}[/tex]

[tex]\theta = cos^{-1}(\frac{583}{728})[/tex]

[tex]\theta = 37[/tex]°

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Complete question -

By using tool, graph of the quadratic function f (x) = x² + 10x + 24 is shown in figure.

And, Vertex = (- 5, - 1)

A point on graph = (- 6, 0)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The quadratic function is,

⇒ f (x) = x² + 10x + 24

Now, By using tool we can draw the quadratic function f (x) = x² + 10x + 24 is shown in figure.

And, By figure of the quadratic function f (x) = x² + 10x + 24, we get;

Vertex = (- 5, - 1)

A point on graph = (- 6, 0)

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Answer:

(-5, -1) & (-6, 0)

Step-by-step explanation:

Just finished the test and this was correct. Hope this was helpful!!

Answer:

rational number, 2/9, 22/100=11/50, rational, no fraction equivalent, perfect square, non-perfect square

Step-by-step explanation:

Answer:

33.33%

Step-by-step explanation:

amount of sugar at first 6x

now 4x

difference 2x,(6x-4x)

"ratio=2/6"

change in percentage:2/6×100%=33.33%

It is a translation of 3 units up and one unit to the left,  then the correct option is D.

For any function y = f(x), we can define:

A vertical translation of N units as:

g(x) =f(x) + N

if N > 0, the translation is up

if N < 0, the translation is down.

A horizontal translation of N units as:

g(x) =f(x + N)

if N > 0, the translation is left

if N < 0, the translation is to the right.

Here we have:

g(x) = f(x + 1) + 3

So we have a translation of 1 unit to the left and 3 units up.

The correct option is d.

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Answer:

[tex] \frac{14}{16} \: and \: \frac{13}{16} [/tex]

Step-by-step explanation:

So we have these two fractions

[tex] \frac{7}{8} \: and \: \frac{13}{16} [/tex]

Does 8 go into 16? Yes. It goes in twice because 8 times 2 is 16. That means 16 is our common denominator.

Because of that, since we multiplied 8 by 2, we will do the same to the 7. 7 times 2 is 14.

Because of that we have 14/16 and 13/16 as our answers.

Answer:

0.707106781187

Step-by-step explanation:

I recommend using the website desmos

Malia can't buy 75 water bottles and 100 pairs of socks because it is not a solution to the system.

System of Inequalities:

The term "system of inequalities" refers to a collection of two or more disparities in one or more variables. When a problem demands a variety of solutions and those solutions must satisfy many constraints, systems of inequalities are used.

Now in the given question,

Here we have a graph of inequalities, and we just need to see if the pair (75, 100) is a solution.

The solutions of the system are all the points in the intersection of the two shaded areas (in this case are all the points in the green area)

Now, clearly the point (75, 100) is not a solution

Even if you evaluate that in the first inequality:

x + y ≥ 200

we get:

75 + 100 ≥ 200

175 ≥ 200

which is false.

So no, Malia can't buy 75 water bottles and 100 pairs of socks.

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Units are a natural number, a natural number that are negative, or zero. The number zero and any number generated by adding one to it repeatedly. A single integer or the product of two integers (division by zero excluded).

What exactly are integers?

In mathematics, integers are the collection of positive and negative numbers. Integers, like whole numbers, do not include the fractional element. Thus, integers are numbers that can be positive, negative, or zero, but not fractions. On integers, we can do all arithmetic operations such as addition, subtraction, multiplication, and division. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. "Z" is the symbol for integers.

The number zero and any number generated by adding one to it repeatedly. A single integer or the product of two integers (division by zero excluded).A natural number, a negative of a natural number, or zero is a unit of an abstract mathematical system according to the principles of arithmetic. 

e.g. 1,2,0, 0+1, 0+2+3, 8, 8/2=4, -8/2=-4 etc. all are units of  an abstract mathematical system subject to the laws of arithmetic.

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The slope of the least-squares regression line is not directly related to the fraction of the variation in the response variable that is explained by the explanatory variable.

The slope of the least-squares regression line is a numerical measure of the rate of change in the response variable for a unit change in the explanatory variable. It does not directly relate to the fraction of the variation in the response variable that is explained by the explanatory variable. This is because the fraction of the variation in the response variable that is explained is determined by the correlation coefficient, which is a measure of how well the regression line fits the data. The slope of the least-squares regression line is unitless, meaning it does not have any specific unit such as meters, seconds, or degrees. The slope of the least-squares regression line is simply a numerical measure of the rate of change in the response variable per unit change in the explanatory variable. This is different from the fraction of the variation in the response variable explained by the explanatory variable, which is determined by the correlation coefficient.

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The number of tractors that should be produced to incur the minimum cost will be 300.

For the maximum value of the function if f''(x) < 0 and for the minimum value of the function if f''(x) > 0.

The maximum and minimum value of the function is at f'(x) = 0.

The function is given below.

C(x) = 11000 − 60x + 0.1x²

Differentiate the function with respect to x, then we have

C'(x) = 0

(d/dx)(11000 − 60x + 0.1x²) = 0

− 60 + 0.2x = 0

0.2x = 60

x = 300

The number of tractors that should be produced to incur the minimum cost will be 300.

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Answer: 9 - 36n

Step-by-step explanation: So, first you multiply 9 by 1 and 9 by 4n, which gives you 9 - 36n.

Answer:

n=1/4

Step-by-step explanation:

9(1-4n)

Distribute the 9 to create the equation 9-36n.

Now set it equal to zero.

9-36n = 0

Add 36n to both sides to get 9 = 36n

Now divide by sides by 36 to get 9/36 = n

Now simplify your fraction 9/36 = 1/4 so 1/4=n

The mean is sensitive to outliers and will not accurately represent the center of the data if the distribution is significantly skewed.

The mean is a measure of central tendency that is calculated by adding up all values in a dataset and dividing by the number of values. It is often used as a measure of average since it takes into account all values in the dataset. However, it is an inappropriate measure of central tendency when the data distribution is severely skewed. A skewed distribution is one in which the data is not distributed evenly around the mean, and the data is either concentrated in the lower or higher end of the range. Since the mean is sensitive to outliers, it will be greatly affected by these values and not accurately represent the center of the data. In this case, it is more appropriate to use the median as a measure of central tendency since it is not affected by outliers. The median is the middle value of a dataset when the data is sorted from smallest to largest and is a better representation of the true center of the data in a skewed distribution.

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The coordinates after the rotation of 90° will be (-2, -3), (3, 4), and (4, -5) respectively.

Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.

Precession, nutation, and intrinsic rotation are the names of these rotations.

Shapes can be rotated by being moved around a fixed point (clockwise or anticlockwise, and by a certain number of degrees).

Although the shape will remain precisely the same, its location within the room will shift.

So, we have:

(-3,2),(4,-3) and (-5,-4)

Now, the graph then as follows.

Now, rotate them to 90°.

(Refer to the graph attached below)

Then, the coordinates after 90° rotation will be:

(-3,2) = (-2, -3)

(4,-3) = (3, 4)

(-5,-4) = (4, -5)

Therefore, the coordinates after the rotation of 90° will be (-2, -3), (3, 4), and (4, -5) respectively.

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Answer:

Time (min) Distance (km)

6       9

12      18

24     36

15     45

Step-by-step explanation:

The table shows equivalent ratios between time in minutes and distance in kilometers. An equivalent ratio means that the ratio of time to distance stays the same, even though the numbers themselves change.

For example, in the first row, the ratio of time to distance is 6 minutes to 9 kilometers. In the second row, the ratio of time to distance is 12 minutes to 18 kilometers. Despite the change in numbers, the ratio of time to distance remains the same. This is why these ratios are considered equivalent.

Answer:

Any odd number multiplied by an even number will make an even number.

Answer:

$26.25

Step-by-step explanation:

25% of 35 can be found by multiplying .25 x 35 to get 8.75

the coupon will reduce the regular price of $35 by 8.75 to produce the new price of $26.25

Answer:

4.84 m

Step-by-step explanation:

V = πr²h

h = V/πr² = (3.8 m³) / π(0.5m)² = 4.84 m

Therefore , the solution of the given problem of standard deviation comes out to be the range rule of thumb is only an approximation and does not take into account the shape of the distribution .

Variance is a measure of variation used in statistics. To calculate the average variance between the data and the mean, use the algorithm below. In opposition to other numerical measures of variability, it incorporates all data points into calculations by comparing each data point's value to the mean. Among the differences are unintentional errors, irrational expectations, and changing market or economic conditions.

Here,

According to the range rule of thumb, the range of the data set is roughly four times the standard deviation. Therefore, we can estimate the standard deviation by dividing the range by 4:

range = 196.9 - 154 = 42.9

estimated standard deviation = range / 4 = 10.725

Comparing this estimate to the actual standard deviation of 8.04 cm calculated using the 149 heights, we see that the estimate is off by about 2.685 cm.

This suggests that the estimate obtained using the range rule of thumb is not very accurate in this case, as it is outside the 1.4 cm threshold for accuracy.

This is not surprising, as the range rule of thumb is only an approximation and does not take into account the shape of the distribution or the sample size.

Therefore , the solution of the given problem of standard deviation comes out to be the range rule of thumb is only an approximation and does not take into account the shape of the distribution or the sample size.

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Answer:

40,000 + 700 + 50 + 3

Step-by-step explanation:

Expanded form requires you to separate the numbers in power of ten

Specific individuals in a population are unfairly left out of a study, which is known as exclusion bias. When researchers design a study that inadequately represents specific segments of the community, undercoverage bias emerges.

When a sample is not chosen that accurately represents the full population of data, a statistical error known as sampling error arises. As a result, the sample's findings do not accurately reflect the outcomes that the complete population would produce.

When a sample is chosen from a population based on the idea of randomization, this practise is known as probability sampling.

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Hi there, here's your answer:

Highest temperature = 18 degrees

Least temperature = -5 degrees

The difference between the two is 18 - (-5) = 18 + 5 = 23 degrees

Hope it helps!

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The equation that determines the intersection of line with a clipping triangle is ax + by + c = 0 [1]. The solution has been obtained by using functions.

What is a function?

A function is described as a relationship between a group of inputs with one output each. A function is, to put it simply, a relationship between inputs in which each input is connected to exactly one output. Every function has a domain and a codomain, or range. A function is typically represented by the notation f(x), where x represents the input. A function is typically shown as y = f(x).

The equation ax + by + c = 0 [1] represents the line in question. A list of pairs of coordinates for each intersection point and the number of intersections (count) should be returned by the function (list).

A list of items can be sent to the function count list, which will return the total number of objects in the list. The function returns the number of objects in the specified list after accepting an array or list of objects.

Hence, the equation that determines the intersection of line with a clipping triangle is ax + by + c = 0 [1].

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Answer:  k=(1/5)

Step-by-step explanation:

The first step is to rewrite the equations in standard form by subtracting the constant from each side.

Standard form is a type of numerical notation used to express large numbers in a concise form. It is based on powers of 10, which means each place value of a number is multiplied by a power of 10. Standard form is typically used in scientific and mathematical applications, and it is also known as scientific notation. To write a number in standard form, the number is written as a coefficient, followed by the base of 10, raised to an exponent.

3x - 2y = 10  becomes  3x - 2y - 10 = 0

3x - y = 17 becomes 3x - y - 17 = 0

Let's multiply the first equation by 2 and the second equation by 3.

2(3x - 2y - 10) = 0

3(3x - y - 17) = 0

6x - 4y - 20 = 0

9x - 3y - 51 = 0

The next step is to add the two equations together.

6x - 4y - 20 + 9x - 3y - 51 = 0

15x - 7y - 71 = 0

The last step is to solve for the variable.

15x - 7y = 71

15x = 71 + 7y

x = (71 + 7y)/15

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