Compare and contrast the relative frequency for the whole table in part B with the two-way frequency table given in the activity introduction. What trends or generalizations can you identify from the data in the tables?

The values of the composite functions are

(1) (f + g)(x) = 4x² + 2x - 2

(2) (fg)(x) = 8x³ - 4x² - 2x + 1

(3) (fⁿ)(x) = (4x² - 1)ⁿ

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

f(x) = 4x² - 1

g(x) = 2x - 1

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

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 4x² - 1 + 2x - 1

Evaluate the like terms

(f + g)(x) = 4x² + 2x - 2

(fg)(x) = f(x) * g(x)

(fg)(x) = (4x² - 1) * (2x - 1)

Evaluate the products

(fg)(x) = 8x³ - 4x² - 2x + 1

(fⁿ)(x) = (f(x))ⁿ

So, we have

(fⁿ)(x) = (4x² - 1)ⁿ

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Answer:

58,565 < 58,566

Step-by-step explanation:

You have to determine which number is greater. I usually start comparing from the farthest left digit (In this case, the ten thousands place.) and work my way up

hope this helped :)

The relative frequency of selecting the number 2 is 0.16 or 16%.

Relative Frequency is a proportion or percentage which is calculated with the help of given frequency.

To calculate the relative frequency of selecting the number 2, you need to divide the number of times 2 was selected by the total number of selections. In this case, 2 was selected 8 times out of a total of 50 selections.

Relative frequency of selecting 2 = (Number of times 2 was selected) / (Total number of selections)

= 8 / 50

= 0.16

Therefore, the relative frequency of selecting the number 2 is 0.16 or 16%.

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Answer: i think c

Step-by-step explanation:

The slope of each line is given as follows:

58) -2.

59) 1.

60) -2/3.

61) 2.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The parameters of the definition of the linear function are given as follows:

When two lines are parallel, they have the same slope, which are the cases for itens 58 and 59, as the slope is given by the multiplier of x.

When two lines are perpendicular, we have that the multiplication of the slopes of the line is of -1, hence the slope for item 60 is given as follows:

3m/2 = -1

3m = -2

m = -2/3.

For item 61, the slope is given as follows:

-m/2 = -1

m = 2.

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The proportion is solved and the variables are a/b = c/d

Given data ,

Let the proportion be represented as A

Now , the value of A is

a / b = c / d

On simplifying the equation , we get

( a + b ) / b = ( c + d ) / d

On dividing the numerator of the fraction by the denominator , we get

( a / b ) + ( b / b ) = ( c / d ) + ( d / d )

On further simplification , we get

( a / b ) + 1 = ( c / d ) + 1

Subtracting 1 on both sides , we get

( a / b ) = ( c / d )

Hence , the proportion is ( a / b ) = ( c / d )

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The probability of the digestive tract disease, given a positive test result, is 45%.

A. Two-Way Frequency Table:

Let's create a two-way frequency table to represent the situation:

                                      Test Positive             Test Negative           Total

Disease Present                   A                                 B              5,000

Disease Not Present           C                                 D              95,000

Total                                   5,000                     95,000     100,000

In this table:

B. Probability of Disease Given Positive Test Result:

P(Disease | Positive)

= (P(Positive | Disease) x P(Disease)) / P(Positive)

= 0.94  x 0.05 / P(Positive)

To calculate P(Positive), we can use the law of total probability:

P(Positive) = P(Positive | Disease) x P(Disease) + P(Positive | No Disease) x P(No Disease)

So, P(Positive | No Disease) = 1 - P(Test Negative | No Disease)

= 1 - 0.94 = 0.06

P(No Disease) = 1 - P(Disease) = 1 - 0.05 = 0.95

Now, P(Positive) = (0.94 x 0.05) + (0.06 x 0.95)

= 0.047 + 0.057

= 0.104

Finally, we can calculate P(Disease | Positive):

P(Disease | Positive) = (0.94 x 0.05) / 0.104

= 0.047 / 0.104

≈ 0.452

Therefore, the probability of the digestive tract disease, given a positive test result, is 45%.

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There are 75 triangles that can be formed using these 9 vertices.

Here we have,

We have 9 vertices arranged in a pattern where 5 vertices are above and 4 vertices are below in a parallel direction.

And we want to know how many triangles can be formed using these vertices.

In order to this,

Count the number of ways to choose 3 vertices from the 9 vertices.

This can be done using the combination formula, which is:

[tex]^{9}C_{3}[/tex] = 9! / (3! * (9-3)!)

      = 84.

Since,

A degenerate triangle is one where all three vertices lie on the same line. To count the number of degenerate triangles,

We need to count how many ways we can choose 3 vertices that lie on the same line.

There are 5 lines with 3 points each (the 5 lines with the upper vertices). So the number of degenerate triangles is:

5 [tex]^{3}C_{3}[/tex] + 4  [tex]^{3}C_{3}[/tex] = 9.

Subtract the number of degenerate triangles from the total number of triangles to get the number of non-degenerate triangles.

Therefore, the number of non-degenerate triangles is:

84 - 9 = 75.

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One-way ANOVA utilizes the five steps of hypothesis testing to determine if there are significant differences among the means of three or more groups.

One-way ANOVA, or analysis of variance, is a statistical test used to compare the means of three or more groups to determine if there are significant differences among them. It helps in determining whether the variations between the group means are due to random chance or if they are statistically significant.

The five steps of hypothesis testing are commonly used in one-way ANOVA to analyze and draw conclusions from the data. These steps are as follows:

1. Formulating the null and alternative hypotheses: In one-way ANOVA, the null hypothesis (H0) states that there are no significant differences between the group means, while the alternative hypothesis (Ha) states that at least one group mean differs significantly from the others.

2. Choosing a significance level: The significance level, denoted as α, represents the threshold below which the null hypothesis is rejected. Commonly used values for α are 0.05 or 0.01, indicating a 5% or 1% chance, respectively, of rejecting the null hypothesis incorrectly.

3. Computing the test statistic: In one-way ANOVA, the test statistic is the F-statistic, which compares the between-group variation to the within-group variation. It measures the ratio of the mean square between (MSB) to the mean square within (MSW).

4. Determining the critical value: The critical value is derived from the F-distribution table and depends on the significance level and the degrees of freedom associated with the numerator and denominator of the F-statistic.

5. Making a decision: If the calculated F-value is greater than the critical value, the null hypothesis is rejected, and it can be concluded that there are significant differences between at least two group means. Conversely, if the calculated F-value is smaller than the critical value, the null hypothesis is not rejected, indicating that there is no significant difference between the group means.

If the null hypothesis is rejected, post-hoc tests can be conducted to determine which specific group means differ significantly from each other.

one-way ANOVA utilizes the five steps of hypothesis testing to determine if there are significant differences among the means of three or more groups.

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Answer:

B} 7/20

Step-by-step explanation:

total: 80

section 1: 28

p(section 1) = 28/80 = 7/20

With the coordinate provided, the lengths of the triangle are Side AB =  5 units, Side BC = 10 units and Side CA = 12.4 units.

To find the side lengths of the triangle using the coordinates provided, we use the distance formul.

The distance between two points (x1, y1) and (x2, y2) is given by √((x2-x1)² + (y2-y1)²).

Side AB: Distance between A(-7, 3) and B(-3, 6)

= √((-3 - -7)² + (6 - 3)²)

= √((4)² + (3)²)

= √(16 + 9)

= √25

= 5 units

Side BC: Distance between B(-3, 6) and C(5, 0)

= √((5 - -3)² + (0 - 6)²)

= √((8)² + (-6)²)

= √(64 + 36)

= √100

= 10 units

Side CA: Distance between C(5, 0) and A(-7, 3)

= √((-7 - 5)² + (3 - 0)²)

= √((-12)² + 3²)

= √(144 + 9)

= √153

= 12.4 units

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Answer: Is it x=y(4)? Can someone tell me if that's right?

Step-by-step explanation:

Sneha actually got 2475 g of sugar instead of 2500 g.

We have,

If the shopkeeper uses a weight of 990 g for measuring 1 kg, it means that he is using a weight that is 10 g less than the actual weight of 1 kg.

So, the actual weight of 1 kg is 1000 g.

Now,
If Sneha bought 5/2 kg of sugar, she should have received:

= (5/2) x 1000 g

= 2500 g

But since the shopkeeper uses a weight of 990 g for measuring 1 kg, the weight of 5/2 kg would be:

= (5/2) x 990 g

= 2475 g

Thus,

Sneha actually got 2475 g of sugar instead of 2500 g.

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The solution to the inequality expression is -8/9 ≤ x ≥ 4/9

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

|3x + 6/9| ≥ 2

Expand the inequality expression

So, we have

-2 ≤ 3x + 6/9 ≥ 2

Subtract 6/9 from both sides

So, we have

-24/9 ≤ 3x ≥ 12/9

Divide through the equation by 3

-8/9 ≤ x ≥ 4/9

Hence, the solution to the inequality expression is -8/9 ≤ x ≥ 4/9

The graph is attached

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Answer:

The correct answer:

(B) reduction

Answer: Blue

Step-by-step explanation:

Half of the entire freaking bag is blue,it states it in the question.If there is so many,unless by pure blind luck you will get that.

I hope it helps!

Between 40 and 60 minutes the target heart rate strictly increasing then strictly decreasing. Therefore, option B is the correct answer.

From the given graph, in the first curve between the interval 0-10 speed is increasing,  between the interval 10-30 speed is constant and  between the interval 30-40 speed is decreasing.

In the second curve between the interval 40-50 speed is increasing,  between the interval 50-60 speed is decreasing, between the interval 60-65 speed is increasing and between the interval 65-73 speed is constant.

In the third curve between the interval 73-85 speed is increasing,  between the interval 85-92 speed is constant and  between the interval 92-100 speed is decreasing.

Therefore, option B is the correct answer.

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Answer:3rd one

Step-by-step explanation:

Median of the set is 34, as it is the middle value of the ordered set (32, 33, 33, 33, 34, 35, 35, 36, 38).

To find the middle of a bunch of numbers, the initial step is to organize the numbers all together from least to most prominent. For this situation, the arranged set is: 32, 33, 33, 33, 34, 35, 35, 36, 38.

The middle is the center number in the arranged set. On the off chance that there is an odd number of values, the middle is the center worth. On the off chance that there is a considerably number of values, the middle is the normal of the two center qualities.

For this situation, there are nine qualities in the set, which is an odd number. The center worth is the fifth worth, which is 34. Thusly, the middle of the set is B. 34.

To confirm, we can count four qualities before 34 and four qualities after 34 in the arranged set. Since there are an equivalent number of values when the middle, we can infer that 34 is for sure the middle.

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Answer:  $130 money did Brenda and Hazel have all together before buying decorations and snacks.

Here, we have,

You want to know Brenda and Hazel's combined money when the ratio of their remaining balances is 1 : 4 after Brenda spent $58 and Hazel spent $37. They had the same amount to start with.

Setup

Let x represent the total amount the two women started with. Then x/2 is the amount each began with, and their fnal balance ratio is ...

 (x/2 -58) : (x/2 -37) = 1 : 4

Solution

Cross-multiplying gives ...

 4(x/2 -58) = (x/2 -37)

 2x -232 = x/2 -37 . . . . . . eliminate parentheses

 3/2x = 195 . . . . . . . . . . . . add 232-x/2

 x = (2/3)(195) = 130 . . . . . multiply by 2/3

Brenda and Hazel had $130 altogether before their purchases.

Alternate solution

The difference in their spending is $58 -37 = $21.

This is the same as the difference in their final balances.

That difference is 4-1 = 3 "ratio units", so each of those ratio units is $21/3 = $7.

Their ending total is 1+4 = 5 ratio units, or $35.

The total they started with is $58 +37 +35 = $130.

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complete question:

Brenda and Hazel decide to throw a surprise party for their friend, Aerica. Brenda and Hazel each go to the store with the same amount of money. Brenda spends $58 on decorations, and Hazel spends $37 on snacks. When they leave the store, the ratio of Brenda’s money to Hazel’s money is 1 : 4. How much money did Brenda and Hazel have all together before buying decorations and snacks?

Part A ;

For Bus:

mean = 17.5

median = 15

mode= 15 and 16

Range= 17

For walking:

mean = 20.5

median = 20.5

mode= 20 and 21

Range= 3

For Bus

To calculate the mean:

= 16+14+15+14+31+15/6

= 105/6

= 17.5

To calculate the median;

= 14,14,15,15,16,31

= 15+15/2 = 15

To calculate the range:

= 31-14 = 17

For walking;

To calculate the mean:

= 19+20+20+21+21+22/6

= 123/6

= 20.5 mins

To calculate the median

= 20+21/2

= 20.5

To calculate the mode:

=20 and 21

To calculate the range:

= 22-19

= 3

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The average rate of change of the function over the interval is 12

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

f(x) = x² + 2x + 1

The interval is given as

From x = 4 to x = 6

The function is a quadratic function

This means that it does not have a constant average rate of change

So, we have

f(4) = 4² + 2(4) + 1 = 25

f(6) = 6² + 2(6) + 1 = 49

Next, we have

Rate = (49 - 25)/(6 - 4)

Evaluate

Rate = 12

Hence, the rate is 12

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The range of the function g(x) = f(x+2)-5 is:

R = [0, ∞)

For a function y = f(x), we define the range as the set of possible outputs of the function.

Here we want to find the range of:

g(x) = f(x+2)-5

Where f(x) = x²

Replacing f(x) in the rule for g, we will get the composition:

g(x) = (x + 2)² - 5

The first part can only be a positive number or 0, then the minimum of the range is -5

And then the function only grows, then the range of g(x) is:

R = [0, ∞)

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The measure of arc angle QTP is 204 degrees.

When a tangent and a secant intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

Therefore, let's find the measure of arc angle QTP as follows:

90 = 0.5(x - 68)

90 = 0.5x - 34

0.5x = 124

x = 124 / 0.5

x = 248 degrees

Where

x = arc angle TSQ

Therefore,

arc QP = 44 degrees

Therefore,

arc QTP = 248 - 44

arc QTP = 204 degrees

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Answer:

48in.²

Step-by-step explanation:

The formula for the area of a triangle is 1/2 x b x h

Since the b = 8 and the h = 12, substitute 8 and 12 for b and h.

1/2 x 8 x 12

4 x 12

48in.²

Answer:

d

Step-by-step explanation:

area= ½ × b × h

= ½ × 8 × 12

= ½ × 96

= ⁹⁶/²

= 48in²

The domain and the range of the graph are Domain = [-10, -8] and Range = [-10, -1]

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

The graph

The above graph can be represented as a list of ordered pairs

The rule of a graph is that

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

Domain = [-10, -8]

Range = [-10, -1]

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Answer:

24 cakes.

Step-by-step explanation:

6 cups of oil divided by 1/4 cup oil per cake = 24 cakes

6/(1/4) = 24

or 6/(0.25) = 24

She can make 24 cakes with 6 cups of oil.

The missing value E, the total revenue for the period 2017/18, is approximately 82.61 billion.

Local government sector's revenue in 2017/18 (L): Missing value (to be calculated)

Provincial sector's revenue in 2017/18 (P): 410.6 (billion)

According to the information provided, L is 20.12% of P. Mathematically, we can write this as:

L = 20.12/100 * P

Substituting the known value of P, we get:

L = 20.12/100 * 410.6

L ≈ 82.61 (rounded to two decimal places)

Therefore, the missing value E, the total revenue for the period 2017/18, is approximately 82.61 billion.

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Answer:

Distance between points is 25 Units.

Step-by-step explanation:

To find the distance between two points, we can use the distance formula. The formula is:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Given the two points: (12, 5) and (-12, -2), we can assign the values as follows:

(x1, y1) = (12, 5)

(x2, y2) = (-12, -2)

Plugging the values into the distance formula, we get:

d = sqrt((-12 - 12)^2 + (-2 - 5)^2)

= sqrt((-24)^2 + (-7)^2)

= sqrt(576 + 49)

= sqrt(625)

= 25

Therefore, the distance between the points (12, 5) and (-12, -2) is 25 units.