What are the two points plotted on the graph?

Data visualization is important because option (a) 90% of the information transmitted to the brain is visual.

Data visualization is important because the human brain is wired to process visual information more efficiently than text or numbers. Research shows that about 90% of the information transmitted to the brain is visual, and we can process visual information much faster than text.

Therefore, data visualization is an effective way to represent complex data in a way that is easy to understand and analyze. It allows us to identify patterns, trends, and outliers that might be difficult to detect in raw data.

Therefore, the correct option is (a) 90% of the information transmitted to the brain is visual.

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The given question is incomplete, the complete question is:

Data visualization is important because: a) 90% of the information transmitted to the brain is visual b) None of these are correct c) People can synthesize data better than visual representation d) Everybody likes chart and graphs

The value of the variable x are;

31. x = 1

32. x = 2

33. x = -3

34. x = 5

35.  x= 17

From the information given, we have to know that;

We then have;

m<2 and m< 7 are corresponding angles

Then,

2x = 8x - 6

collect the like terms

x = 1

m<1 = m< 8; corresponding angles

3x - 2 = 5x - 4

collect the like terms

x = 1

m<2 = m<5

6x + 4 = 8x + 10

collect the like terms

x = -3

m<1 = m< 6

2x - 5 = x

collect the like terms

x = 5

m<3 + m< 4 = 180

3x + 6 + 7x + 4 = 180

collect the terms

10x = 170

x = 17

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Answer:

Yes, the 3-4-5 triangle and the 1.5, 2, 2.5 triangles are both working right triangles.

Step-by-step explanation:

I am assuming that the triangle we are given below is 1.5, 2, 2.5, and not necessarily a Pythagorean triple (we are asked to check if it is). We can check if this triangle meets the Pythagorean Theorem, which states that:

a^2+b^2=c^2

Where a and b are both the legs of the triangle and c is the hypotenuse (longest side). Now we can simply plug in 1.5, 2, and 2.5 and see if we get a working Pythagorean triple (if so, then the equation will be true).

(1.5)^2+2^2= 2.25 + 4= 6.25

and

(2.5)^2=6.25

This works! Giving that:

(1.5)^2+2^2=(2.5)^2 in the form of: a^2 + b^2=c^2

Now for the second part of the problem, how can we figure out if a 3,4, and 5 triangle is also a working Pythagorean triple by using our existing knowledge about the 1.5, 2, 2.5? Well, the 3, 4, and 5 triangle is also the right triangle! This is because every number in the set "1.5, 2, 2.5" is simply multiplied by 2, which is alike to scaled triangles. We can see so like this:

1.5*2=3

2*2=4

2.5*2=5

It is scaled up from the 1.5, 2, and 2.5 triangles! Now lets double check our work and see if we are correct.

3^2+4^2=9+16=25

5^2=25

Thus,

(3)^2+(4)^2=(5)^2

So, yes, the 3, 4, and 5, triangles and the 1.5, 2, 2.5, triangles are both working Pythagorean triples, we were able to prove this by scaling up and existing triple to find new ones. Have a great day!

The value of angle R is 28.03( nearest hundredth)

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

The two legs of the right angled triangle are opposite sides and adjascent while he third side is hypotenuse.

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

Here, using angle R, opp = 8cm , adj = 15cm and hyp = 17cm

Therefore sin(R) = 8/17

sin(R) = 0.47

R = sin^-1( 0.47)

R = 28.03( nearest hundredth)

therefore the value of angle R is 28.03°

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The p-value for the hypothesis test is approximately 0.65.

To find the p-value for the hypothesis test, we need to determine the test statistic and the corresponding probability.

First, we need to state the null and alternative hypotheses:

Null Hypothesis: The mean number of alcoholic drinks for college students at the liberal arts college is equal to the mean number of alcoholic drinks for U.S. college students in general, which is 4.73.

Alternative Hypothesis: The mean number of alcoholic drinks for college students at the liberal arts college is not equal to the mean number of alcoholic drinks for U.S. college students in general.

Next, we need to determine the test statistic, which is calculated as follows:

t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))

t = (4.45 - 4.73) / (3.92 / sqrt(70))
t = -0.28 / 0.47
t = -0.596

Using a t-distribution table with 69 degrees of freedom (70 - 1), we find the corresponding two-tailed probability to be 0.553.

Therefore, the p-value for the hypothesis test is 0.553. This means that if we assume the null hypothesis is true, there is a 55.3% chance of observing a sample mean of 4.45 drinks per week or more extreme. Since this p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the mean number of alcoholic drinks for college students at the liberal arts college differs from the mean number of alcoholic drinks for U.S. college students in general.
To find the p-value for the hypothesis test, we first need to set up the null and alternative hypotheses:

Null hypothesis (H₀): The mean number of alcoholic drinks for college students at this liberal arts college is equal to the national mean (µ = 4.73).
Alternative hypothesis (H₁): The mean number of alcoholic drinks for college students at this liberal arts college is different from the national mean (µ ≠ 4.73).

Next, we'll perform a t-test, since we have a sample mean, standard deviation, and sample size, but not the population standard deviation.

First, calculate the t-statistic:
t = (sample mean - population mean) / (sample standard deviation / √sample size)
t = (4.45 - 4.73) / (3.92 / √70)
t ≈ -0.46

Now, we need to find the degrees of freedom (df) for the t-distribution:
df = sample size - 1
df = 70 - 1 = 69

Using a t-table or t-distribution calculator, we can find the p-value for a two-tailed test (since we're testing for a difference, not specifically greater or lesser) with t ≈ -0.46 and df = 69. The p-value is approximately 0.65.

Your answer: The p-value for the hypothesis test is approximately 0.65.

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Step-by-step explanation:

just find the cubic of 16

[tex] {16}^{3} = {2}^{12} = 4096[/tex]

The answer in the form of polynomial is:

x² + 2/(x-1) = x + 3 + 1/(x-1)

An expression that consists of variables, constants, and exponents and that is combined using mathematical operations such as addition, subtraction, multiplication, and division (no division operation by a variable) is referred to as a polynomial.

To write x² + 2/(x-1) in the form of p(x) + k/(x-1), we need to perform partial fraction decomposition:

x² + 2/(x-1) = (Ax + B)/(x-1) + Cx + D

Multiplying both sides by (x-1), we get:

x² + 2 = (Ax + B) + (Cx + D)(x-1)

Expanding the right-hand side, we get:

x² + 2 = Ax + B + Cx² - Cx + Dx - D

Matching coefficients on both sides, we get the following system of equations:

C = 1

D - B = 2

A - C = 0

-B + D = 0

Solving for A, B, C, and D, we get:

A = 1

B = -1

C = 1

D = 1

Therefore, we have:

x² + 2/(x-1) = (x-1)/x-1 + x + 1

                   = x + 2 + 1/(x-1)

Hence, the answer is:

x² + 2/(x-1) = x + 3 + 1/(x-1)

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Answer:

Domain: {4, 3, 2}

Range: {-7,0}

This IS NOT a function

Step-by-step explanation:

Since x=4 produces y=−7 and y=0, the relation (4,−7),(3,−7), (2,0),(4,0) is not a function.

have a good day :)

(a) There are 81 different sequences of sandwiches are possible

(b) The total number of different (unordered) collections of sandwiches is 3.

First, we need to determine the number of ways the four tuna fish sandwiches can be ordered. Since all four sandwiches are the same, there is only one way to order them. Similarly, there is only one way to order the two chicken sandwiches and the two roast beef sandwiches. For the two people who can choose any sandwich, there are three options for each person, giving a total of 3 x 3 = 9 possible sandwich combinations.

Therefore, the total number of different sequences of sandwiches is:

1 (tuna fish) x 1 (chicken) x 1 (roast beef) x 9 (any sandwich) x 9 (any sandwich) = 81

For part (b), we need to determine the number of different (unordered) collections of sandwiches. We can use combinations to solve this problem. We need to select 10 sandwiches from the total of 10 sandwiches available. Since there are four tuna fish sandwiches, we need to select four of them.

Similarly, we need to select two chicken sandwiches and two roast beef sandwiches. Finally, we need to select two more sandwiches from the remaining three (since two people can choose any sandwich). The number of ways to select these sandwiches is:

combination(4,4) x combination(2,2) x combination(2,2) x combination(3,2) = 3

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By using the level of significance and p-value method with the TI-84 Plus calculator, we can determine if the mean number of dinners changed while the free dessert offer was in effect.

To perform the one-sample t-test on the TI-84 Plus calculator, we need to input the sample data and the null hypothesis. We will use the following steps:

Press STAT and then ENTER to access the list editor.

Enter the sample data into a list.

Press STAT again and then scroll right to TESTS.

Select t-Test and then highlight "Stats."

Enter the sample list name, the null hypothesis, and the level of significance.

Press ENTER and the calculator will output the t-statistic, degrees of freedom, and the p-value.

If the p-value is less than 0.05, we can reject the null hypothesis and conclude that the mean number of dinners changed while the free dessert offer was in effect.

If the p-value is greater than or equal to 0.05, we cannot reject the null hypothesis and conclude that there is insufficient evidence to suggest that the mean number of dinners changed.

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The slope of the linear equation:

y = -4x + 2/5

is -4.

A general linear equation is written as:

y = ax + b

Where a (the coefficient that multiplies the variable) is called the slope, and b is the y-intercept.

Here the linear equation is:

y = -4x + 2/5

We can see that the coefficient that multiplies the variable is -4, so that is the slope of the line.

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For a normal distribution of SAT, scores of students particular high school over the last 8 years. The actual SAT score is equals the 224.213.

A normalized value called z-score can be associated to every data, (x) which is normally distributed. The z-score formula is an extremely used way of comparing data sets which are normally distributed. We have a study of students which is conducted from a particular high school over the last 8 yrs. In case of SAT scores

Mean of score, μ = 1019

Standard deviations of score, σ = 201

The scores on sat test are normally distributed. In case of ACT score, Mean of score = 20

Standard deviations of score = 5.1

Now, if a student got sat score that is the 27-percentile. We have to determine actual sat score. Probability value for varible, p value = 0.27

So, using normal distribution table or P value to Z-score calculator value of 27th percentile corresponds to a z-score of 0.613. Using Z-score formula,

[tex]z = \frac{ X - \mu}{ \sigma}[/tex]

so, [tex] 0.613= \frac{ X - 1019}{ 201}[/tex]

Solve the expression,

=> 201 × 0.613 = X - 101

=> X= 101 + 123.213

=> X = 224.213

Therefore, a score of 224.213 corresponds to the 27th percentile .

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The statements regarding the triangles can be completed with the following:

The converse Pythagoras theorem states that a triangle is a right triangle if the square of its longest side equals the sum of its squares on the other two sides.

The converse Pythagoras theorem can be used to determine whether a triangle is acute, right, or obtuse by comparing the sum of its two sides to the square of its third side.

Proof: If the square of the longest side in a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right-angled traingle.

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50

Step-by-step solution:

    0.3x-42=0.1x-32

    -0.1x

    0.2x-42=-32

                   +42

      0.2x=10

               0.2                

        x=50

A factor of the polynomial graphed is

The zeros, which is the solution of the graph is used find the factor of the polynomial on the graph.

The graph shows that zeros includes

x = -2, x = 0 and x = 3

x = -2 is same as x + 2 = 0 hence this is a factor as in the third option.

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Answer:

Step-by-step explanation:

The function g(x) is a dilation of the parent function f(x) = 1.035^x.

Specifically, g(x) = 4000(1.035)^x is a vertical dilation of f(x) = 1.035^x by a factor of 4000.

This means that the graph of g(x) is the same shape as the graph of f(x), but it is vertically stretched by a factor of 4000.

In other words, the values of g(x) are 4000 times greater than the values of f(x) for any given value of x.

For example, when x = 1, f(1) = 1.035 and g(1) = 4000(1.035) = 4140. This means that the amount of money in Destiny's account after one year is 4000 times greater than the initial amount she invested.

Overall, the dilation in g(x) as it relates to the parent function f(x) is a vertical dilation by a factor of 4000.

The box and whisker plot that matches the data-set is given as follows:

Second plot.

A box and whisker plots shows these five features from a data-set, listed as follows:

The ordered data-set for this problem is given as follows:

13, 18, 18, 20, 27, 27, 27, 31, 31, 33, 37, 37

Hence the halves are given as follows:

The median of the data-set is given as follows:

(27 + 27)/2 = 27.

Hence the second plot is the correct plot.

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Answer:

3) Plot the points on the graphing calculator. Then generate a linear regression function. That function is:

y = -.112x + 23.448

4) (2) is correct.

Answer:

-8 (or) 5 and 5 (or) -8

Step-by-step explanation:

Let one of the numbers = x

Let other number = y

As the sum of two numbers = -3

x + y = -3

x = -3-y

As the the result of multiplication = -40

xy = -40

(-3-y)*y = -40

-3y-y² = -40

-y²-3y+40 = 0

-(y²+3y-40) = 0

-(y+8)(y-5) = 0

(-y-8)(y-5) = 0

-y-8 = 0 (or) y-5 = 0

-y = 8 (or) y = 5

y = -8 (or) y = 5

when y = -8

x = -3-y

x = -3-(-8)

x = -3+8

x = 5

when y = 5

x = -3-y

x = -3-5

x = -8

The volume of one marble is 27 cubic centimeters.

First, let's calculate the initial volume of water in the container. We know that the container is 8 cm long, 9 cm wide, and filled with water to a depth of 6 cm. Therefore, the initial volume of water in the container can be calculated as follows:

Volume of water = length x width x height

= 8 cm x 9 cm x 6 cm

= 432 cm³

Next, we need to find the final volume of water in the container after the 12 marbles were added. We are given that the depth of the water increased from 6 cm to 7.5 cm. Therefore, the final height of the water can be calculated as follows:

Final height of water = 7.5 cm - 6 cm

= 1.5 cm

Now, we can find the final volume of water in the container as follows:

Volume of water = length x width x height

= 8 cm x 9 cm x 1.5 cm

= 108 cm³

The difference between the initial volume of water and the final volume of water is equal to the volume of 12 marbles that were added to the container. Therefore, we can calculate the volume of one marble as follows:

Volume of one marble = (Final volume of water - Initial volume of water) / Number of marbles

= (108 cm³ - 432 cm³) / 12

= 324 cm³ / 12

= 27 cm³

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The value of the inverse function at x = 4 is:

[tex]y = g^-^1^(^4^) =-5[/tex]

From the attachment of graph :

Points available on the graph 'g' are (-5, 4), (-2, 1), (0, -1), (4, -2).

Since, rule to get the points lying on the graph of the inverse of the given function is,

(x, y) → (y, x)

And, (x, y) is the function of g and (y , x) is the inverse function of the g.

By the given rule, points on [tex]g^-^1^(^x^)[/tex]  will be,

(4, -5), (1, -2), (-1, 0), (-2, 4)

Therefore, value of the inverse function at x = 4 will be:

[tex]y = g^-^1^(^4^) =-5[/tex]

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The probability that both marbles are red is 0.33

The probability formula defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes.

P(A) = Number of favorable outcomes/ total no. of possible outcomes

We have the information from the question:

Total marbles are there in bag is = 6

Red Marbles = 2

Green Marbles = 2

Yellow Marbles = 2

To find the probability that both marbles are red.

Now, According to the question:

The probabilities that are desirable for our cases are:

P(RR) = 2/6 = 1/3 = 0.33

Hence, The probability that both marbles are red is 0.33

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The standard error of estimate can be used for constructing a confidence interval about a value.

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. inside a specific degree of confidence, this is the range of values you anticipate your estimate to fall inside if you repeat the test. In statistics, confidence is another word for probability.

The size of a 90% confidence interval for a given estimate is one method to gauge how "good" it is; the greater the range, the more care must be used when utilizing the estimate. A crucial reminder of the limits of the estimations is provided by confidence intervals.

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Answer:

99

Step-by-step explanation:

The circle graph shows that the "Sports" section represents 24% of the total. To find out how many students that corresponds to, we can calculate 24% of the total number of students:

24% of 450 = 0.24 × 450 = 108

Therefore, there are 108 students who prefer the Sports television genre. However, none of the answer choices match this result exactly. The closest option is 99, which is approximately 91.7% of 108. If we round 91.7% up to the nearest whole number, we get 92, which is closer to 99 than any of the other answer choices. So we can conclude that the answer is:

99 (approximately)

Answer:

  (a)  99

Step-by-step explanation:

You want to know the number of middle school students who prefer the Sports television genre, given 14, 24, 20, and 20 percent of 450 students prefer drama, documentaries, reality, and sci-fi, respectively.

The percentage of students who prefer Sports is the difference between 100% and the sum of the other percentages:

  sports = 100% -(14 +24 +20 +20)% = 22%

This fraction of the 450 students is ...

  0.22 × 450 = 99

99 middle school student prefer the Sports genre, choice A.

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Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{10400}\qquad \leftarrow 6400+4000\\ a=\stackrel{adjacent}{4000}\\ o=\stackrel{opposite}{SP} \end{cases} \\\\\\ SP=\sqrt{ 10400^2 - 4000^2}\implies SP=\sqrt{ 108160000 - 16000000 } \\\\\\ SP=\sqrt{ 92160000 }\implies SP=9600~mi[/tex]

The value of x for the right triangles is derived to be x = 1 or x = -2/3 using the trigonometric ratio of tangent for the angles a and b

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

tan a = (x + 2)/x and tan b = 4/(3x - 1) {opposite/adjacent}

(x + 2)/x = 4/(3x - 1)

(3x - 1)(x + 2) = 4x {cross multiplication}

by expansion we have a quadratic equation;

3x² - x - 2 = 0

we can rewrite the equation and factorise as follows;

3x² + 2x - 3x - 2 =0

x(3x + 2) - 1(3x + 2) = 0

(x - 1)(3x + 2) = 0

x = 1 or x = -2/3

Therefore, the value of x for the right triangles is derived to be x = 1 or x = -2/3 using the trigonometric ratio of tangent for the angles a and b.

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The bar graph representing a frequency of 20 will be the tallest

Given data ,

The tallest bar in a bar graph will represent the highest frequency. So, in the given options:

A) a bar representing a frequency of 15

B) a bar representing a frequency of 5

C) a bar representing a frequency of 20

D) a bar representing a frequency of 10

The tallest bar will be C) a bar representing a frequency of 20, as it has the highest frequency among the options given.

In a bar graph, the frequency or count of a certain category or data point is represented by the height of the bars, with larger bars denoting greater frequencies or counts.

Hence , the bar graph is solved

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Answer:

$8421.60

Step-by-step explanation:

First, we need to convert the dimensions of the deck from yards to square yards, since the cost is given per square yard.

The area of the deck is the product of its length and width:

8 yards * 12 yards = 96 square yards

So, the cost to build the deck is:

$87.85/square yard * 96 square yards = $8421.60

Therefore, it cost $8421.60 to build the deck.